摘要:

Faraday Discuss. Chem. SOC., 1991,91,97-110 Metal-Metal and Metal- Hydrogen Reactive Transition States William C. Stwalley,*t Paul D. Kleiber,S Kenneth M. Sando,? A. Marjatta Lyyra,?S Li Li, Sharath Ananthamurthy,S Solomon Bililign,S He Wang,S Jiaxiang WangS and Vassilios Zafiropulos Center for Laser Science and Engineering, University of Iowa, Iowa City, IA 52242, USA Atomic line broadening has traditionally emphasized resonance broadening by like atoms and ‘inert perturber’ broadening by rare gases and hydrogen. Such methods are ideal for qualitative and quantitative understanding of reactive transition states, including especially non-adiabatic interactions and polarization, orientation and alignment effects. Experiments at Iowa include a variety of such studies with alkali-metal and alkaline-earth metal atoms, e.g.diatomic photodissociation (including state-selected photodissociation through quasibound resonances) and reactive transition-state absorption. In each case theoretical information is available concerning the relevant potential-energy curves (or surfaces) and their couplings, and there are approximate dynamical theories (e.g. orbital locking) to be tested. A sum- mary of recent experimental results and theoretical comparisons emphasizing diatomic photodissociation and its relation to transition state absorption will be presented. The concept of a transition state involves a transient configuration of atoms during the dynamic evolution of reactants into products. Normally, one takes the simplest chemical reaction to be a bimolecular exchange reaction: A+BC + AB+C ( 1 ) but one may also consider the conceptually simpler photoassisted two-atom ‘half- collision’ reactions, e.g. diatomic photodissociation:’-3 A,+hv + A*+A (2) This two-atom process can be viewed as fundamental from the perspective of atomic line broadening as well as from the perspective of chemical physics, as can related processes such as energy-transfer collision^^-^ and bound-free emi~sion.~-’~ The idea of a transition state for a two-atom system is non-standard, since there is only a single internuclear coordinate with no transverse degrees of freedom for nuclear motion. However, critical issues concerning the coupling of electronic and nuclear motion remain ( e.g.when is orbital angular momentum ‘unlocked’ from the internuclear axis as a diatomic dissociates).These issues are, of course, also important for standard polyatomic transition states. Likewise, questions of polarization, orientation, alignment and angular-momentum distributions arise. Even in polyatomic systems, an approximate one-dimensional model can often lead to valuable insight into the reaction dynamics. In our studies of metal-atom-H, transi- tion-state spectroscopy, for example, a phenomenological one-dimensional model relying on potential-energy curves for selected approach geometries has demonstrated semiquan- titative agreement with experimental As the metal atom M approaches HZ, i Also at the Department of Chemistry. $ Also at the Department of Physics and Astronomy. 9798 Metal Reactive Transition States I free ( 5 0 % ) \ bound / RM--H* + Fig.1 Schematic diagram of a simple model for reaction probability in Mg+ H, transition-state excitationI6 photon absorption from a free (continuum) state of relative M-H2 motion on the ground-state potential surface produces the excited transition complex ( MH2)* in one of three types of states (Fig. 1): ( 1 ) bound-quasibound states, (2) continuum states above a barrier, and (3) continuum states outside a barrier. [In cases where there is no barrier (3) does not occur.] A one-dimensional model is particularly appropriate for near-spherical H2 , especially since no excited vibrational levels and only a few rotational levels are usually populated. The transition-state absorption probability can be treated quite accurately.The subsequent dynamical evolution on the excited-state potential- energy surface is, of course, determined by the details of the surfaces and any important non-adiabatic effects. Without detailed quantitative knowledge of the relevant surfaces and coupling elements it is impossible to model a priori the excited-state dynamics. However, it is still possible, and indeed very valuable, to evaluate the reaction probability on various excited-state surfaces by a heuristic model chosen to fit the experimental data. For example, in the Mg + H2 reaction (Fig. 1 ) for the Mg + H2 system, the reaction probabilities for MgH formation are taken to be 100% for the bound-quasibound states, 50% for continuum states above a barrier (50% corresponding to an incoming wave react and 50% corresponding to an outgoing wave do not) and 0% for continuum states outside a barrier. An average is taken over the potential surfaces involved.'6 Thus these barrier maxima (corresponding to transition states) are critical points with abrupt changes in reaction probability as one goes from above to below the barrier or inside to outside the barrier.This simple (and certainly incomplete) model agrees reasonably well with many observations, and can in principle be tested further, e.g. by studying photodissoci- ation of the van der Waals molecules MH2. A severe limitation at present is the lack of accurate and complete ab initio potential-energy surfaces. Note also it is a model appropriate for other cases with a so-called early barrier in the entrance valley of the reactive potential-energy surface.Truly one-dimensional analogues occur for this model, e.g. diatomic photodissoci- ation over a potential barrier, as in the B 'nu state of K2 and other alkali-metal dimers (Fig. 2). In the case of photodissociation, the potential-energy curves and even theW. C. Stwalley et. al. 99 I free free M + M* 1 free M + M Fig. 2 Schematic diagram of diatomic photodissociation, an analogue of Fig. 1 radiative transition probabilities are well known from both experimental and theoretical results. It is suggested here that the powerful new techniques being applied, e.g. to state-selective photodissocation, are potentially applicable to the analogous triatomic transition states. In a sense, a half-collision photoexcitation corresponds to directly producing an excited wave packet in the Franck-Condon region of absorption which evolves to the ‘diatomic transition state’.Note, however, the far greater specificity of the half-collision approach. Assume, for example, that a process such as photodissociation is studied as described below for a single rovibrational level. Then the photodissociation can be readily studied with energy resolution << 1 cm-’, which is much better than in almost all collision experiments and readily allows observation of sharp resonances. More impor- tantly, the number of partial waves involved in the photodissociation will be 3, 2 or even 1 from a given J level. Of particular interest are the states near the barrier maxima, where the model reaction probability varies rapidly with energy (or also angular momentum).States slightly below the barrier are called quasibound states, since they can decay by tunnelling through the barrier and are not truly stationary states. In scattering terminology, such states also correspond to shape resonances above or below the barrier maxima. 19,20 Such resonances are also called orbiting resonances, since classical collisions at impact parameters and asymptotic kinetic energies corresponding precisely to barrier maxima in the effective potentials give rise to infinite classical defection or orbiting. Such quasibound states are well known in classical diatomic spectroscopy from the broadening of molecular spectral lines.” Bernstein and co-workers contributed greatly to their study, e.g.their important relation to long-range forces,19 different ways of determining their position and width,22 and their contribution to atom-atom re~ombination.~’ Their study is a particularly accurate method of determining dissociation ene~gies*~-~’ and potential- energy barrier^.^'-^' In the case of the B ‘nu state of K2, line-broadening of molecular transitions involving quasibound states has been previously reported.’” This work extends those results by directly observing state-selective photodissociation to produce100 Metal Reactive Transition States Table 1 Summary of processes and systems surveyed herein type of process species excitation laser involved wavelength/ nm ref. diatomic photodissociation transition-state absorption K2 580-670 132 NaK 550- 585 3 Mg+H, ca.285 15,16 ca. 230 17 Na+H2 ca. 330 18 atomic fluorescence (as well as diminished intensity of molecular fluorescence). A long-term goal is to observe similar resonances in triatomic transition states. Thus an atomic half-collision perspective also leads naturally to a direct probe of the transition-state region in triatomic systems: A+BC+hv --* [ABC]* --* AB+C (3) In studies of processes corresponding to reactions (2) and (3), we have focused on using simple alkali and alkaline-earth metal atoms. The interactions of these atoms with each other and with H2 have then been studied (Table 1). In this discussion the focus is on diatomic photodissociation, especially where initial state selection is possible, e.g. using the efficient STIRAP t e c h n i q ~ e , ~ ~ - ~ ~ and then its relation to transition-state absorption.Experimental The reported experiments were carried out with a molecular-beam apparatus with laser beam(s) at right angles to the molecular beam and atomic or molecular fluorescence detection in a third direction perpendicular to the laser and molecular beams (Fig. 3). The K2 effusive molecular beam was created by heating potassium to 620 K, corre- sponding to a vapour pressure of K2 of ca. 1 x lo-* Torr,? and expanding the vapour through a 0.5 mm nozzle into a stainless-steel vacuum chamber with a background pressure of 3 x Ton. This operating temperature is slightly lower than that used in ref. 1 in order to eliminate a weak molecular fluorescence which may influence the polarization measurements as discussed below.In thermally averaged experiments, a Coherent 599-21 CW broad-band dye laser, pumped by a Coherent CR-6 argon-ion laser, was used to irradiate the potassium effusive molecular beam ca. 8 mm downstream from the nozzle. Two dyes were used to cover the whole bound-free absorption profile of K2 (583-665 nm): rhodamine 6G for the range 583-643 nm and DCM for the range 617-665 nm. Before entering the vacuum chamber, the laser beam was modulated at 1 kHz and then passed through a high-extinction prism polarizer (extinction ratio better than lop5). The laser beam was ca. 2 mm in diameter in the region where it crossed the molecular beam; tighter focusing was avoided to alleviate saturation effects. The laser power was 530 mW, and the observed signals were determined to be linear in laser power.In state-selected triple resonance experiments, the experiments were similar except that the lasers involved were three single-mode scanning tunable dye lasers with 1 MHz linewidth (Coherent 699-29) pumped by Ar+ lasers (sometimes one Kr+ laser was used) operating with the above dyes and also LD 700. Normally either the pump (laser L1) or the probe (laser L3) was modulated, and phase-sensitive detection was used. Dye-laser frequencies were calibrated using the standard I2 spectrum as a reference. The dye-laser t 1 Tom= 101 325/760 Pa.W. C. Stwalley et. al. 101 Photon-Counting I Fig. 3 Experimental diagram of all-optical triple-resonance state-selective photodissociation of K2. PMT indicates photomultiplier tube beams were superimposed in the molecular beam and in a five-armed stainless-steel cross heat-pipe oven operated at 1-2 Torr with argon buffer gas. The strong molecular fluorescence from the heat-pipe oven was used to set the frequencies of two lasers, and then the frequency of the third laser was scanned continuously.The molecular fluores- cence was detected using a Spex 1404 double monochromator set to the wavelength of an appropriate B 'nu( u' = 43, J ' ) --* X 'X;( d' = 60, J") transition. The atomic fluorescence was observed in a direction mutually perpendicular to the laser beam and the molecular beam. For polarization experiments, the fluorescence first passed through an analysing polarization filter and then through a reference polarizer oriented at 45". The purpose of the reference polarizer was to eliminate the polarization sensitivity of the detection apparatus.The fluorescence was detected with a filtered photomultiplier. Two narrowband pass filters were used in series: a 2 nm FWHM filter centred at the potassium D2 line (766.5 nm); and a 10 nm FWHM filter centred at 766 nm. This double filtering was used to improve dramatically the rejection of scattered laser light and other molecular emissions over the conditions of ref. 1. The phototube output was detected with a lock-in amplifier. The total atomic fluorescence excitation and the linear polarization of the atomic fluorescence, given by were determined as a function of excitation laser wavelength. To verify that the system did not introduce spurious polarization results, it was tested in several ways.An unpolarized incandescent white light source was placed in the observation zone and the detection system checked for zero polarization. In a second test, the K D-line filters were replaced with Na D-line filters and trace atomic Na in the beam was used to check the atomic fluorescence polarization following resonance excitation on either the D1 or D2 lines of Na. The measured values of -1 f 2% for D, and 18f3% for D2 agree well with the theoretical values (corrected for hyper- fine depolarization). In a third test, the molecular beam was run with sodium and the polarization of the Na D-line emission following Na, photodissociation at A = 457.9 nm was measured to be -6%, in good agreement with the earlier result (-5%) of Rothe et C L Z .~ ~102 20 16 - I E p 12 \ 4 8 4 C Metal Reactive Transition States Fig. 4 The potential curves of K2 involved in the X 'Xi --+ B 'nu photodissociation (ao = 5.29177 x IO-" m) Results on Diatomic Photodissociation Thermally Averaged Photodissociation Perhaps the simplest chemical reactions are diatomic photodissociations. Our initial studies of photodissociation in thermal molecular beams included both homonuclear',' K,+hv -+ K*+K (4) and heter~nuclear~ NaK+hv -+ K*+Na ( 5 ) examples. In both cases the total photoabsorption profiles calculated from the relevant potential (X and B) potential curves were in very good agreement with experiment. This is illustrated for K2 in Fig. 4 and 5. More significantly, the polarization of atomic fluorescence for K2 was again found to be significantly negative in all regions of strong absorption (Fig.6). Such results are consistent with theoretical assuming a fully adiabatic dissociation from small [ Hund's case (a)] internuclear distances to intermediate [ Hund's case (c)] inter- nuclear distances, followed by a sudden approximation dissociation from intermediate to large [ Hund's case (e)] internuclear distances. The fully quantum-mechanical treat- ment of dissociation by Dubs and Julienne37 turns out to be very well approximated by the semiclassical approach of Kleiber et a1.' In particular, one finds that the atomic fluorescence polarization P depends only on a single parameter a, the angle through which the diatomic rotates as it dissociates (Fig.7). First note that semiclassicallyW. C. Stwalley et. al. 103 A/nm Fig. 5 The total photodissociative absorption cross-section of K,: (-) calculated and (0) experimental 1 I I I I I I I I I 1 '"1 P 610 620 630 640 i(nm) T -5 h/nm Fig. 6 The polarization as a function of wavelength: (-) theory (thermally averaged and corrected for hyperfine depolarization, (A) experimental set from ref. 1, (0) new experimental set. Note that for overlapping experimental error bars, the error bars are shown only for the new results; the error bars in ref. 1 (not shown) are comparable where E is the continuum energy, V ( R ) the excited-state potential energy, EROT(R) the local rotational energy, EKIN(R) the local kinetic energy, p the reduced mass and J the rotational angular-momentum quantum number.The integration is carried out from the inner classical turning point Ro to a final decoupling distance, R,,, beyond104 Metal Reactive Transition States Z x . Fig. 7 Geometry of the photodissociation process which the molecular axis is no longer followed by rotation of the electronic cloud (for K2 one finds negligible rotational coupling consistent with R,, + a). In K 2 , because of a potential barrier of ca. 300 cm-’ in V ( R ) , EKIN(R) is large for most R and thus (Y is small ( S T ) . If one calculates P ( a ) for the transformation Hund’s case (c) - Hund’s case (e) transformation,* one sudden adiabatic Hund’s case (a) - finds 3 COS* (Y -6 cos (Y - 5 P ( a ) = cos2 (Y -2 cos a + A further correction is needed because hyperfine depolarization causes the decay of K” alignment on the timescale of the hyperfine procession frequency.38,39 The final thermally averaged predicted polarization profile is given in Fig. 6 along with two different sets of experimental results.”* The agreement is very good, except that the first set of experiments disagrees somewhat at wavelengths corresponding to very weak absorption (605 and 650nm). The agreement between theory and experiment suggests that the current interpretation of dissociation dynamics in this thermally averaged K2 case is correct. State-selected Photodissociation A superior approach for molecular photodissociation is to photodissociate state-selec- tively an individual vibrational-rotational level. In that case, a particular vibrationally excited level (prepared by a two-laser double-resonance te~hnique)~’ is photodissociated with a third laser (Fig.8). Such all-optical triple resonance (AOTR) spectroscopy is a direct extension of purely bound-state techniques, both ordinary4’ and perturbation- fa~ilitated.~’ The initial experiments have involved quasibound levels or orbiting reson- ances in the B ‘nu state of K2. Excitation to such levels can produce either ordinaryW. C. Stwalley et. al. 105 25 20 - 15 2 3 \ 10 5 0 3 3 , 2 9 / 2 8 / 2 ; L3 1 ( 1 7 , 2 8 1 + 2 , 2 K, + hv -+ K;-bK*+ K 7 B1l-IU 0 2 4 6 8 10 12 14 16 R I A Fig. 8 Triple-resonance photodissociation of K2 through the B 'nu( u = 43, J ) quasi-bound levels. Note that interference can occur if v,= v m 600 400 300 Y ul .- 5 U ._ 200 100 0 / 8 10 12 14 16 18 20 22 24 28 28 30 P ( J ) Fig. 9 Predicted and observed intensity of molecular fluorescence from B 'nu( u = 43, J ) levels.The prediction ignores predissociative tunnelling. Thus the difference clearly indicates the magni- tude of the dissociation by tunnelling106 Metal Reactive Transition States J = 2 0 .': . . J = 2 1 . . I. . . .. : . . .- . . . . . . - .. . . . . I . . . ...... .... ,..:: : : ..I .. '.. '.: . . . . . . .\. . . - . . . . . . . Fig. 10 Observed all-optical triple-resonance signals as a function of the frequency of laser L, detected by observation of atomic fluorescence with a K D2 filter for six selected B 'XIu( u' = 43, J ' ) levels. Frequency markers are spaced 10 GHz apart molecular fluorescence3' or photodissociation by tunnelling to K" + K (with subsequent atomic fluorescence). In addition to the linewidth of the molecular fluorescence, the decreased intensity of molecular fluorescence for higher, more rapidly tunnelling levels is evident in Fig.9. More significantly, the direct production of K" has been detected in all-optical triple resonance state-selected photodissociation experiments (Fig. 3). Selected triple reson- ance signals are shown in Fig. 10, which clearly show increased linewidths (detected by atomic fluorescence as laser L3 is scanned) for the more rapidly tunnelling higher J levels. At lower J these linewidths agree (Fig. 1 1 ) with those (detected by molecular fluorescence) of Heinze and Engelke." Energy and width calculations, based on a B 'IT, potential-energy curve derived from ref.30, give agreement with observed energy levels to <0.1 cm-' and with observed widths as shown in Fig. 1 1 . Note that the radiative lifetime and AC Stark contributions to the linewidth are small compared to the tunnelling contribution at high J. The Doppler effect is also small for the sub-Doppler triple- resonance technique. It is also worth noting that, in principle, the molecular and atomic fluorescence processes (Fig. 8) could interfere if molecular emission occurs at precisely the atomic frequency. This is the analogue of bound-free interference effects (e.g. ref. 8, 10, 11, 14 and 42) in the limit that the internuclear distance of one branch of the MullikenW. C. Stwalley et. al. 8 ’ ’ + m .+++++ , 107 a0 Fig. 11 Linewidths (FWHM in GHz) for B ‘nu( u ’ = 43, J ’ ) levels from the earlier molecular fluorescence results3’ ( x ) from the triple resonance atomic fluorescence experiments reported here (M) and from calculations which assume the linewidth is due to tunnelling only (+) difference potential goes to infinity. It is also worth recalling that such quasibound levels are sometimes called orbiting resonances, because classically they correspond to rotating diatomics in metastable equilibrium right at barrier maxima. Such levels thus correspond to extremely large values of a, and thus one expects to observe large changes in polarization per rotational angular momentum increment. Once these quasibound resonances in the photodissociation cross-section are fully characterized (e.g.the polarization of their atomic fluorescence measured), the plan is to also study the state-selected ‘ordinary’ continuum above the centrifugal barrier, both experimentally and theoretically. The resonance structure does continue slightly above the barrier maxima.24 Discussion The thermally averaged experimental results for absorption and polarization (Fig. 5 and 6 ) for the X ‘Xl---* B ‘nu photodissociation are in remarkably good agreement with fully quantum-mechanical close-coupled calculation^^^ and also with a simple semiclassical theory based on a fully adiabatic dissociation from small [Hund’s case (a)] distances to intermediate [ Hund’s case (c)] distances, followed by a sudden dissociation to large [ Hund’s case (e)] distances.* State-selected photodissociation uia quasibound states has been characterized as to both energy and width, each in very good agreement with theoretical calculations.It is clear that further, even more experimentally challenging measurements are highly desirable. In particular, plans include attempts to observe the polarization of atomic emission from state-selected excitation of quasi-bound states and also to observe the state-selected non-resonant background photodissociation onset and continuum. The excellent theoretical framework available for precisely predicting the results of these photodissociation measurements is of great value in these endeavours.108 Metal Reactive Transition States j I 3 E O X l F I 39195 6 cm-' 1 x ) o o o ' ' ' 5 ' " " " ' ' " ' ' ' ~ J I0 15 20 R I A Fig. 12 The proposed stimulated radiative dissociation process Finally, it should be noted that there is an additional triple resonance photodissoci- ation technique of high promise suggested by Lyyra: stimulated radiative dissociation (SRD). This process is illustrated for Na, in Fig.12, where the upper 4 'C+ state is a very unusual 'shelf' state studied extensively by optical-optical double resonance spec- t r o ~ c o p y . ~ ~ Note that the outer turning point of the upper 4 ' C l state (which can be increased to very large distances) should roughly match the inner turning point (outside the potential barrier) in the lower B 'nu state. Thus, if normal X + B photodissociation is a 'half-collision', the SRD process corresponds to an increasingly small fraction of a collision. In principle, one can now directly probe regions of angular momentum recoupling, e.g.where C3/ R3 approximately equals the spin-orbit splitting. Another diatomic of high interest for photodissociation studies is the heteronuclear molecule NaK3 Preliminary NaK results are more complex, and the theoretical and experimental results are much less complete. First, unlike K2, where only the *P3/2 state (which correlates adiabatically with the excited B 'll, state) is produced, both 'P3/2 and 2P1,2 atoms are produced in NaK photodissociation, in a ratio which varies strongly with wavelength. Experimental studies of the polarization have not yet been completed, and a series of incompletely determined curve crossings are involved in the t h e ~ r y .~ Secondly, there is no barrier in the upper-state potential, so the continuum energy can approach zero (an ultracold half-collision at ca. lop3 K is possible), and a can become very large.W. C. Stwalley et. al. 109 Relation to Transition-state Absorption In these experiments, neither the metal atom nor the H2 molecule absorbs laser On the contrary, the only absorption which takes place does so as a result of metal-hydrogen collisions. In the relatively well studied Mg + H2 system, as noted above, a model (Fig. 1) based on a6 initio potential-energy surfacesu for CZv amd C,, geometries qualitatively (and semi-quantitatively) predicts the detuning profiles for Mg", MgH( o = 0, N = 6) and MgH( ZI = 0, N = 23) production.16 More extensive calculations based on more complete potential-energy surfaces are planned.45 The one-dimensional model assumes no reaction if absorption occurs outside (and below) a barrier in the one-dimensional effective potential, unit probability of reaction if absorption occurs inside (and below) a barrier and 50% reaction probability if absorption occurs above a barrier. One of the more remarkable results is summarized in Fig.6 of ref. 16 (see also ref. 46), i.e. blue-wing (repulsive potential-energy surface) reaction is nearly as probable as red-wing (attractive potential-energy surface) reaction. This suggests a high probabil- ity of reaction once the excited metal atom-hydrogen molecule system is in close proximity, i.e. once the system is inside the barrier.Recently, experiments have been extended to the interesting Na(4p) + H2 system.'* Preliminary results clearly indicate that reaction on repulsive surfaces (2Z+ in C,,, 2A1 in C2, geometry, corresponding to blue detuning) leads preferentially to low product rotation, while reaction on attractive surfaces ('n in C,,, 2B1 in C2, geometry, corre- sponding to red detuning) leads preferentially to high product rotation. It might also be noted that the repulsive surface is'predicted to have a barrier in both C,, and C2, Assuming these surfaces are reasonably accurate, a state-selective Franck- Condon excitation of the van der Waals NaH, molecule could access the region of the 2X+/2A, barrier and directly test the strong inside/ outside and above/ below-barrier asymmetries in the simple model (Fig.1).l6 Similarly, it could directly probe resonant structure near the barrier maxima. The many contributions of Professor R. B. Bernstein to inspiring interest in the study of quasibound states/orbiting resonances and their possible importance in chemical reactions are gratefully acknowledged. References 1 V. Zafiropulos, P. D. Kleiber, K. M. Sando, X. Zeng, A. M. Lyyra and W. C. Stwalley, Phys. Rev. Lett., 2 P. D. Kleiber, J.-X. Wang, K. M. Sando, V. Zafiropulos and W. C. Stwalley, J. Chem. Phys., submitted. 3 J. X. Wang, P. D. Kleiber, K. M. Sando and W. C . Stwalley, Phys. Rev. A, 1990, 42, 5352. 4 K. C. Lin, P. D. Kleiber, J. X. Wang, W. C. Stwalley and S. R. Leone, J. Chem. Phys., 1989, 89, 4771. 5 S. Ananthamurthy, P. D. Kleiber, W. C .Stwalley and K. C. Lin, J. Chem. Phys., 1989, 90, 7605. 6 S. Ananthamurthy and P. D. Kleiber, to be published. 7 J. T. Bahns, W. C . Stwalley and G. Pichler, J. Chem. Phys., 1989, 90, 2841. 8 K. K. Verma, J. T. Bahns, A. R. Rajaei-Rizi, W. C . Stwalley and W. T. Zemke, J. Chem. Phys., 1983, 9 J. T. Bahns, K. K. Verma, A. R. Rajaei-Rizi and W. C. Stwalley, Appl. Phys. Lett., 1983, 42, 336. 1988,61, 1485. 78, 3599. 10 G. Pichler, J. T. Bahns, K. M. Sando, W. C . Stwalley, D. D. Konowalow, L. Li, R. W. Field and 11 W. T. Luh, J. T. Bahns, K. M. Sando, W. C. Stwalley, S. P. Heneghan, K. P. Chakravorty, G. Pichler 12 W. T. Luh, J. T. Bahns, A. M. Lyyra, K. M. Sando, P. D. Kleiber and W. C. Stwalley, J. Chem. Phvs., 13 W. T. Luh, K. M. Sando, A. M. Lyyra and W.C . Stwalley, Chem. Phys. Lett., 1988, 144, 221. 14 M. Masters, J. Huennekens, W.-T. Luh, L. Li, A. M. Lyyra, K. Sando, V. Zafiropulos and W. C . 15 P. D. Kleiber, A. M. Lyyra, K. M. Sando, S. P. Heneghan and W. C. Stwalley, Phys. Rev. Lett., 1985, W. Miiller, Chem. Phys. Lett., 1986, 129, 425. and D. D. Konowalow, Chem. Phys. Lett., 1986, 131, 335. 1988,88, 2235. Stwalley, J. Chem. Phys., 1990, 92, 5801. 54, 2003.110 Metal Reactive Transition States 16 P. D. Kleiber, A. M. Lyyra, K. M. Sando, V. Zafiropulos and W. C. Stwalley, J. Chem. Phys., 1986, 17 P. D. Kleiber, Phys. Rev. A, 1988, 37, 2719. 18 S. Bililign and P. D. Kleiber, Phys. Rev. A, 1990, 41, 6938. 19 R. B. Bernstein, Phys. Rev. Lett., 1966, 16, 385. 20 W. C. Stwalley, A. Niehaus and D. R. Herschbach, J.Chem. Phys., 1975, 63, 3081. 21 G. Herzberg, Spectra of Diatomic Molecules, Van Nostrand, New York, 2nd edn., 1950, p. 425. 22 R. J. Le Roy and R. B. Bernstein, J. Chem. Phys., 1971, 54, 5114. 23 R. E. Roberts, R. B. Bernstein and C. F. Curtiss, J. Chem. Phys., 1969, 50, 5163. 24 K. R. Way and W. C. Stwalley, 1. Chem. Phys., 1973, 59, 5298. 25 W. C. Stwalley, J. Chem. Phys., 1975, 63, 3062. 26 W. T. Zemke and W. C. Stwalley, Chem. Phys. Lett., 1988, 143, 84. 27 W. T. Zernke, W. C. Stwalley, J. A. Coxon and P. G. Hajigeorgiou, Chem. Phys. Lett., in the press. 28 M. M. Hessel and C. R. Vidal, J. Chem. Phys., 1979, 70, 4439. 29 H. J. Vedder, G. K. Chawla and R. W. Field, Chem. Phys. Lett., 1984, 111, 303. 30 J. Heinze and F. Engelke, J. Chem. Phys., 1988, 89, 42. 31 W. T. Luh and W. C. Stwalley, J. Mol. Spectrosc., 1991, 145, 200. 32 U. Gaubatz, R. Rudecki, M. Becker, S. Schiemann, M. Kulz and K. Bergmann, Chem. Phys. Lett., 33 J. Kuklinski, U. Gaubatz, F. T. Hioe and K. Bergmann, Phys. Rev. A, 1989, 40, 6741. 34 U. Gaubatz, P. Rudecki, S. Schiemann and K. Bergmann, J. Chem. Phys., 1990, 92, 5363. 35 H. G. Rubahn and K. Bergmann, Annu. Rev. Phys. Chem., 1990, 41, 735. 36 E. W. Rothe, U. Krause and R. Diiren, Chem. Phys. Lett., 1970, 72, 100. 37 R. Dubs and P. S. Julienne, J. Chem. Phys., submitted. 38 U. Fano and J. H. Macek, Rev. Mod. Phys., 1973,45, 553. 39 M. D. Havey and L. L. Vahala, J. Chem. Phys., 1987, 86, 1648. 40 A. M. Lyyra, H. Wang, T.-J. Whang, L. Li and W. C. Stwalley, Phys. Rev. Lett., submitted. 41 L. Li, T.-J. Whang, H. Wang, A. M. Lyyra and W. C. Stwalley, to Phys. Rev. Lett., submitted. 42 J. Tellinghuisen, in Photodissociation and Photoionizations, ed. K. P. Lawley, Wiley, New York, 1985, p. 299. 43 H. Wang, T.-J. Whang, A. M. Lyyra, L. Li and W. C. Stwalley, J. Chem. Phys., in the press. 44 P. Chaquin, A. Sevin and H. Yu, J. Phys. Chem., 1985, 89, 2813. 45 K. Morokuma, personal communication. 46 W. H. Breckenridge and H. Urnemoto, J. Chem. Phys., 1984, 80, 4168. 47 F. Rossi and J. Pascale, Phys. Rev. A, 1985, 32, 2657. 85, 5493. 1988, 149, 463. Paper 1/00231G; Received 16th January, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100097

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1991, 91, 111-172 GENERAL DISCUSSION Prof. J. C. Polany (University of Toronto) said: I should like to make two simple points, one in regard to the work of Weaver and Neumark’ and one concerning the paper of Schatz et a1.*. These points hark back to earlier discussions of reaction dynamics. Prof. Neumark’s success in ‘parachuting’ from an anionic state, FHS, to the transition- state region of the F+ H2 + HF+ H reaction (to cite only the present example) represents a breakthrough in the field of ‘transition-state spectroscopy’. My comment is largely pedantic. In saying (as these authors do when comparing their findings with those derived from early dynamical studies) that the F+ H2 ‘reaction has an early barrier in the reactant valley’ one is making a true but perhaps misleading statement.Though the barrrier crest is indeed in the entry valley (as is commonly the case for exoergic reactions), for this reaction only a minor fraction of the energy-release is in the entry valley: this is therefore a repulsive potential-energy surface (p.e.s.). By referring only to the barrier location and describing it as ‘early’, one invites the misunderstanding that the downhill portion of the p.e.s. is predominantly in the entry valley, which it is Ref. 2 is an important theoretical adjunct to Ref. 1; it looks at the effect on the transition-state photodetachment spectrum of increases in barrier height on a LEPS p.e.s. Here again it may be worth recalling that in earlier studies4 an increasing barrier height correlated strongly with a shift in the (classical) barrier to late positions along the entry valley.If, for example, for these authors’ surface A (low barrier) the IHI- anion were to form IHI” in the region of the barrier crest, for surface D it would be likely to form IHI” in advance of the barrier crest. This would not in any sense invalidate the findings, but should be born in mind in attempting to conceptualise them. 1 A. Weaver and D. M. Neumark, Furuday Discuss. Chem. SOC., 1991, 91, 5. 2 G. C. Schatz, D. Sokolovski and J. N. L. Connor, Furuday Discuss. Chem. SOC., 1991, 91, 17. 3 J. C. Polanyi and J. C. Schreiber, Furaduy Discuss. Chem. SOC., 1977, 62, 267. 4 M. H. Mok and J. C. Polanyi, J. Chem. Phys., 1969, 51, 1451. Prof. D. M. Neumark (University of California, Berkeley) replied: Prof.Polanyi’s comment pertaining to the F+H2 barrier is quite relevant. We merely wished to point out that the barrier is early enough in the entrance channel so that the FH, anion has good overlap with the neutral transition-state region. Our earlier photodetachment studies of heavy + light-heavy reactions used strongly hydrogen-bonded (Do - 1 eV) XHY-. anions as the precursor to the neutral transition-state region. In these anions the HX and HY distances are known (or predicted) to be substantially longer than in diatomic HX or HY, leading one to expect good overlap with the neutral transition-state region. In contrast, FH, is calculated by Nichols et al. to be much less weakly bound (Do= 0.20 eV) than the bihalide anions, and, in the anion equilibrium geometry, the calculated H-H distance of 0.770 8, is very close to that of diatomic H2 (0.742 A).Thus, FH, can be thought of as H2 weakly perturbed by F-. Under these circumstances one might expect photodetachment to access the asymptotic region of the F+ H2 entrance valley, yielding a rather uninteresting photoelectron spectrum. However, because the barrier occurs sufficiently early in the entrance channel, one instead probes the neutral transition-state region. 1 J. A. Nichols, R. A. Kendall, S. J. Cole and J . Simons, J. Phys. Chem., 1991, 95, 1074. Prof. G. Schatz ( Northwestern Uniuersity ) also responded: Prof. Polanyi correctly notes that for LEPS surfaces there is usually an important correlation between barrier height and saddle-point location.One exception to this occurs for symmetrical reactions 111112 General Discussion like I + HI, where for a wide range of Sat0 parameters the saddle point has a symmetrical geometry which does not change significantly with barrier height. However, even in this case the location of the eflective reaction barrier can vary with barrier height. Indeed we find strong evidence for this, with the effective barrier becoming tighter and more symmetrical as barrier increases. This plays an important role in determining reaction thresholds, as we noted in our paper, and it also causes the peak locations in the photodetachment spectra to shift gradually below these thresholds as the barrier is increased. Prof. D. G. Truhlar ( University of Minnesota) said: Prof.Neumark and his co-workers make the statement that incorrect product distributions may reflect inaccuracies in the 5a potential surface in the product-like region. We have carried out accurate quantum dynamics on four different F+H, surfaces,’ and one of our results is very striking in this regard. Two of the surfaces we studied differed significantly only in the reactant-like region, but nevertheless the change has a very significant effect on the product vibrational distribution. which shows that sometimes the product distribution for exothermic regions correlates much better with attributes of the region of high reaction-path curvature (even when it is energetically more similar to reactants than to products) than it does with those of the product-like region.In addition there is strong theoretical evidence based on electronic structure c a l c ~ l a t i o n s ~ - ~ ~ that surface 5a is more accurate in the product valley than near the saddle point. Thus we should not conclude that the reactant-like region is better known than the product-like region for the F + H2 surface. In addition I wish to call attention to other 1 G. C. Lynch, P. Halvick, M. Zhao, D. G. Truhlar, C.-h. Yu, D. J. Kouri and D. W. Schwenke, J. Chem. 2 J. W. Duff and D. G. Truhlar, J. Chem. Phys., 1975, 62, 2477. 3 D. G. Truhlar and D. A. Dixon, in Atom- Molecule Collision Theory, ed. R. B. Bernstein, Plenum, New York, 1979, p. 505. 4 D. G. Truhlar, F. B. Brown, D. W. Schwenke, R. Steckler and B. C. Garrett, in Comparison of Ab Initio Quantum Chemistry with Experiment .for Small Molecules, ed. R.J. Bartlett, Reidel, Dordrecht, 1985, p. 95. Phys., 1991, 94, 7150. 5 R. Steckler, D. W. Schwenke, F. B. Brown and D. G. Truhlar, Chem. Phys. Lett., 1985, 121, 475. 6 D. W. Schwenke, R. Steckler, F. B. Brown and D.G . Truhlar, 1. Chem. Phys., 1986, 84, 5706. 7 C. W. Bauschlicher Jr., S. P. Walch, S. R. Langhoff, P. R. Taylor and R. L. Jaffe, J. Chem. Phys., 1988, 88, 1743. 8 C. W. Bauschlicher Jr., S. R. Langhoff and P. R. Taylor, in Supercomputer Algorithmsfor Reactivity, Dynamics and Kinetics of Small Molecules, ed. A. Laganii, Kluwer, Dordrecht, 1989, p. 1 9 C. W. Bauschlicher Jr., S. R. Langhoff and P. R. Taylor, Adu. Chem. Phys., 1990, 77, 103. 10 G. C. Lynch, R. Steckler, D. W. Schwenke, A. J. C. Varandas, D.G. Truhlar and B. C. Garrett, J. Chem. Phys., 1991, 94, 7136. Prof. Neumark responded: We base our statement that the reactant region on the T5a surface is well characterized on the overall agreement between our experimental FH, photoelectron spectrum, which probes this region, and the simulations on this surface by Zhang and Miller. The key question is whether the product vibrational distribution or the photoelectron spectrum is more sensitive to the details of the surface in this region. It would be of considerable interest to simulate the anion photoelectron spectrum using one of Professor Truhlar’s new F+ H2 surfaces. Prof. J. J. Valentini (Columbia University) said: It is a little disappointing to see the apparent difficulty that is encountered in analysing the beautifully detailed photodetach- ment spectra from Professor Neumark’s experiments.Professor Schatz’s attempts to fit the IHI- spectra by varying potential parameters is at least partially successful, but the impression I get from his paper is that we can really understand the details of the photodetachment spectra only if we know the potential-energy surface for the reaction.General Discussion 113 However, if we really knew the surface we would not need the photodetachment experiments. Can we not find a way to get information on the potential-energy surface and dynamics directly from the photodetachment spectra, i.e. a way in effect to ‘invert’ the spectra to determine the shape of the potential-energy surface and the nature of the scattering wavefunctions in the transition-state region? What kind of detail in the photodetachment spectra would make such an approach feasible? Do we need not only the present spectra but also the final state distributions of the products of the photodetach- ment? Do we need better information on the structure of the ion? Separability of the motion along and perpendicular to the reaction coordinate makes resonances, and therefore peaks in the photodetachment spectra, prominent in the kinematically extreme heavy-light-heavy systems like IHI.Should not this separability also make the ‘inversion’ of the photodetachment spectra that I ask about relatively easy? Prof. Neumark answered: The inversion of the IHI- photoelectron spectrum should be reasonably straightforward if you restrict the neutral potential-energy surface to be collinear.However, in three dimensions the IHI antisymmetric stretch and bend appear to be strongly coupled.’ Nonetheless, approximate inversion schemes which assume separability would probably be of value. 1 C. Kubach, G. Nguyen Vien and M. Richard-Viard, J. Chem. Phys., 1991,94, 1929. Prof. H. Taylor (University of Southern California) said: The position of the resonances may not be too sensitive to the static hypersurface because the resonance is trapped and caused by a local adiabatic potential embedded in the total static potential. If this adiabatic local potential region does not touch the walls of the static potential then the resonances depend mostly on the adiabatic potential. The widths are more sensitive to the true potential since they are obtained from a matrix element that couples the local trapping region to the exterior region which does touch the walls of the static potential.In short we believe that in general fitting the true static potential is not an easy task, as at least the resonance positions are weakly connected to the static potential. I predict that such fittings, when successful, may not be unique. Dr. G. G. Balins-Kurti ( University of Bristol) continued: Prof. Valentini commented that Prof. Neumark’s beautiful results might be inverted to yield a potential-energy surface for the IHI system. I note that even in the simplest case two surfaces need to be involved in the modelling, namely that of IHI- and that of IHI. Secondly, it is almost certain that many IHI potential-energy surfaces, and not just one, participate in the process. Prof.Neumark answered: Dr. Baht-Kurti’s point about the importance of the IHI- surface is well taken. In our simulations of the IHI- photoelectron spectrum (and in all the others as well), harmonic potentials were used for all modes of IHI- with frequencies determined from matrix-isolation spectroscopy. An inter-iodine equilibrium distance of Re = 3.88 A was also assumed. Recent (unpublished) calculations by Bauschlicher on IHI- yield a value of Re close to our estimate, but show the potential- energy surface to be highly anharmonic. It will clearly be of interest to perform simulations with more realistic anion wavefunctions; we expect this to have a larger effect on the peak intensities than on the positions or widths.With regard to multiple neutral potential-energy surfaces, three potential-energy surfaces result from the interaction of the two spin-orbit states of I with HI; only one, the ground-state surface, adiabatically correlates with ground-state products. We observe transitions to the ground-state surface and at least one of the excited-state surfaces in the 213 nm photoelectron spectrum of IHI-; the two sets of progressions corresponding to these transitions are separated by 1 eV (near the I atom spin-orbit splitting). The114 General Discussion question remains whether transitions to the other excited-state surface overlap with the ground-state or with the excited-state band seen in the 213 nm spectrum. 1 R. B.Metz, S . E. Bradforth and D. M. Neumark, Adv. Chem. Phys., in the press. Dr. D. E . Manolopoulos (University of Nottingham) said: One or two rather simple observations can be made regarding the extraction of electronic potential-energy surfaces from the anion photodetachment spectra of Weaver and Neumark. These observations, in common with other related theoretical work,’-3 are based on the assumption that the experimental electron kinetic-energy distribution a( ekE) is proportional to a simple Franck-Condon factor, P( E f ), which can be written equivalently as3 and Here is a scattering wavefunction at energy E f with asymptotic fragment quantum numbers n on the final (neutral) electronic potential-energy surface Vf, p is the density of scattering states at energy Ef, which depends on the normalisation chosen for +E,n , and 4i is a rovibrational boundstate wavefunction with energy Ei on the initial (anion) electronic potential-energy surface V , .The electron kinetic energy ekE, final neutral energy E f , and initial anion energy Ei are related by total energy conservation Ef-Ei=hw-(ekE) (4) where o is the (fixed) photodetachment laser frequency. Supposing for simplicity that the anion electronic potential-energy surface V , and the initial bound rovibrational wavefunction +i are both known, and that one has some given functional form for the neutral electronic potential-energy surface Vf , one can envisage fitting the parameters in this functional form to the experimental data of Weaver and Neumark in a variety of ways.One might, for example, perform the time-indepen- dent quantum reactive scattering calculations implied by eqn. ( l ) , or equivalently the time-dependent quantum reactive scattering calculations implied by eqn. (2), for a variety of different parameter sets and see which set gives the best fit to the experimental results. In fact this is precisely the approach taken by Schatz et al. in their study of the IHI- photodetachment spectrum presented at this Discu~sion.~ Full 3D quantum reactive scattering calculations are still quite expensive to perform, however, and one wonders whether there might not be a more direct approach. One possible direct approach is based on spectral moments,and follows immediately from the third expression for the Franck-Condon factor in eq.(3): The first few moments ( n = 0, 1 , 2 , . . .) on the left-hand side of this equation are easily extracted from the experimental spectrum, and can be regarded as providing a compact representation for the averaged structure of the experimental results. The expectation values on the right-hand side are also far easier to compute, at least for small n, than the full quantum scattering calculations are to perform. Therefore, by adjusting the parameterisation of Vf to fit only the first few spectral moments, rather than the entire spectrum, considerable efficiencies might be gained.General Discussion 115 Of course this argument assumes that the first few spectral moments do indeed contain the required potential-energy surface information. To establish that this is so it is instructive to look at the n = 0, n = 1 and n = 2 cases in more detail.First, for n = 0, we obtain an appropriate normalisation for the experimental spectrum: Secondly, using Hi 1 +J = Ei is the same in both Hf = T + Vf and Hi = T + n = l and n = 2 : and the fact that the nuclear kinetic-energy operator T , we can simplify the expressions for and Unfortunately this simplification cannot be carried beyond the second moment, because Hf and Hi do not in general commute. Nevertheless, it is clear that the first two moments of P(Ef), which are related to the average position and width of the photodetachment spectrum a(ekE), depend only on the difference between the anion (V,) and neutral ( V,) electronic potential-energy surfaces in the neighbourhood of the anion rovibrational wavefunction.In this sense, then, the first few moments of an anion photodetachment spectrum do indeed contain valuable information about the excited (neutral) electronic potential-energy surface. This information becomes all the more valuable when the equilibrium geometry of the anion happens to lie close to the transition state of the neutral Indeed Neumark and co-workers have often remarked that their experiments are most interesting under these circumstances, being tantamount to direct ‘spectroscopy of the transition state’. Eqs. (7) and(8), which are exact within the usual theoretical assumptions, seem to quantify this idea. The average position and width of the experimental spectrum only ever depend on the final potential-energy surface near the equilibrium geometry of the anion, and under these circumstances this geometry coincides with the transition- state region of the neutral reaction.Incidentally, since reactive scattering resonances have now been conclusively iden- tified in some of the spectra of Neumark and co-~orkers’-~ one might question whether a neutral surface with parameters fit to moments of the experimental spectrum is also likely to reproduce the resonance positions and widths. At first sight one might think not, especially if only the first two moments ( n = 1 and n = 2) are used to fit the potential, because resonant scattering states often access a far larger region of the available coordiate space than the initial anion wavefunction. Moreover, calculated resonance positions and widths are known to be extremely sensitive to fine details of the potential- energy surface used.However, assuming that the usual theoretical assumptions used to model these spectra are valid,’-3 at least one neutral potential-energy surface must exist which reproduces, via eqn. (3), both the first few moments of the spectrum and the resonance positions and widths. Therefore, if one has some sensible parametric form for the reactive neutral surface, with the correct dissociation properties and long-range interactions, optimising the parameters in this form to fit the moments of the spectrum does at least make sense. Whether or not the resulting optimised surface reproduces the resonance positions and widths can then be determined in a full-blown reactive scattering calculation, and so serves as an a posteriori check.116 General Discussion While these simple ideas are probably well known to a number of people at this Discussion, I believe that they have not yet been used as much as they should.In fact, since they apply equally well to straightforward molecular photodissociation, albeit with a minor modification regarding the relationship between the Franck-Condon factor and the experimental absorption spectrum, a variety of possible applications come to mind. Initial model applications are currently planned for several of the anion photodetachment spectra of Neumark and co-workers, especially those (like IHI-) for which both the anion and neutral potential-energy surfaces still remain largely unres01ved.~ 1 G.C. Schatz, J. Chem. Phys., 1989, 90, 3582. 2 B. Gazdy and J. M. Bowman, J. Chem. Phys., 1989, 91, 4615. 3 J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1990, 92, 1811. 4 G. C. Schatz, D. Sokololvski and J. N. L. Connor, Faraday Discuss. Chem. Soc,, 1991, 91, 17. 5 R. B. Metz, T. Kitsopoulos, A. Weaver and D. M. Neumark, J. Chem. Phys., 1988, 88, 1463. 6 A. Weaver, R. B. Metz, S. E. Bradforth and D. M. Neumark, J. Phys. Chem., 1988, 92, 5558. 7 R. B. Metz, A. Weaver, S. E. Bradforth, T. N. Kitsopoulos and D. M. Neumark, J. Phys. Chem., 1990, Dr. M. S. Child (University of Oxford) commented: Concerning the possibility of inverting the resonance data on IHI to determine the potential function, I wonder how far it is possible to isolate different features of the surface and to relate them to different observations.For example, the existence of such resonances requires that the frequencies o1 and o2 of transverse motion to the reaction path depend on the reaction coordinate, say Q3. How well do the resonance energies for the two isotopic species determine wl( Q3) and w2( Q3)? Secondly the resonance widths no doubt have tunnelling contribu- tions and vibrationally non-adiabatic contributions, of which the latter must depend in part on (do,/dQ3) and (doJdQ3) and in part on the curvature of the reaction path. Can either Prof. Neumark or Prof. Schatz give a ‘score card’ to show which aspects of the experimental data are best accounted for and which features of the potential surface are thought to be best understood? 94, 1377. Prof.Neumark responded: In our analysis of the BrBHr- and BrDBr- photoelectron spectra’ we devoted considerable effort to the construction of an ‘effective’ collinear potential-energy surface (one with the zero-point bending motion implicitly included) for the Br + HBr reaction which reproduced our experimental spectra in simulations. The experimental spectra show progressions in the V3 antisymmetric stretch mode of the neutral complex, and the simulated peak positions were very sensitive to the double minimum potential along the Q3 coordinate in the Franck-Condon region. We feel that this aspect of the surface is reasonably well characterized. In addition, the existence of resonances and the simulated peak widths in general were found to depend on the slope of the minimum energy path in the Franck-Condon region of the surface; a more steeply rising path resulted in broader peaks from direct scattering and smaller contributions from resonances, and it was necessary to construct a surface with a steeply rising path in order to obtain sufficiently broad peaks in the simulated spectra.We found that the minimum energy path on LEPS surfaces tended to rise too gradually, resulting in simulated features much narrower than the experimental peaks. However, these conclusions are drawn on the basis of collinear simulations only. 1 R. B. Metz, A. Weaver, S. E. Bradforth, T. N. Kitsopoulos and D. M. Neumark, J, Phys. Chem., 1990, 94, 1377. Prof. J. Manz ( Universitat Wiirzburg ) (communicated): Resonances at the transition state of IHI or similar systems (as observed by Neumark and coworkers’ by means of photoelectron detachment of anions IHI- and analysed by Schatz et a1.* Kubach3 and previously by Bowman et al.4) had been predicted first in quantum evaluations of reaction probabilities in the I + IH reaction, using the collinear Later they were rational- ized by means of the diagonally corrected vibrationally adiabatic hypersphericalGeneral Discussion 117 (DIVAH) t h e ~ r y , ~ which exploits a Born-Oppenheimer-type separation of hyper- spherical radial and angular coordinates’ representing essentially the motions of heavy (I) and light (H) atoms, similar to the usual separation of nuclear and electronic degrees of freedom. Kubach’s approach3 may be considered as substantial extension yielding, in part, similar results and interpretations (e.g.the analogy of IHI ‘hydrogenic’ states and H i = pep ‘electronic’ states),’ but also substantial new insight (e.g. the selective role of rotational excitations in three-dimensional (3D) models: for previous 3D evalu- ations of IHI, see ref. 2,4,9 and 10). The analyses of Neumark’s’ photodetachment spectra of IHI by Schatz2 and by Kubach3 are also similar in several aspects; however, they differ in an important detail which has substantial consequences. On the one hand, Kubach3 obtains good agreement with Neumark’s’ spectra, using our original empirical LEPS potential-energy surface A.5 This surface has a rather low barrier of 0.048 eV, supporting vibrational bonding.’-’’ However, the bound states of IHI lie outside the Franck-Condon region of IHI-; therefore they do not yield any prominent peaks in the original photodetachment spectra.On the other hand, Schatz2 obtains the best agreement with Neumark’s results’ if he uses a modified potential-energy surface (surface C in Ref. 2) with a slightly higher barrier of 0.161 eV. As a consequence, this surface does presumably (?) not support vibrational bonding. Thus there are no peaks for IHI bound states in the simulated photoelectron detachment spectra of IHI-. My question to Professors Schatz and Kubach is: Does vibrational bonding in IHI exist or not? Or should this be considered as an open question, calling for new analyses of new, refined measurements, preferably in the low-frequency part of the original spectra ?’ Of course, the confirmation of vibrational bonding in IHI should be fascinating.In any case, this new type of chemical bonding may exist in other weakly bound molecules.’* 1 A. Weaver, R. B. Metz, S. E. Bradforth and D. M. Neumark, J. Phys. Chem., 1988, 92, 5558; I. M. Waller, T. N. Kitsopoulos and D. M. Neumark, J. Phys. Chem., 1990, 94 2240; R. B. Metz, S. E. Bradforth and D. M. Neumark, Adv. Chem. Phys., in the press; see also A. Weaver and D. M. Neumark, Famday Discuss. Chem. Soc., 1991, 91, 5. 2 G. C. Schatz, J. Chem. Phys., 1989,90,4847; J. Phys. Chem., 1990,94,6157; G. C. Schatz, D. Sokolovski and J. N . L. Connor, Faraday Discuss. Chem. SOC., 1991, 91, 17. 3 C. Kubach, Chem. Phys. Lett., 1989, 164,475; C. Kubach, Faraday Discuss.Chem. SOC., 1991,91, 118. 4 B. Gazdy and J. M. Bowman, J. Chem. Phys., 1989, 91, 4615. 5 J. Manz and J. Romelt, Chem. Phys. Lett., 1981, 81, 179. 6 J. A. Kaye and A. Kuppermann Chem. Phys. Lett., 1981,77, 573. 7 J. M. Launay, J. Phys. B, 1982, 15, L455; J. Romelt, Chem. Phys., 1983, 79, 179; D. K. Bondi, J. N. L. 8 A. Kuppermann, J. A. Kaye and J. P. Dwyer, Chem. Phys. Lett., 1980,74,257; G. Hauke, J. Manz and 9 J. Manz, R. Meyer and J. Romelt, Chem. Phys. Lett., 1983, 96, 607. Connor, J. Manz and J. Romelt, Mol. Phys., 1983, 50, 467. J. Romelt, J. Chem. Phys., 1980, 73, 5040. 10 D. C. Clary and J. N. L. Connor, Chem. Phys. Lett., 1983, 94, 81; J. Phys. Chem., 1984, 88, 2758. 1 1 E. Pollak, in Intramolecular Dynamics, ed. J. Jortner and B. hllmann, Reidel, Dordrecht, 1982, p.1; J. Manz, R. Meyer, E. Pollak and J. Romelt, Chem. Phys. Lett., 1982, 93, 184; J. Manz, R. Meyer, E. Pollak, J. Romelt and H. H. R. Schor, Chem. Phys., 1984, 83, 333; J. Manz, R. Meyer and H. H. R. Schor, J. Chem. Phys., 1984,80, 1562; J. Manz and J. Romelt, Nachr. Chem. Tech. Lab., 1985,33, 210. 12 B. S. Ault and J. Manz, Chem. Phys. Lett., 1985, 115, 392. Prof. Schatz replied: Dr. Child, Prof. Manz and several others raise important questions concerning how much information can be derived from the photodetachment experiments about the properties of the IHI potential surface. Let me respond by first noting that the most unambiguous properties available from the measurements are the symmetric and antisymmetric stretch frequencies. These are matched very well by our theoretical simulations using surface A.They are not, however, very sensitive to barrier118 General Discussion height, so it is likely that our other surfaces will give similar frequencies to A (although we have not explored that point in detail yet). It does not appear that the transition-state bend frequency can be derived from the spectra. Photodetachment should be able to provide an accurate estimate of the I + HI barrier height (through the location of the resonance peaks relative to the I + HI asymptote), but unfortunately there is a 0.13 eV uncertainty in the location of the asymptote because of a similar uncertainty in the IHI- dissociation energy. This makes it possible for us to match the measured peak energies using all four of the surfaces we considered, despite their huge range of barrier heights (0.05-0.24 eV).It is precisely this problem with barrier height that makes it difficult to give a definitive answer to Professor Manz’s question concerning vibrational bound states. Only surface A of our surfaces has such a bound state, but the Franck-Condon overlap with that state is so small it may not be observable in the measurements. Since the locations of the peaks using surface A are consistent with experiment (admittedly they are just on the edge of the energy uncertainty), we cannot rule out that surface. However, we feel the higher barrier surfaces, especially surface C, are slightly to be preferred, because the fine structure of the v3 = 0 region (spacing and widths) is in better agreement with experiment.The photodetachment peak widths may also provide important clues concerning the correct IHI potential surface. These widths are for the most part not limited by instrumental resolution or rotational broadening, so they should reflect the intrinsic lifetimes of the transition-state resonances. In the u3=2 region of the spectrum, the measured peak widths are all ca. 12 meV, while those calculated for surface A are ca. 2 meV. We have not determined these widths for surfaces B-D, but they are presumably larger, since the adiabatic well which supports the resonances (see comments by Manz and Kubach) must be shallower. For the v 3 = 0 region of the spectrum, the measured widths are roughly 15 meV, which agrees best with our calculated results for surface C.For surface A we find both narrow and broad peaks in the u 3 = 0 region, and some peaks are much narrower than 15 meV. Dr. Child also raises the question of how to interpret the resonance widths. Within the context of the adiabatic models mentioned by Manz and Kubach, the resonances can decay either by tunnelling or by nonadiabatic coupling. For the v3 = 2 resonances, the widths are independent of resonance energy, which suggests that nonadiabatic coupling is the dominant mechanism. These resonance widths increase substantially (over a factor of 10) on going from collinear to three dimensional models of I + HI, which indicates that decay in three dimensions is controlled by bending motions. These results are consistent with Kubach’s picture of resonance decay via coupling to excited rotational states that are accessed by bending away from linear IHI.One hopes that a more detailed theory of resonance widths that incorporates these concepts will soon be developed so that the widths may be used to derive specific features of the IHI surface. Prof. C . Kubach (University of Paris-Sud) (communicated): My point of view is that the occurrence of vibrational bonding in IHI is still an open problem for theoretical and experimental reasons. The theoretical point is that this bonding would require a very specific barrier (smaller than 0.052 eV, which is the ground-state vibrational energy of the IH molecule). This accuracy, for such a system, is a challenge for theoreticians working on calculations of potential energy surfaces.The experimental point is that the photodetachment of the IHI anion performed by Neumark and co-workers is presently the only experimental way to investigate the IHI system. Despite the fact that this experiment has provided renewed interest in this system, the detailed analysis of the results is limited by uncertainties in the spectroscopic constants of the IHI anion. Furthermore, this kind of experiment could only determineGeneral Discussion 119 the electronic surface in the Franck-Condon region, which may be far from the location of bound states of the IHI system. The partial agreement obtained by Schatz et al. between the calculated and experi- mental photodetachment spectra by increasing the barrier might also be achieved by acting on other parameters of the electronic surface.In conclusion, additional experimental investigations involving in particular IH + I collisions could contribute to answer the question of the vibrational bonding in IHI or other systems, which is (as mentioned by Manz) a fascinating topic. Prof. Neumark asked Prof. Schatz: You have shown that the u3=0 features in the simulated IHI- spectrum are very sensitive to changes in the barrier height on the model I + H I potential-energy surface used in the calculation. Have you looked at the effect of these changes on the u3=2 and u3=4 peaks? One might find markedly different effects, since these peaks are due to localized resonances while the u3=0 features are due to direct transitions. Prof. Schatz replied: As the IHI barrier is increased, the resonances associated with the u3 = 2 and 4 regions of the spectrum will both increase in energy and become less stable.An important worry then is whether the higher barrier surfaces will still have the resonance structure that we know from your experiments must be present. We have not yet examined this point in our computations, but it is reasonable to predict that at least some resonance structure will be present. This is because the highest barrier we have considered is still well below that found in our Cl+HCl calculations (0.24 us. 0.37 eV). The latter calculations show that one v3 = 2 resonance exists (the v3 = 4 region has not been studied). For I + HI on surface A we have found seven resonances in the u3=2 region. Surfaces B, C and D will probably have fewer, but it is likely that our most reasonable surface, namely C, has at least the three resonances that have been found in your measurements.Prof. Manz said to Prof. Neumark: In a paper with Bisseling, Gertitschke and Kosloff' we carried out the first time-dependent model simulations of resonance decay in an asymmetric triatomic system: F+DBr + FDBr" + FD+Br ( 1 ) somewhat similar to the dissociation F+H, +- FH,* -+ FH+H (2) which has been studied experimentally by Neumark and co-workers2 by means of photoelectron-detachment spectroscopy of the anion FH y . We also discovered strong correlations of the unimolecular decay ( 1 ) with the bimolecular reaction F+DBr+ FDBr" + FD+Br (3) at energies close to those of resonances FDBr". By analogy, it is of course fascinating to see corresponding correlations of Neumark's spectra' for process (2), and possible resonances in the reaction F+H, + FH,* + FH+H (4) as discussed in ref.3. Moreover, we predicted that the branching ratio of products F + DBr/ FD + Br in process ( 1 ) should depend selectively on the specific resonance FDBr" that is excited initially.' This conclusion has been confirmed by similar model simulations of selective resonance decay4 H+OD + HOD + HO+D ( 5 )120 General Discussion and isotopomers,’ inducing specific bond ruptures. I should like to ask Professor Neumark whether he already has any experimental evidence for similar selective branch- ing ratios in reaction (2), analogous to our predictions,’.435 in addition to stimulating correlations with theoretical model^?^ This would establish a new technique of selective bond fissions induced by photoelectron detachment, complementary to other methods such as the IR+VIS-UV two-photon strategy suggested by Imre et a1.6 and verified by Crim et al.’ and Bar et aL:* for a recent survey.See ref. 4. 1 R. H. Bisseling, P. L. Gertitschke, R. Kosloff and J. Manz, J. Chem. Phys., 1988, 88, 6191; see also J. Manz and J. Romelt, J. Chem. SOC., Furuduy Trans., 1990, 86, 1689. 2 A. Weaver and D. M. Neumark, Furuduy Discuss. Chem. SOC., 1991, 91, 5: R. B. Metz, S. E. Bradforth and D. M. Neumark, Adv. Chem. Phys., in the press. 3 D. M. Neumark, A. M. Wodtke, G. N. Robinson, C. C. Hayden and Y. T. Lee, J. Chem. Phys., 1985 82, 3045; D. M. Neumark, A. M.Wodtke, G. N. Robinson, C. C. Hayden, K. Shobatake, R. K. Sparks, T. P. Schafer and Y. T. Lee, J. Chem. Phys., 1985, 82, -1067; Z. Bacic, J. D. Kress, G. A. Parker and R. T Pack, J. Chem. Phys., 1990, 92, 2344; C.-H. Yu, D. J. Kouri, M. Zhao and D. G. Truhlar, Chem. Phys. Left., 1989, 157, 491; J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1990, 92, 1811: D. E. Manolopoulos, M. D’Mello and R. E. Wyatt, J. Chem. Phys., 1990, 93, 403; J. M. Launay and M. LeDourneuf, Chem. Phys. Lett., 1990, 169, 473. 4 B. Hartke, J. Manz and J. Mathis, Chem. Phys., 1989, 139, 123. 5 B. Hartke and J. Manz, J. Chem. Phys., 1990, 92, 220. 6 D. G. Imre and J. Zhang, Chem. Phys., 1989, 139, 89. 7 R. L. Vander Wal, J. L. Scott and F. F. Crim., J. Chem. Phys., 1990, 92, 803; F.F. Crim, Science, 1990, 8 I.Bar, Y. Cohen, D. David, S. Rosenwaks and J. J. Valentini, J. Chem. Phys., 1990, 93, 2146. 249, 1387. Prof. Neumark responded: Prof. Manz raises a very interesting point. One would like to measure not only the branching ratio between F+ H2 and HF+ H resulting from dissociation of the FH2 complex formed by photodetachment, but also the HF product vibrational distribution. We are unable to do this at present. However, we are nearing completion of an instrument that may allow us to do this for peak A in our photoelectron spectrum, which we assigned to a near-threshold reactive resonance. Prof. J. M. Bowman (Emory University) addressed Prof. Schatz: From the text of your paper it may appear that all of my calculations of the photodetachment spectra of IHI- and ClHCl- were done with the adiabatic-bend approximation.I wish to point out that the 1989 paper by Gazdy and Bowman’ made no approximations other than to represent the wavefunction of both the anion and neutral systems in L2 bases. I would also like to note that those calculations extended to energies above your scattering calculations, and did find the peak in the experimental spectrum of Neumark and co-workers corresponding to the resonance (v, = 0, v, = 0, v9 = 4) for IHI. I have a question about the interesting test of the J-shift model to obtain cross-sections from the reaction probability for J = 0. It appears that the model works somewhat better for the small cross-sections than for the large ones. Could this be due to a variational effect which becomes important for J >> 1, and which would have the effect of increasing the transition-state rotation constant B * which appears in the energy-shift factor B’J(J+ l)? 1 B.Gazdy and J. M. Bowman, J. Chern. Phys., 1989, 91, 4615. Prof. Schatz responded: Prof. Bowman has correctly pointed out that the J-shift model that we used works better for small cross-sections than for large ones. This results from the larger partial waves J that contribute to the larger cross-sections. The J-shift model that we have used assumes that the saddle point defines the bottleneck to reaction, and thus it is the saddle-point rotational energy that is subtracted from the total energy in determining energy available for overcoming the barrier to reaction. For large J, the true bottleneck occurs at larger Cl-Cl separations than the saddle point because ofGeneral Discussion 121 centrifugal effects.This makes the rotor constant larger, lowering the rotational energy, and raising the energy available to ovecome the barrier. Thus the J-shifted cross-sections would have been larger had we included for this effect. However, this has little influence on the cross-sections that are most strongly influenced by the resonance, as these are cross-sections that are determined by small J values. Prof. Taylor said: The purpose of this comment is to present the application of a classical mechanical method of spectral analysis’ and to apply it to the Neumarks’ experiments on the ClHCl transition state. The purpose of the method is not to compute spectra, energy levels or even cross-sections but to extract the nuclear motions whose quantization causes the experimental result.As input to the theory the experimental spectrum, I ( E ) or a quantum simulation thereof can be used. The quantity to be computed first by use of experimental or quantum-calculated data and second by using classical mechanics is the spectral density S ( o ) . This quantity, which is the FTlFTI(E)(,* can be shown to be the Fourier transform of an initial wavepacket correlation function and therefore emphasizes the periods, T, and frequencies (o = 27~/ T) of the motion of the transition state. Frequencies of motion, unlike spectra and energy levels have a classical analogue, and as such the classical analogue of S( o) exists and can be computed by running on a potential hypersurface for ClHCl, the classical trajectories dictated by an ensemble that depends entirely on the known initial sate and the energy range of the spectrum to be interpreted.As shown, S ( w ) computed both ways has similar peak frequencies. Each peak frequency in the classical version can be traced back to trajec- tories that are trapped in different parts of the transition region. The trapping is related to local adiabatic dynamic potentials at the bottom of whose wells lie periodic orbits that are almost evident from the trapped part of the trajectories and can therefore be located precisely. The frequency and stability frequencies of these periodic orbits correspond to the peaks in S ( o ) , and the periodic orbits and nearly trapped trajectories are the desired motions whose quantization gives the spectrum.For ClHCl the motion was mainly a three-mode one, consisting of an antisymmetric stretch motion and a lower-frequency degenerate symmetric and bend motion. The motions are not related to the col of the potential but are related to the normal modes of the adiabatic bound-type potential that is embedded in the true repulsive static potential hypersurface. The results explain not only the observed periods but by comparing small peak splittings in the experimental or quanta1 S ( w ) to the classical ones it can be concluded that tunnelling is important in the hydrogen exchange reaction of H with HCl. Isotope effects are also treated, and will soon be published. The method used here can also be used to explain diffuse structures in absorption spectra accompanying photodissociation and low-resolution features in chaotic spectra.2 The method yields the motions that underlies all these processes and as such is the ‘assignment’ of the spectra.1 0. Hahn, J. M. Gomez Llorente and H. S. Taylor, J. Chem. Phys., 1991, 94, 2608. 2 J. M. Gomez Llorente and H. S. Taylor, J. Chem. Phys., 1989, 91, 933. Prof. A. Lagana (University of Perugia) and Prof. A. Aguilar, Dr. X. Gimenez and Dr. J. M. Lucas (University of Barcelona) said: In ref. 1 the dependence of the state (vj) to state (vlj‘) CSH2 cross-sections of the C1+ HC1 reaction from the collision energy has been discussed. The curves show a smooth behaviour that seems to exclude resonance effects.With the aim of singling out possible resonances, in the same paper the differential cross sections were also analysed. Using the same LEPS3 potential-energy surface (PES) we have carried out reactive infinite-order sudden approximation4 (RIOSA) calculations. Also, our calculations were aimed at the investigation of possible resonant structures. To this end the RIOSA code was implemented on a parallel computer and restructured to partition the computational122 General Discussion 0 100 I 200 Fig. 1 Plot of single 1, single collision angle ( y = 180 ") and single energy ( E = 0.5 eV) contributions to the RIOSA cross-section of the C1+ HC1 reaction effort on concurrent processor^.^ The particular structure of the RIOSA calculation has allowed a distribution of the entire single energy, single angle and single angular momentum propagation from the separating surface to the asymptotes on a single processor.This has made it possible to profit from the large number of processors available on local-memory highly parallel machines to scan the energy range using a fine grid.6 Using parallel machines it has been possible to investigate the range of total energy up to 1 eV. In spite of the fine grid used, no structure was detected in the energy dependence of the cross-section. For o = 0, however, the cross-section shows a small knee just past the threshold that might have a resonant nature. A similar knee was found by Miller and Zhang7 for the H+H2 reaction. Such a feature was analysed in terms of broad and narrow resonances in angular-momentum space.For this reason we have plotted the fixed angle cross-section S( y ) as a function of the value of the orbital angular momentum 1. The plot obtained at y = 180" and a total energy of 0.5 eV is shown in Fig. 1. The plot shows two distinct regions. At low e values there is a broad maximum, while at high 1 values there is quite a sharp peak. Work is in progress to rationalize this structure and build simple models of the behaviour of reactive heavy-light-heavy systems. 1 G. C. Schatz, D. Sokolovski and J. N. L. Connor, Faraday Discuss. Chem. SOC., 1991, 91, 17. 2 G. C. Schatz, Chem. Phys. Lett., 1988, 150, 92. 3 D. K. Bondi, J. N. L. Connor, J. Manz, and J. Romelt, Mol. Phys., 1983,50, 467; D. K. Bondi, J. N. L. 4 A. Lagana, E. Garcia, 0.Gervasi, J. Chem. Phys., 1988, 88, 7238. 5 A. Laganl, 0. Gervasi, R. Baraglia and D. Laforenza, in High Peflormance Computing, ed. J. L. Delaye 6 A. Lagani, X. Gimenez, E. Garcia and 0. Gervasi, Chem. Phys. Lett., 1991, 176, 280; A. Aguilar, X. 7 W. H. Miller and J. Z. H. Zhang, J. Chem. Phys., 1991, 95, 12. Connor, B. C. Garrett and D. G. Truhlar, J. Chem. Phys., 1983, 78, 5981. and E. Gelenbe, North Holland, Amsterdam, 1989, p. 287. Gimenez, J . M. Lucas, 0. Gervasi and A. LaganB, Theor. Chim. Acta, 1991, 79, 191. Prof. Schatz responded: Prof. Lagani points out an interesting feature of the collinear reaction dynamics of C1+ HC1 and many other heavy-light + heavy reactions, namely the existence of strong reactivity oscillations as a function of energy. His RIOSA calculations suggest that such oscillations may also show up in three-dimensional scattering.General Discussion 123 It has been our experience based on coupled-channel hyperspherical (CCH) reactive- scattering calculations' that reactivity oscillations are often quenched in three dimensions, especially when significant reaction can occur through noncollinear path- ways2 The potential surface that we used for our CCH calculations3 is one which disfavours reactivity oscillations because of its relatively small transition-state bending frequency.It is our feeling, based on comparison with ab initio surface^,^ that this sort of surface is correct for describing Cl+HCl. We have studied this point for other reactions5, but do not have enough evidence from ab initio calculations or comparisons with experiment to say if this quenching of reactivity oscillations is a general property of real systems.1 G. C. Schatz, Chem. Phys. Lett., 1988, 151, 409. 2 B. Amaee, J. N. L. Connor, J. C. Whitehead, W. Jakubetz and G. C. Schatz, Faraduy Discuss. Chem. 3 D. K. Bondi, J. N. L. Connor, J. Manz and J. Romelt, Mol. Phys., 1983, 50, 467. 4 G. C. Schatz, B. Amaee and J. N. L. Connor, J. Phys. Chem., 1988, 92, 3190. 5 H. Koizumi and G. C. Schatz, in Molecular Vibrations, ed. J. M. Bowman and M. A. Ratner, JAI Press, SOC., 1987, 84, 387. Greenwich, CT, 1991, in the press. Prof. Kubach said: I would like to point out that a new method has been proposed for the treatment of the dynamics of heavy-light+heavy systems and applied to the IH + I prototype.' This method starts with a Born-Oppenheimer type separation between the light and heavy nuclear motions.Accordingly, the dynamics are treated in two steps. In the first step, the hamiltonian describing the light particle (H) is considered holding the iodine nuclei fixed. This provides hydrogenic wavefunctions, potential-energy curves and couplings that govern the motion of the iodine nuclei. The latter is treated in the second step. This approach has been shown to produce accurate results and to lend itself to a detailed understanding of the dynamics. The energy location of the computed resonances is in very good agreement with results obtained from other calculations. The properties of hydrogenic states enables one to easily establish the origin of those resonances.2 The proposed method reveals the particular hydrogenic states that play a central role in the H-atom exchange process in IH+I collisions.It can be applied to calculate fully quanta1 3D state-to-state cross-sections. 1 C. Kubach, Chem. Phys. Lett., 1989, 164, 475. 2 C. Kubach, G. Nguyen Vien and M. Richard-Viard, J. Chem. Phys., 1991, 94, 1929. Dr. Balint-Kurti commented: Schinke et al. report calculations on the photodissoci- ation of H2S and stress the differences with our previous modelling work on this system.' We would like to point out the great similarities between the calculations presented by Schinke er al. and our own modelling of the process. We found it necessary to use two interacting excited electronic states to model the photodissociation process.As remarked by Schinke et al., this was not accepted as the necessary mechanism beforehand. In our paper we correctly modelled three different aspects of the experimental observations, namely the absorption spectrum, the HS photofragment vibrational quantum state distribution and the emission spectrum of the dissociating molecule. In Fig. 2 we show our modelled electronically excited dissociative potential-energy surface. It is clear that this surface is very similar to that given in Fig. 7 of Schinke er al. No qualitative model of the form we previously presented can fully identify all the sources of coupling between potential-energy surfaces. This can only be accomplished through unambiguous ab initio calculations; Schinke et al. have produced diabatic states from their ab initio computations using a generally accepted procedure (see their ref.44). They state that their diabatic states are strongly coupled. It is possible that an alternative adiabatic-to- diabatic transformation may eventually be found which would lead to a weakly coupled diabatic representation. This would clearly represent an improvement on their current model. 1 G. G. Balint-Kurti et al., J. Chern. Phys., 1990, 93, 6520.124 General Discussion 10 8 6 RE8 4 2 Fig 2 Modelled electronically excited dissociative potential-energy surface. Key to energy contours as follows: (1) 33457, (2) 36584, (3) 39711, (4) 42838, (5) 45965, (6) 49092, (7) 52219, (8) 55 346, (9) 58 473; (10) 61 600, (1 1 ) 64 727, (12) 67 854 cm-I. Vertical dashed line shows R , = R,, Prof.R. N. Dixon (University of Bristol) said: Dr. Baht-Kurti has highlighted the similarities of conclusions between our empirical modelling of the first absorption continum of H2S and that calculated a6 initio by Dr. Schinke. We do not doubt that accurate theoretical knowledge of all relevant potential-energy functions, and of the detail of nuclear kinetic matrix elements, provides a benchmark for the calculation of all observables; and that the complexity of systems that are amenable to such a treatment is increasing rapidly. I wish to address the reverse problem of inverting experimental data from photodissociation experiments to derive molecular potential-energy surfaces where these are not known. It is essential in this context that the modelling should combine information from a wide range of experimental data.As Dr. Schinke has commented, a broad absorption continum contains information only about the slope of the upper dissociative surface in the Franck-Condon region. A more highly structured spectrum, as in H2S, implies a recurrence to the Franck-Condon region in time, and therefore contains information about the more remote regions of the surface visited before the recurrence. The more experimental data that are used inGeneral Discussion 125 the inversion the less the ambiguity that will be associated with the derived potential. Thus absorption spectra probe the Franck-Condon region and beyond, resonance Raman spectra of dissociating molecules probe more towards the transition region, and product distributions probe the flux evolution in the exit channel(s).The variation of any of these with change in the initial state provides a valuable addition. For example, in H2S the one-photon excitation from the ground 'A, level to all 'A2 vibronic levels is dipole-forbidden, but could become allowed through a two-photon excitation or through a one-photon excitation from the v3 = 1 ( 'B2) level of the ground state. Most observables relate to the amplitude of a wavefunction, but not its phase, thereby introducing some ambiguity into the inversion process. In particular, there are three unique vibrational operators (two diagonal and one off-diagonal) for a coupled nuclear motion on two surfaces, so that a number of model Hamiltonians related through unitary transformations may fit the same data.Since applications to many-body systems will remain beyond the scope of accurate ab initio work for some years to come, it is essential that we learn how to maximise the reliability of the inversion process, and that we also design the most informative experiments. I would urge Dr. Schinke to compute the predicted values of all known observables from his ab initio approaches for comparison with experiment, and to address the problems of the implementation of reliable inversion procedures. Theory and experiment can thereby help one another to the benefit of both. Prof. J. P. Simons ( University of Nottingham) commented: While the analysis yhic,h Dr. Schinke presents is able to explain the origin of the diffuse structure in the B+X absmption spectrum of H20, it does not explain other indicators of the dynamics on the B 'Al PES.In particular, it does not address the dependence of the OH(A) fragment yields, rotational state distributions and rotaticnal alignments on the parent molecular rotational state, following dissociation on the B 'A, potential. These are all well docu- mented,' although not referenced in Dr. Schinke's stimulating paper. For example, detailed state-to-state investigations"* of the dynamics of OH/OD( A) production, fol- lowing predissociation of H20/ D20(c 'B,) establisted: (i) that OH/OD(A) was gener- ated via the heterGgeneous predissociation of the C state, through electronic Coriolis coupling with the B state; (ii) that the yields of OH/OD(A) passed through a maximum as the component of the parent rotational angular momentum, J, increaseci; (iii)_ that this was associated with the 'leakage' of trajectories which passed through the B 'A,-A 'B1 intersection ( inside the conical intersection with the ground-state potential); and that (iv) while the shortest-lived trajectories generated fragments with the highest rotational angular momentum, less excited fragments were associated _wi_th longer-lived 'reson- ances', able to survive more than one excursion through the B-A, Renner-Teller inter- section at linearity.These results re-inforced the spirit, if not the letter, of the predictions made nearly ten years ago by Segev and Shapiro.' They cannot be explained without invoking some contributions from trajectories which pass inside the conical intersection and which retain, at least initially, a high degree of bending character.Assuming the calculations presented ?t this Discussion are restricted to states of zero total angular momentum (where the B-A path is closed), is it possible to predict the manner in which the calculated trajectories might be influenced by the inclusion of angular momentum in the photo- excited molecule? 1 M. P. Docker, A. Hodgson and J . P. Simons, in Molecular Photodissociation Dynamics ed. M. N. R. Ashfold and J. E. Baggott, Royal Society of Chemistry, London, 1987, ch. 4, p. 115. 2 M. P. Docker, A. Hodgson and J. P. Simons, Mol. Phys., 1986, 57, 129. 3 E. Segev and M. Shapiro, J. Chem. Phys., 1982, 77, 5604. Dr. Schinke replied: A wealth of detailed experimental data on the photodissociation of H20 in the second absorption band have indeed been collected over the past ten126 General Discussion years or so.As Prof. Simons notes, they are all well documented in the literature. Our contribution to this Faraday Discussion exclusively deals with the diffuse absorption structures and their (possible) explanation in terms of a simple unstable periodic trajectory. We did not aim to explain all the interesting facets of this important system. With regard to the question at the end of Prof. Simons’ comment, I do not think that the generic structure of this particular periodic orbit will qualitatively change if the restriction to zero total angular mcmentum is lifted. The photodissociation of H20( B) is a very complicated process.A rigorous theoreti- cal treatment should involve three electronic states, three nuclear coordinates, as well as nonzero angular momentum states. Such calculations are not feasible at present and will probably never be possible. Dr. G. Hancock (University ofoxfird) said: Some aspects of the dynamical behav- iour of H20 molecules excited to the B ‘A, state can be studied by observations of the polarization of fluorescence from the nascent A 2Z+(OH) fragment. There have been two studies above 130 nm corresponding to the region in which strong undulations are seen in the spectra calculated by Schinke et al. [Fig. l ( b ) of their paper), namely one-photon excitation at 130.4 nm’ and two-photon excitation at 266.2 nm2, the latter energy hitting the maximum of one of the undulations in the calculated spectrum.Although rotational energy distributions in the two cases were very similar, polarisation results were not: in the one-photon case, high N’ values in OH ( v = 0) show alignment parameters AC) which are close to the maximum possible values,’ whereas at the equivalent of 133.1 nm, AS) is close to zero.2 I wonder if such dramatic differences would be expected from the range of trajectories that excitation at these different energies would produce. If not, then the alternative explanation of involvement of ,an initially produced state in the two-photon case which is of different symmetry to the B ‘A, state, for example, a ‘A2 state which can be accessed in two- but not one-photon excitation, may need to be invoked.1 J. P. Simons, A. J. Smith and R. N. Dixon, J. Chem. Soc., Faruday Trans. 2, 1984, 80, 1489. 2 C. G. Atkins, R. G. Briggs, J. B. Helpern and G. Hancock, J. Chem. SOC., Faraday Trans. 2,1989,85,1987. Dr. K. H. Gericke (Uniuersity of Frankfurt) said: We have investigated the hoto- OH(211, v, J) + H(2S), at 157 and 177 nm. This fragmentation process is treated as a benchmark system for the direct photodissociation of simple molecules, since a variety of experimental facts can be well explained by theoretical calculations: (i) the low rotational excitation of the OH product at a photolysis wavelength of 157 nm, (ii) the complete OH fine-structure product-state distribution in a state-to-state experiment in which a single rovibrational level of H20 was prepared by infrared excitation before photolysis at 193 nm and (iii) the branching ratio OH/OD in the photodissociation of HDO.Iv2 However, the vibrational state distribution of the OH product, which directly reflects the dynamics of the H20(’A,) decay, is experimentally known only for u” = 0 and v” = 1.’ Fragments in higher vibrational states were not investigated quantitatively.Theoretical calculations predict OH to be vibrationally excited up to v” = 6 when water is excited at 157 nm. We have observed the complete rovibrational state distribution of the OH product (including A and spin-orbit states) by laser-induced fluorescence. Since the vibrational levels higher than v’= 1 of the first electronic excited state of OH are predissociative, we excited the OH fragments from all v” states to u’= 0 and v’ = 1, so Av = u’- v” = 0, -1, -2, bands were used to probe the products.’ In all populated vibrational states no preferential OH production in one of its spin-orbit, states, 2111,2 and 2113,2, or its A states, II(A’) and II(A), is observed.The rotational excitation is low, and the distribution can be described by a rotational dissociation dynamics of H20 from its first excited electronic state, H20( P A,) +General Discussion 127 Table 1 Observed, Pexptl, and calculated, Ptheory, vibrational distributions and observed rotational temperature, Trot, in each vibrational state for the photodissociation of H 2 0 at 157 nm 0 0.59 0.32 620 1 0.33 0.27 450 2 0.06 0.17 440 3 0.014 0.11 500 4 0.002 0.07 I 5 - 0.02 - 6 - 0 - 0 1 2 3 4 5 6 vibrational state Fig.3 OH vibrational state distribution in the photodissociation of water observed experimentally at 157 nm (+) and predicted by theoretical calculations for ., 156.9 and +, 172.2 nm temperature Table 1. Only in u” = 4 are the higher rotational levels populated slightly more strongly than expected for a Boltzmann distribution. The OH spatial distribution was determined by high-resolution measurements of Doppler profile^.^ These results are in agreement with the theoretical expectations. However, the vibrational distribution differs significantly from the calculated one. The observed magnitude of the vibrational excitation is much smaller than expected. The calculations predict u” = 6 to be populated, but we did not even observe any transitions which probe the u”= 5 level.From the noise we estimate an upper limit of 0.02% for this state. Fig. 3 shows the observed OH(*lI, u”) distribution and the calculated distribution at 156.9 and 172.2 nm. Obviously the form of experimental distribution resembles the calculated distribution for a photolysis wavelength of 172.2nm rather than that of 156.9nm. A shift of the upper potential surface by ca. 0.5 eV may explain the deviation between experimental and thoretical results. It should be mentioned that completely different transition probabilities would influence the observed vibrational state distribution.128 General Discussion 308 310 312 wavelength/ nm Fig. 4 Scan of the OH2(L211) system in the photodissociation of ater at 177.3 nm.OH products are formed exclusively in the u" = 0 state However, the use of former Einstein B coefficients' would even reduce the amount of vibrational excited OH products. Furthermore, we used a lower excitation energy of 177.3 nm (two-photon excitation of H 2 0 via the third harmonic of a Nd: YAG laser), where theory still predicts a significant amount of OH vibration (roughly the OH distribution at 172.2nm in Fig. 3). However, a scan of the 'Z + 'll system around 3 12 nm does not show any transition which can be assigned to a v' = 1 + v'' = 1 transition (Fig. 4). Even a strong increase of dye-laser energy and H20 pressure, which should increase the detection efficiency of OH by two orders of magnitude, yields negative results. Thus the OH products are formed only in the lowest vibrational state, in contrast to the theoretical predictions. In conclusion, the dynamics in the photodissociation of water from the first absorption band are still open to discussion.1 P. Andresen, G. S. Ondrey, B. Titze and E. W. Rothe, J. Chem. Phys., 1984,80, 2548. 2 P. Andresen and R. Schinke, in Molecular Photodissociation Dynamics, ed. M. N. R. Ashfold and J. E. 3 K. Mikulecky, K.-H. Gericke and F. J. Comes, Chem. Phys. Lett., 1991, 182, 290. 4 K.-H. Gericke, S. Klee, F. J. Comes and R. N. Dixon, J. Chem. Phys., 1986, 85, 4463. 5 W. L. Dimpfl and J. K. Kinsey, J. Quant. Spectrosc. Radiat. Transfer, 1979, 21, 233; C. B. Cleveland, Baggott, Royal Society of Chemistry, London, 1987, p. 61. G. M. Jursick, M. Trolier and J. R. Wiesenfeld, J. Chem.Phys., 1987, 86 3253. Dr. M. N. R. Ashfold (University of Bristol) and Dr. L. Schnieder and Prof. K. H. Welge (University of Bielefeld) said: We would like to offer two comments relating to the beautiful calculations of Schinke et al.' First, it should perhaps be emphasised for the-benefit of those not intimately acquainted with the photofragmentation dynamics of B-state water molecules that the dominant dissociation channel yields ground-state OH(X) radicals with high levels of rotational excitation.2 It is specifically stated thatGeneral Discussion I I I I I I I 129 I I I I I I ] 0 0.05 0.10 0.15 0.20 0.25 0.30 internal energy/eV Fig. 5 ( a ) Internal energy spectrum of SH(X 211)u=o fragments resulting from H2S photolysis at 193.3 nm together with ( b ) best-fit simulation of this spectrum.The various rotational levels of the two spin-orbit components are indicated above the experimental spectrum thesresent calculations do not allow for any non-adiabatic coupling to the lower A 'B1 or X 'Al states ofyater, but the statement (section 4 of ref. 1 ) that 95% of the trajectories launched on the B-state surface vertically above the ground-state equilibrium configur- ation yield OH(*E+) fragments with high rotational excitation could be _misleading if it is not realised that this is only true for trajectories that remain on the B-state surface. Most do not. Non-adiabatic coupling- mechanisms to both of the lower-lying singlet potential-energy surfaces (A 'B1 and X 'A,), both of which correlate with the major dissociation products H + OH(X), have been discussed, although their relative import- ance does remain a matter of some We now focus attention on the very detailed treatment of the photodissociation of H2S molecules following excitation within their first absorption continuum and, in particular, on the statement that calculations which explicitly include the bending degree of freedom, and thus allow prediction of the SH(X) product rotational state population distribution, are now underway.Clearly, any assessment of the accuracy of these proposed calculations will be aided by the availability of accurate experimental data for the rotational energy disposal in the SH(X) fragments. Thus it is appropriate to report the results of a recent reinvestigation of the 193.3 nm photodissociation of a jet-cooled sample of H2S molecules employing the technique of Rydberg H atom photo fragment translational spectros~opy.~,~ Fig.5 shows the internal energy spectrum of the SH(X),=, fragments so obtained, together with a best-fit simulation of this130 1.0- 4 0.6 1 a a 0 .C U 9 0.4- !i 0.2 General Discussion O 1 _ 1 - 0 2 4 6 8 1 0 1 2 1 4 N )I Fig. 6 Plot of relative populations of the various Fl rotational levels of the SH(X),,, fragments produced in the 193.3 nm photolysis of jet-cooled H,S: 0, this work, 0, population distribution deduced from earlier LIF studies8 after correction for the rotational level dependent predissociation of the SH(A),,o.9 The two data sets are scaled to be equal for N"=2 spectrum which employs SH( X) , =, rotational term values determined from conventional electronic absorption spectroscopy.' The spin-orbit branching ratio for the SH( X),,, fragments is found to be Fl : F2 = 1.0: 0.7; the deduced population distribution for the F1(2113,2) rotational levels is plotted in Fig.6. Comparing this distribution with that deduced from analysis of the most recent laser-induced fluorescence studies of the SH(X),,, fragments produced in this dissociation' clearly shows that the LIF study underestimated the relative yield of fragments in the higher rotational states. This underestimate can be directly attributed to neglect of the rotational level dependent predissociation of the excited SH( A),=, fragments;' after correcting the previously reported population distribution' to allow for the rotational level dependence of the SH(A),,, fluorescence quantum yield we find the two determinations of the SH(X),,, rotational state population distribution to be in reasonable accord.1 R. Schinke, K. Weide, B. Heumann and V. Engel, Furuduy Discuss. Chem. SOC., 1991, 91, 31. 2 H. J. Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold, Furaduy Discuss. Chem. SOC., 1986, 82, 99. 3 R. N. Dixon, Mof. Phys., 1985, 54, 333. 4 K. Weide and R. Schinke, J. Chem. Phys., 1987, 87, 4627. 5 L. Schnieder, W. Meier, K. H. Welge, M. N. R. Ashfold and C. M. Western, J. Chem. Phys., 1990,92,7027. 6 L. Schnieder, K. Seekamp-Rahn, F. Liedeker, H. Steuwe and K. H. Welge, Furuduy Discuss. Chem. 7 J. W. C. Johns and D. A. Ramsay, Can. J. Phys., 1961, 39, 210.8 B. R. Weiner, H. B. Levene, J. J. Valentini and A. P. Baronavski, J. Chem. Phys., 1989, 90, 1403. 9 W. Ubachs and J. J . ter Meulen, J. Chem. Phys., 1990, 92, 2121. Soc., 1991, 91, paper 14.General Discussion 131 Prof. Taylor addressed Dr. Schinke: First, two technical comments. Diffuse structure need not be caused only by unstable periodic orbits. In ClHCl a stable one causes such structure.' In Na, low-resolution SEP spectra, diffuse structure is caused by a 2D, reduced-dimension torus.2 Secondly, I wish to emphasize the fact made in Fig. 5 of your paper that the trajectories for the motion of carbon dioxide molecules are governed, i.e. guided, in the transition region by periodic orbits. This result, in the case of C 0 2 , is in accord with the historical physical chemical view of the photodissociation. From Fig.5 we see that the system is excited to a point on the symmetric stretch periodic orbit and moves out along it till it reaches and moves onto the antisymmetric periodic orbit. At this point the molecule can either go to dissociation, larger PI, or P,*, or it can retrace its steps back to its region of origin. The arrival times at the latter transition region gives Fig. 4 of your paper, which shows the peak periods of the correlation function whose Fourier transform gives the absorption spectra. Each period is a given periodic orbit in Fig. 4. Now the symmetric followed by antisymmetric motion is what would have been predicted by the traditional chemical picture. This picture recognises that in order to dissociate, the molecule must vibrate antisymmetrically, but that to do this as a final step would compress one bond so much as to require high energies.As such C 0 2 lengthens its bonds by executing first a bond-enlarging symmetric motion, followed by the dissociative antisymmetric motion. 1 0. Hahn, J. M. Comes Llorente and H. S. Taylor, J. Chem. Phys., 1991, 94, 2608. 2 J. M. Comes Llorente and H. S. Taylor, J. Chem. Phys., 1989, 91, 953. Mr. M. Hippler and Prof. J. Pfab (Heriot- Watt Uniuersity) (communicated): The beautiful work reported by Schinke et al. in their paper reminds us of the fact that diffuse vibrational structures are very common in the electronic spectra of polyatomic molecules. Since spectral congestion often obscures diffuseness one expects the clearest examples to be found in light triatomics without low-frequency vibrations that might lead to thermal (i.e.hot band) congestion. The discrimination between vibrational diffuseness and broadening that is heterogeneous becomes increasingly difficult in 300 K electronic spectra of larger polyatomic molecules. Methyl nitrite affords a good example, for which Schinke et al. predict sharp resonances,172 but the experimental spectra available for comparison are broadened heterogeneously. Proper homogeneous widths of the predissociated features in the near-UV spectra of alkyl nitrites are not yet available, and their measurement remains a challenge for the experimentalist. In comparing theory with experiment in the predissociation of alkyl nitrites final state distributions of the NO fragment have also proved to be valuable in deducing information about the upper-state potential surface which includes the region of the transition state involved in the dissociation To what extent are these NO state distributions affected by the averaging involved in photolysing a broad thermal ensemble of parent molecules? Almost without exception the final-state distributions reported in the literature for the near-UV photolysis of alkyl nitrites refer to experiments conducted with 300 K vapour For t-butyl nitrite the averaging over parent internal states at 300 K must be extensive and should lead to a broadening of the NO state distributions.Yet experiments do not appear to confirm this.778 Radhakrishnan and Estler report that the rotational energy of nascent NO from the near-UV photo- dissociation of alkyl nitrites decreases with increasing complexity of the alkyl group.4 The large density of vibrational states associated with the t-butyl group might lead to competition between dissociation and intramolecular vibrational energy randomisation (IVR) during the lifetime of the electronically excited state.Evidence for this has been seen in the cooling of the NO fragment rotation with increasing complexity of the alkyl group.4132 General Discussion 1.0 I 1 I 1 o*2L-A - & i 0.0 1 I I 1 1 51000 51500 52000 52500 53000 53 500 two-photon wavenumber/cm-' Fig. 7 C 211 + X 211 2+ 1 REMPI spectra of NO: ( a ) from the photodissociation of CH30N0 in a pulsed supersonic expansion of Ar; ( b ) simultaneously recorded room temperature NO reference spectrum We have recently studied the photodissociation of the series of five alkyl nitrites RON0 in a supersonic jet of Ar, where the alkyl group R ranges from CH3 to t-butyl via C2H5 and isopropyl in the hope of reproducing the results of Radhakrishnan and E ~ t l e r .~ ' ~ The rotational temperature of NO expanded under our conditions together with the parent and Ar carrier gas is less than 5 K. One may assume that parent rotation and low-frequency torsional and bending modes are cooled similarly, and that the parent akyl nitrites are very cold. Thus interference from 300 K contaminant NO or partially relaxed NO photofragment can be excluded in our experiments, but not in those of the previous room-temperature Fig.7 shows the C-state 2 + 1 REMPI spectrum of NO obtained by photodissociation of CH30N0 jet-cooled to a rotational temperature likely to be <10 K and a simul- taneously recorded reference spectrum of 300 K gaseous NO. In this one-colour experi- ment photolysis of CH30N0 in the supersonic jet and probing of the nascent fragment occur simultaneously in the focal region of the tuned pulsed dye laser beam. Although the excess energy above threshold varies slightly with the wavelength of the scanning laser, we anticipate that the experimental errors in the 0- N bond dissociation energies" and the average rotational energy of NO outweigh the error incurred by assuming Eavl, i.e. the available excess energy to be constant during scans. For all five nitrites examined we find Gaussian-shaped rotational population distributions peaking near J = 33 with a full width at half height of 14.An average rotational energy of 1900 cm-' corresponding to 15% of the available excess energy is partitioned into NO, independent of the size and complexity of the alkyl group. Our results indicate clearly that the energy disposal into rotation of NO does not vary significantly for the five alkyl nitrites examined. We conclude that rotational energy randomisation is slow on the timescale of the dissociation process ( a 0 0 fs). 1 S. Hennig, V. Engel, R. Schinke, M. Nonella and J.R. Huber, J. Chem. Phys., 1987, 87, 3522. 2 R. Schinke, S. Hennig, A. Untch, M. Nonella and J. R. Huber, J. Chem. Phys., 1989, 91, 2016. 3 U. Briihlmann, M.Dubs and J. R. Huber, J. Chem. Phys., 1987, 86, 1249.General Discussion 133 4 G. Rhadakrishnan and R. C. Estler, Chem. Phys. Lett., 1983, 100, 403. 5 0. Benoist d’Azy, F. Lahmani, V. Lardeux and D. Solgadi, Chem. Phys., 1985, 94, 247. 6 C. G. Atkins and G. Hancock, Laser Chem., 1988,9, 195. 7 R. Lavi, D. Schwartz-Lavi, I. Bar and S. Rosenwaks, J. Phys. Chem., 1987,91, 5398. 8 D. Schwartz-Lavi and S. Rosenwaks, J. Chem. Phys., 1988, 88, 6922. 9 M. Hippler, F. Al-Janabi and J. Pfab, to be published. Deriuatiues, Interscience, New York, 1982, p. 1035. 10 L. Batt and G. N. Robinson, in The Chemistry of Amino, Nitroso and Nitro Compounds and their Prof. Pfab (communicated): Drs. M. R. S. McCoustra and P. G. Giovanacci have shown some time ago in our laboratories that the diffuse vibrational structure revealed by the visible absorption spectra of t-butyl thionitrite is due to absorption to a state that is unstable with respect to dissociation of the S-N bond.’-* Fig.8 shows the absorption spectrum of gaseous But SNO at 300 K. The maximum is shifted to significantly longer wavelengths compared to CH3SN0,3 and the peaks may be labelled as members of a progression in the N-0 stretching frequency with a companion progression due to a lower-frequency bending or torsion vibration. We have briefly studied the photolysis of But SNO jet-cooled in He at 603 nm. The NO rotational state distributions are narrow and Gaussian-like, peaking near J” = 2@ with a full width at half maximum close to 16. Less than 1 % of NO is formed in the v ” = 1 level, and the dissociation at this wavelength must be largely adiabatic indicating the importance of tunnelling if there is a minimum at all along the S-N single bond dissociation coordinate. For CH3SN0 we have studied the photodissociation following absorption into the much more weakly structured S,(n, v * ) state in much greater detail, as reported briefly el~ewhere.~ In that case dissociation was also shown to be direct, and the results nicely confirm the previous calculations of Schinke et aL3, indicating that the potential along the S-N dissociation coordinate must be rather shallower than in the case of the analogous akyl nitrites.1 P.A. Giovanacci, Ph.D. Thesis, Heriot- Watt University, 1989. 2 P. A. Giovanacci, M. R. S. McCoustra and J.Pfab, to be published. 3 R. Schinke, S. Hennig, A. Untch, M. Nonella and J. R. Huber, J. Chem. Phys., 1989, 94, 2016. 4 J. Nab, D. M. Wetzel and V. M. Young, Ber. Bunsenges. Phys. Chem., 1990, 94, 1322. 450 550 650 wavelength/nm Fig. 8 Absorption spectrum of gaseous tert-butyl thionitrite in the visible at ambient tem- perature(ca. 300 K). The absorption to lower wavelength is due to a much stronger continuum centred with a maximum near 350 nm134 General Discussion Mr. A. E. Janza (Freie Universitat Berlin), Dr. W. Karrlein (Siemens-Nixdorf AG, Munich) and Prof. J. Manz (Universitut Wiirzburg) commented: The evaluations of three-dimensional (3D) resonances in systems such as FHF- by Dr. Yamashita and Prof. Morokuma' may be considered as extensions of our previous evaluations of 2D resonances in many systems, including models of XHY systems such as FHBr and isotopomers: dihydrides such as H20: CH; or similar ABA-type systems' and their isotopomers.6 Here we should like to present some of our extensions yielding 3D and even 4D resonances, e.g. in the systems H20, CH20,7-9 HCCH, HNNH'"' and HNCND.' For example, a highly excited 3D local-mode resonance of H20 with essentially 1 + 24 vibrational quanta in the (anti-symmetrized) stretches plus zero quanta in the bend7 is illustrated in Fig.9. A 4D local-mode resonance of HNCND with essentially nine quanta in the NH stretch plus zero quanta in all other stretches is shown in Fig. 10. These types of 3D resonances have been evaluated by means of the techniques of ref. 11.For H20 we employ the elaborate spectroscopic Hamiltonian of Carrington and Halonen,'* whereas HNCND is modelled by Morse and harmonic oscillators for the 10 i \ 2' H20* ( a ) i 10 L t a 0 1 1 ' ' ' I " 0 5 10 %la0 Fig. 9 Local-mode resonance of H 2 0 with essentially 24 plus 1 vibrational quanta in the (anti- symmetrized) stretches, plus zero quanta in the bend. The three-dimensional resonance is illus- trated by contour diagrams us. bond coordinates qa, q b for fixed bond angles, e.g. 8 = 90.76 and 99.93 O in panels (a) and (b). Close to the equilibrium bond angle, 8 = 104.51 O, the numbers of quanta (1, 24, 0) are indicated roughly by the nodal structureGeneral Discussion 135 2.5 O I NCN-H 10 0 0 %/a0 -0.03 1.75 t l PS 0 Fig. 10 Decay of local-mode resonance of HNCND with essentially nine quanta in the dissociative HN stretch, plus zero quanta in all other (NC, CN, ND) stretches.The four-dimensional resonance is indicated by equidensity contours us. coordinates qa and q b for the HN and ND bonds, respectively: complementary bond coordinates are not visible in this presentation. Panels (a) and (b) show the resonance at the start ( t = 0.00 ps) and at the end ( t = 1.93 ps) of the propagation, illustrating stability within graphical resolution. The corresponding long lifetime has a lower limit of 7 > 4000 ps, as deduced from the decay of the absolute square of autocorrelation function l(T(t = 0) IT(t))l2 versus time t, see panel ( c )136 General Discussion dissociative HN (or ND) and NC (or CN) bonds, respectively. The corresponding parameters: D = 2.25 eV, p = 1.684a,', re = 0.979 66ao and k = 0.008 586Eh/ai2, re = 1.232 69ao, respectively, are derived from MNDO calculations by means of the methods in ref.13. The bond angles HNC (or CND) and NCN are fixed to constant values, 126.75 and 164.71 O, respectively. The masses used are rnH = 1.0079, rn, = 2.0158, rnc = 12.01 1 , mN = 14.0067 and mo = 15.9994 amu; for further details, see ref. 7-10. In contrast, Yamashita and Morokuma' use high-quality quantum-chemical ab initio methods for evaluations of the potential-energy surface of their molecules. The time evolutions of the resonances are evaluated by extending the fast Fourier transform propagation techniques of Kostoff, et al. (see e.g. Ref. ( 5 ) ) to higher (three or four) dimensions.* As an example, we present preliminary results for the first 4D FFT propagation of the HNCND resonance (up to 1.93 ps) in Fig.10. The stability of the resonance points to surprisingly long lifetimes, T >> 1000 ps, which might be due to a decay mechanism first proposed for HNNH local resonances in ref. 10. In short, this hypothesis combines the heavy-atom blocking effect with the Feshbach mechanism to predict extremely long decay times, if the dissociative bonds are not directly coupled. Resonances of this type call for more efficient propagation techniq~es.'~ The 4D FFT propagations of the HNCND resonance shown in Fig. 10 approach the limit of our available technology; i.e. they were carried out on the maximum grid (= 128 x 32 x 16 x 16 gridpoints for the HNxNCxCNxND bonds) that could be loaded into the central memory of the Cray Y-MP 4/432 computer at LRZ Munchen, and the propagation illustrated in Fig.2 consumed more than lo5 s CPU computer time for 80 000 time steps. The limitations of the grid caused an artificial increase of the resonance energy for 0.18 to 0.55 eV, just above the threshold for dissociation, 0.16 eV: cJ the well depths of the dissociative HN bond, 2.25 eV. We gratefully acknowledge fruitful discussions with Drs. B. Hartke, V. Mohan and H.-J. Schreier, kind and efficient help of Dr. U. Howeler and Professors M. Klessinger and W. Thiel with their MNDO programs, as well as generous financial support by the Deutsche Forschungsgemeinschaft and the Fonds der Chemis- chen Industrie.1 K. Yamashita and K. Morokuma. Furuduy Discuss. Chem. SOC., 1991, 91, 47. 2 R. H. Bisseling, P. L. Gertitschke, R. Kosloff and J. Manz, J. Chem. Phys., 1988, 88, 6191; J. Manz and J. Romelt, J. Chem. SOC., Furuduy Trans., 1990, 86, 1689. 3 T. Joseph, T.-M. Kruel, J. Manz and I. Rexrodt, Chem. Phys., 1987, 113 223. 4 T. Joseph, J. Manz, V. Mohan and H.-J. Schreier, Ber. Bunsenges. Phys. Chem., 1988,92, 397. 5 R. H. Bisseling, R. Kosloff and J. Manz, J. Chem. Phys. 1985, 83, 933; R. H. Bisseling, R. Kosloff, J. Manz, F. Mrugala, J. Romelt and G. Weichselbaumer, J. Chem. Phys., 1987,86, 2626: R. H. Bisseling, Ph.D. Thesis, Hebrew University of Jerusalem, 1986. 6 B. Hartke, J. Manz and J. Mathis, Chem. Phys., 1989, 139, 123. 7 A. E. Janza, Diploma Thesis, Universitat Wurzburg, 1989. 8 W.Karrlein, Ph.D. Thesis, Universitat Wiirzburg, 1990. 9 B. Hartke, A. E. Janza, W. Karrlein, J. Manz, V. Mohan and H.-J. Schreier, to be published. 10 B. Hartke and W. Karrlein, Chem. Phys., in the press. 11 W. Karrlein, J. Manz, V. Mohan, H.-J. Schreier and T. Spindler, Mol. Phys., 1988,64, 563: W. Karrlein, 12 L. Halonen and T. Carrington, J. Chem. Phys., 1988, 88, 4171. 13 W. Thiel, Tetrahedron, 1988, 44, 7393. 14 R. Kosloff and A. Hammerich, Furuduy Discuss. Chem. SOC., 1991, 91, 239. Prof. K. Morokuma (Institute for Molecular Science, Okazaki) replied: It is nice to hear Dr. Manz's achievement of three- and four-dimensional resonance. We are trying to say that our ab initio MO-based potential-energy surface for FHF is realistic and that this system is probably a good candidate for transition-state spectroscopy of unimolecular reactions. Prof.M. H. Alexander (University of Maryland) and Prof. H.-J. Werner (University of Bielefeld) said: Have Dr. Yamashita and Prof. Morokuma investigated other algorithms to determine the adiabatic -+ diabatic transformation in NaI? In particular, J. Phys. Chem., 1990, 94, 8530.General Discussion 137 one approach might be to characterize the transformation angle 8 as’ where Cj denotes an expansion coefficient in the CASSCF or CASSCF-MRCI wave- function. The sum in the numerator runs just over those configurations with nominal ionic electron occupancy, while the sum in the denominator runs over all configurations. Our previous work indicates2 that the transformation angle so defined is relatively independent of the size of the configuration space in the MCSCF wavefunction so long as natural CASSCF orbitals are used.Alternatively the approach described by Patcher et aL3 could be used. 1 H.-J. Werner, B. Follmeg and M. H. Alexander, J. Chem. Phys., 1988, 89, 3139. 2 H.-J. Werner, B. Follmeg, M. H. Alexander and D. Lemoine, J. Chem. Phys., 1989, 91, 5425. 3 T. Patcher, L. S. Cederbaum and H. Koppel, J. Chem. Phys., 1988, 89, 7367. Prof. Morokuma replied: In this system of NaI, where one covalent and one ionic state cross, the dipole moment is probably the best quantity to be used to separate non-adiabatic states. Of course there are other methods one can use. One of the difficulties in using CI coefficients is how to distinguish between ionic and covalent terms.Prof. H. Metiu (University of California) commented: All dynamicists are grateful to Dr. Yamashita and Prof. Morokuma for performing the kind of calculations presented here. However, to interpret the pump-probe experiments in detail we need to know a lot more about the state populated by the probe and the coordinate dependence of the transition moment to this state. Engel and I’ have attempted to construct a detailed model for Zewail’s pump-probe experiments on NaI and failed: too little is known about the final state. Even simple information, such as which state (or states?) is populated and whether that state is bound or repulsive, would be useful. I also want to make a general comment regarding Heller’s absorption formula, which has been used in several presentations. It is common to use the time evolution of the absolute value of the correlation function to interpret the spectrum in terms of the nuclear dynamics on the excited state.However, the correlation function is a complex quantity, and in many cases the time evolution of its phase determines the spectrum in an essential way.2 Physical pictures ignoring the role of this phase can be incomplete. 1 V. Engel and H. Metiu, J. Chem. Phys., 1989, 91, 1596. 2 V. Engel, R. Schinke, S. Henning and H. Metiu, J. Chem. Phys., 1990, 92, 1 Prof. Lagana said: A bottle-neck to the use of ab initio potential-energy values in dynamical calculations is the difficulty in building a suitable analytical representation of the potential-energy surface (PES).An analytical representation of the PES can be either local or global.’** The local formulation of a PES relies on the adoption of simple functionals accurately describing the interaction in a limited region of the configuration space. Global interpolators have a more complex analytical form tailored to provide an accurate fit of the potential over the whole configuration space. A popular way of formulating a global analytical representation of the atom-diatom interaction is to perform a many-body expansion (MBE).’ MBE terms are then expressed as polynomials in the internuclear distances (physical space) damped by appropriate exponential-like functions. As an alternative to the physical space, other kinds of spaces and associated coordin- ates can be used to perform a MBE expansion.In particular, potential-energy values can be mapped onto the space of bond-order (BO) variable^.^ The ( n i ) BO variables are defined as the exponential of the weighed diatomic displacement4 ( n , = exp [ -bi( ri - r o i ) ] , where bi is a constant related to one or more diatomic force constants,138 3.0 2.0 lb S E: 1 .o 0 General Discussion 0 1 .o 2.0 nLiF 3.0 Fig. 11 Isoenergetic contours of the LiFH potential-energy surface plotted as a function of the LiF and FH bond-order coordinates at 8 = 170 O roi is the equilibrium diatomic distance and r, is the familiar atom-atom internuclear distance of the ith diatom. A property of the BO space is to have the origin at infinite internuclear distances and to confine the physical space inside the limiting value exp (bir&) (r$ is the largest equilibrium distance of the considered diatoms).This makes the BO space of particular interest for dynamical studies. BO coordinates have already been used for some theoreti- cal investigations of atom-diatom reactivity.’ Work aimed at reformulating scattering equations in the BO space is also being carried out in our laboratory.6 The potential- energy surface of several alkali-metal or alkaline-earth atom hydrogen halide systems having a bent transition state and a structured minimum-energy path to products have been fitted using BO polynomials.’ In this spirit we have recently proposed’ a re-examination of the rotating model potential (RMP) approach in BO space. In a RMP approach, the reaction channel is described by a diatomic model potential rotating around a turning centre, TC.The distortion of the channel on going from the reactant to the product asymptote is accounted for by a variation of the model potential parameters.In the physical space, however, an inappropriate choice of the TC may cause some problems. On the contrary, in BO space the TC is naturally set at the axes origin. Cuts of the potential-energy surface are then obtained by drawing the line p = (n:+ n:)*’* at fixed value of the angle a. [a, = arctan ( n , / n 2 ) ] and of the third coordinate (say the collision angle 6 ) . Although a detailed discussion of the properties of the cuts of the reactive potential channel along p will be given elsewhere,’ for illustrative purposes we show in Fig.1 1 the isoenergetic contours of the potential-energy surface of the prototype Li+HF system drawn at e= 170”. As can be easily seen from Fig. 11, the BO circular coordinates are a more appropriate set of reaction coordinates than those defined using straight cuts centred on an arbitrarilyGeneral Discussion 139 chosen point on the ridge in the fixed angle-of-approach cross-section of the potential in physical space. The figure also suggests that fixed-a cuts have a smooth, single- minimum shape. This makes it possible to represent the fixed-8 cross-section of the potential-energy surface as where D is the depth of the one-dimensional cut of the potential along p that is a function of a and 8. In eq. (1) P"' is a polynomial of order m whose coefficients can be chosen to reproduce the structure of the one-dimensional cut of the potential-energy surface along p.Of particular interest is the case m = 2. In this case one obtains a BO analogous to the rotating Morse potential. 1 J. N. Murrell, S. Carter, S. C. Farantos, P. Huxley and A. J. C. Varandas, Molecular Potential Energy 2 J. N. L. Connor, Comput. Phys. Commun., 1979, 17, 117; N. Sathyamurthy, Comput. Phys. Rep., 1985, 3 E. Garcia and A. LaganP, Mol. Phys., 1985, 56, 521; 529. 4 L. Pauling, J. Am. Chem. SOC., 1947, 69, 542. 5 H. S. Johnston, Adu. Chem. Phys., 1960, 31, 31; H. S. Johnston and C. Parr, J. Am. Chem. SOC., 1963, 85,2544; R. A. Marcus, J. Phys. Chem., 1968,72, 891; C . M. Marschoff and A. Jatan, Chem. Phys. Lett., 1978,56,35; N.Agmon and R. D. Levine, J. Chem. Phys., 1979,71,3034; N. Agmon and R. D. Levine, Isr. J. Chem., 1980, 19, 330; N. Agmon, J. Chem. Phys., 1982, 71, 3034. Functions, Wiley, New York, 1984. 3, 1. 6 G. Ferraro and A. Laganh, unpublished results. 7 A. LaganA, 0. Gervasi, and E. Garcia, Chem. Phys. Lett., 1988, 143, 119; P. Palmicri, E. Garcia and A. LaganA, J. Chem. Phys., 1988, 88, 81; A. Lagank, P. Palmieri, J. M. Alvarifio and E. Garcia, J. Chem. Phys., 1990,93, 8764; P. Palmieri and A. Lagani, J. Chem. SOC., Faraday Trans. 2, 1989, 85, 1056. 8 A. Lagana, J. Chem. Phys., 1991,95, 2216. 9 E. Garcia and A. Laganl, in preparation. Prof. Valentini commented: I am pleased to see an a6 initio calculation of global potential-energy surfaces for the UV photodissociation 03.Several years ago we carried out state-to-state dynamics experiments'** on the photodissociation of ozone that revealed an anomalous alternation in the populations of the even and odd rotational states of the O,( 'Ag) photofragment. This is illustrated in Fig. 12. We proposed that this behaviour was the result of nuclear exchange symmetry restrictions in the curve cross between the B and R potential-energy surfaces, and experiments with '*O-enriched O3 supported this proposal. However, uncertainty about the potential-energy surfaces precluded us from carrying out a more rigorous analysis of the curve-crossing process. 1 J. J. Valentini, Chem. Phys. Lett., 1983, 96, 395. 2 J. J. Valentini, D. P. Gerrity, D. L. Phillips, J.-C. Nieh and K. D. Tabor, J. Chem.Phys., 1987, 86, 6745. Dr. Yamashita and Prof. Morokuma (communicated): We would like to comment on our study of ozone photodissociation based on some new insights' which are found after we submitted our paper. The first point is on the accuracy of our new a6 initio PES. Fig. 13 shows a comparison of the width of the absorption spectrum (excluding the structures) between the calculations using (a) the Sheppard and Walker PES and (6) our new a6 initio PES. Our new PES produces a correct width for the spectrum, and this again indicates that the repulsive part of the B state, which corresponds to the Franck-Condon region of the ground equilibrium geometry, is well reproduced by our calculation. It should be emphasized here that this comparison provides a very severe test for quantum chemists, since we are examining a very small residual of the initial wavepacket (<1 %).The second point is why the calculated recurrence intensities are stronger than the experimental ones. Several causes can be considered. One is the role of the transition dipole moment p between the ground and the excited B states. The autocorrelation function in the paper was calculated assuming that p is independent of140 General Discussion 10 - 8 - 6 - 4 - 2 - v = o x 21- 4 = 0 'It! Fig. 12 Populations of rotational states for O,( 'Ag); hdiss = 240 nmGeneral Discussion 141 \ .P 750 Y 1 500 2 E .C1 P 4 250 30 35 40 3 0 3 5 40 frequency/ lo3 crn-’ frequency/ lo3 crn-’ Fig. 13 Comparison of spectrum width between (a) Sheppard and Walker PES and ( b ) our new PES.The curve with structures is the experimental spectrum by Freeman et al. geometry. Our new result with the ab initio p ( R ) , however, shows that the geometry dependence has only a minor effect on the recurrence peaks. In a simple approach, Le Quere et aL2 have estimated the rotational contribution CR( t ) to the total autocorrelation function C ( t ) as the convolution product, C ( t ) = C,( t ) CR( t ) , where CR has been computed as the inverse Fourier transform of a pure rotational spectrum at 195 K, the experimental temperature. They found that the rotation effect appears only after 200 fs. We suspect that the discrepancy between experiment and theory in the recurrence intensity is due to a nonadiabatic process among the several electronic states.Le Quere and Leforestier3 have recently found that a wavepacket can arrive at the nonadiabatic region between the repulsive R and B states within a very short time of <lo fs. 1 K. Yamashita, K. Morokuma, F. Le Quere and C. Leforestier, to be published. 2 F. Le Quere, C . Leforestier and P. Lombardi, personal communication. 3 F. Le Quere and C . Leforestier, personal communication. Prof. Bowman said to Prof. Morokuma: With regard to the ab initio calculation of the FHF- potential and the vibrational calculations of bound and unbound resonance and ‘scattering’ states by Dr. Yamashita and yourself, I would like to mention similar work in support of your approach. In collaboration with Dr. A1 Wagner and Dr. Seon-Woog Cho I have calculated L2 vibrational wavefunctions for resonances in HCO using an ab initio potential calculated by Dr.L. B. Harding and fitted by Dr. K. T. Lee and myself. The resonance energies agree with converged scattering results to within 1-3 cm-’ for nine resonances calculated thus far. Comparisons of these and bound-state energies with experiment reveal some small errors in the potential-energy surface. However, by making very minor adjustments to the surface it was possible to improve agreement with experiment considerably. Prof. Neumark asked Prof. Morokuma: Your prediction of highly vibrationally excited FHF- resonances above the dissociation threshold is quite interesting. If they are sufficiently long-lived and could be populated to an appreciable extent, one could probably observe them in an ion photodissociation experiment.I wonder if it would be possible to calculate the resonance lifetimes. A promising approach to populating these resonances may be stimulated emission pumping uia an excited electronic state.142 General Discussion Dr. F. Temps (Max Planck Institute, Gcttingen) said: With reference to the comments of Professors Morokuma and Bowman, who mentioned experimental observations of highly excited states of the molecules HFCO' and HC0,2*3 I would like to report on results concerning the CH30 radical that were obtained in our laboratory. CH30 constitutes a unique model system for investigating at a rotation-vibration state-resolved level of detail the unimolecular dissociation reaction CH30 + H+H,CO for which the asymptotic reaction enthalpy and threshold energy are AHio == 7000 cm-' and Eo == 8500 cm-'. We have observed highly excited short-lived quasibound resonance states of CH30 in the X 2E ground electronic state at energies significantly above the H-CH20 dissociation threshold.495 Experiments were carried out using the optical double-reson- ance method of stimulated emission pumping (SEP) spectroscopy.6 A pulsed dye laser (PLJMP) was employed to transfer molecules to a selected rotation vibration level in the A 2A1 excited electronic state, which can be detected by the associated laser-induced fluorescence (LLF).A second dye laser (DUMP) served to access via stimulated emission highly excited X states, from the bottom of the CH30 potential well up to above the H-CH20 dissociation limit. Transitions induce by the_DUMP were detected by observ- ing the corresponding dips in the LIF intensity from A.Fig. 14 depicts some typical SEP spectra, ploited Girectly versus the ? term energy, that were obtained with the PUMP tuned to the A + X, 3 $,_A" AJFSF" (J", K") = 3; 4R21 (7.5, - 8 ) line and the DUMP scanned over the regions of the X, v3 = 6,8 and 9 vibrational states.' These windows refer to energies slightly below the asymptotic C-H dissociation energy, just at the reaction threshold, and significantly above the top of the dissociation barrier, respectively. At these high energies only the total energy E and total angular momentum J remain as 'good quantum numbers'. The features in the spectra shown in Fig. 14 must be assigned to individual rotation- vibration states with J = 9.5.The complex line structure arises from coupling of a single 'bright' zero-order state ( J = 9.5, K = 10, C = -0.5 and v3 = 6, 8 or 9, respectively) which carries the oscillator strength to the manifold of (in zero-order) dark background states, which receive some transition moment by intensity borrowing. Below the reaction threshold [see e.g. the 6500 cm-' region, Fig. 14(a)] the observed spectra exhibit sharp line structure which reflects the vast density of states at the high energy. Above the dissociation limit the spectrum of a diatomic molecule would be a true continuum. However, in a polyatomic like CH30 one has short-lived quasibound 'resonance' states. Fig. 14( 6) and ( c ) shows two such spectra. Just at threshold (middle trace) the spectrum still consists of sharp lines, although a careful inspection reveals some evidence for the onset of line broadening.However, at energies around 9500 cm-', significantly above the reaction barrier [Fig. 14( c ) ] the spectrum reveals strongly broadened features, which reflect the shortening of the lifetimes [increasing unimolecular rate constants k ( E, J ) ] with increasing energy. Note that the calculated density of states increases only by a factor of four from 6500 to 8500 cm-' and by a factor of two from 8500 to 9500 cm-'. The comparison of the spectra rules out the possibility of purely inhomogeneous broadening in the 9500 cm-' spectra, although some inhomogeneous contribution cannot be excluded. It is noted that the observed linewidths are in accord with results from unimolecular rate theory, assuming that the K-rotor is strongly coupled to the vibrational degrees of freedom.1 Y. S. Choi, P. Teal and C. B. Moore, J. Opt. SOC. Am., Part B, 1990, 7 , 1829. 2 A. D. Sappey and D. R. Crosley, J. Chem. Phys., 1990, 93, 7601. 3 X. Zhao, G. W. Adamson and R. W. Field, personal communication. 4 A. Geers, J. Kappert, F. Temps and J. W. Wiebrecht, J. Chem. Phys., 1990, 93, 1472. 5 A. Geers, J. Kappert, F. Temps and J. W. Wiebrecht, Ber. Bunsenges. Phys. Chem., 1990,94, 1219.General Discussion 143 I I 1 9455 9460 9465 a495 8500 8505 I I I 6 5 8 5 6 5 9 0 6595 energy/ cm-' Fig. 14 Typial SEP spectra (see text). PUMP: 3:, rRZl (7.5,8) 6 C. A. Hamilton, J. L. Kinsey and R. W. Field, Annu.Rev. Phys. Chem., 1986, 37, 493. 7 A. Geers, J. Kappert, F. Temps and J. W. Wiebrecht, J. Opt. SOC. Am., Part B, 1990, 7, 1935. Summarizing, Prof. Morkuma said: Though good a6 initio calculations are reliable semiquantitatively, they may require modifications for the accurate reproduction of dynamics. In response to Prof. Newmark, he said: The lifetime of the resonance states of FHF- will be calculated by the complex scaling method. Concerning the request of Prof. Metiu to calculate the excited state of NaI which the probing laser is to excite, he said one has to examine several states of various origins, e.g. excited states of I and excited states of Na. Prof. Morokuma continued: The formic acid system studied by Brouard and Simons is large, and for a qualitative discussion of the reactant and product mode specificity of its reaction, the concept of the intrinsic reaction coordinate (IRC) and its coupling with normal coordinates would be useful.Such a calculation has not been made, as far as I am aware, for excited states, but is feasible.144 General Discussion In this connection I would like to comment on our reaction-coordinate justification of the recent SEP spectra of HFCO. Choi and Moore, in their recent SEP study, found at energies higher than the dissociation threshold several quasi-stable high overtone states of the out-of-plane bending mode (Q5) in combination with the CO stretch mode (Q2). They also observed an increase in the spectral linewidth when internal energy is shifted from Q5 to Q2. We have traced the IRC at the correlated MP2/6-3lG * level for the unimolecular decomposition HFCO ---* HF+ CO, and calculated along the IRC the frequencies of normal vibrations, their coupling elements with the IRC (curvature coupling) and those with the other normal coordinates (Coriolis coupling).' The out-of- plane bending Qs mode has no coupling with any vibration mode or the IRC, all of which belong to the total1,y symmetric representation, and therefore Q5 overtomes should have the longest lifetime for IVR or reaction. Q2, among the totally symmetric modes, has been found to have the smallest Coriolis and curvature coupling until the system goes beyond the transition state, which gives the largest lifetime to its overtone modes.However, a small amount of coupling that exists for Q2, in contrast to none for Q5, must be responsible to the observed increase in linewidth when energy is moved from Q5 to 4 2 .1 K. Kamiya and K. Morokuma, J. Chem. Phys., 1991, 94, 7287. Prof. J. Pfab and Mr. A. W. Simpson (communicated): Brouard et al. have shown in their paper on the predissociation dynamics of formic acid well above threshold that almost all the available excess energy appears in the recoil of the OH and HCO fragments. This prompts the question to what extent the product internal state distributions are statistical, particularly for dissociation closer to threshold. This is surely of some interest, since the nature of the product state distributions should be indicative of the timescale of the dissociation and might reflect the influence of state couplings in the transition state.We have previously studied the predissociation dynamics of CF3N0 close to threshold in the visible' using jet-cooling and pump-probe experiments not dissimilar to those performed by Brouard et al. but probing NO rather than OH by LIF. Fig. 15 shows a 5 , 4 -i 3 2 : 1 4 c 3 12 8 12 5 I 12 ; 680 690 700 710 720 wavelength/ nm Fig. 15 Power-corrected fluorescence excitation spectrum of jet-cooled CF3N0 in the visible spectral regionGeneral Discussion 145 corrected fluorescence excitation spectrum of CF3N0 jet-cooled with Ar, indicating that vibronically state-selected photolysis is achieved readily for this compound. Here the 13 980 f 60 cm-’ dissociation threshold virtually coincides with the Franck-Condon- forbidden electronic origin.The fluorescence decays bi-exponentially, with the short-life time component ranging from ca. 300 ns for the origin level down to 74 ns for the 127e level close to the barrier for internal rotation in the electronically excited state. Here the torsion (i.e. normal) mode 12 is clearly only weakly coupled to the dissociation coordinate. We were led to conclude from the bi-exponential fluorescence decay behaviour that intersystem crossing (ISC) to the triplet state was important for all but the lowest A-state levels. Is there any indication that the predissociation of formic acid might also involve ISC and dissociation from the triplet surface? 1 J. A. Dyet, M. R. S. McCoustra and J. Pfab, J. Chem. SOC., Faraday Trans. 2, 1988, 84, 463.Dr. M. Brouard, Prof. J. P. Simons and Dr. J.-X. Wang (communicated): The involvement of the triplet surface cannot, at present, be discounted, although its role would appear to be unimportant (for the OH+ HCO dissociation channel?) given the similarity of the spin-orbit populations in the OH products.’ Note also that triplet states have not been invoked to explain the analogous dissociation process in HONO. As regards whether or not the product rovibrational state distributions are statistical, it seems unlikely to us that a simple statistical model could account for the very large translational energy releases (fT = 80 %) we observe, both close to and up to ca. 4500 cm-’ above the threshold for OH production. Certainly, very simple phase-space calculations predict significantly greater rovibrational excitation in both HCO and OH fragments, even if it is assumed that only the energy above the 2400cm-’ barrier is free to be distributed among the internal modes of the products.We feel that the pattern of energy disposals observed for HC02H photodissociation is determined largely in the exit channel, in which presumably the coupling between the C-OH dissociation coordinate and the remaining modes is very weak. As with H2C0 dissociation to H2 and CO, product siate distributions alone may not have much to tell us about the region of the HC02H(A) surface prior to and at the transition state. 1 M. Brouard and J. O’Mahony, Chem. Phys. Lett,, 1988, 149, 45. Prof. M. Henchman (Brandeis University) said: Prof. Katz’s conclusions that the reaction H + SiD4 = D + SiHD3 proceeds via inversion at energies of ca.2 eV is based on four findings: (i) The H and D atom velocity distributions show similar directional properties. (ii) Energy transfer from H to D is efficient. (iii) The threshold energy is lower than that for the corresponding H + CD4 reaction. (iv) There are isotope effects for the reaction cross-sections. These findings can be used to argue a contrary conclusion. Direct displacement, as shown in the nuclear recoil studies, in the probable energy range 2-10eV, involve atom/atom interactions. Hence (i) displacing and displaced atoms are collinear; (ii) energy transfer is maximised more effectively than for inversion; (iii) a stable intermediate SiH5 is not impossible (SiH; is stable whereas CHT is not) such that oxidative addition/reductive elimination would occur, yielding racemization not inver- sion; (iv) mechanistic deductions from isotope effects are fraught with ambiguity, as I have discussed elsewhere.The authors could be right; but they could equally well be wrong. t Below the OH + HCO threshold, fluorescence lifetime measurements indicate the presence of other dissociation channels, which may involve internal conversion to So and/or intersystem crossing to the T, surface.146 General Discussion Reaction (1) may well occur with inversion at threshold. I am pessimistic about showing this with kinetic evidence. 1 R. Wolfgang, Progr. React. Kinet., 1965, 3, 97. 2 D. J. Hajdasz and R. R. Squires, J. Am. Chem. SOC., 1986, 108, 3139.3 M. Henchman, in Ion Molecule Reactions, ed. J. L. Franklin, Plenum Press, New York, 1972, vol. 1, p. 101. Prof. B. Katz (Ben-Gurion Uniuersity) replied: After the submission of this paper the exchange reaction H + CD, --+ CD3H + D at 2 eV was studied.' Similar features to the reaction H+SiD, were found. The absolute cross-section for H+CD, was about five times smaller than the one of H + SiD, , but the cross-section per D of H + CH3D was about 1.7 larger than that for H + CD,. The velocity of the D product was found to be correlated with the velocity of the reacting H atoms, and about 80% of the translational energy of the H atoms is carried by product D atoms. At the same collision energy, when CH3CD3 was substituted for CD,, no D signal was detected. This finding excludes the direct mechanism, and further supports the inversion mechanism at this collision energy. Regarding the claim that SiH5 may be a stable radical, we mention a paper published last year by Volatron et a1.* They used an a6 initio study to show that SiH5 is not a stable radical, but rather dissociates spontaneously into H + SiH, even at no extra energy.In our experiment at a collision energy of ca. 2 eV we deduced from the correlation of the velocities of the reactant H and product D and from the fact that most of the reactant translational energy remains as product translation, that the reaction is direct and that SiH5 is a transition state. 1 A. Chattopadadhyay, S. Tasaki, R. Bersohn and M. Kawasaki, J. Chem. Phys., 1991, 95, 1033. 2 F. Volatron, P.Maitre and M. Pellisier, Chem. Phys. Lett., 1990, 166, 49. Prof. Henchman (communicated): Prof. Katz's failure to observe displacement with ethane shows that the threshold energy for that reaction exceeds 2eV. The nuclear recoil experiments show that the displacement reaction is efficient at higher energies (probably 2 < E/eV < lo).' Again nuclear recoil experiments suggest that the displace- ment will be direct (90 * 10 %). This leaves open the question of whether displacement could occur with inversion at threshold. 1 R. Wolfgang, bog. React. Kinet., 1965, 3, 97 Prof. Valentini said: One possible explanation for the apparent difference in mechan- ism of the substitution reaction in the T+ CHXYZ and H + CD, (H + SiD,) systems that Prof. Henchman has described is kinematic.At the high collision energies at which the experiments have been carried out the motion of the T atom will be sudden with respect to the motion of the heavy X, Y and Z species. The inversion mechanism will be disfavoured because the reaction coordinate for it requires that these heavy atoms undergo a large displacement that is synchronized with the approach of the attacking T atom. Because the inversion route is essentially blocked by the disparity in timescales for the motion of the light T and the heavy X, Y and Z, the reaction will have to proceed by displacement of the H atom by the attacking T atom, with retention of configuration as is experimentally observed. The case of the H+CD, (H+SiD,) systems is much different. Here the attacking D atom and the H atoms have comparable timescales for their motions, so the inversion of the H atoms about the C atom and the attack of the D atom can occur synchronously, and the inversion route is no longer disfavoured.Prof. Henchman (communicated): I agree with Prof. Valentini's summary. At low energies (ca. 1 eV), the collision lifetime is long enough to allow the atom to interact with the whole molecule: at high energies (ca. 10 eV) the lifetime is too short and theGeneral Discussion 147 interaction consists of atom-atom interactions. A particularly beautiful illustration of this is provided by the work of the late Bruce Mahan, in his study of O++ HD.' Displacement can only occur with inversion at the lowest energies. At high energies it can only occur by a direct, 'knock-on' mechanism.There is indirect evidence for mechanism changing with energy for the nucleophilic displacement reaction OH- + CH3Cl = CH30H + C1- At thermal energies it proceeds on almost every collision, almost certainly with inversion. Yet at higher energies ( 2 2 eV) it still shows a measurable cross-section (ca. 1 A') with little energy dependence. The energy range and the energy dependence imply direct displacement.2 1 B. H. Mahan, in Interactions between Ions and Molecules, ed. P. Ausloos, Plenum Press, New York, 1975, p. 220. 2 P. M. Hierl, A. F. Ahrens, M. J. Henchman, A. A. Viggiano and J. F. Paulson, Furuduy Discuss. G e m . Soc., 1988, 85, 37. Prof. Katz said: I would like to mention the work of Dr. I. Schechter on the modelling of the isotope effect in Walden-inversion reactions.' The model assumes that a T-V energy transfer from the attacking atom to the proper vibrational mode is essential for the reaction to occur.The assumption of the regular line-of-centres is kept, while the T-V process is performed by the vertical to the line-of-centres velocity component of the attacking atom. In the process all three atoms to be inverted get the required momentum from the colliding atom, and it is assumed that the energy transfer occurs in the spectator limit. Assuming a constant barrier along the line-of-centres Eo within a cone of reaction yo, a formula for the reaction cross-section was derived: where d is the sum of the H-Si bond length and the H atom radius, Eh is the energy supplied in the perpendicular to the line-of-centres, and cos2 p is given by where mA is the mass of the attacking atom, mB the mass of the three atoms to be inverted, and mc is the mass of the central atom.yo was taken to be 156", which makes a reasonable cone for hard spheres in a tetrahedral molecule. EL was taken to be 0.6 eV, in agreement with an a6 initio calculation.* Eo was taken to be zero for simplicity, since almost all the energy required to cross the barrier is for the inversion mode. Using these parameters the experimental cross-section at a collision energy of 2 eV could be repro- duced. They were 0.36 A2 for H+SiD4 and 0.17 A2 for H+ SiH,D. Moreover, the ratio of the isotopic variants is: (ET- Eo) - Eb/(4 cos2 p1 sin2 pl) (ET- Eo) - Eh/(4 cos2 p2 sin2 p2) s = This ratio does not depend on the geometrical parameters d and yo, but on energetics only.With the parameters above a value of 0.58 for (H + SiD4)/( H + SiH3D) was attained, which reproduces nicely the experimental ratio of 0.55. 1 I. Schehter, Chem. Phys. Lett., 1991, in the press. 2 F. Volatzon, P. Maitze and M. Pellissier, Chern. Phys. Lett., 1990, 166, 49. Prof. P. Casavecchia, Dr. N. Balucani, Dr. L. Beneventi, Dr. D. Stranges and Prof. G. G. Volpi (University of Pemgia), said: In relation to the paper presented by Dr. Hancock and his co-workers, aimed at deriving the scattering dynamics of atomic oxygen148 General Discussion 6 C 4c T 2c d z 9 0 - A F E -2c -4c - 6 ; - 8( E2 I I I I E -4 “ O e ) + H,S OSH (3A -I- - - - - - \ I I \ I \ I HOSH(N Fig.16 The energy level and correlation diagram for the O(3P, ‘D) + H2S system reactions using laser-based methods, we would like to make a brief comment, present a short communication, and finally ask a question. The utility of laser-based methods for deriving the dynamics of elementary chemical reactions under experimental conditions which do not involve the use of molecular beams is well established. The specific approach of Hancock and co-workers is quite interesting and promising. However, we would like to remind Dr. Hancock of the ‘venerable’ technique of crossed molecular beams with mass-spectrometric detection as a very powerful tool for providing detailed information on the dynamics of elementary chemical reactions. To do so, we wish to present some recent results obtained in our laboratory by the crossed-beam method on oxygen atom reactions which may be amenable to complementary investigation by the laser-based technique discussed by Hancock and co-workers.Furthermore, we would like to stress that methods based on molecular beams and lasers should be seen as, and actually are, complementary to each other, and that an array of experimental data as wide as possible is usually needed to characterize in detail the many facets of a complex physical problem. In our laboratory we have studied the reactions of both ground-state, 3P, and excited-state, ID, oxygen atoms with H2S by using the method of crossed molecular beams.’ The apparatus is an optimized version of the universal high-resolution machine employed for elastic scattering experimenk2 Recently, the reactions of O( ‘D) with hydrogen halides were also inve~tigated.~ Fig.16 shows an energy-level and correlation diagram for the O(3P, ‘D)+H2S system. Note that all three possible reaction channels are exoergic for both O(3P) and O(’D), but the O(3P)+H2S reaction is known4 to have an activation energy of 4.3 * 0.4 kcal mol-I. Using continuous and intense seeded super- sonic beams containing both O(3P) and O(’D), which are generated by a high-power radiofrequency discharge in high-pressure 02-rare-gas mixture^,^'^ we have investigated the reaction channels leading to HSO + H and SO + H2 at several collision energies, Ec, ranging from ca. 3 to ca. 12 kcal mol-’. At collision energies lower than, or comparable to, the threshold for the O(3P) reaction, we observe HSO(H0S) product coming essen- tially only from the O( ‘D) reaction.The laboratory angular and velocity distributionsGeneral Discussion 149 1.0 U ._ v) e 0.5 6 " 0 a 5 V C ,$ @' I I Fig. 17 Laboratory angular distribution and velocity spectrum at 0 = 32 O of m / z = 49 (HSO) product at E, = 11.8 kcal mol-' for the O(3P, 'D) + H2S reactions. The corresponding Newton diagram is shown, indicating the maximum velocity of the products from the ground- and excited-state reactions when all the available energy is assumed to go into translation. Solid lines: calculated curves with the best-fit CM angular and translational energy distributions. The separate contributions from the O('D) and O(3P) reactions are also shown with dashed and dotted lines, respectively can be fitted with a translational energy distribution which peaks at CQ.30 % of the total available energy and with a symmetric centre-of-mass (cm) angular distribution, which indicates that the O( 'D) reaction proceeds through the formation of a long-lived complex, presumably a thioperoxide (HOSH) intermediate, following O( 'D) insertion. The cm angular distribution is weakly polarized along the relative velocity vector, suggesting that there is a weak (k, k') correlation, i.e. the initial ( L ) and final (L') orbital angular momenta are weakly correlated as a consequence of a non-coplanar intermediate complex. For this specific mass combination angular-momentum partitioning arguments predict a significant ( k , J') correlation between the initial orbital angular momentum L and the final rotational angular momentum J'.As we raise the collision energy, the experimental data show clearly that a contribution from both ground- and excited-state reactions is occurring. This is not surprising, considering that the cross-section for O( 3P) reaction become significant at collision energies well above thre~hold,~ and that the concentration of O(3P) is dominant in the beam. Fig. 17 shows the m/Z = 49 angular distribution measured at Ec = 11.8 kcal mol-', together with the most probable Newton diagram and the velocity spectrum at 0 = 32 O. Time-of-flight spectra were recorded every 2 O from 0 = 12 to 52 O using 5 pslchannel pseudo-random chopping. The very different energetics and dynamics produce distinct150 General Discussion features in the angular and velocity distributions of the HSO (HSO) products that can be unambiguously attributed to the reactions of atomic oxygen in the two different electronic states.The angular and translational energy distributions in the cm frame were determined for each reagent electronic state by forward convolution of trial distributions.6 The dashed and dotted lines in Fig. 17 are the laboratory distributions generated by the best-fit cm parameters for the two reactions. The contribution from O(3P) to the total laboratory number density signal is estimated to be about one half that from O('D). The dynamics of the O(3P) reaction at Ec = 11.8 kcal mol-' is found to be drastically different from that of O(lD), being characterized by a completely backward cm angular distribution and by a very large fraction (ca.60 %) of energy released into translation. This indicates that the reaction proceeds by a direct, rebound type, mechanism and that the barrier is located in the exit channel. A good qualitative agreement is noted with the results of an earlier low-resolution crossed-beam study' of this reaction. The resolution of the present experiment permitted a refinement of the heat of formation of the HSO radical. O('D) instead yields a scattering which, while it is symmetric at Ec = 3-5 kcal mol-', becomes slightly forward at the higher Ec of 11.8 kcal mol-', with a much smaller average fraction of available energy going into translation than for the O(3P) reaction. The results for the O( 'D) reaction are interpreted in terms of a long-lived complex at low Ec and of an osculating complex at high Ec.Again, from the derived cm distributions it is possible to infer qualitative, and to some extent quantitative, ( k , k') and (k, J ' ) correlations. In surxmary, the triplet reaction proceeds via a short-lived, weakly bound, triplet intermediate with an energy barrier on the exit channel (Fig. 16) and is characterized by a direct mechanism, whereas the singlet reaction proceeds with virtually no barrier via a singlet surface that correlates with a strongly bound intermediate (Fig. 16) and therefore is characterized by a mechan- ism forming a long-lived complex. 176 As far as the SO + H2 reaction channel is concerned, this is not observed to occur in the investigated range of collision energies, in line with an expected very high barrier for the three-four centre elimination of molecular hydrogen from a collision adduct.The other relevant reaction channel in the reactions O(3P, 'D) + H2S is the one leading to OH + SH. While this channel has been characterized to some extent for the excited- state reaction by laser-induced fluorescence and infrared chemiluminescence tech- niques,' very little is known about the dynamics of the O(3P) reaction. The channel leading to OH formation is unfavourable to our cross-beam technique for the present system. Could your technique, Dr. Hancock, be applied to the investigation of the dynamics of the reaction channel O(3P) + H,S -+ OH + SH? Our understanding of the mechanism and dynamics of the reactions of atomic oxygen with H2S, which are the prototype of the atmospheric oxidation reactions of sulfur compounds and are also relevant in the combustion of sulfur-contaminated fossil fuels, would benefit considerably from a detailed investigation of the above reaction channel. It would be interesting to see if there is also a dramatic effect of electronic excitation on the dynamics of the OH-forming channel.A more clear correlation between reaction dynamics and potential- energy surfaces could be made. 1 N. Balucani, L. Beneventi, P. Casavecchia, D. Stranges and G. G. Volpi, J. Chem. Phys., 1991,94,8611. 2 L.Beneventi, P. Casavecchia and G. G. Volpi, J. Chem. Phys., 1986, 85, 7011. 3 N. Balucani, L. Beneventi, P. Casavecchia and G. G.Volpi, Chem. Phys. Letr., 1991, 180, 34. 4 R. F. Hampson, Chemical Kinetics and Photochemical Data Sheets for Atmospheric Reactions, Report 5 S. J. Sibener, R. J. Buss, C. Y. Ng and Y. T. Lee, Rev. Sci. Znstr., 1980, 51, 167. 6 N. Balucani, L. Beneventi, P. Casavecchia, D. Stranges and G. G. Volpi, to be published. 7 F. E. Davidson, A. R. Clemo, G. L. Duncan, R. J. Browett, J. H. Hobson and R. Grice, Mol. Phys., 8 S. Klee, H. Gericke, and F. J. Comes, Chem. Phys. Lett., 1985, 118, 530, P. M. Aker, J. J. A. O'Brien No. FAA-EE-80-17 to US Department of Transportation, 1980. 1982, 46, 33. and J. J. Sloan, Chem. Phys., 1986, 104, 421.Genera I Discussion 151 Dr. Hancock replied: The O(3P)+H2S reaction is very well suited to study via the production of velocity-aligned O(3P) atoms.The activation energy (3.6 kcal mol-')* for the overall reaction, and the threshold kinetic energy for the formation of HSO+ H products (3.4 kcal mol-'),2 can both be exceeded by the energies of O(3P) formed by the 355 nm photolysis of NO2. The predominant channel, producing OH+SH, which, for kinematic reasons, is hard to observe in conventional molecular-beam scattering experiments, could be studied in great detail, as both products can be detected by laser-induced fluorescence of their A *X+-X 211 transition. A further advantage in com- parison with the present experiments is that, as one of the reagents is a stable molecule, it could be prepared in a facile way in low rotational levels by nozzle expansion, so that the initial angular momentum of the reactants would come predominantly from their translational motion.1 Chemical Kinetics and Photochemical Data for Use in Stratospheric Modeling, Evaluation Number 9, JPL Publication 90-1, 1990. 2 A. R. Clemo, F. E. Davidson, G. L. Duncan and R. Grice, Chern. Phys. Lett., 1981,84, 509, 1981; F. E. Davidson, A. R. Clemo, G. L. Duncan, R. J. Browett, J. H. Hobson and R. Grice, Mol. Phys., 1982,46, 33. Dr. J. C. Whitehead (communicated): Prof. Casavecchia asked Dr. Hancock if it would be possible to use his pulse-probe arrangment to study the reaction O(3P)+ H2S --P OH + SH. Dr. Hancock replied that on energetic grounds it would be possible. However, we have found' that using NO2 as a precursor for 0(3P) renders the pulse-probe arrangement unsuitable for this reaction because of a rapid gas-phase reaction between NOz and H2S which produces, amongst other things, sulphur and nitrous acid.Thus the photolysis-probe arrangement actually studies the well known production of OH from the 351 nm photolysis of nitrous acid.2 This is pertinent to the discussion of the merits of molecular-beam experiments versus pulse-probe experiments for studying the dynamics of elementary chemical reactions. The pulse-probe method is restricted to reactions for which one reagent can be generated by photolysis of a suitable precursor at a wavelength at which the other reagent does not absorb, and to systems for which there is no significant dark reaction between the precursor and the other reagent.3 To find an O('P) precursor other than NO2 for the reaction O(3P) + H2S that satisfies these conditions is extremely difficult.1 N. M. Ferber, Ph.D. Thesis, University of Manchester, 1989. 2 R. Vasudev, R. N. Zare and R. N. Dixon, J. Chem. Phys., 1984, 80, 4863. 3 J. C. Whitehead, J. Phys. B, 1991, 23, 3443. Dr. Hancock replied: Dr. Whitehead raises the problem of reaction of H2S with the NO2 precursor. If this did occur to form HONO, which was then photolysed at 355 nm to produce OH, then it would complicate the measurement. However, we need to look at the time of mixing of reagents that can be reasonably achieved and the rate of the dark reaction at the typical pressures that are used. Mixing of reagents in a static cell might cause problems, but this can be overcome by pulsed valve injection of one reagent into a low pressure of the other.For pressures similar to those that we use in the 0 + CS experiment (i.e. ca. 5 x lop3 Torr each of H2S and NO2), then mixing 2 cm away from a pulsed inlet valve (a similar geometry to that in our present apparatus) would take at the most a few hundred microseconds. If we allow an upper limit of 500 ps, then for 1 % dark reaction during that time, the bimolecular rate constant would have to be of the order of lo-" cm3 molecule-' s-l. Although Dr. Whitehead suggests that the H,S+ NO2 reaction is rapid, the only reference in the literature that we can find gives the rate constant as being extremely slow, <6 x lop2' cm3 molecule-' s-l, and possibly heterogeneous in nature.' Even if this value is six orders of magnitude too slow, it would still not affect the proposed method.152 General Discussion In general, though, it is perfectly true that there are restrictions in the systems that can be studied by the laser pump and probe technique, just as there are restrictions on the crossed-beam scattering experiments that can produce both velocity- and quantum- state-resolved data.Both techniques have already made important and often complemen- tary contributions to molecular dynamics, and both are edging towards full quantum-state resolution of of both vector and scalar properties in reactants and products. 1 C. A. Cantrell, J. A. Davidson, R. E. Shetter, B. A. Anderson and J. G. Calvert, J. Phys. Chern., 1987, 91, 6017. Dr. V. Wei-Keb Wu (Victor Basic Research Lab., Bielefeld) commented: My experi- mental and simulational experiences have shown that in order to conclude if the products are scattered forwards or backwards, the simulated angular distribution p ( 9 ) of the products in the CM (centre-of-mass) system cannot be obtained from only the in-plane angular distributions of the products.It can, however, be obtained in combination with the in-plane TOF distributions of the products, but in a rather untrustworthy state or with bad resolution.lY2 The better way should be from the measurement of the in-plane and out-of-plane angular distributions of the products; the most reliable one is the measurement of the in-plane and out-of-plane TOF distributions. ‘*2 1 V. W.-K. Wu, Abstracts of the 10th ICAP, 25-29, August 1986 Tokyo, Japan, p.514. 2 V. W.-K. Wu, Abstracts of the 8th MOLEC, 10-14 September 1990, Bernkastel-Kues, Germany, p. 113. Prof. Casavecchia responded: It is well known that when cylindrical symmetry exists around the relative velocity (i.e. when unpolarized beams are used in the absence of orienting fields), one can obtain complete information on the scattering process, i.e. on the angular distribution and the translational energy distribution of products in the centre-of-mass (CM) system, by measuring angular and velocity distributions of products in the plane defined by the two crossing beams.’ Dr. Wu’s comment that the CM angular distribution derived from in-plane measurements is ‘in a rather untrustworthy state or with bad resolution’ clearly refers to the specific case (K+ HBr 4 KBr+ H) discussed in the references he quotes, but does not have general validity.In fact, the accuracy of the derived CM functions, although it may be limited by an unfavourable kinematics usually associated with a large mass ratio of the products, depends in general on the level of experimental resolution. As can be seen from our experimental results on the reactions O(3P) + H2S + HSO + H and O( ‘D) + H2S -+ HSO + H,2*3 although the reaction kinematics is unfavourable ( mHso/ mH ==: 50 >> l), we have been able to un- ambiguously CM angular and translational energy distributions with small error bars because of the high resolution of the experimental conditions (i.e. high angular and velocity resolution). For instance, as can be seen from Fig.17 in our comment’ to the paper by Green et al.,5 using a sufficiently high angular and velocity resolution it was possible to measure the angular and velocity displacement of the product from the centre-of-mass angle and velocity, respectively. Similar accurate results were also obtained for other kinematically unfavoured reactions, such as O( ‘D) + HCI + ClO + H ( mCIO/mH = 50)6 and O( ‘D) + HBr + BrO+ H ( mBrO/mH == loo).’ Obviously, in experi- ments with polarized beams where cylindrical symmetry is lost, it becomes necessary either to perform out-of-plane measurements or to study the in-plane scattering as a function of the orientation of the reagents to obtain complete information on the scattering process ( i e . reliable CM functions). In addition, caution has to be used when products are detected out-of-plane, since product molecules with small recoil velocity will not be detected.’ Because of this, out-of-plane measurements have always to be complemented by in-plane measurements. In conclusion, information obtained from out-of-plane angular and velocity distributions is, in general, complementary to that obtained from in-plane distributions. While this may be useful in some cases, in others, as discussed above, it is unnecessary.General Discussion 153 Y.T. Lee, in Atomic and Molecular Beam Methods, ed. G. Scoles, Oxford University Press, New York, Oxford, 1988, vol. 1, ch. 22. P. Casavecchia, N. Balucani, L. Beneventi, D. Stranges and G. G. Volpi, Faraday Discuss. Chem. Soc., 1991, 91, 148. N. Balucani, L.Beneventi, P. Casavecchia, D. Stranges and G. G. Volpi, J. Chem. Phys., 1991,94, 8611. N. Balucani, L. Beneventi, P. Casavecchia, D. Stranges and G. G. Volpi, to be published. F. Green, G. Hancock and A. J. Orr-Ewing, Faraday Discuss. Chem. Soc., 1991,91,79. N. Balucani, L. Beneventi, P. Casavecchi and G. G. Volpi, Chem. Phys. Lett., 1991, 180, 34. N. Balucani, L. Beneventi, P. Casavecchia, D. Stranges and G. G. Volpi, in Ecological Physical Chemistry, ed. C. Rossi and E. Tiezzi, Elsevier, Amsterdam, 1991, in the press; N. Balucani, L. Beneventi, P. Casavecchia, D. Stranges and G. G. Volpi, to be published. Prof. Simons said: The two papers presented by Dr. Hancock' and Dr. Katz2 signal the arrival of a new experimental strategy, 'molecular-beam dynamics in a bulb', which promises to be a powerful complement to conventional crossed-beam studies.Doppler resolution of the polarised laser-induced fluorescence (or ionisation) spectra of nascent bimolecular reaction products can allow the determination of their scalar quantum state distributions and vector correlations, initially referenced to the laboratory frame, but after a simple transformation, to the bimolecular collision frame. Fortunately, the lack of product rotational alignment found for the CO molecules generated in Dr. Hancock's experiment is the exception rather than the rule (given that the alignment found in two other systems constitutes a 'rule'). The two systems include the reaction of velocity aligned H atoms with 02:3 H+0, --* OH+O where a reanalysis4 of Wolfrum's data leads to an estimate of (P2(JOH k)) - -0.5; and the reaction of velocity-aligned O( 'D) atoms with N20? O('D)+N20 + 2N0 ( u s 18) Analysis of quantum-state distributions and scalar pair correlations in the nascent NO fragments establishes the operation of two parallel mechanisms.One generates NO( v = 0 ) with very low translation and rotational excitation in partnership with NO excited into very high vibrational (v 18) and rotational levels; the other generates both NO molecules in rotationally and vibrationally excited states (see Table 2). The first pathway implies a stripping mechanism, the second implies reaction via a short-lived complex: the absence of any detectable (k, k') correlation for NO( v = 3,lO) reinforces this view. The 'spectator' NO( u = 0) is found (surprisingly) to be aligned with Ah2) - --0.1.The non-zero alignment establishes the (currently unknown) translational alignment of the O( 'D) atoms derived from photodissociation of N20 at 193 nm, as 2 2 p 2 0.5. Table 2 Approximate energy disposals in selected vibrational states of NO generated uia the reaction O('D) + N 2 0 -+ NO( u , ) + NO( u ~ ) ~ 0 0 200 110 16-20 1 1876 4000 690 d 17 > 4000 1350 d 13 1280 s 4 3 5 540 10 17 600 h a Note the positive correlation between vibrational and rotational excitation: the behaviour reported by Valentid at this Discussion is not unique! ' Not determined.154 General Discussion 1 F. Green, G. Hancock and A. Orr-Ewing, Furuduy Discuss. Chem. Soc., 1991,91, 79. 2 B. Katz, J. Park, S.Satyapal, S. Tasaki, A. Chattopadhyay, W. Yi and R. Bersohn, Furuduy Discuss. 3 J. Wolfrum, in Selectivity in Chemical Reactions, ed. J. C . Whitehead, Kluwer, Dordrecht, 1988, p. 23. 4 M. Brouard and J.P. Simons, unpublished work. 5 M. Brouard, S. P. Duxon, P. A. Enriquez, R. Sayos and J. P. Simons, J. Phys. Chem. (Bernstein Issue), 6 J. J. Valentini, P. M. h e r , G. J. Germann and Y.-D. Huh, Furuduy Discuss. Chem. SOC., 1991, 91, 173. Chem. Soc., 1991,91, 73. in the press. Dr. Hancock and Mr. Om-Ewing replied: The O( *D) + N20 experiments illustrate very nicely the potential of laser pump and probe experiments to quantify vector correlations in bimolecular reactions. They emphasise the importance of sub-Doppler spetroscopy, as there is a wealth of dynamical information contained within the Doppler profiles. In addition to the study of reagent and products' relative velocity (k and k') correlations as discussed in the paper by Bersohn and co-workers, if the products of a bimolecular reaction have rotational angular momentum, J', the Doppler profiles of rotational spectral lines can be analysed to obtain bipolar moments of the k', J' distribution, essentially as detailed by Dixon' for photodissociation. For bimolecular reactions these bipolar moments will be referenced to the k vector rather than to the transition dipole moment for photodissociation, p.The transformation from centre-of- mass to laboratory frames will differ because the distribution of k about E,, the electric vector of the photolysis laser, will not have the pure cosine squared form of p about E, except in the limiting case of p = 2, but the modifications to Dixon's analysis are -0.4 -0.2 0 0.2 0.4 frequency shiftlcm-' Fig.18 Q( 17) Doppler profiles for CO(u = 14) from the O+CS reaction, taken with an angle between E , and the probe laser propagation dirrection of ( a ) 90 and ( 6 ) 30"Genera 1 Discussion 155 small. The bipolar moments will characterise all the correlations between the three vectors k, k' and J' that can be measured by single-photon laser pump and LIF probe techniques. This procedure may be complicated by any dependence of the reaction probability on reagent translational energy, since a velocity-dependent reaction cross- section will affect the form of the product Doppler profiles. In Fig.18 we show recent measurements of Doppler profiles of the Q(17) line of the (6,14) band of the A 'n-X 'Zc.+ transition of CO formed from the O+CS reaction. They were recorded at two different values of the angle between E~ and the propagation direction of the probe laser, 90 and 30 O. The profiles are very similar, confirming that the scattering is nearly isotropic in our experiments, but the slightly broader 30 O profile suggests that there is a small preference for forward/backward as opposed to sideways scattering, i.e. a small, positive k, k' correlation. [The same behaviour is observed for the Q(28) transition.] These profiles show some discrepancies with the expected form for isotropic scattering, and we are trying to explain these in terms of a J', k' vector correlation and a velocity-dependent reaction cross-section. 1 R.N. Dixon, J. Chem. Phys., 1986, 85, 1866. Dr. Gericke said: Prof. Casavecchia has reported on the reaction of O('D) atoms with H2S where one reaction channel leads to OH and HS products: O('D)+H2S -+ OH+HS ( 1 ) The OH product is formed vibrationally excited, while HS is generated in low vibrational states.172 Similar behaviour is observed by Simons and co-workers in the reaction of O('D)+N20 -+ NO+NO (2) where a bimodal distribution in terms of the population of vibrational states is observed. This implies a vibrational excited new bond and an old bond which is more a spectator during the reaction process. We have studied the reaction of electronically excited oxygen atoms with water.3 However, isotopic labeling allowed a direct discrimination between the old and new OH bond: 160(lD)+ H2 I8O -+ 160H+180H (3) Indeed, the 160H product (newly formed bond) was found to be vibrationally excited, while the other 180H product (old bond) is formed essentially in the d'= 0 state.Only a few percent of 180H are in the first vibrational excited state. However, the high rotational excitation is the same for both OH fragments. In reactions (1)-(3), although completely different in electronic structure, the old molecular bond is conserved and acts as spectator. The reaction time should be very short and of the order of the time needed by the O('D) atom to pass the molecular reaction partner. The high values of the reaction rate for processes (1)-(3) and the absence of a reaction barrier also confirm this finding.1 S. Klee, K.-H. Gericke and F. J. Comes, Chem. Phys. Lett., 1985, 118 530. 2 P. M. Aker, J. J. A. O'Brien and J. J. Sloan, Chem. Phys., 1986, 104, 421. 3 K.-H. Gericke, F. J. Comes and R. D. Levine, J. Chem. Phys., 1981,74 6106; F. J. Comes, K.-H. Gericke and J. Manz, J. Chem. Phys., 1981, 75 2853. Dr. B. Whitaker ( University ofLeeds) said: In their paper Green et al. are despondent at the small values of the translational anisotropy parameter, p, that have been reported in the literature for the ca. 355 nm photodissociation of N02,'-4 since a small value of p reduces the precision in the measurement of (P2(J- k)). Consequently they reflect that photolysis of NO2 is less than ideal as a source of translationally ordered O(3P) atoms for use in this kind of reactive scattering experiment.I would now like to show some recent experimental results that have been obtained, in collaboration with Prof.156 General Discussion i Fig. 19 Photofragment image obtained by photoionising NO in the region of the u”= 1, = 1/2, Q1 bandhead following 355 nm photodissociation of NOz P. L. Houston and Mr. V. P. Hradil at Cornell University, on the 355 nm photolysis of NO2 using the molecular imaging technique,’ which I hope will encourage Dr. Hancock and his co-workers. Our experimental apparatus differs from earlier designs in that the photofragment ions are detected orthogonally to the molecular beam and laser axes. Very briefly the experiment involves photolysing molecules in a skimmed molecular beam using a linearly polarised laser beam pulse.Following this ‘pump’ pulse the photofragments are allowed to recoil briefly (< 100 ns) before a second linearly polarised ‘probe’ pulse is fired. This is to avoid any distortion due to space charge effects. The frequency of the probe laser is tuned so as to ionise state-selectively one of the photofragments by REMPI. The ions are then extracted from the photolysis region using a Wiley- McClaren arrangement of charged grids, and the ion cloud, still transversely expanding, is projected onto a dual-chevron microchannel plate detector. By suitable adjustment of the voltages on the repeller plate and acceleration grids the ion cloud is focussed in such a way that it becomes a ‘pancake’ as it arrives on the detector.The resulting electrons at the rear of the MCP are then further accelerated onto a phosphor-coated (P47) fibre optic bundle which couples the (now optical) signal through the vacuum chamber walls. The resulting image is then recorded by means of a gateable image-intensified CID camera, which in turn is connected to a signal averager and micro-computer. Typically we average 2’’ laser shots and then subtract an equal number of images with the pump laser blocked, thus minimising the effects of any probe-alone signal. The resulting image (Fig. 19) represents the projection of the three-dimensional velocityGeneral Discussion 157 Fig. 20 Transformed photofragment image showing a slice through the 3D velocity distribution for a state-selected photofragment distribution of the state-selected photofragment onto the imaging plane.In order to extract the anisotropy parameter we need to transform the image to obtain the true (3D) velocity distribution. Because of the cylindrical symmetry of the system this can be done by means of a Hankel transform,6 and the result of this procedure is shown in Fig. 20. This shows a slice through the 3D velocity distribution for NO( ZI” = 1) recorded in the region of the II1,* band-head. By integrating the transformed image over all angles, and knowing the flight time, we obtain the speed distribution of the photofrag- ment, and by integrating along radial lines we obtain the angular distribution. The speed resolution (FWHM 50 cm-’) is limited by the width of molecular beam in the interaction region (ca.1.5 mm). The fit to the angular distribution to the familiar function, I ( @ ) cc (1 + pP2 cos 0) yields a value for p of 1.50 * 0.05 (60 % confidence), which is roughly twice the values previously reported. This value may not be the true translational anisotropy, however, because of the effects of v J correlation. Since for a triatomic dissociation we expect ulJ, this vector correlation means that we may not photoionise the photofragment molecules uniformly. Since we detect the NO by 1 + 1 REMPI and if we assume that the ionisation step is saturated, it is easy to calculate the effect. For a Q-branch transition (which predominates in the band head region) the detection efficiency should go as sin2@. This would lead to a distortion of the image and a decrease in the effective p parameter.Since we do not see this distorted image we conclude that we must be saturating the resonant transition with the first photon, and it is difficult to imagine any effect which will lead to an enhanced p value. Why is our158 General Discussion determination of /3 so high? It is interesting to note that all the previous determinations of the anisotropy have been made in thermal beams with about 300cm-' of internal energy in the parent NO2 molecule Providing that we have not made some fundamental mistake it is possible that we are observing an enhanced p value as a result of rotational cooling in the parent molecule which effectively changes the rotational clock speed. I understand that Dr. J. Frey has recently observed similar effects.research grant. Prof. Houston and I gratefully acknowledge support from NATO for a col 1 G. E. Busch and K. R. Wilson, J. Chem. Phys., 1972,56, 3626; 3638. 2 M. Mons and I. Dimicoli, Chem. Phys. Lett., 1986, 131, 298. 3 M. Mons and I. Dimicoli, Chem. Phys., 1989, 130, 307. 4 M. Kawasaki, H. Sato, A. Fukodora, T. Kikeuchi, S. Kobayashi and T. Arikawa, J. Chem. 86, 4431. aborative Phys., 1987, 5 T. Suzuki, V. P. Hradil, S. A. Hewitt, P. L. Houston and B. J. Whitaker, Chem. Phys. Lett., 1991, submitted. 6 R. N. Strickland and D. W. Chandler, Appl. Opt., 1991, 30, 1811. Dr. J. G. Frey (University of Southampton) said: Dr. Whitaker has described results on the photolysis of NO2 which indicate much larger p values in the dissociation than the literature values used by Green et al.in their analysis. I wonder if the larger values could be due to differences in the extent of rotational cooling in the beams used in different experiments, as the lower the rotational excitation the longer the classical rotational period and so the larger will be the observed p value for the same actual dissociation time. Dr. Hancock responded: We are grateful for Dr. Whitaker's encouraging experiments and Dr. Frey's comment suggesting the possibility of greatly enhancing the sensitivity of our experiments by rotationally cooling the NOz in a molecular beam. The suggestion that rotational cooling will give a substantially higher value of the anisotropy parameter for photodissociation, p, through the slowing of the rotational period of the parent molecule is supported qualitatively by a simple picture for the dependence of p on the angular velocity ( w ) and lifetime (7) of this parent in its excited state.' As the angular momentum, and hence the angular velocity, of the NO2 decreases for a fixed lifetime, so p increases towards a limiting value (which is less than the limit of +2 expected for prompt dissociation of a linear molecule via a parallel transition, since the photofrag- mentation proceeds through a bent excited state).From an estimate of the change in the average value of o on rotational cooling of the parent NO2, and with the inclusion of the parameters given by Busch and Wilson that influence the angular distribution of the photofragments, it becomes apparent that a value of p = 1.5 as observed by Whitaker et al.is attainable via this mechanism. We note that with a value of p of the order of twice that assumed in our experiments, the scatter on the centre-of-mass alignment data would be reduced by a factor of two, and we might expect that any features of the Doppler profiles masked by insufficiently anisotropic O-atom recoil velocities would be more pronounced. 1 G. E. Busch and K. R. Wilson, J. Chem. Phys., 1972, 56, 3638. Dr. Frey said: Unless the initial state of the molecules in a dynamics study is specifically selected it is possible for there to be a difference in the results of a gas-cell study and a molecular-beam study, since the range of rotational states populated can be quite different; effusive and supersonic beams can also differ in this respect.The work presented by Dr. Hancock on O(3P) + CS(X 'Z+) used a thermal distribution of CS, which means a number of the CS rotational levels will be populated. The averaging over the initial rotational states could contribute the small alignment effectsGeneral Discussion 159 observed. I wonder if it would be possible to generate the CS in a different manner (laser photolysis?) so as to allow it to be rotationally cooled by a supersonic expansion? Dr. Hancock replied: We suspect that the rotational angular momentum of the thermal CS does reduce the measurable alignment, although if there were a very pronounced correlation between J' and k we might expect it to survive this additional smearing. This is supported by quasi-classical trajectories performed on an empirical potential energy surface with sampling of initial conditions that mimics our experiments.The generation of rotationally cooled CS might be possible either by laser photolysis at the point of expansion of a molecular beam, or by electrical discharge in CS2 directly behind the supersonic nozzle, but as yet we have not attempted this experiment. Prof. M. Shapiro ( The Weizmann Institute, Rehovot ) commented: When considering photodissociation from multiply interacting electronic states of different electronic angular momenta, it may not be possible to describe the angular distribution in the usual form: where fc = &, & ) is the direction of the departing fragments and P is the anisotropy parameter. This is mainly due to the fact that detection of a specific electronic state of the fragments is in some cases equivalent to the specification of the projection of the electronic angular momentum of the parent molecule.Under these circumstances the general theory of photodissociation' dictates a more complicated angular distribution. In particular, for linear molecules, if this enables one to resolve A, the projection of the electronic angular momentum along the molecular axis, then, as shown by us previously,2 the general shape of the Mi averaged differential cross-section is g ( i ) = a[ 1 + Pp2(cOs e k ) ] ( 1 ) In this expression, in addition to the ordinary anisotropy parameter, ( i e . Po), two other anisotropies, PI and P2, are seen to exist. All three anisotropies may be calculated from a single expression for the differential cross-section: cr(hv, i, A I Ei, J i ) = 16.n3vpk/( h2c) fAtA'(-l)J+J'+A'+Ji [1 + p ( - l ) J + l + J q J,J',p,p',A,A' ( J 1 "i)( J' 1 J ) x [ 1 + p'( - 1 ) "'"'~](2J + 1 )( 2J' + 1 ) -A A 0 -A' A' 0 x ( 1 q)[1 ") 0 0 0 J ' J Ji x { ( J A -A' J' A ' - A ' ) Y9,A-A'(ek7 0) A A' - A ' - A ) Y9.A+A'( ek 7 O)} (3) where v is the photolysis frequency, p is the reduced mass in the dissociation coordinate, tA = [ 2 ( 1 + and p determines the parity of the excited state(s).Tp,A( E, J, A I Ei, J i ) are dynamical amplitudes,2 which contain all the potential-surface dependence (and hence determine the real dynamics of the process), Ei and Ji are the initial energy and total angular momentum of the parent molecule, and J is the final total angular momentum.160 General Discussion As a result of the above, the calculation of vector properties must include the possibility of the more complex form for the differential cross-sections described here.The effect of the additional anisotropies on the Doppler lineshapes is discussed in more detail in a forthcoming p~blication.~ 1 G. G. Balint-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137. 2 I. Levy and M. Shapiro, J. Chem. Phys., 1988, 89, 2900. 3 G. G. Balint-Kurti and M. Shapiro, to be published. Dr. Frey said: Levy and Shapiro’ have shown that if two electronic surfaces are involved in the initial excitation producing an atomic fragment in which the electronic state can be resolved then the angular distribution involves three not one anisotropy parameters, essentially due to interference effects: (1) 1 47r P ( y ) = - [ 1 + POP;( cos y ) + p1 Pi( cos y ) + p2P:( cos y ) ] The experimental consequences of these three terms are not immediately obvious with the distribution shown in this form.However using the expressions for the Legendre polynomials: 3 Cos2 7 - 1 - 1 + 3 cos 2y 2 4 - P;(cos y ) = 3 sin 2 y 2 P l ( C 0 S y ) = - P:(COS y ) = 3 sin2 y = 2[1- P;(COS y)] allows the important parts of the angular dependence to be displayed in any of the following three forms (3) 1 P ( Y ) =&(I +2P2)+(Po-2P2)P;bs y)+BA(cos r)I (4) 1 47r P( y ) = - (A+ B cos 2y+ C sin 27) 1 471. P( y ) =- {A + (Y cos [2( - a)]} where the coefficients in eqn. (4) are given in eqn. (6) and in those for eqn.(5) 4 + PO + 6P2 A = 4 in eqn. (7). 2P 1 ( P o - 2/32] tan 6 =General Discussion 161 At this point it is instructive to compare the results obtained here for the two-surface case with the single-surface dissociation including the possible effects of experimental error. The true zero of the polarisation angle may be difficult to determine, and this would introduce an offset in to the angular distribution: A comparison of this distribution with the two-surface case, eqn. (5) 4+P 3 P 4dexpr( y ) = - + - cos 2( y - 8 ’ ) 4 4 (9) 4+ Po+6P2+ a cos 2( y - 6) 4 4TP( y ) = shows that there may be an experimental problem in ensuring that any offset that is obtained is due to the presence of the extra anisotropy terms and not an indication of an experimental error.1 I. Levy and M. Shapiro, J. Chem. Phys., 1988,89, 2900. 2 Y. B. Band and K. F. Freed, Chem. Phys. Left., 1981,79, 238; S . J. Singer, K. F. Freed and Y. B. Band, Chem. Phys. Lett., 1982, 91, 12 and J. Chem. Phys., 1983, 79, 6060. Dr. Hancock commented: With regard to the point made by Prof. Shapiro and expanded by Dr. Frey, the photodissociation of NO2 at 355 nm results in the formation of O(3P) atoms in three spin-orbit states and N0(211) fragments in two. The angular distribution of oxygen atoms [predominantly O(3P2)1 might then not be correctly rep- resented just by one anisotropy parameter because of the effect of interference. Any offset observed in the experimental photofragment angular distribution [eqn. (9) in Dr. Frey’s comment] may then be due to additional anisotropy terms rather than experimental error in the determination of the true zero of the polarisation angle. However, the data upon which we base the analysis of our experiments2 shows an offset which, when corrected for the laboratory to centre-of-mass frame transformation, is small compared to the experimental uncertainty in the angular alignment of the apparatus.The data fit the functional form of eqn. ( 3 ) of our paper well, and hence we are confident that the effect of multiple electronic surfaces on the photofragment velocity distribution is, for our experiments, small. We agree that caution should be employed when using laser photolysis/laser probe methods to meaure alignment parameters to ensure that the angular distribution of photofragments can be characterised by a single anisotropy parameter, P .1 J. Miyawaki, T. Tsuchizawa, K. Yamanouchi and S. Tsuchiya, Chem. Phys. Let?., 1990, 165, 168. 2 G. E. Busch and K. R. Wilson, J. Chem. Phys., 1972, 56, 3638. Prof. Truhlar said: The papers by Hancock and McCaffery make strong cases for measuring the vector-vector correlations. Accurate quantum scattering matrices contain a wealth of information that can be analysed in terms of such correlations, and prototype experiments will provide a critical stimulus to carrying out such analyses. I would like to mention a related vector correlation that I have observed in some of our quantum scattering calculations on the reaction H + D2 + HD+ D. As an example, consider the converged quantum results’ for this reaction with total angular momentum J = 2 and total energy E,,, = 1.49 eV.For this total angular momentum, there are three initial channels with rotational quantum number j = 1, namely I = 1,2 and 3. For each of these channels I calculated the average value o f j ‘ for HD produced with each value of the final vibrational quantum number v’. The results are shown in Table 3 .162 General Discussion Table 3 Average value of j ’ for H+D,(v = 0, j = 1 specified 1- HD v‘)+D as calculated by converged quantum dynamics for E,,, = 1.49 eV and J = 2 in ref. 1 ( j ‘> V ’ 1 = 1 1=2 1 = 3 0 3.3 4.4 3.3 1 2.7 4.7 3 .O 2 2.6 3.5 2.7 The results, perhaps surprisingly, are non-monotonic in 1. We may interpret these results as follows: 1 = 1 , 2 and 3 correspond to j being respectively parallel, perpendicular and antiparallel to 1.Clearly the alignment effect is larger than the effect of changing the magnitude of 1; the product rotational excitation is enhanced in the perpendicular alignment, which involves intrinsically nonplanar collisions. Any interpretation of the angular dependence of (j’) must certainly take account of this correlation. Since classical trajectories have been shown to reproduce the accurate quanta1 o’, j’ distributions quite well even at these low values of the quantum numbers,’ it may be possible to trace these effects to specific features of the distributions of reactive transition states using trajectory analysis. 1 M. Zhao, D. G. Truhlar, N. C. Blais, D. W. Schwenke and D. J. Kouri, J. Phys. Chem., 1990,94,6696; M.Zhao, D. G. Truhlar and D. W. Schwenke, unpublished work. Prof. Simons said: One vector correlation which has not been too heavily stressed at this Discussion is that of electronic orbital alignment. Prof. Dudley Herschbach once remarked that ‘if one really wanted to understand reactive collisions one should ask what the electrons are doing’;’ in a sense, at the range where it really matters, the nuclear motions come second. In particular, while there have been many examples of orbital alignment propensities in the products2 ( e.g. preferential A-doublet population) or orbital selectivity in the I am not aware of any full state-to-state studies which include both these indicators in a reactive encounter. 1 D. R. Herschbach, personal communication in a Gottingen ‘pub’.2 See e.g. M. H. Alexander, P. J. Dagdigian and H.-J. Werner, Furuduy Discuss. Chem. SOC., 1991,91, 319. 3 See e. g. C. T. Rettner and R. N. Zare, J. Chem. Phys., 1981,75, 3636; 1982, 77, 2416. 4 Cf: B. Soep, C. J. Whitham, A. Veller and J. P. Visticot, Furuduy Discuss. Chem. SOC., 1991, 91, 191. Dr. H.-G. Rubahn (Max Planck Institute, Gottingen ) (communicated): Implementing laser polarization techniques Hancock and co-workers have shown that it is possible to extract information about reactive ( k, J)-correlations for atom-diatom scattering from a bulk experiment. Here, k denotes the velocity vector and J the angular momentum vector of the diatomic. Using a bulk implies a limitation in that sense that the reactants can hardly be state selected before the reaction, although state-resolution is possible.In particular, the initial vibrational state of reactants within the electronic ground state cannot be varied as one might wish in order to probe the r-coordinate ( r is the bond distance) of the potential hypersurface.’ Thus a molecular-beam scattering experiment seems to be more appropriate to perform investigations of this kind. Here some results from trajectory calculations are presented in order to investigate the correlation between relative velocity vector and product rotational angular momen- tum vector as a function of the initial vibrational state of the diatomic. The system is Li2( q)-Na, vi = 0 and oi = 20. This alkali-metal exchange reaction is currently underGeneral Discussion 163 planarity angle, O / O Fig.21 Calculated reactive cross-sections (arbitrary units) are shown as function of planarity angle 8 for Liz - Na at a CM collision energy of 500 meV. In the upper part of the figure the initial vibrational state of Liz is set at u = 0, in the lower part u = 20. The rotational states are marked beside the blocks. The error bars represent single standard deviations and correspond to the J-averaged values (shaded blocks) study in a crossed molecular beam laser experiment,2 and the results from the trajectory study shown here may serve as complementary computational experiments, helping to understand in more detail the reaction mechanisms. The trajectory calculations have been performed via standard computational methods3 with Monte-Carlo selection of initial conditions except for the rovibrational state and impact parameter.A recently developed semiempirical valence bond LEPS surface by Varandas and co-workers4 has been used. Per rovibrational state about 2000 trajectories were run in the impact parameter range between 0 and 4 A. In Fig. 21 total reactive cross-sections are shown as a function of planarity angle 8 in increments of A8=20° for vi=O and vi=20, a collision energy of 500meV and different initial rotational states Ji = 0, 1,2,4,8, 10 and 15. The angle 8 is measured between the rotational angular momentum vector of the product LiNa and the relative velocity vector. Since there is no evident dependence on the rotational state, J-averaged values are presented as shaded blocks. The typical error bars given are single standard deviations.164 General Discussion Only a slight preference for 8 to occupy values between 8 = 40 and 140 O with a minimum at 8 = 90 O is observed for vibrational ground-state molecules.In case of highly vibrationally excited molecules a more pronounced preference for values around 8 = 98 O is observed. Note that 8=Oo is expected to be the preferred value for a statistical distribution of rotational angular momenta of the reaction products. Thus the preference of 8 = 9 0 ° shows that the reaction proceeds in a direct and coplanar manner for vibrationally excited reactants. The initial plane of the reaction is conserved, and the lithium atom takes away negligible angular momentum. This significant vibrational dependence of the coplanarity apparently results from the fact that high vibrational excitation is very effective in weakening the bond of the reactant Liz.1 H.-G. Rubahn and K. Bergmann, Annu. Rev. Phys. Chem., 1990,41 735. 2 A. Slenczka, work in progress. 3 J. C . Polanyi and J. L. Schreiber, in Physical Chemistry, ed. H. Eyring, D. Henderson and W. Jost, 4 A. J. C. Varandas, V. M. F. Morais and A. A. C . C . Pais, Mol. Phys., 1986, 58, 285. Academic Press, New York, 1974, vol. 6A. Prof. J. N. Murrell (University of Sussex) said: In considering the relative merits of spectroscopic and molecular-beam experiments as probes of the potential-energy surface I would have to point out the inbuilt averaging of collision vectors which is always there in the spectroscopic experiment and which I believe will always average out any quantum features of the collision (e.g.oscillation in the differential cross-section). Spectroscopically determined cross-sections are likely to be interpretable by classical collision theory; no less valuable for that but a less sensitive test of the potential-energy surface than quantum calculations. Of course one has to accept that the ideal crossed- beam experiment is very rare; most such experiments at present also entail some averaging over states, velocities etc. Prof. W. C. Stwalley (University of Iowa) replied: I wish to emphasise the advantages of 'spectroscopic' half-collision experiments in contrast to 'molecular beam' full-collision experiments. Not only can the energy of a state-selected half-collision experiment be very accurately defined (e.g. to 1 MHz == 3 x lop5 cm-' with commercial lasers) compared to the best energy resolution in a crossed molecular beam (>> 1 cm-I), but also the angular momentum can be specified to 3 , 2 or even 1 h.Thus the results are much more directly connected to theory. Prof. Murrell responded: I do not consider photochemical experiments to be equivalent to scattering experiments; if you are interested in only half the potential-energy surface you need do only half an experiment! To which Prof. Stwalley answered: One can of course carry out both 'half-collision' experiments separately. For example, one can see both Mg" and MgH in MgH2 photofragmentation. Prof. R. Grice (University of Manchester) commented: Prof.Murrell has pointed to the additional resolution which may be obtained by undertaking scattering measurements in crossed molecular beam experiments. This is certainly important in the study of reactive collisions, where the angular distributions of scattering for collisions with high initial orbital angular momentum will often involve sharp peaks with widths A 8 =: 10 O. The experiments reported by Prof. Welge later in this Discussion and measurements from other laboratories' demonstrate that angular distributions can now be determined for specific product vibrational-rotational states for the hydrogen exchange reaction. Such techniques will surely be extended to other reactions, and crossed-beam experi- ments are to be preferred, all other things being equal. When other things are not equal,General Discussion 165 which mostly they are not, the reaction-dynamics community is well versed in combining information from complementary techniques to create a whole which is hopefully greater than the sum of its parts.1 R. E. Continetti, B. A. Balko and Y. T. Lee, J. Chern. Phys., 1990,93, 5719. Prof. Casavecchia said: Following the comments of Prof. Murrell and Prof. Grice, which have been stimulated by the papers of McCaffery et al., Stwalley et al. and Hancock and co-workers, on the desirable fruitful combination of laser and beam techniques to unravel the dynamical details of an elementary chemical reaction, I would like to point out that the ideal output of an experimental investigation at microscopic level is the reactive differential cross-section for a single quantum state, starting from reagents in well defined quantum states.This quantity could then be directly compared with the 'normal' output of exact, or approximate, dynamical theoretical calculations which readily provide differential cross-sections for a single quantum state. We have in this regard the beautiful example of the theoretical work' on the fundamental H + H2 reaction, for which impressive progress has been made in the laboratory of Prof. Welge towards the measurement of the reactive differential cross-section for a single quantum (vibrational and rotational) state by using a sophisticated combination of beam and laser techniques and exploiting the novel technique of hydrogen Rydberg atom time-of-flight spectroscopy as a detection scheme.2 Attempts towards the same goal for the same system are also pursued in the laboratory of Prof.Lee in Berkeley, also by using laser and crossed beams, but with the REMPI technique as detection scheme. I would like to indicate another reaction which is suitable with the present technology for similar detailed investigation. This is the reaction of electronically excited oxygen atoms with H2: This reaction was first studied in crossed-beam experiments with mass-spectrometric detection at Berkeley;' the internal states of OH were not resolved. In our laboratory we are investigating this reaction with the same technique at very low collision energies in order to resolve the vibrational states of the OH product and gain deeper insight into the reaction dynamics, which is still not well understood.The experiments are based on the capability of generating continuous and intense supersonic beams of O('D,) by radiofrequency discharge in 0,-rare-gas By combining the crossed-beams method with the technique laser-induced fluorescence (LIF) for detecting OH as a function of scattering angle, it should be possible to measure the reactive differential cross-section for a single electronic, vibrational, rotational and A-doublet product quantum state. The high sensitivity of the LIF technique to OH species would be exploited. This represents a long-term project in our laboratory. The O( ID2) + H2 system is still relatively simple, and thus amenable to accurate theoretical treatment, and therefore useful comparisons between experiment and theory could be made.1 J. Z. H. Zhang and W. H. Miller, J. Chem. Phys., 1989,91,1528; M. Zhao, D. G. Truhlar, D. W. Schwenke 2 L. Schnieder, K. Seekamp-Rahn, F. Liedeker, H. Steuwe and K. H. Welge, Faraday Discuss. Chem. 3 R. J. Buss, P. Casavecchia, T. Hirooka, S. J. Sibener and Y. T. Lee, Chem. Phys. Lett., 1981, 82, 386. 4 N. Balucani, L. Beneventi, P. Casavecchia and G. G. Volpi, Chem. Phys. Lett., 1991, 180, 34. and D. J. Kouri, J. Chem. Phys., 1990, 94, 7074. SOC., 1991, 91, 259. Prof. B. Girard, Dr. N. Billy, Dr. G. Gouedard and Dr. J. Vigue, (Paul Sabatier University, Toulouse) said: The ideal experiment mentioned by Prof. Murrell and several other speakers has already been realized at least twice in the past few years.'-' It consists of measuring doubly differential cross-sections (angular distribution as a function of166 General Discussion the product internal state).Two different experimental techniques can be used in order to achieve this goal. If the internal states of the molecular product are widely spaced, measuring its recoil velocity can be sufficient to determine the internal state. This requires in general a diatomic molecule containing a hydrogen atom. Up to now, only the vibrational distribution of the product has been determined as a function of the scattering angle, using time-of-flight measurements combined with mass-spectrometer detection for the F+ H2, HD, D2 reactions3 or with laser-induced fluorescence of the atomic product in the H + D2 r e a ~ t i o n .~ Another competing technique uses laser-induced ffuorescence in order to probe a given internal state (u, J) of the diatomic molecule. If the spectral width of the laser is sufficiently narrow, the velocity distribution of the product along the laser axis can be deduced from the Doppler profile of the resonance line.5 The actual determination of the angular distribution from the Doppler profile requires several assumptions (which are satisfied here); (i) the total energy of the system must be well defined or at least the total energy spread must be small compared to the recoil energy of the product (this almost requires the use of supersonic beams); (ii) the product atom must not have any excited state accessible with the available energy [total energy minus the internal energy of the probed molecular state (0, J ) ] ; and (iii) the laser must be shone along the relative velocity of the reagents, which is the axis of cylindrical symmetry.Under these conditions there is a one-to-one connection between the Doppler shift Av and the scattering angle e: V(u, J ) cos A v = v 0 - C where V(u, J) is the modulus of the recoil velocity of the internal state (u, J). Vetter and co-workers have studied the Cs(7p) + H2 reaction under crossed-beam conditions; probing the CsH product by laser-induced fluorescence they have deduced the angular distribution as a function of the internal state and of the collision energy.2 With a similar experimental set-up, we have studied the F+12 reactive collision and measured the differential cross-section as a function of the internal state of IF( v, J).' These measurements exhibit a significant variation of the angular distribution with the rotational state.Fig. 22 presents the Doppler profiles of ( a ) the ( u ' = 5)-( u = 11) P( 107) and (b) the (u' = 6)-( u = 13) R(25) transitions. The six vertical lines marked on each spectrum indicate the position of the six hyperfine components of the transition. The observed profile is therefore the superposition of the Doppler profiles of the six hyperfine components. This hyperfine structure is almost the same in both spectra, and the main difference observed between these Doppler profiles is due to a change in the differential cross-section, as can be seen in Fig. 23 (these angular distributions have been deduced assuming the same differential cross-section for all the hyperfine sublevels): sharply forward peaked for the 6-13 R(25) line and nearly isotropic for the 5-11 P(107) line.Around 60 lines have been recorded exhibiting similar behaviour.6 This strong variation of the differential cross-section with the rotational state of the product may be due to bimodality (two different reaction paths: direct and migratory reactions) which has been predicted by trajectory calculations7 and probably observed in the experiments (angular distributions' and internal state distributions'). Also, dynamical models which could predict such behaviour are actually investigated." 1 B. Girard, N. Billy, G. GouCdard and J. Viguk, J. Chem. Soc., Furuday Trans. 2, 1989,85,1270, Europhys.Leu., 1991, 14, 13. 2 J. M. L'Hermite, G. Ramat and R. Vetter, J. Chem. fhys., 1990, 93, 434. 3 D. M. Numark, A. M. Wodtke, G. N. Robinson, C. C . Hayden and Y. T. Lee, fhys. Rev. Lett., 1984, 53, 226; J. Chem. Phys., 1985, 82, 3045.General Discussion 167 Fig. 22 Doppler profile of the 5-11 P(107) (left) and of the 6-13 R(25) (right) lines. The six vertical lines on each spectrum indicate the position of the hyperfine components of the transition. The full line corresponds to the best fit of the data which is obtained with the differential cross-section shown in Fig. 23 Fig. 23 Differential cross-sections extracted from the Doppler profiles shown in Fig. 22. The broken lines represent the *la error limits. The two cross-sections are scaled to have the same average value, represented by the horizontal line168 General Discussion 4 L.Schnieder, K. Seekamp-Rahn, F. Liedeker, H. Steuwe and K. H. Welge, Furuduy Discuss. Chem. 5 J. L. Kinsey, J. Chem. Phys., 1977, 66, 2560. 6 B. Girard, N. Billy, G. GouCdard and J. ViguC, J. Chem. Phys., in the press. 7 I. W. Fletcher and J. C. Whitehead, J. Chem. SOC., Furuduy Trans. 2, 1982, 78, 1165; 1984, 80, 985; 8 N. C. Firth; N. W. Keane, D. J. Smith and R. Grice, Furuduy Discuss. Chem. SOC., 1987, 84, 53; Mol. 9 B. Girard, N. Billy, G. GouCdard and J. ViguC, J. Chem. Phys., 1988, 88, 2342. SOC., 1991,91, paper 14. N. W. Keane, J. C. Whitehead and R. Grice, J. Chem. SOC., Furuduy Trans. 2, 1989,85, 1081. Phys., 1989, 66, 1223. 10 N. Billy et ul., in preparation. Prof.Alexander and Prof. Werner said to Prof. McCaffery: A new ab initio potential energy surface for the Li2(A 'X;) + Ne system has recently been determined and fitted to a global functional form. ' The magnitude and velocity dependence of rotationally inelastic cross-sections resulting from close-coupled calculations based on this new potential-energy surface* are in exellent agreement with earlier experimental estimates by Smith and co-~orkers.~,~ Calculations of differential cross-sections with this new potential could be used to calibrate the accuracy and resolution of the novel experimental technique described by Collins et al. 1 M. H. Alexander and H.-J. Werner, J. Chem. Phys., 1991, in the press. 2 N. Smith, T. P. Scott and D. E. Pritchard, J. Chem. Phys., 1984, 81, 1229.3 T. P. Scott, N. Smith and D. E. Pritchard, J. Chem. Phys., 1984, 80, 4841. Prof. A. J. McCaffery (University of Sussex) responded: In reply to Prof. Murrell I emphasize that spectroscopic techniques enhance traditional beam methods and are not intended to replace them. The advantage that a purely spectroscopic method of obtaining the differential cross-section has over beam methods is the speed at which systems may be changed. This should widen the base of the state-to-state differential cross-sections available at present and could lead to inversion routines to obtain the intermolecular potential. As an indication of the sensitivity of a polarisation-selective spectroscopic method such as that we have reported is given in a paper by Schawlow and co-workers.' They were interested in developing polarisation labelling as a method of simplifying molecular spectra and noticed a transfer of the polarisation label to Av = 2 levels.This process has an approximately two orders of magnitude smaller cross-section than the rotationally inelastic transitions we report and is of the same order of magnitude as reactive collisions. In reply to the comment by Prof. Alexander I welcome the news that he and his co-workers have developed an ab initio Li,(A)-Ne potential, and we will endeavour to provide state-to-state measurements for this system for comparison with calculations based on his potential. 1 R. W. Teets, R. Feinberg, T. W. Hansch and A. L. Schawlow, Phys. Rev. Lett., 1977, 37, 1725. Dr. M. R. Levy (Newcastle Polytechnic) said: I am particularly interested in the report of Stwalley et al.' on their studies of metal-atom-H, transition states, and their ability to describe the Mg-H2 and Na-H, systems by a simple one-dimensional model.I have recently employed a beam-gas configuration to investigate multiple potential surface interactions in collisions of Mn atoms with D2 molecules.2 As reported at an earlier Discussion3 and the Mn atom beam is produced by pulsed laser ablation of a solid metal target, and consists of a number of metastable states in addition to the ground state. Atomic velocities vary typically from ca. 14 to ca. 1.4 km s-*, and can be separated by time-of-flight, so that excitation functions CT( ET) for luminescent processes can be determined. In the present system, both Mn*(z "PJ + a %) collision-induced emission and MnD* chemiluminescence (b 'X- + a 'X+, A 711 + X 'X+ or c 511 + a ?Z'-) can in principle beGeneral Discussion 169 a 6~ / 100 k J m o l - ' I Fig. 24 Correlation diagram for the Mn + H2 reaction in the C, point group. On the reagent side, full lines indicate long-lived states which are expected to be present, to some degree at least, in the pulsed atomic beam; broken lines indicate short-lived radiative states. Vertical arrows show anticipated emission processes resulting from Mn-H2 collisions. Connecting lines between reagent and product states show allowed correlations of different multiplicity: (-) sextet; (-) quartet; ( - * - ) octet detected and isolated. As Fig. 24 the Mn + H2 reaction is much more endo- thermic than the Mg analogue, with several metastable states below the z 6PJ resonant state; but molecular-orbital interactions' (Fig. 25) suggest that all of these low-lying metastable states should have facile access to formation of a bound HMnH intermediate. Although MnH*(A 711 -+ X 7.C+) luminescence at ca. 586 nm has been observed in collisions of Mn atoms with hydrocarbons,2 the analogous MnD* emission is absent in the present case. No (b5.C--,a5.C') signal at ca. 849nm could be found either. However, MnD*(c 'II -, a 'C') chemiluminescence at ca. 478 nm is detected, along with the ca. 403 nm Mn*(z 6PJ -+ a %) collision-induced emission.170 General Discussion /" H 'H MOLECULAR ORBITAL I H M n INTERACTIONS Mn a6S Q 6D z $a4D z 6P 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I t 1 11 1 1 \ \ \ \ \ 3d df 0 0 0 0 d Fig. 25 Molecular-orbital interaction diagram for Czv approach in Mn-H, collisions (adapted from Elkind and Armentrout).' The orbital occupancy of different Mn atomic states is also shown Fig. 26 presents yield functions Y(&) = ~ r ( & ) & - for these two processes (here I?, is the nominal collision energy, very close to the average in this beam-gas configuration). This form of display is preferred to the simple cross-section a(&), since it allows more straightforward analysis of the data in terms of Gonzilez Urefia's microcanonical transition-state theory model," Y ( E T ) = ( 1 ) where n is the number of active modes at the transition state and Eo its energy above the reagent asymptote. Application of eqn. ( 1 ) shows that two separate processes, identified by E, =: 60f 5 and 187 f 12 kJ mol-I, and n = 2.0-2.5 and 2.5-3.0, respectively, contribute to MnD*(c 'Z+) production. The collision-induced emission channel is a little more problematic, but it appears that there is an initial process with n = 2 from Eo= 12 kJ mol-I, followed by a change in dynamics to n =: 1 at E,=65 kJ mol-I. The spread of collision energies in the beam-gas arrangement makes the thresholds in Fi . against I?,- for different values of n until linearity is a ~ h i e v e d . ~ The endothermcity of the Mn + D2 reaction is uncertain, since only an upper limit has been determined for the MnH bond energy.7 However, from this it is clear6,' that 2575 kJ mol-I, in the form of reagent translational/electronic excitation, would have to be supplied for MnD*(c5Z+) to be produced. Since the observed thresholds are so low, highly excited Mn* states must be involved; and this, together with the absence of MnD*(A 'II + X 7Z+ and b 5C- --* a 5X+) luminescence, demonstrates the breakdown of simple adiabatic state correlations. Mn*( z 6P,) production likewise must involve violation of spin conservation, since only a 4D, atoms are sufficiently energetic to give rise to either threshold. All this indicates that there must be strong interactions between potential surfaces in the close-coupling region. The derived values of n are particularly relevant to the present discussion. For either two or three modes to be active at the transition state, as implied by the data, an insertion mechanism must be involved, since only an HMnH intermediate would have the 26 appear lower than they really are; the true value of E, is found by plotting Y' B "General Discussion 171 0 &/ kJ mol-' LOO ET/ kJ mol-' Fig. 26 Yield functions Y(&) for Mn+ D2 luminescent processes: ( a ) MnD* ( c 'll 4 a 'E+) emission at ca. 478 nm; ( 6 ) Mn*(z "PJ 4 a 'S) emission at ca. 403 nm. Arrows indicate the different thresholds necessary stability. The higher n-value from the ca. 187 kJ mol-' MnD* threshold perhaps indicates a tighter exit transition state for reaction from the less excited Mn" reagent state. In the collision-induced emission channel, the change in n at &-= 65 kJ mol-' implies a shift to more direct dynamics at that point. 1 W. C . Stwalley, P. D. Kleiber, K. M. Sando, A. M. Lyyra, L. Li, S. Ananthamurthy, S. Bililign, H. Wang, J. Wang and V. Zafiropulos, Faraday Discuss. Chem. Soc., 1991, 91, 97. 2 M. R. Levy, to be published. 3 M. R. Levy, Faraday Discuss. Chem. Soc., 1987,84, 120. 4 M. R. Levy, J. Phys. Chem., 1989, 93, 5185. 5 M. R. Levy, J. Phys. Chem., 1991, in the press. 6 K. Huber and G. Herzberg, Constants of Diatomic Molecules, Van Nostrand, New York, 1979. 7 A. Kant and K. A. Moon, High. Temp. Sci., 1981, 14, 23. 8 W. J. Balfour, J. Chem. Phys., 1988, 88, 5242. 9 J. L. Elkind and P. B. Armentrout, J. Phys. Chem., 1987, 91, 2037. 10 A. Gonzilez Ureiia, Mol. Phys., 1984, 52, 1145.172 General Discussion Dr. K. Burnett (University of Oxford) commented: We have recently performed experiments on photodissociation of the Hg-Ar van der Waals molecule. We were able to vary the kinetic energy of the fragments from close to threshold up to energies around 40 cm-I. In this region the alignment of the Hg fluorescence increases from a low (large rotation) value near threshold to a high (recoil) value at higher kinetic energies. We feel this shows that photodissociation of a van der Waals molecule is a good way to study orbital locking models. Prof. Stwalley summarized: I wish to emphasise that a major reason for studying the 'one-dimensional transition state' corresponding to diatomic photodissociation is to understand non-adiabatic electronic effects. In the most studied system [ K2 (B 'll")] we find adiabatic electronic behaviour from short distances (Hund's case a) to intermediate distances (Hund's case c), followed by sudden (recoil) behaviour to asymptotic atoms (Hund's case e). In our initial NaK experiments we find strongly wavelength-dependent non-adiabatic behaviour producing both P3,, and PI,? atoms. Theory here must involve coupling of several potential curves at short to intermediate distances. In addition, since there is no B 'll potential barrier, very low asymptotic kinetic energies can be accessed. Also in Na,, one can hope to stimulate emission pump to continuum states on the B 'llU potential barrier, perhaps reaching the angular momentum recoupling region (where C,/ R3 == Aspin-orbit) directly, approximately a 'quarter collision'.

ISSN:0301-7249    

DOI:10.1039/DC9919100111

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991, 91, 173-182 Transition-state Control of Product Rotational Distributions in H + RH -+ H, + R Reactions (RH = HCI, HBr, HI, CH4, C2H6, C,H,) James J. Valentini,” Pamela M. Aker,? Geoffrey. J. GermannS and Young-Duk Huh Department of Chemistry, Columbia University, New York, NY 10027, USA Measurements of the rotational state distributions for the H2 product of the H + RH -+ H2 + R reactions (RH = HC1, HBr, HI, CH4, C2H6, C3H8) at a collision energy of 1.6 eV are reported. For the reactions with the hydrogen halides we also have carried out quasiclassical trajectory calculations for conditions that mimic those of the experiments. We find that the rotational state distributions are quite characteristic and distinguishing in these systems. The combination of experiments and calculations allows us to provide some compelling explanation of how the structure and dynamics in the transition state are coupled to the product rotational state distributions.Not surpris- ingly, mere measurement of the rotational state distributions is insufficient to establish this connection, as illustrated by the results of the state-to-state experiments with the alkanes as reactants. These reactions give anomalous rotational state distributions, showing rotational excitation that actually increases with increasing product vibrational energy, rather than decreasing, as has been observed for all other reactions whose rotational and vibrational state distributions we know have been measured. State-to-state dynamics experiments do not provide the capability for ‘direct’ probing of the transition state in chemical reactions.In fact, in such experiments the transition state is effectively treated as a ‘black box’, into which reactants flow and from which products emerge, but into which we cannot peer. The hope of course is that the multitude of couplings of particular reactant quantum states with specific product quantum states revealed in such an experiment will provide a picture of what transpires in the black box. Ideally this revelation will be detailed enough to allow unambiguous interpretation, although it is quite difficult to realize this ideal. Even if this ideal is realized, the indirect nature of this type of transition-state probing has interpretation as a key element. Such interpretation usually takes the form of some theoretical description or model.Despite these limitations imposed on interrogating the transition state through the indirect route of state-to-state dynamics measurements, it is possible to use this indirect route to gather a large amount of significant information about the transition state. This is particularly true when individual rotational states of the reactants and products are detected. While the information so obtained is less easily interpreted than that provided by some of the direct probes of transition-state structure and dynamics reported elsewhere in this Discussion, this indirect information is much more easily obtained and can be obtained for a wider variety of reactions. This contribution reports a combination of state-to-state dynamical observation coupled with both theoretical calculations and model descriptions to provide an indirect, but nonetheless very detailed, look at how product rotational distributions are controlled by transition-state structure and dynamics in one particular class of reactions.These ?Present address: Department of Chemistry, University of Wisconsin, Milwaukee, WI 53201, USA. $ Present address: IBM, 650 Harry Road, San Jose, CA 95120, USA. 173174 Control of Product Rotational Distributions are the hydrogen-atom abstraction reactions, H + RH + H2 + R, where RH is HCl, HBr, HI, CH4, C2H6 or C3Hs. The experiments are carried out using reactants at ambient temperature, so individual quantum states of the reactants are not prepared.However, the reactions are studied at high collision energy, typically 1.6 eV, so that the reactant internal (thermal) energy is only a very small part of the total energy, and reactant orbital angular momentum dominates the reactant rotational angular momentum. Thus, further state preparation would probably provide little additional insight at a rather substantial increase in technical complexity. However, the individual ro-vibrational states of the H2 product are detected, using coherent anti-Stokes Raman scattering (CARS) spectroscopy under single-collision or near-single-collision conditions. State-to-state dynamics experiments and complementary quasiclassical trajectory calculations seem to indicate that the way in which the transition-state structure and dynamics control the rotational distributions is relatively simple and fairly clear in the case of the H-atom abstraction reactions with the hydrogen halides.However, for the H-atom reactions with the alkanes the connection between the transition-state charac- teristics and the H2 product rotational state distributions is apparently more complicated and more difficult to understand, although the important theoretical calculations that will probably allow their interpretation have not been carried out yet. Experiment The experimental approach used here has been described in detail in a previous report of some of these results,’ so only a brief review will be provided. The experiments use HI as a photolytic precursor for the H-atom reactant. The HI precursor and the RH reactant are flowed through a reaction cell at ambient temperature and a few Torr pressure, with the pressure maintained by a mechanical vacuum pump.The apparatus employs a Quanta-Ray Nd : YAG laser, the 523 nm second-harmonic output of which is split into three parts. One part pumps a Quanta-Ray PDL-2 pulsed dye laser, that provides typically 5 mJ pulses to be used as the tunable Stokes frequency, w,, for the CARS process. Some of the remaining 532 nm light is doubled to provide ca. 15 mJ of the 266 nm light (cod) that photolyses HI to make the H-atom reactant. The last part of the 532 nm light, ca. 20 mJ of each laser pulse, is used directly for the pump frequency, wp, in the CARS process. The wp, w, and wd beams are collinearly combined using dichroic mirrors and focused into the reaction cell, where they are precisely overlapped spatially and have coincident foci.Delay lines provide the temporal control necessary to keep the up and w, pulses temporally overlapped, and delayed with respect to the arrival of the @d pulse at the cell by ca. 4 ns. The HI precursor and RH reactant are flowed through the reaction cell at a rate sufficient to ensure renewal of the gas in the sampled volume between laser shots at the 10 Hz repetition rate of the Nd: YAG laser. The CARS beams generate a signal beam at the anti-Stokes frequency, was= 20, - w, = up + ( wp - 0,) = up + w,, where w, is the Raman transition frequency of the molecules being probed.2 The intensity of this signal is proportional to the difference in population between the two particular ro-vibrational states (v’,j’ and v’+ 1,j’) of the H2 product that are connected by the specific Q-branch Raman transition being probed.Thus, by scanning o, and measuring the signal intensity of was an intensity vs. frequency spectrum is obtained that can be analysed to give the H2 product state population distributions. Results and Discussion Fig. 1 and 2 show the rotational state distributions of the H2 product of the H + HCl and H + HI reactions at 1.6 eV collision energy. The rotational distributions are quiteJ. J. Valentini et al. 175 160 120 s .- - 80 a a a 4 0 0 0 10 J ’ 20 16 12 a 4 0 0 10 J’ Fig. 1 Rotational state distribution for the H2 product of the H + HCI reaction at 1.6 eV collision energy. The populations in even-j‘ states have been multiplied by a factor of three to smooth out the even-j‘-odd-j intensity alternation associated with the different nuclear spin degeneracies of the even-j’ (degeneracy = 1) and the odd-j’ (degeneracy = 3) rotational states.The solid lines are linear surprisal analysis best fits’ to the experimental measurements, with the rotational surprisal parameters (6,) 3.7 (a) and 7.4 (b) 16 12 s .- U 2 8 a 4 a 0 16 12 32 24 16 8 0 0 10 20 0 10 20 J’ J’ 0 0 10 20 0 4 8 12 J’ J’ Fig. 2 Rotational state distribution for the H2 product of the H + HI reaction at 1.6 eV collision energy. The solid lines are simple smoothe curves drawn through the data to aid the eye. As with the data in Fig. 1 the even-j’ populations have been multiplied by three176 Control of Product Rotational Distributions characteristic.The 1.42 eV exoergic H + HI -+ H2 + I reaction produces H2 over a broad range of rotational states, with a distribution that is highly dependent on the vibrational state of the product (fairly high rotational states in the lower vibrational states) while the nearly thermoneutral (AH = -0.04 eV) H + HCl -+ H2 + Cl reaction yields H2 product in low rotational states only. The H + HBr -+ H2 + Br reaction, which is intermediate between the H + HI and H + HCl reactions thermochemically (AH = -0.72 eV) produces rotational state distributions (not shown here) that not surprisingly are intermediate between those observed in the H + HI and H + HCl reactions. One characteristic of these three reactions that makes for an interesting comparison is that they differ energeti- cally, and therefore in their potential-energy surfaces, but are kinematically effectively identical, having reactant reduced masses, preactants, of 0.97,0.99 and 0.99, for HCl, HBr and HI, respectively.Although the trend observed in the rotational state distributions among these three reactions appears simply to track the thermochemistry of the reactions, the individual rotational state distributions are not so simple. Each of these reactions has a potential- energy surface with a collinear minimum-energy path, yet only for the H + HCl reaction are the rotational distributions peaked at the low j ’ typical of collinearly dominated reactions. The reason is that although the minimum-energy path is collinear, for the 1.6 eV collision energy at which the reactions are studied the H + HI reaction, and to a lesser extent the H + HBr reaction, are not dominated by collinear transition-state geometries, rather non-collinear transition-state geometries are dominant.Based on an examination of just the experimental observations this would be nothing more than a supposition. However, quasiclassical trajectory (QCT) calculations show, to the extent that such calculations can, that the rotational state distributions we observe for the H + HI, H + HBr and H + HCl reactions are a direct reflection of the transition- state structure. The QCT calculations are carried out on approximate potential-energy s~rfaces,~ and the calculations are themselves only an approximation to the ‘true’ quantum dynamics of the system, so the QCT results can be used as an interpretation of the experimental results only if they can be corroborated.The required corroboration is provided by a comparison of the rotational state distributions predicted by the calculations, with those actually observed e~perimentally.~ Such a comparison is presented in Fig. 3 and 4. The plotted QCT results are actually a combination of the results obtained in calculations at 1.6 and 0.68 eV. This is necessary because the photolysis of HI at 266nm that we use to generate the H-atom reactant produces both H + I(2P3/2) and H + I(2P1/2) fragment channels, with the former, dominant channel giving the nominal 1.6 eV collision energy, while the latter, minor channel yields collisions of 0.68 eV. For comparison with the experimental measurements the trajectory results at the two energies are combined in a ratio that reflects the [H + I(2P3/2)]/[H + I( 2P1/2)] photolysis branching ratio as well as the difference in reactive cross-sections at the two energie~.~ The QCT and experimental data in Fig.3 and 4 are scaled such that both give the same total reaction cross-section, so the figures actually compare ro-vibrational distribu- tions, not simply rotational distributions. Because of this, and because the QCT vibra- tional distributions are not in quite as close accord with experiment as are the rotational distributions, the agreement between the experimental and calculated rotational distribu- tions is actually slightly better than that indicated by the comparison shown in the figures.Nonetheless, this comparison reveals the fidelity of the description of the rotational dynamics provided by the QCT approach. Given the accurate description of the H + HI, H + HBr and H+ HCl reactions pro- vided by the QCT results, we can use the calculations to provide a ‘direct’ probe of the transition-state structure and dynamics. The transition state is certainly more accessible computationally than experimentally, and the trajectory calculations lend themselvesJ. J. Valentini et al. 177 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0.06 0.05 0.04 0.03 0.02 0.01 0.00 0 4 8 1 2 0 4 8 1 2 J ’ J’ Fig. 3 Comparison of experimental rotational state distributions (points with error bars, as in Fig. 1) with those derived from QCT calculations (-) for the H + HCl -D Hz + C1 reaction.The experimental results and the QCT results have been scaled to have equal total cross-sections. (a) u’=O, ( b ) v ’ = 1 0.06 - 0.04 - U 0 5 10 15 20 0.06 0.04 U 0.02 0.00 0 5 10 15 20 J ’ 0.10 0.08 0.06 0.04 0.02 0.00 0 5 10 15 0.02 p--T 0.00 0 5 10 J ’ Fig. 4 Comparison of experimental rotational state distributions (points with error bars, as in Fig. 2) with those derived from QCT calculations (-) for the H + HI + H2 + I reaction. The experimental results and the QCT results have been scaled to have equal total cross-sections. (a) u’=O, ( b ) o’= 1, ( c ) v ’ = 2 , ( d ) u ’ = 3178 Control of Product Rotational Distributions % o o o , , , , , , I 30 0 L - _ L _ L . L - 1 I I I 0 . 0 0.5 1.0 1.5 2 .0 2 . 5 3 . 0 3 . 5 impact parameter/ A Fig. 5 Scatter plot of H-H-I angle us. H+HI impact parameter for those trajectories that to reaction to produce H,+ I. X, trajectories at 1.6 eV collision energy; 0, at 0.68 eV led readily to quite revealing interpretative analysis. For example, scatter plots of the H-H-X angle vs. impact parameter for those trajectories that react reveal a fairly strong correlation between these two variables. Such a scatter plot, for the H + HI + H2 + I reaction, is shown in Fig. 5 . The observed correlation approximately follows the relation b = ( r H , + r ~ ~ ) s i n 8 ( 1 ) where 6 is the impact parameter and 8 is the H-H-X angle at the transition state. The distances rHX and rHH are, respectively, the saddle-point distance between the halogen atom X and the H atom bonded to it, and the saddle-point distance between the two H atoms.This implies that the reaction occurs for transition-state structures that orient the H of the hydrogen halide such that it is directly in the path of the incoming H atom. Put another way, it means that reaction is dominated by those trajectories in which the impact parameter between the H reactant and the H of the HX is near zero, not by those trajectories for which the nominal impact parameter, 6, defined in terms of the HX centre-of-mass, is near zero. At the high energies of these collisions the barrier height energetic constraints that favour collinear H - H -X transition-state geometries are relaxed, and replaced by geometric constraints that cause the impact parameter and input angle to be correlated such that the transition-state geometry favours H-H-X geometries that minimize rHH irrespective of the H-H-X angle.Because of the sin 8 weighting of the input angle 8, non-collinear H-H-X geometries are much more probable than nearly collinear geometries. This weighting and the correlation expressed in eqn. (1) dictate that the opacity function should be maximized at b#O if the barrier height energetic constraints that favour collinear transition-state geometries are sufficiently overcome by the collision energy. This condi- tion is satisfied for the H + HI and the H + HBr reactions at the 1.6 eV collision energy of our experiments and calculations, as the barrier height for 8 = 90" is only 0.1 eV for H + HI and 1.1 eV for H + HBr.3 The opacity functions of both these reactions show a maximum at 6 # 0 for 1.6 eV collision energy, as indicated in Fig.6. However, for the H + HCl reaction this condition is not satisfied, since the barrier height exceeds the collision energy for angles ca. 90", and Fig. 6 shows that the opacity function for this reaction has a maximum at 6=0, not b>O. At the 0.68 eV collision energy both the H + HCl and the H + HBr reaction opacity functions have maxima at 6 = 0, while the H+ HI reaction still has a peak at b # 0, but it is a much weaker maximum than atJ. J. Valentini et al. I I I 1 1 1 I - - 0.10 - 179 0.08 0.06 0.04 0.02 0.00 0.00 0.60 1.20 1.80 2.40 3.00 impact parameter/ A Fig. 6 Opacity functions for the H + HX - H2 + X reactions at 1.6 eV collision energy.(-) X = I, (- - -) X = Br, ( - * -) X = Cl 80 60 h 1 si 40 z v 20 0 20 16 12 8 4 0 0 . 0 0 . 2 0 . 4 0 . 6 0 . 0 0 . 2 0 . 4 0 . 6 ‘rot1 ( ‘tot - Evib) Erotl(Eto1- Evib) Fig. 7 Experimental rotational population distributions for the HD product of the H + CD4- HD+CD, reaction (-) and for the H2 product of the H+HCl- H2+C1 reaction (---). ( a ) u’=O, ( b ) u ’ = 1 1.6 eV collision energy. For the H + HI reaction at 1.6 eV collision energy the impact parameter at which P ( b ) is a maximum agrees well with what a simple geometrical model would predict in the absence of any energetic constraints on the transition-state geometry., The H+CH,, H+C2H, and H+C3H, reactions are all very similar to one another energetically, with A H = -0.06, -0.26 and -0.26 eV, respectively, and similar kinemati- cally as well, having preactants = 0.94, 0.97 and 0.98, respectively.All three are also very similar in both regards to the H + HCl reaction already discussed, which has AH = -0.04 eV and prLreactants = 0.97. However, the rotational state distributions of the molecular hydrogen products of the H + alkane reactions are characteristically different from and more complicated than the H2 rotational state distributions of the H + HCl rea~tion.~ This is shown by the data in Fig. 7. Our experiments on the hydrogen atom plus methane reaction were actually done with the methane isotopomer CD,. The small cross-section for this reaction (see below) makes it difficult to investigate the H + CH4 + H2 + CH3 reaction without interference180 Control of Product Rotational Distributions a v z 80 60 4 0 20 0 20 16 12 8 4 0 0 .0 0 . 4 0 . 8 0 . 0 0 . 4 0 . 8 ‘rot/(‘tot- E v i b ) E r o t / ( E t o t - Evib) Fig. 8 Experimental rotational population distributions for the H2( HD) product of three H+ alkane reactions. (-) CD4, (- - -) C2H6, ( a * .) C3H8. ( a ) u’ = 0, ( b ) u’ = 1 from the H+HI -+ H2+ I reaction that is also taking place as a consequence of the presence of unphotolysed HI precursor in the reaction cell. Thus, to allow a true comparison of rotational energy disposal in the two reactions, the rotational distributions of the HD product of the H + CD, reaction and the H2 product of the H + HCl reactions compared in Fig. 7 are plotted vs. rotational energy rather than rotational angular momentum.The product state distributions in this figure have been normalized such that the total cross-section is the same for both reactions, to allow an unbiased comparison of rotational distributions independent of total cross-section. (The experimental total reaction cross-section for the H+ HCl- H2+C1 reaction, 2 A2, is much larger than the cross-section for the H + CD, -+ HD + CD, reaction, 0.15 A2.) In v’ = 0 the alkane reaction yields product that is much colder rotationally than the HC1 reaction. One would be tempted to associate this difference readily with the higher barrier to reaction in the alkane reaction, Eb = 0.54 eV,6 as compared to that for the HCl reaction, 0.22 eV, and possibly a faster increase in the barrier height upon distortion away from the collinear minimum-energy path.The disparity in reaction cross-sections lends support to this supposition, but the rotational distribution in v’ = 1 certainly does not. The v’ = 1 rotational distribution of the HD from the H + CD4 reaction is actually hotter than that of the H2 from the H + HCl reaction. In fact, the v’= 1 HD product is hotter rotationally than the v’ = 0 product! This is an unusual result, as the normally observed behaviour, so common as to be generally regarded as universal, is that product rotational energy decreases as product vibrational energy increases. For the H + CD4 + HD + CD, reaction, product rotational excitation and product vibrational excitation are not negatively correlated, they are positively correlated.It is not just the H+CD, reaction that shows this behaviour; in fact the H-atom abstraction reactions of the heavier alkanes show it even more clearly. This is evident in the data presented in Fig. 8 for all three H +alkane reactions we have studied so far. The hydrogen-atom abstraction reactions of the ethane and propane have experimental total cross-sections (1.5 A’ for H + C2H6 and 2.9 A2 for H + C,H,) that are sufficiently large that interference from the reaction of H with the unphotolysed HI is not significant, so we used the perproto isotopomers, rather than the very expensive perdeutero com- pounds. Thus, the comparison of the rotational distributions from the three alkane reactions also involves comparison of HD and H2 products, and here in Fig. 8, as inJ.J. Valentini et al. 181 Table 1 Rotational energy disposal in the H + RH(RD) + H,(HD) + R reactions H+HC1 H+CD4 H + CzH, H + C3Hs EavailleV 1.65 1.64 1.86 1.86 Emtl Eavail v ’ = O 0.21 *0.01 0.08*0.01 0.11 fO.01 0.12f0.01 v”1 0.08f0.01 0.11 f0.01 0.16f0.01 0.19f0.01 v’=O 0.21 f 0.01 0.08 0.01 0.1 1 f 0.01 0.12 f 0.01 v’= 1 0.12 f 0.01 0.15 f 0.01 0.22 f 0.01 0.27 f 0.01 Erotl (Eavail- Evib) Fig. 7, we also plot the rotational distributions vs. rotational energy rather than vus. rotational angular momentum. While the v’ = 0 rotational energy distributions for all three alkanes are very similar, the v‘ = 1 rotational energy distributions are very different and quite characteristic for each reaction. As the complexity of the alkane increases, the v’= 1 product becomes rotationally hotter. The one behaviour that all three reactions have in common is that the rotational energy in the v’ = 1 product is greater, for H + C2H6 and H + C3H8 much greater, than that in the v’ = 0 product, as indicated by the data in Table 1. (In all three reactions, as with the energetically nearly identical H + HCl reaction, the only product vibrational states observed are v f = 0 and v f = 1, and population in higher vibrational states must not be more than 5% of the total population.) Thus, all the H+alkane reactions we have investigated, and probably all H + alkane reactions in general, have an anomalous and surprising positive correlation of the rotational and vibrational excitation of the product. Although we can put forth purely speculative rationalizations of this behaviour, we cannot provide a compelling explanation of the connection of this behaviour with the structure and dynamics of the transition states involved in these reactiorrs.However, such a connection must obtain. Given the apparent success of QCT calculations in elucidating this connection in the H + HX reactions, we expect that similar calculations on the alkane reactions will explain what features of the H + alkane transition-state structure and dynamics are responsible for this unusual behaviour. Conclusion Rotational state distributions measured for the H2 product of the H + RH -+ H2+ R Reactions (RH = HCl, HBr, HI, CH4, C2H6, C,H8) provide a very detailed, if indirect, probe of the transition-state structure and dynamics in these atom-transfer reactions.However, the measurements certainly require that theoretical calculations be carried out and model descriptions be developed in order to determine how the transition state controls the rotational distribution in the reactions. This is positively illustrated by the apparent success of QCT calculations in providing a compelling interpretation of the results obtained in the H + HI, H + HBr and H + HCl state-to-state dynamics experiments. The difficulty of establishing the connection between the product rotational state distribu- tion and the transition-state properties in the absence of such interpreting calculations is illustrated by the state-to-state results we have obtained for the H+CH,, H+C,H6 and H + C3& reactions, for which we observe surprising and not yet explained rotational state distributions. This work was supported by the Division of Chemical Sciences, Office of Basic Energy Sciences Office of Energy Research, US Department of Energy.182 Control of Product Rotational Distributions References 1 P. M. Aker, G. J. Germann and J. J. Valentini, J. Chem. Phys., 1989, 90, 4795. 2 J. J. Valentini, in Spectrometric Techniques, ed. G. A. Vanasse, Academic Press, New York, 1985, vol. 3 M. Baer and I. Last, in Potential Energy Surfaces and Dynamics Calculations, ed. D. G. Truhlar, Plenum 4 P. M. Aker and J. J. Valentini, Isr. J. Chem., 1990, 30, 157. 5 G. J. Germann, Ph.D. Thesis, University of California, Irvine, 1990. 6 T. Joseph, R. Steckler and D. G. Truhlar, J. Chem. Phys., 1987, 87, 7036. 7 R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity, Oxford 4, ch. 1, pp. 1-62. Press, New York, 1981, ch. 21, pp- 519-534. University Press, London, 1987, pp. 260-276. Paper 0/05726F; Received 19th December, 1990

ISSN:0301-7249    

DOI:10.1039/DC9919100173

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991,91, 183-190 Indirect Information on Reactive Transition States from Conservation of Angular Momentum Christine A. Leach,” t Athanassios A. Tsekouras, Patrick H. Vaccaro,$ Richard N. Zare and Daqing Zhao Department of Chemistry, Stanford University, Stanford, CA 94305-5080, USA By choosing a kinematically constrained bimolecular reaction of the type H + H’L + HH’+ L, where H and H’ are heavy atoms and L is a light atom, the orbital angular momentum, L, of the reagents appears almost exclusively as HH‘ product rotation, J. It follows that the magnitude of J is given by ILI = pvrelb, where p is the reduced mass of the reagent collision partners, vre, is their relative velocity and b is the impact parameter, i.e. the distance of closest approach if the reagents moved in undeflected straight-line paths.Hence, by measuring both the product rotational distribution and the relative velocity distribution of the reagents, it is possible to deduce the range of impact parameters resulting in specific vibrational levels of the HH’ product. A prototype system is Ba + HI + BaI + H. Experimental results for BaI ( v = 0) are presented for this kinematically constrained reaction showing that the range of b is restricted, peaking at or near the energetic cut-off. Obtaining real-time information on the transition state of a bimolecular reaction, A+ BC -+ AB + C, is a daunting task that challenges chemists. We present indirect measure- ments of the approach geometry that leads to a reaction resulting in a specific product state.In particular, we are able to estimate the impact parameter distribution which describes the entrance way to the transition state leading to formation of a specific product. The impact parameter is defined as the distance of closest approach if the reagents were to move in undeflected straight-line paths.’ Currently, little experimental evidence is available about which values of impact parameter lead to a specific product state. This lack of information is largely because the impact parameter cannot be controlled in reactive scattering experiments. The observed reaction cross-section, u ( v r e l ) , as a function of the relative velocity of the reagents, ureI, is given by U(vre1) = I,: I,: P ( b , vrel, y ) f ( Y ) d y 2Tb db ( 1 ) where the impact parameter, b, and the reagent orientation, y, are each averaged over the appropriate distribution function, 2 ~ b and f( y ) , respectively.P( b, urel, y ) is known as the total opacity function. This fundamental dependence of reactivity on impact parameter is usually concealed in an average over the impact parameter in state-to-state experiments where there is no angular distribution analysis. However, as first suggested by Herschbach2 in a 1962 Faraday Discussion, the dependence of the reaction probability on the impact parameter, b, can be determined if a kinematically constrained reaction of the type H + H’L + HH’+ L is chosen, where H and H’ are heavy atoms and L is a light atom. The special combination of masses in this class of reaction systems means that the reagent orbital t Nee Montgomerie.4 Present address: Department of Chemistry, Yale University, New Haven, C T 06511, USA. 183184 Specific Opacity Function for Ba + HI angular momentum, L, is channelled almost exclusively into product rotational angular momentum, J : L - J . ( 2 ) ILI = ~ v r e l b (3) IJI = Pvre16. (4) The magnitude of the reagent orbital angular momentum is given by: where p is the reduced mass of the reagents. Hence we obtain: The reduced mass, p, is known. Thus, by measuring the rotational distribution of the HH' product at a known relative velocity of the reactants, the reactive impact parameter distribution can be deduced. In particular, the specific opacity function, Pu( 6, vrel, y ) describing the probability of obtaining products in a vibrational level, u, can be deter- mined.The total opacity function is a sum of the individual specific opacity functions: The shape of Pu( 6, vrel, y ) provides the dependence of the final-state distribution on the initial approach geometries of the reactants. When there is no experimental control over the orientation of the reactants an orientation-averaged specific opacity function is obtained: We have chosen the kinematically constrained reaction Ba( 'So) + HI(X 'X+) + Bal(X 2X+) + H(2S1,2) (7) for our studies. By measuring the rotational distribution of product BaI molecules formed in v = 0 and by measuring the velocity of the reagents, Ba and HI, we aim to determine Pu,o( b, vrel) for this reaction. Earlier work in this laboratory' was involved with rotational distributions of BaI ( v = 8 ) product molecules formed in the same reaction by using selectively detected laser-induced fluorescence.In that work, a thermal Ba beam reacted with background HI gas. As the range of collision energies was large, the shape of a velocity-averaged opacity function could be estimated but not uni uely determined. The opacity function (FWHM) of 1.0 A. In the experiments presented in this paper a beam-beam study of the reaction Ba + HI is described in which the translational energy spread of the reactants is narrower than that in the earlier beam-gas study. was found to be a maximum at close to 2.6 x with a full-width at half-maximum Experimental There have been studies of other kinematically constrained reactions, but none has been able to resolve rotational product states.This is mainly because one of the essential features of these reactions is that the product diatomic molecule must contain two heavy atoms. This means the reduced mass of the product is large and consequently the rotational constant is small. This results in very congested spectra which can only be rotationally resolved with narrow-band lasers and sub-Doppler techniques. Such tech- niques are used in our experiment. Fig. 1 shows a schematic cross-section through the apparatus. A full description of this experiment has been given elsewhere4 so only a brief summary follows. A Ba beam from an oven source (1300 K) intersects at right angles a supersonic HI beam. TheC. A. Leach et al. 185 I Interaction ~ ~ H I b e a m \ ; I 1 HI source Mass spectrometer Fluorescence Ba beam Fig.1 Schematic horizontal cross-section through the apparatus. The laser beam is directed perpendicular to the plane of the diagram and passes through the interaction region nascent product BaI molecules are probed by a laser beam which is perpendicular to both molecular beams. Laser-induced fluorescence is used to measure the rotational distribution of the BaI X 'X+ products formed in ZI = 0. The velocity of the Ba beam is determined by Doppler spectroscopy and the velocity of the HI beam is measured by time-of-flight mass ~pectrometry.~ A beam from a continuous-wave single-mode ring dye laser (Coherent 699-29) containing rhodamine 560 dye is used to excite the BaI C 2Kt-X 2C+ transition. The total fluorescence from the C211 state is collected using a photomultiplier as the laser is scanned.One rotational branch (either PI2 or P2) is measured to determine the relative populations of the different J states resulting from the reaction. To obtain accurate rotational distributions, the laser is actively power-stabilised as it is scanned using a servo-locked acousto-optic modulator. In addition, a Keplerian telescope/ spatial filter collimates the light at the same time as converting any movements of beam position into amplitude fluctuations which are therefore compensated for by the power stabilisa- tion. Attenuation of the laser beam is carried out by two polarisation cubes to reduce the power to 5 mW. This prevents saturation of the BaI transitions.The HI beam is formed by expansion of a mixture of 6% HI in N2 at a stagnation pressure of 250 kPa through a 100 pm diameter nozzle. The beam then passes through a 1 mm diameter skimmer before entering the main reaction chamber. The distance from the nozzle to the interaction region is ca. 20cm. The HI beam is directed into a quadrupole mass spectrometer which is used to obtain a time-of-flight spectrum of the HI beam for determining the velocity distribution for a particular set of expansion conditions. When carrying out the time-of-flight measurement a chopper inside the vacuum system is moved to intersect the HI beam. A Ba oven consisting of a steel crucible heated to 1300 K is used as a source for a beam of ground-state Ba atoms. The Ba beam emerges from the crucible through a 0.8 mm diameter orifice and is collimated by several apertures before entering the main reaction chamber.The velocity of the Ba beam is measured using Doppler spectroscopy of the two-photon transition 3D2-1S0 at 36 200.42 cm-1.6 A sub-Doppler spectrum is measured with the laser beam vertical, and hence perpendicular to the Ba beam (as in Fig. 1) and a Doppler-limited spectrum is recorded by bringing the laser beam in horizontally, at an angle of 45" to the Ba beam. The laser-induced fluorescence is collected using single-photon counting of the emission through the 3D2-3Po transition at 440 nm which is isolated using a narrow-bandpass interference filter placed in front of the photomultiplier.186 Specijic Opacity Function for Ba + HI I I I I I 25 20 .I.Y I a 0) 15 .CI Y -..I c 10 0' I I I I 1 0 100 200 300 400 500 J Fig. 2 Rotational distribution of the BaI ( ZI = 0) product Results Both the Ba and HI velocity distributions were modelled to the equation: f(u) = ( u - u,J2 exp [-(')'I. 0 i < 0 0 . 0 Convolution of the known pulse temporal profile of the HI beam with the velocity distribution gives a simulation of the time-of-flight spectrum. Similarly, a convolution of the Doppler-free spectrum with the Ba velocity distribution gives a simulation of the Doppler-limited spectrum. A thermal distribution of the Ba velocities was found to give a very poor simulation; thus eqn. (8) was The values of the parameters, vo, 21, and a,, determined from non-linear least-squares optimisations of the simulations are 183, 282 and 296 m s-' for Ba and 0, 785 and 31 m s-' for HI, respectively. From these results the relative velocity distribution was calculated to have a mean velocity of 976ms-' and an FWHM of 108 ms-'.The rotational distribution measured for v = 0 is found to be very highly excited. A rotational analysis of the BaI C 211 - X *X+ (0,O) band has been carried out.' We are able to assign rotational quantum numbers to the lines measured and thus know the rotational angular momentum of the BaI products formed in u = O . The resulting rotational distribution is given in Fig. 2. The maximum of the distribution is at J = 428.5 and the FWHM is 29. This corresponds to an energy distribution with a maximum at 13.8 kcal mol-' and an FWHM of 1.77 kcal mol-I. Opacity Function Models From our experiment we have obtained the rotational distribution for products formed in u = 0 and the relative velocity distribution of the reagents. We are now in a position to use eqn.(4) to deduce an impact parameter distribution for a particular velocity. To determine the specific opacity function, we choose a number of models for P ( 6, vreJ and investigate how well they can simulate the experimental rotational distribu- tion. Three models are described.C. A. Leach et al. 187 The principle of conservation of energy constrains all models by providing a velocity- dependent maximum allowed impact parameter, b,,,(u, J ) . As J increases for a given value of urel, a point is reached when there is no longer enough energy available for products to form.Thus we can write the inequality, where Erel is the energy of the reactants, AE is the difference between the dissociation energies, D: of BaI and HI: AE = D:( BaI) - D:( HI) (10) and EBal(u, J ) is the total internal energy of the BaI molecules. The restriction placed on vrel by energy conservation is For a particular value of J this results in a maximum reactive impact parameter of Our experiment is very sensitive to the exothermicity of the reaction, AE, as given in eqn. (1 1). D:( HI) is 70.429 * 0.025 kcal mo1-1.8 We have recently recommended a value of 77.7*2.0 kcal mol-' for DE(Ba1); based on our observations of the highest occupied rotational and vibrational levels from the beam-beam reaction Ba + HI, which gave a lower limit,4 and earlier work by Johnson et aZ.,9 which used the observation of the onset of predissociation from the C 211 state to give an upper limit.The models can determine D:( BaI) to better than the uncertainty of k2.0 kcal mol-I. Thus, D:( BaI) is treated as an adjustable parameter in our simulations of the rotational distribution for the different specific opacity function models. Model 1: Step Function In this model all collisions between the reactants below a certain impact parameter are assumed to have the same probability of reacting. The maximum impact parameter is determined by the energy cut-off at each reagent velocity as given in eqn. (12). A non-linear least-squares fit to model this data to the experimental rotational distribution is performed in which Dz(Ba1) is the only adjustable parameter.Fig. 3 shows the results of this fit. D:(BaI) is determined to be 79.16 kcal mol-I. The insert shows the specific opacity function for the mean relative velocity where the maximum impact parameter is 4.57 A. Model 2: Isosceles Triangle In this model an isosceles triangle is moved along the energy cut-off with its high-b vertex on the energy cut-off. To keep this model as simple as possible we choose to maintain the width and height of the triangle constant as the relative velocity is changed. There are two fitting parameters in this model, the len th of the base of the triangle and D:(BaI). The optimised values of these are 0.036 fi and 76.59 kcal mol-'. Fig. 4 shows the results of this fit, including an insert showing the impact parameter distribution for the mean relative velocity.188 E ." C c( a a c.6" El .- C C Specijk Opacity Function for Ba + HI I I I I I I 00 0 0 P .OO 0 0 0 6 0 15 - 10 - 0 O I 0. ooo Q 0 23 O e 8 o,.: 5 - 0 1 I I I 1 I 360 380 400 420 440 460 J Fig. 3 Simulation of the BaI ( u = 0) rotational distribution using a step function as an opacity function. The insert shows the form of the opacity function for the mean relative velocity 30 25 E *; 20 - a c. 51 15 E .- J lo El 5 0 360 380 400 420 440 460 J Fig. 4 Simulation of the BaI ( u = 0) rotational distribution using an isosceles triangle as an opacity function. The insert shows the form of the opacity function for the mean relative velocity. The triangle is so narrow that it appears as a line Model 3: Truncated Gaussian In this model the opacity function is assumed to be a Gaussian in b of the form: P,,o( b, v,,,) = exp[ -:( y)2] (13) The constraints associated with energy conservation cause this Gaussian distribution to be truncated according to eqn.(12). In this model the parameters which are derivedC. A. Leach et al. 189 30 25 20 15 10 5 0- I I I I 360 380 400 420 440 460 J Fig. 5 Simulation cif the BaI ( u = 0) rotational distribution using a truncated Gaussian as an opacity function. The insert shows the form of the opacity function for the mean relative velocity. The complete Gaussian is also shown (dotted line) from a non-linear least-squares fit of the data are the maximum of the Gaussian, 60, its width, c b , and @( BaI). The values of these parameters are found to be 5.07 A, 0.526 A, and 78.42 kcal mol-I. The resulting fit is shown in Fig.5. Discussion As can be seen in Fig. 3 the fit of a step function is very poor. The very narrow, highly excited rotational distribution which we obtain in our experiments can be reproduced only by a model which has a maximum close to the energy limit and has a narrow width. Using a simple model of this type (model 2) improves the fit considerably over the step function, although it still does not closely reproduce the experimental distribution. In particular, it can be seen that the triangular model fails at the rising edge of the rotational distribution. This is because the model does not allow any reactive collisions to happen at impact parameters well below b,,,( v, J ) and thus restricts the recoil energy to a very narrow range.The fit using the Gaussian distribution is much better (Fig. 5 ) . This model allows for both a sharp maximum close to the energy limit and some reactivity at lower impact parameters. In models 2 and 3 the specific opacity function is found to have a maximum at or near the energy cut-off and consequently predicts that the most probable impact para- meter reacts to give products with (nearly) zero recoil velocity. However, this is not a serious problem because of the uncertainty in the dissociation energy of BaI and the small mass of the H atom relative to the BaI product. If there is just 0.1 kcalmol-’ energy in recoil the H atom escapes from the BaI product at a velocity of 980 m s-l. Work is underway to carry out a direct inversion of the rotational distribution to find Pu=o(b, vreJ and the present simulations should be regarded as preliminary. Nevertheless, we can draw some conclusions about the necessary form of P,,o(b, vre,), namely, that it peaks at or near the energy cut-off and its width is narrow. Thus, spectroscopic study of kinematically constrained reactions can determine the location of the ‘door’ that opens to the transition state and can provide an estimate of how wide the entrance is.190 Specijc Opacity Function for Ba + HI C.A.L.thanks the Lindemann Trust and NATO for postdoctoral fellowships. This work was supported by the U.S. National Science Foundation under grant NSF CHE 89-21 198. References 1 I. W. M. Smith, Kinetics and Dynamics of Elementary Gas Phase Reactions, Butterworths, London, 1980; R. D. Levine and R. B. Bernstein, Molecular Reaction Dynamics and Chemical Reactivity, Oxford University Press, New York, 1987. 2 D. R. Herschbach, Faraday Discuss. Chem. Soc., 1962, 33, 281. 3 C. Noda, J. S. McKillop, M. A. Johnson, J. R. Waldeck and R. N. Zare, J. Chem. Phys., 1986,85, 856. 4 P. H. Vaccaro, D. Zhao, A. A. Tsekouras, C. A. Leach, W. E. Ernst and R. N. Zare, J. Chem. Phys., 5 D. J. Auerbach, in Atomic and Molecular Beam Methods, ed. G . Scoles, Oxford University Press, New 6 W. Jitschin and G. Meisel, Z. Phys. A, 1980, 295, 37. 7 D. Zhao, P. H. Vaccaro, A. A. Tsekouras, C. A. Leach and R. N. Zare, J. Mol. Spectrosc., in the press. 8 K. P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, I V . Constants of Diatomic 9 M. A. Johnson, J. Allison and R. N. Zare, J. Chem. Phys., 1986, 85, 5723. 1990,93, 8544. York, 1988, vol. 1, ch. 14. Molecules, Van Nostrand Reinhold, New York, 1979. Paper 0/05695B; Received 14th December, 1990

ISSN:0301-7249    

DOI:10.1039/DC9919100183

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991,91, 191-205 Observation of the Reactive Potential-energy Surface of the Ca-HX* System through van der Waals Excitation B. Soep and C. J. Whitham Laboratoire de Photophysique Molkulaire, Universite' Paris-Sud, Orsay 91 405, France A. Keller and J. P. Visticot Service de Physique des Atomes et des Molkcules, CENSaclay, Gif-sur Yvette 91 191, France The potential-energy surface of the excited-state reactions of calcium with halogen halides has been explored by the optical excitation of a Ca-HX van der Waals complex prepared in a supersonic expansion. Resonances and intense vibrational progressions of van der Waals modes have been observed, and the spectra have been analysed on a local-mode basis. It is seen that the excitation promotes modes involving the Ca-HCI bending coordinate, which appears to be different from the reaction coordinate.There is a renewed interest in the experimental investigation of the transition region in photodissociations and chemical reactions. Energy-resolved and time-resolved experi- ments have been devised which allow the direct exploration of regions of the potential- energy surface that are only indirectly accessible t3 scattering experiments. 1-4 All these experiments make use of the transformation of a bimolecular reaction in a photodissoci- ation-like experiment:'-' the reagents are condensed within a weakly bound species (van der Waals or ion) and the reaction is initiated by optical means. Through the optical selection rules a specific surface will be excited, and through Franck-Condon excitation there will be access to a localized region of a reactive potential-energy surface (PES).In this case, unlike the case of a direct photodissociation experiment, the excited coordinate can be different from the dissociation (reactive) coordinate. From a spectro- scopic point of view this will result in resonances in the spectrum, and from a time- resolved point of view there will be time recurrences due to oscillations on the excited potential-energy surface. These osci!lations, which may exist even in the case of an entirely repulsive surface, are a consequence of the selectivity induced by the optical e ~ c i t a t i o n . ~ ' ~ Two factors will determine the region accessed: first the initial geometry of the ground state complex, resulting from the intermolecular forces; secondly the Franck- Condon factors, which depend upon the relative changes between the ground- and excited-state PES.Among the possible reaction schemes, we have chosen a metal- molecule reaction which is initiated by excitation of the metal part of a van der Waals complex. In this kind of reaction, which is of the harpoon type, occurring at large internuclear distances (3-4 A), Franck-Condon excitation of the complex may allow one to probe the transition state region. We report here the reactions with a van der Waals complex of calcium with hydrogen halides (HCl and HBr) leading to electronically excited calcium halides. These reactions have been quite extensively studied in full collisions of excited calcium beams.''-I4 The electronic excitation of the calcium atom results in a strong chemiluminescence under collisional conditions. The efficiency of this chemiluminescence depends upon the electronic state and the fine-structure component, and the final product state is influenced by the preparation conditions of the collision. In the reaction Ca(4s4p 'PI) + HCl, the direction of the polarization of the P orbital with respect to the collision relative velocity (p, or p,) has an effect on the branching ratio to the products CaC1, A *I3 or B 2Z+.13,14 191192 PES of the Ca-HX* System In the complex, transitions to electronic states correlating at infinite distance to the 4s4p 'P, and 4s3d ID2 states of calcium have been observed in the spectra of the laser-induced reactions.We have analysed the spectra in terms of a local excitation of the calcium and internal van der Waals coordinates (stretching and bending). Indeed, strong resonances are observed in these spectra which can be assigned to van der Waals modes. The excitation of these vibrations allows the exploration of an important region in the excited PES. It should be mentioned that this exploration is more extensive when the laser-excited coordinate is different from the reaction coordinate. In such a case, the longer-lived is the reaction intermediate, the more of the PES will be explored. The excitation of different resonances is reflected in the different widths of the transitions, which are an indication of their reactivities. Experimental Set-up The reaction of the complex Ca*-HX -+ CaX*(A 'IT, B 2Z+), with X = C1, Br, was observed in the silent zone of a pulsed supersonic expansion after excitation of the Ca-HX complex with a pulsed, tunable dye laser. The complex was formed by laser evaporation of a rotating calcium rod in a classical arran ernent.I5-l9 The resulting on a phototube.The tunable laser was generated in the range 4000-43OOA by mixing the fundamental frequency of a YAG laser with the output of a red dye laser (DCM, LDS698) pumped by the same YAG laser. In the range 4300-5OOOA direct pumping of coumarin dyes by the third harmonic of the YAG laser was used. Great care was taken to eliminate super-radiance light in the case of direct pumping, while frequency mixing acted almost completely as a filter of this super-radiance.A delay of a few microseconds between the laser vaporization pulse (created by the second harmonic of another synchronized YAG laser) and the laser excitation pulse was needed to allow the calcium atoms or complexes to reach the excitation zone. This delay depended upon the carrier gas (10 ps for He and 35 ps for Ar), and its accurate adjustment was crucial for the observation. A temperature of 5 K was achieved in argon expansion, allowing the formation of complexes. We found, as in our study of calcium free radicals, that helium was less efficient a coolant in our beam configuration.18 The expansion was characterized by the weak appearance of the Ca, bands at 4840A; the rotational contour of the B-X(13-0) band in the expansion of calcium in pure argon corresponded to a temperature of 5 K.The calcium evaporation power was kept low, typically at 0.7 mJ, in order to optimize the formation of calcium metal with respect to metal clusters and to obtain the lowest beam temperatures. A 1% mixture of HX in argon was further diluted in argon in a continuous fashion, allowing the concentration range of HX to be varied between and emission was dispersed through a small monochromator (50 1 resolution) and collected Characterization of the Ca-HCl Complex We made three observations. First, the chemiluminescence signal of CaX resulting from the complex excitation was linear with HX concentration. Secondly, it was only observed intensely in the expansion of argon (with HX). Thirdly, when HCl, HBr or HF was added in minute quantities to the pure argon expansion, the Ca, dimer signal disappeared.We concluded (from the linear dependence on HX and cold expansion) that the observed chemiluminescence originated from a Ca- HX complex whose the binding energy was greater than that of Ca2 (1075 cm-').20321B. Soep, C. J. Whitham, A. Keller and J. P. Visticot C a + H + X C a ( ' P ) + H X Ca('D)+ HX,\T ~ CaXIB2X*l + H C a X ( A * f l ) + H D$HX) I I hu I I I I I To(A->X 1 I I I I I 193 Ca-HX Fig. 1 Schematic diagram of the energetics of the Ca+ HX reaction. The optical excitation takes the Ca-HX van der Waals complex from the ground state to an excited state correlated with the Ca 'P or 'D states, which then reacts and forms the excited CaX* product Resu 1 t s Several types of experiment have been conducted: ( 1 ) dispersed fluorescence of the product CaX*; (2) action spectra, where the reaction product fluorescence is monitored as a function of the excitation laser; (3) pump-and-probe experiments, where the excitation laser is tuned to a particular resonance of the action spectrum and the state distribution of CaX is probed with a second laser. These last experiments will be reported in a forthcoming paper.Ca-HCI Action Spectra Action spectra have been recorded in long scans between 4000 and 5000 A, monitoring the CaCl A-X (or B-X) emission. This region covers the Ca('S,-ID,) and ('So-'P1) transitions and does not overlap with CaCl transitions. No chemiluminescence signal is observed at wavelengths >5000 A as a result of the energetic threshold for CaX* formation (see Fig.1 and the Discussion section). The action spectrum presented in Fig. 2 reveals two sets of bands localized near each of the two calcium transitions. Both sets extend over about 1000 cm-', with broad structures in their red part and narrow structures in their blue part. A close-up of the band corresponding to the Ca('So-'P1) transition is presented in Fig. 3 ( a ) , and the pattern of a vibrational progression merges from the figure. This pattern is slightly complicated by satellites within the bands which either appear as non-symmetrical in shape or display shoulders. The ultimate width of the transitions may be given by one band, located at 24 360 cm-', which appears sharp and therefore has been recorded under a higher laser resolution (0.1 cm-') in Fig.4. It exhibits a quasi-lorenztian lineshape with no fine structure indicative of rotational transitions; therefore the band- width depends only on the diffuseness of the transition.194 PES of the Ca-HX* System Cr..HCl-> CICI(A) + H 2oooo 2 lo00 22OOo 23000 24000 25000 26000 Elcm-' Fig. 2 Action spectrum of the Ca-HC1 van der Waals complex. The laser exciting the complex has been swept between 21 000 and 25 000 cm-' while recording the intensity of the CaCl(A-, X) transition The large spacing between the bands in Fig. 3(a) (the 'PI region) must correspond to vibrational transitions in the excited Ca-HCl complex. In order to assign these bands, we have substituted DC1 for HCl. The corresponding spectrum is displayed in Fig.3( 6). A strong isotopic effect is observed resulting in a considerable decrease of the band spacings. The spectrum of the deuterated complex also has narrow structures in the blue part and broader structures in the red part, and the separation between these two sets of bands is even more conspicuous here. It is obvious that the motion of the H/D atom is involved in these progressions. In the discussion sectim, we shall demonstrate that the main features of the transitions within the blue envelope of the spectrum pertain to the Ca-HCl bending. A similar effect of the deuteration on the band spacing has been observed in the 'D2 region, but because of the smaller number of identified transitions, we could not make a conclusive assignment. Ca-HCl Fluorescence Spectrum The spectrum obtained by dispersing the fluorescence when fixing the excitation laser frequency on a transition of the Ca-HCl complex is displayed in Fig.5. This spectrum is characteristic of the CaCl A *n-X *E+ and B *E+-X 'E+ emission. It consists of two series of short vibrational progressions that are well separated. The spectral resolution is, however, insufficient to resolve either the band sequences (a few cm-') or the spin-orbit separation in the A 211 state (60 cm-'). The spectrum in Fig. 5 permits the estimation of the branching ratio of the reaction to the A or B states of CaC1. This ratio is approximately statistical and is the same as for the gas-phase reaction Ca(4s4p 'PI) + HCl.14 We observed in two ways that this ratio remained constant throughout the excitation spectrum: first by recording this fluores- cence spectrum for various excitation frequencies and secondly by observing identical action spectra with the A-X or B-X transition.Ca-HBr Action Spectra The spectra have been recorded in the eame conditions as for HCl and are very similar in appearance. In Fig. 6 ( a ) , an overview of the action spectrum is presented. As for23000 23400 23800 24200 24600 25000 E l m - ' I v = 3 1 - 23000 23400 23800 Elcm-' = 4 j = 5 1 I v $ 1 Y .- [ I Y .- I 23000 23400 23800 24200 24600 25000 E l m - ' j = ! v = 3 ::i2, j v = o 23000 23400 23800 24200 24600 25000 24200 24600 25000 Elcm-' Fig. 3 ( a ) Expansion of Fig. 2 in the region of the Ca('P) state. The sharp line at 23 652 cm-' is the Ca('S ---* 'P) resonance line: the excited Ca atoms are reacting with the background HCl gas.( b ) The same as part (a), but replacing HCl by DCl. (c) Simulation of the Ca-HCl action spectrum with a bending model. The bending potential has been adjusted to reproduce the positions of the lines in the short-wavelength part of Fig. 3(a). The intensities have been obtained with the assumption of a harmonic ground-state potential with a 70 cm-' bending frequency (ref. 19). They should be compared to the integrals of the bands in Fig. 3(a). (d) Isotopic substitution of H by D in the simulation. This should be compared with the action spectrum in Fig. 3 ( b ) Q 3196 PES of the Ca-HX* System L -10 -5 0 5 10 Elcm-' Fig. 4 Band of the Ca-HCl van der Waals complex at 24 360 cm-' recorded with a higher resolution of the exciting laser (0.1 cm-').The band appears to be continuous and has a quasilorentzian shape Ca-HC1, the spectrum consists of two regions close to the calcium atomic transitions; these regions can also be further divided into two sets of bands. The main differences from the Ca-HCl spectra appear in the ID2 region, where the red part is now structured with a regular separation of about 60 cm-', decreasing slightly towards the blue. In the 'PI region, although the bands exhibit the same spacing as in the Ca-HCl spectrum, their width is somewhat broader. A spectrum has also been recorded with DBr and is presented in Fig. 6 ( 6 ) ; unfortunately, the spectral structures have vanished throughout the spectrum of the deuterated compound, except for the band at 23 400 cm-', which splits into three sub-bands.CaCl B2C + I 0 550 600 650 A/nm Fig. 5 Fluorescence spectrum of the Ca-HCI van der Waals complex. The excitation laser has been fixed on an absorption band of the complex (see Fig. 2) and the fluorescence has been dispersed. The saturated line at 532 nm originates from the scattered light of the evaporation laserB. Soep, C. J. Whitham, A. Keller and J. P. Visticot 1.2 1 197 1 0.8 5 0.6 2 .E 0.4 0.2 .- Y n 23000 21200 22400 23600 24800 26000 Elcm-' 2.5 2 1.5 5 .9 1 Y .- v) Y 0.5 0 20000 21000 22000 23000 24000 25000 26000 Elcrn-' Fig. 6 (a) Action spectrum of the Ca-HBr van der Waals complex. The laser exciting the complex has been swept between 20 000 and 25 000 cm-' while recording the intensity of the CaBr(A + X) transition. ( b ) The same as part (a), but replacing HBr by DBr Ca-HBr Emission Spectra A typical spectrum is shown in Fig.7. The main features are the same as for Ca-HCI, i.e. the observation of the A and B states of CaBr with short progressions. However, in contrast, the ratio of the A to B emission strikingly depends on the excitation region ('PI or 'D2), or on which set of bands is excited in each region. In summary, the decay pattern is characteristic of each set of bands previously mentioned, to the blue or red of each atomic line 'PI or 'D2, thus contributing further to the individuality of each set. This will be analysed in detail in a forthcoming paper. Discussion We now describe the nature of the observed transitions in the action spectra in terms of local excitation and local modes.Before this discussion, it seems necessary to summarize what can be stated about the structure of the Ca-HCI van der Waals complex and what can be inferred with regard to the energetics of the reaction.198 PES of the Ca-HX* System 57 0 59 4 618 64 2 666 6 90 A/nm Fig. 7 Fluorescence spectrum of the Ca-HBr van der Waals complex. The excitation laser has been fixed on the absorption band at 4175 A of the complex [see Fig. 6(a)J and the fluorescence has been dispersed Structure of the Ca-HCl Complex The geometries of the known complexes of an atom with HCl are linear, with the hydrogen atom lying between the two heavy partners.22 This also applies to the Hg-HCl van der Waals complex23 and should also be true for Ca-HCl in the ground state, as the calcium atom is even more polarisable (25 A)24 than Hg (5.1 A3)25 and interacts strongly with the HCl quadrupole.Following Buckingham’s developments, Hutson calculated the anisotropy of rare-gas-HX complexes and found that the major contribu- tion arose from the induction forces.26 In this model the HCl dipole imposes a linear geometry, and the HCl quadrupole leads to H having the central position. Therefore, in Ca-HCl, with a 3.5 A centre-of-mass separation, the barrier to linearity is high (ca. 700 cm-’) and the second well is shallow. This value is not inconsistent with the existence of a deep well, as stated in the Experimental section. We cannot make such definitive statements in the case of HBr because of the possible failure of a point-charge electrostatic model for a bulkier atom such as Br: nevertheless, we can safely assume a linear geometry for Ca-HBr, once this complex is also strongly bound.In conclusion, for HCl, the structure of the complex is a linear Ca-HCl geometry which is further confirmed by the initial results of a6 initio calculation^^^ in accordance with the intuitive partial charge transfer between the calcium and the HX. This charge transfer will involve the S orbital of Ca and the antibonding orbital of HX located mainly on the H atom. Experiments would be welcome to confirm this structure. Energetics of the Ca + HX Reactions The schematic diagram in Fig. 1 represents the various levels of the reagents and of the products. At first, a lower limit to the CaX dissociation energy may be found in the frequency extension of the observed action spectra.In order to produce chemilumines- cence, the energy given to the Ca-HX complex by optical excitation should exceed the energy of the first excited state of the CaX product. This sets the limit: DG(CaX)l T,(A -+ X)+DG(HX)+DG(Ca-HX)-hv where v is the frequency of the reddest band in the action spectra. Assuming a 0.2 eVt binding energy for the Ca-HX complex, we obtained DG(CaC1) L 4.03 eV and Tl eV= 1.60218 x J.B. Soep, C. J. Whitham, A. Keller and J. P. Visticot 199 DG(CaBr) I 3.44 eV. The first value compares with the previous experimentally deter- mined D: of CaCl (4.28 eV)," while the value determined by Hildenbrand for CaBr (3.18 eV)28 must be an underestimate.Note that these limits are compatible with the preparation of a Ca-HX complex in the ground state, even in the absence of a barrier. In such a case, for a complex to be formed in the calcium ground state, the reaction should be endoergic, implying a larger binding energy for HX than for CaX, i.e. D:(CaCl) 5 4.34 eV and D",CaBr) I 3.76 eV. Nature of the Action Spectra Localization of the Excitation Energy The Ca-HX complex is a weakly bound species in the ground state, as we have seen in the preceding sections. How can we then describe the optically accessed states when we know that these excited states are reactive and probably react through the harpoon mechanism? This mechanism has been po~tulated'~"~ by analogy with reactions of an excited alkaline earth with an alkali metal (in the ground state) and HX.The open shell Ca(4s4p) of the ionisable calcium can easily yield an electron jump to HX,t the crossing radius being 3.5 f 0.1 A for Ca'P+ HCl between the covalent and Ca+, HC1- surfaces. Therefore the vertical excitation of the complex should lead directly to the reaction domain. The ionic curve is directly attained by optical excitation neither for Ca-HCl nor for Ca-HBr, as can be seen by inspection of the action spectra in Fig. 2 and 6. If it were, the spectrum should be continuous and unstructured, as are the charge-transfer spectra; this results from the rapidly varying nature of the ionic potential (ca. 1 eV k'). Rather, the spectra display sets of bands close to the calcium singlet transitions at strikingly similar positions for both the Ca-HCl and Ca-HBr complexes.We therefore think that the observed transitions derive their oscillator strength from the calcium transitions. In such conditions, the reaction surfaces correlating at an infinite distance with Ca('P, 'D) + HX should split into several A components under the molecular field.677 We thus expect two classes of transitions (2' and 'TI') as allowed by electric dipole transitions for each excited atomic configuration. Indeed, in the spectra displayed in Fig. 2 and 6, the structures correlating with Ca('P, 'D) are split into two groups of bands which appear in all cases, i.e. HCl, DCl, HBr and DBr. Vibrational Excitation A closer examination of the previous spectra reveals vibrational structures that we shall analyse as follows in terms of Iocal modes of the excited complex Ca-HX.We therefore assume that the optical excitation process allows us to make one-dimensional cuts through the excited potential-energy surface along the van der Waals stretch and bend and the HCl coordinates. We shall combine the information contained in the spectra of both Ca-HC1 and Ca-HBr, provided that they bear a close resemblance. The ID2 Ca-HBr Stretching Progression At the long-wavelength end of the CaHBr spectrum (the 'D region), we notice a long progression of closely spaced peaks (ca. 60 cm-I). These peaks, which have a width of ca. 40 cm-', can be described by a one-dimensional Morse oscillator with o, = 70 cm-' w,x, = 0.24 cm-' (assuming that the first band observed corresponds to the origin).This long low-frequency progression suggests a van der Waals mode. The first observed band P The isolated HCI- ion is unstable but is easily stabilised in the Ca+ field in the range of distances of the complex (3-4 A).PES of the Ca-HX* System is located at 1580 crn-' to the red of the 'D line; thus the potential-energy surface in the excited state of the complex is deeper by at least 1580 cm-'. In such case the Ca-HCl distance should be appreciably reduced in the excited state, and the progression must pertain to the van der Waals stretching mode. The resulting dissociation energy is Do = w:/4w,xe = 5000 cm-' in the excited state. The order of magnitude of the stretching frequency in excited states of Ca-HX will be kept in the following as <70cm-' (depending on the well depth of the relevant potential).The same portion of the CaDBr spectrum is reproduced in Fig. 6(6): to our dis- appointment, it does not display the same stretching progression that would be expected in a local-mode analysis. Rather, the observation of a quasicontinuum is surprising. The onset of a continuum could be due to a greater number of bands, possibly of increased breadth as a result of an increase in reactivity. The increase of the bending level density on going from Ca-HBr to Ca-DBr may cause the appearance of a great number of bend-stretch combination bands. Such an increase of the complexity of the spectra as a result of deuteration has already been observed at a certain level of excess energy in the Hg-NH3 and Hg-H20 van der Waals complexes.29730 This complexity could be combined with a larger width of the individual peaks. The reaction can have a very strong angular dependence, with a maximum close to the equilibrium angle.As the vibrational amplitude will be smaller for Ca-DBr than for Ca-HBr, one could expect a greater reactivity for the deuterated compound. In any case, the long progression ( 1 100 cm-') with a small positive anharmonicity observed in Ca-HBr must be assigned to the Ca-HBr stretch. The 'P Ca-HX Bending Progressions We shall now analyse the spectra displayed in Fig. 3. A progression in the blue part of Ca-HCl spectrum is observed with an irregular spacing of ca. 200 cm-', a value implying a van der Waals mode progression. We already noticed a large H/D isotope effect on the band spacing.Furthermore, the relative positions of the four bands in the shortest- wavelength part of the spectrum closely match the energy separations of free HCl rotor lines for J = 4-7 [EJ = bJ(J+ l ) , where 6 is the HCl ground-state rotational constant]. This is confirmed by the observation in the corresponding Ca-DCl spectrum of four transitions matching the J = 5-8 line positions of a free DCl rotor. This correspondence indicates that these ensembles of transitions lead to upper levels beyond the barrier to free rotation of HCl/DCl within the excited state of the complex. On the contrary, the other members of the progression relate to the bending motion associated with the anisotropy of the excited Ca-HCl potential. The observation of quasi-free rotation has also been reported recently in the transition region of IHI.8 To be more quantitative, we have used a bending model described in the Appendix with its selection rules (Amj=O).The transitions in the Ca-HC1 complex arise from the vibrationless state of the linear geometry, without angular momentum mj along the complex axis. The selection rules allow only the access of excited mi = 0 states, as it is shown in the Appendix that for Z -j I3 transitions the AA = 1 change is cancelled by the change in the total angular momentum projection, AhR = 1. Therefore these Amj = 1 transitions should be minor, as they are only due to Coriolis coupling, which we have neglected. Such transitions have been observed by Nesbitt et al. in the case of strong Coriolis coupling of degenerate levels.31 We have fitted the bending potential V(0) of the excited state to reproduce the positions and intensities of most of the transitions of the Ca-HC1 'P region.The result of the fit is presented in Fig. 3 ( c ) and the best potential in Fig. 8. The calculated levels and intensities reproduce correctly the pattern of the blue bands in Fig. 3 ( a ) , with the origin taken on the calcium line. The details of the fit have been given in a previous article." We mention here the essential points of this fit for Ca-HC1: the barrier to freeB. Soep, C. J. Whitham, A. Keller and J. P. Visticot \ 840 - P) M 9 560 E s 280 I----- j = 8 I - J = 7 j = 5 j = L I' - 201 "0 45 90 135 180 Fig. 8 Bending potential of the excited state of Ca-HCl corresponding to the fits in Fig.3. It has been obtained under the assumption of a linear ground-state complex and a bending model described in the text. The parameters have been adjusted to reproduce the positions of the bands in the short-wavelength part of Fig. 3(a) rotation in the excited state has been deduced from the onset of the free rotation in the spectrum, the geometry changes from a linear ground state to a T-shaped excited state and the well depth is the same in the ground and excited states. With these parameters, we could directly obtain the Ca-DC1 transitions in Fig. 3 ( d ) by only changing the masses. This indicates that the main progressions in the blue part of the spectra in Fig. 3 are bending progressions of the Ca-HCl complex. This agreement between experi- mental and calculated positions of peaks for Ca-HCl and Ca-DCl also implies that the origin of this progression changes by only 30 cm-' upon deuteration.This is compatible with a local-mode description in which the HCl bond is reduced in the excited state by only ca. 200 cm-'. This model was designed to give the framework of the transitions showing that one-dimensional local-mode excitation was promoted by the optical pulse. However, it does not account for all the transitions observed in Fig. 3. If we look more closely at the blue part of the spectrum of Fig. 3, we see some unassigned transitions appearing as satellites or shoulders displaced by 20-50 cm-' from the main peaks of the bending progression. This separation is compatible with a stretching mode spacing in a shallower potential (1500 cm-') than the potential of Ca-HBr in the 'D2 region.Therefore a possible explanation for the existence of such bands relies on a combination of bend- stretch modes which are not easily predicted in the model. Inspection of the Ca-HBr spectrum in the same 'P region shows a very similar pattern for the transitions, similar spacings but a more diffuse appearance. We have not attempted a bending analysis because the Ca-DBr spectrum is almost continuous, as in the 'D2 domain, and probably for the same reason, i.e. a greater bend-stretch coupling. The previous analysis clearly confirms the existence of a second group of transitions which appear most distinctly in the red part of the Ca-DCl (Ca-DBr) spectrum (Fig. 3) and bear no relation to the group of bending transitions.We can exclude the contribution of Ca-(HX),, n > 1, in both the HCl and HBr spectra, as these bands are sensitive to H/D substitution. Another interpretation for this group of bands would be the existence of a Ca-XH isomer in the ground state, which, on the basis of electrostatics, seems unlikely. The correlation of atomic and complex states implies, in the case of calcium 'P, the presence of a second electronic state. We have already noticed the separation into two groups of the transitions observed in the spectra of Ca-HBr and Ca-DBr, a result which fits this interpretation.202 Reactivity of the Ca-HX States The purpose of the previous analysis has been to show that one could represent the excited complex by one-dimensional modes on surfaces correlated to excited atomic calcium. This description may appear surprising, for we have been probing a reactive surface, and we could conclude from the observation of structured spectra and resonances that we only had access to the entrance valley of this reaction. On the other hand, the chemiluminescent reaction of excited calcium with HCI is known to occur with high cross-sections, ranging from 25 A2 (ID2)'' to 68 A' ('P).l4 These cross-sections agree with a crossing of the ionic and covalent surfaces without a barrier at 3.5 Hence, we must expect a direct and fast reaction. In addition, in Fig.3(a) the bending bands become increasingly sharp with excitation, so that the bending Ca- HCl vibration displaces the system away from a favourable conformation.We thus interpret the observation of distinct progressions, as opposed to featureless continua, in the action spectra as due to the excitation of local modes perpendicular to the reaction coordinate. PES of the Ca-HX" System Appendix: The Ca-HX Bending Model We describe here a simple to calculate the bending levels of a Ca-HCl van der Waals complex and to yield selection rules for the optical transitions. The levels of Ca-HCI have been calculated within the hindered rotor model in a body-fixed frame ( O X ~ Z ) . ~ ~ To describe the internal degrees of freedom we use the Jacobi coordinates R, r and 8, which are well adapted to this type of problem; here they have the following meanings: R is the distance between the calcium atom and the HCl centre of mass, r is the HCI bond length and 8 is the angle between the vectors R and r.We shall also make the following approximations. We separate the electronic and nuclear motion in the Born-Oppenheimer approximation. Furthermore, we consider, as justified in the text, the electronic excitation to be localized on the calcium atom, and thus the electronic wavefunction to be a perturbed atomic Hence, the perturbation of an excited calcium atom with angular momentum L by the HCl molecule splits up the components of L. In a linear geometry of the complex, the projection A of L on the body-fixed Oz axis is a constant. However, states of the complex correlating with different values of L may be mixed. The 'P and 'D atomic states will be mixed in the complex, as their separation (1803 cm-I) is comparable to the interaction energy between Ca and HC1 (ca.1500 cm-I). This is the origin of the absorption observed in the complex in the 'D region, while it is forbidden within the atom by the optical selection rule AL = 0, *l. Here this absorption becomes allowed owing to the interaction between states of same .A (X and ll states, respectively). We shall make an additional approximation in considering A to be a good quantum number even in the case of a bent geometry, as R >> r in the complex. In other words, we assume the electronic cylindrical symmetry to be little perturbed in twisting the geometry of the Ca-HCl complex. A model for the bending will be made in the approximation of the separation of the internal coordinates ( R , r, 8 ) .While the separation of r and ( R , 0) is justified by a large difference in the frequencies of the HC1 stretching (ca. 3000 cm-I) and van der Waals (ca. 100 cm-I) modes, the separation of R and 8 is much cruder, and this will be improved in the future. The bending wavefunction is a solution of the Schrodinger equation with the H a m i l t ~ n i a n ~ ~ b B A A H => j 2 + i l ' + V " ( 8 ) where j is the angular momentum of the HCI molecule, 1 is the angular momentum forB. Soep, C. J. Whitham, A. Keller and J. P. Visticot 203 the overall rotation of the complex, V(6) is the bending potential for the A electronic state considered, and 6 and B are the rotational constants of HC1 (10.6 cm-') and of the overall rotation of the complex ( B =: 0.15 cm-' for R =: 3.5 A), respectively.The wavefunction is expanded* over the basis set IJMfl)ljmj) where IJMfl), the Wigner rotation matrix element DLn(Q>, 0, +), describes the rotation of the molecular frame in space, and Ijmj) = Y i , ( 0,O) describes the rotation of HCl in the molecular plane.34 J is the total angular momentum, M its projection on the space-fixed axis and SZ its projection on the body-fixed axis ( R ) . We have the relation J = j + l + L where it follows, projecting j on the body fixed axis 02, that mj = SZ - A because Z, = 0. Finally, the wavefunction is written as m J c C;yblJMfl)ljmj) j = O R=-J where ub labels the bending level and the coefficients Ci;.'"b may be obtained by diagonalizing H. In this basis, the matrix elements o f j 2 and Z2 are easily calculated: 1' = ( J - L - j ) 2 = J 2 + L2 +j2 - ( J + j - + J-j+ + J+ L- + J-L+ - j , L- -j-L+) Z2 can couple the function corresponding to the quantum numbers SZ, M and A to the functions f l f 1, M f 1 and A f 1.This is the Coriolis interaction due to the overall rotation of the complex. These terms can be neglected here because B << 6, and therefore fl is a good quantum number. The wavefunction can be written as J M A n = f CjM '3n"hlJMfl)ljCl -A) j = O Ub j' is diagonal in this representation, and, as V(0) is taken to depend solely on 6, it couples functions corresponding to different j only. In the framework of these approximations, to obtain the main transitions we must solve the Schrodinger equation with the hamiltonian: h A H => j ' + V(6) To solve this eigenvalue problem, we expand the potential V ( 6) in Legendre polynomials: hmdx 0) = c CkPk[COS ( 0 ) l k = O and the bending wavefunction is expanded over spherical harmonic functions: 'ma, J =o xl#, = c 'l#,,J q,o( '7 O) With these requirements, the matrix elements of H are analytic.The diagonalization of this matrix gives the energy levels and the wavefunction describing the bending motion of HCl in the V(6) potential. Transition Selection Rules Because the geometry of the ground-state Ca-HCI complex will be taken as linear, fixing the J, M quantum numbers, the lower bending state corresponds to Z)b=0, f l = O and the first excited state to ?& = 0, fl= 1. The energy gap between these two states is204 PES of the Ca-HX* System approximately the bending frequency cob (of the order of 100-200 cm-').In the super- sonic beam, where the temperature is <10 K, only the ground bending state will be populated, thus J, M, f2 = 0, A = 0 and mj = f2 - A = 0. The intensity of the absorption is proportional to where E is the polarization of the electric field and p the dipole operator for the molecule. E is defined in the space-fixed frame, whereas p is defined in the molecular frame, thus &P = c (-1)p&-pP9D;9(@, @,#I p , q = o=t 1 where pq and E~ are the usual tensorial notations for vector component operators. We can thus write Afe = ( ~ o ~ I x v f > c (-l)p&-p(J~M,szelo;(CP, @,#)IJfMffifXAelpqIAf) p.9 =o+ 1 As usual, two types of transitions can occur: ( a ) if q = 0, then Ae = Af (2 + I; transitions); ( b ) if q = kl, then A, = Afk 1 (I; -+ TI or n -+ I; transitions).When q = 0 the selection rules come from the terms: The integration over the angles 0 and CP gives the usual selection rules: ]Jf - lI(Je(lJf+ 11, and Me = Mf, Mf f 1, depending on the value of p . The integration over the # angle gives sze = Rf This last relationship, combined with the fact that A, = A,, implies: mj, = mj, fie = f2f+ 1 When q = f l the selection rules can be derived in the same way, yielding: but in this case A, = Af* 1 and we again have m. = m . Jc JI We see that only states with mj = 0 may be accessed from the ground state, mi = 0, which is the only state populated in the supersonic expansion. References 1 P.R. Brooks, Chem. Rev., 1988, 88, 407. 2 A. H. Zewail, Science, 1988, 242, 1645. 3 M. Gruebele and A. H. Zewail, Phys. Today, 1990, 43, 24. 4 S. K. Shin, Y. Chen, S. Nickolaisen, S. W. Sharpe, R. A. Beaudet and C. Wittig, Adv. Photochem., 5 R. B. Metz, S. E. Bradforth and D. M. Neumark, Adu. Chem. Phys., submitted. 6 C. Jouvet, M. Boivineau, M. C. Duval and B. Soep, J. Phys. Chem., 1987, 91, 5416. 7 C. Jouvet, M. C. Duval, B. Soep, W. H. Breckenridge, C. J. Whitham and J. P. Visticot, J. Chem. Soc., 8 S. E. Bradford, A. Weaver, D. W. Arnold, R. B. Metz and D. M. Neumark, J. Chem. Phys., 1990,92,7205. 9 R. T. Pack, J. Chem. Phys., 1976, 65, 4765. submitted. Faraday Trans. 2, 1989,85, 1133. 10 U. Brinckmann and H. Telle, J. Phys. B, 1977, 10, 133. 11 U. Brinckmann, V. H. Schmidt and H. Telle, Chem. Phys. Lett., 1980, 73, 530. 12 H. Telle and U. Brinkmann, Mol. Phys., 1990, 39, 361. 13 C. T. Rettner and R. N. Zare, J. Chem. Phys., 1981, 75, 3636. 14 C. T. Rettner and R. N. Zare, J. Chem. Phys., 1982, 77, 2416. 15 R. E. Smalley, Laser Chem., 1983, 2, 167.B. Soep, C. J. Whitham, A. Keller and J. P. Visticot 205 16 V. E. Bondybey, Science, 1985, 227, 125. 17 J. P. Visticot, B. Soep and C. J. Whitham, J. Phys. Chem., 1988, 92, 4574. 18 C. J. Whitham, B. Soep, J. P. Visticot and A. Keller, J. Chem. Phys., 1990, 93, 991. 19 A. Keller, J. P. Visticot, S. Tsuchiya, T. S. Zwier, M. C. Duval, C. Jouvet, B. Soep and C. J. Whitham, in Dynamics of Polyatomic van der Wads Complexes, NATO AS1 Series, ed. N. Halberstadt and K. C. Janda, Plenum, New York, 1990, p. 103. 20 W. J. Balfour and R. F. Whitlock, Can. J. Phys., 1975, 53, 472. 21 V. E. Bondybey and J. H. English, Chem. Phys. Lett., 1984, 111, 195. 22 S. E. Novick, K. R. Leopold and W. Klemperer, in Atomic and Molecular Clusters, ed. R. E. Bernstein, 23 J. A. Shea and E. J. Campbell, J. Chem. Phys., 1984, 81, 5326. 24 T. M. Miller and B. J. Bederson, Adv. At. Mol. Phys., 1977, 13, 1. 25 R. R. Teachout and R. T. Pack, At. Data, 1971, 3, 195. 26 J. M. Hutson, J. Chem. Phys., 1989, 91, 4448. 27 J. P. Daudey and A. Keller, to be published. 28 D. L. Hildenbrand, J. Chem. Phys., 1977, 66, 3526. 29 M. C. Duval, B. Soep, R. D. van Zee, W. B. Bosma and T. S. Zwier, J. Chem. Phys., 1988, 88, 2148. 30 M. C . Duval and B. Soep, J. Phys. Chem., to be published. 31 D. J. Nesbitt, C. N. Lovejoy, T. G. Lindeman, S. V. O’Neil and D. C. Clary, J. Chem. Phys., 1989,91, 722. 32 B. P. Reid, K. C. Janda and N. H. Halberstadt, J. Phys. Chem., 1988, 92, 587; J. M. Hutson, J. Chem. Phys., 1989, 92, 157. 33 G. C. Schatz and A. Kupperman, J, Chem. Phys., 1976,65, 4642. 34 C. Jouvet and A. Beswick, J. Chem. Phys., 1987, 86, 5500. 35 R. N. Zare, Angular Momentum, Wiley Interscience, New York, 1988. Elsevier, Amsterdam, 1990, p. 359. Paper 1/00446H; Received 30th January, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100191

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991, 91, 207-237 Femtosecond Transition-state Dynamics Ahmed H. Zewail Arthur Amos Noyes Laboratory of Chemical Physics, California Institute of Tcchnohgy, Pasadena, California 91 125, USA This article presents the progress made in probing femtosecond transition- state dynamics of elementary reactions. Experiments demonstrating the dynamics in systems characterized by a transition region and by a saddle- point transition state are reported, and comparison with theory is made. 1. Introduction Since the early days of the transition-state theory of Eyring, Evans and Polanyi,' the fleeting nature of the state as the reaction proceeds from reagents to products has been known. The lifetime of the state is typically s, and hence to observe these transition states in real time the temporal resolution must be on the femtosecond scale.Progress has been made in probing transition states of elementary reactions and in studying the dynamics in real time.2 The objective of this account is not to review all the work done in this area (for a review, see ref. 2). Instead, I wish to discuss recent developments with particular focus on two- and one-dimensional reactions. The dimensionality (D) of the potential-energy surface (PES) determines the nature of the transition state, TS. In 1-D systems there is only one vibrational coordinate, and the motion can be mapped out as atoms recoil along this coordinate in the transition region. In 2-D (or more) systems, there may be a saddle point, and the dynamics would involve both the translational motion along the antisymmetric coordinate and vibrational motion (dynamical resonance) along the symmetric coordinate.In this case the saddle point defines clearly a TS, and the system spans both bound and repulsive features of the PES. Experiments demonstrating the dynamics in such systems are reported, and comparison with theory is made. 2. A Prototype Case: the Transition Region of Alkali Halide Reactions We consider first the simplest case of two atoms with a single internuclear coordinate in the half-collision dissociation of a diatomic. This example we use to demonstrate the concepts involved and to report on the recent progress made on these alkali halide (MX) reactions: MX* --* [M.**X]'* --* M+X (1) As discussed by Berry,3 the PES for this class of reactions is well described by the covalent (M+X) and ionic (M++X-) curves, which cross at a given internuclear distance, R, (Fig.1). Actually there are more curves, but they are not relevant here. When an alkali atom (e.g. Na) is brought closer to a halogen atom (e.g. I), according to the molecular-states picture [Hund's case (a); A = O ( 2 ) and A = l(II) etc.], II and 2 singlet and triplet states are formed. However because of spin-orbit coupling, Hund's case (c) is invoked, and the states are actually indexed according to the projection of the total angular momentum along the bond axis giving rise to R = 0'- and 1 states. In a correlation scheme, the O+ state correlates with the B 'Z+ and the 1 state correlates with the A'II (and triplet) state.The ground state is of type X (or 0), and therefore 207208 4 2 % fi 5 0 E \ - .CI U U a - 2 - 4 Gemtosecond Transition-state Dynamics Na' + I 0 5 10 1 5 20 internuclear separation/ A Fig. 1 The covalent (M + X) and ionic (M+ + X-) potential energy curves for the reaction of alkali halides the covalent Of and the ground state interact at the crossing point R, to form the avoided crossing region between the covalent and ionic curves (Fig. 1). The covalent curve is essentially non-bonding (except for van der Waals attraction) until it reaches the repulsive branch. This reaction of alkali halides represents an ideal test case for using femtosecond transition-state spectroscopy (FTS) to probe the nuclear motion as the system proceeds from MX" to [M...X]S* and then finally to M+X.Over the past years we have studied these systems with different time and spatial resolutions in order to observe the nuclear motion in real time. In this section we discuss the femtosecond dynamics, particularly for the NaI system, and the new findings. 2.1. The Activated Complex: Motion between the Covalent and Ionic Potentials As the wave packet, prepared at time zero, moves from the covalent to the ionic curve, the bond changes its characteristic from being purely covalent to a mixture of covalent and ionic. As discussed by Pauling? the crossing (or closeness) of the covalent and ionic potentials is a general phenomenon which describes the nature of the chemical bond. The dynamics of the bond is that of the activated complex, as termed by Atkins,' in the transition region and its decay toward final products.Classically, the probability209 A. H. Zewail I I -2 0 2 4 6 0 10 -2 0 2 4 6 8 time delay/ps Fig. 2 Top: the oscillatory (resonance) behaviour observed by detecting the activated complex [Na.-.I]S* in the transition region. In the insert, both the peak area (solid) and peak height (hatched) of the oscillations are shown to indicate the leakage through the Landau-Zener region and the dephasing of the wave packet. Bottom: detection of free fragments ( a ) and the activated complex ( b ) of going out to form M+X depends on the coupling between the two potential curves (a Landau-Zener type of interaction). Quantum-mechanically, this coupling changes the nature of the wavefunction as the internuclear separation, R, changes.If we probe the motion in the transition region, [M...X]$*, we should observe the resonance motion between the covalent and ionic curves, with a damping determined by the leakage probability through the Landau-Zener region. On the other hand, if free M atoms are detected, one should see an increase in the number of M atoms every time the system executes a resonance period, i.e. a series of steps of increasing signal intensity determined by the period of covalent to ionic motion. Such observations (see e.g. Fig. 2) have been made by Rose et al. and Rosker et ~ 1 . ~ and related to the resonance period, the lifetime of the activated complex, the escape probability and the magnitude of the coupling (covalent/ionic). [The iR = 1 curve is a repulsive curve and has dynamical characteristics similar to other reactions studied by Dantus et al.and Rosker et al. (ICN),' and by Glownia et al. and Bowman et a1 (Bi2).'] For example, at a total energy of 6850 cm-' above the Na+ I channel, the period is 1.25 ps, the lifetime of the complex210 Femtosecond Transition-state Dynamics 4 4 3 3 - i i 2 2 .C. 1 1 time delay/ ps time delay/ps Fig. 3 The change in the period of the resonance as a function of total energy. Left: the wavelength A , changes from (a) 300, to (b) 311 to ( c ) 321 and to (d) 339 nm, respectively. (Right): A l is (a) 332, (b) 344, (c) 354 and (d) 364 nm. The change of packet resonance frequency with energy over a wider range is given in ref. 6 is 34 fs, the recoil velocity is 0.029 A fs-’ and the Landau-Zener escape probability is 18% (the largest value at this energy).The total splitting between the adiabatic curves at R , is 0.1 eV. As discussed below, the wave packet spreads, and the spreading in time is larger than the lifetime of the complex; it can be observed experimentally (Fig. 2) hemiire the nrnhino window h2c ciifficient A R recnliitinn. 2.2. The Two Potentials Involved In probing the transition region, we use laser-induced fluorescence and ionization/mass- spectrometric methods with a time delay resolution of ca. 10 fs. In principle, we have to consider the two potentials involved, the lower potential V, and the upper potential(s) V,. As discussed by Bernstein et a ~ , ~ FTS enables determination of V, if V, is essentially flat at large R.In general, however, one probes A V ( t ) , and this A V can be deciphered into V,( r) and V,( t ) by changing the two wavelengths of the pump and probe, A, and AZ, in addition to scanning the delay time; i.e. measurements involve I ( A l , h2 ; t ) . In the centre-of-mass frame, E = ~ I Y : , and by changing A*, we can change vr, the recoil velocity. Thus, for a fixed probe wavelength (A2), the total energy can be changed systematically to observe the effect of v, on the dynamics of the motion between covalent and ionic curves. In Fig. 3 this behaviour is shown for NaI dissociation. Clearly, the potential is far from harmonic, and ‘opens up’ as we increase the total energy. There is another measurement that helps us determine the nature of the V, potential.It is called a clocking e~perirnent.~”’ If t=O is determined precisely, then we can measure the time it takes the wavepacket to travel from Ro at t = 0 to R of the probe. This time, T, must change depending on E and the shape of V , . As shown in Fig. 4, strongly repulsive V, and weakly repulsive V, have different temporal dynamics. For a fixed probe A,, we change the available energy (A, tuning) and determine clocking times T ( E ) . By self-consistency between the values of T and E we determine a unique length parameter L for the repulsive branch [see eqn. (3)], and from the periods we determine the outer turning points at different values of E. For illustration, we consider R( t), from conservation of energy: 1/2 R ( r ) = R o + I ‘ ( Z { E - o m VJR(r’)]}) dt’A.H. Zewail 211 I 8 - .n c) E c) a * O m m 0 2 4 6 8 1 0 2000 2 4 6 8 10 internuclear separation/ A internuclear separation/ A 2 : 1 I 0 100 200 2+ I . I 0 100 200 t/fs t l f s Fig. 4 The internuclear separation as a function of time, R ( t ) , at two different energies [(c) and ( d ) ] and for the two different potentials V ( R ) = Voexp [-cu(R-R,)] in ( a ) and ( 6 ) . V,= 8000 cm-', Ro = 2.7 A, ry = 4.0 A-' ( a ) and 1.0 A-' ( b ) As an example, if V,=Aexp(- 3 - Ro) ) then one can calculate the time it takes the particle to travel from R, to R. Solving the equation for R( t), and taking AR >> L, one obtains The first term describes the kinetic energy (velocity) effect; i.e. fragments begin at Ro with the terminal velocity or. The second term gives the influence of the exponent L of the potential.As an example, for L = 0.4 A and vr = 0.018 A fs-' (total energy= 2570cm-I; 391 nm), T is 171 fs for R to change from 3.07 to 5.6A. This value is determined experimentally to be 175 fs, as discussed below. One can define a finite time for dissociation, T~ , as the limit of the difference between T and (R - Ro)/ or and obtain the effect of L on T, by analogy with particle physics definitions; for more discussion, see ref. 11. The value of T is different from a characteristic time, T;, defined to include the window of the probe; during this time the potential drops to a value equal to y (the energy width of the probe window) the absorption of free fragment reaches half of its maximum value: L 4E T; = - In - - or Y (4) For the same L, E and v,, mentioned above, = 94 fs.This indicates that for this type of strongly repulsive (L = 0.4 A) branch, the potential drops to the y-value and the212 Femtosecond Transition-state Dynamics t 2 - b E 1 - E 1 x t? CI .- U U a 0 - 0 2 4 6 8 10 12 ' ' I ' internuclear distance/ A -1 ' ' I ' ' I ' ' ' ' ' I ' I " " ' I ' ' ' I ' ' I 1 l 1 ' I ' ' ' ' ' ' ' " " ' ' ' ' I ' I Fig. 5 ( a ) The PE curves of the NaI reaction and the experimental range of points reached in the FTS studies by changing the total energy A,(R,) and the probe position AT(R), and by measurement of the period T ~ . (b) and ( c ) The experimentally deduced V, ( c ) and V, (b). For V, there are two sets of data, using different ways of measuring the clocking times, and the results give the potential well discussed in text.The dotted curve in (b) is the one deduced in ref. 12. For V, , the experimental points give the repulsive branch, with L = 0.4-0.5 A, and the coulombic branch. The value of 0.4-0.5 A is consistent with other studies,64 but larger than the value of 0.245 8, reported in ref. 65. We have taken a simple repulsion form, eqn. (2), and this can be modified in form to include other terms (see ref. 66 and 67). The dotted line is the potential predicted by inversion of the data, and the circles give the RKR p0tentia1.l~'~~ The solid line is the potential from ref. 6, which has been used in many calculations. These studies will be discussed and compared in more detail in ref. 68 absorption of free fragment (50%) appears after 94 fs.In this 94 fs, R is 4.2 A. In the case of NaI, there is an avoided crossing (not just a simple repulsive curve) and free fragments are born after the crossing point. Also, eqn. (4) assumes V, to be flat over the region of interest. The important point about this equation is that it describes the physics of the probing window and the role played by the weak dependence on y in defining the bond-breaking time, as discussed in ref. 7, 9 and 10. Fig. 4 illustrates R ( t ) 11s. t in two regimes, emphasizing velocity and distance effects on two different potentials, and the self-consistency between R ( t ) and E to determine L. The data obtained in Fig. 5 give L = 0.4-0.5 8, for the repulsive branch and the 1/R dependence for the coulombic branch.(A more precise determination of L is currently underway.) To probe V2, we then fix the total energy and change A, systematically. These experiments, which sweep the absorption (in time) from the free fragment to the transition region, give the nature of the upper potential reached by A 2 . In Fig. 5 we summarizeA. H. Zewail 213 3 4000 A t? g 2000 -. .CI U OI 3 U a -2000 b 10000 8000 6000 4000 2000 0 i 2 4 6 8 10 12 14 internuclear separation/ A Fig. 5. (continued) our findings for both V, and V2, probed by FTS. The well found in V2 is deeper (ca. 0.2 eV) than that previously deduced (530 cm-') by Bower et u1.,l2 and is consistent with a recent spectroscopic study by Bluhm et uZ.'~ For V , , our probing distance of the potential is over the range of R from cu.2.7 to 12 A. 2.3. Dynamics of the Activated Complex Motion and Recurrences From the damping of the resonance oscillations, we obtained the coupling matrix element (415 cm-') between the covalent/ionic curves, which is in good agreement with the theoretical calculation by Grice and Her~chbach'~ (400 cm-'). From the period of resonance oscillations and the clocking times, we deduced the PES (Fig. 5) and the dynamics (Fig. 2 and 3). However, the quantum nature of wave-packet spreading with time can be obtained only if the window's resolution is sufficient to observe the coherent/incoherent changes in the motion. For a free particle, a wave packet spreads appreciably for times given by 2m h T,=- (A&)* showing the natural relationship to the mass, m.For NaI, T, = 6 ps. Accordingly, a 1 A wave packet in R-space will begin to spread appreciably after 6ps. Manifestations of this spreading come from the change of the width of the observed resonance with time (Fig. 2 ) . Thus, both the spreading or dephasing of the wave packet and the population214 Femtosecond Transition-state Dynamics 0.5 - 0.0- JU 1 . , . . 1 . . . . 1 . , , . , . . . . I , , . . , . , , , 1 . . , , , & -1.5 1 I I I...,,....I....,....I....,,...I....l 0 10 20 30 40 time delay/ps Fig. 6 (a) The oscillatory behaviour of the activated complex [ N a - .I]$* and the rephasing (echo) at long times, 30-40 ps. ( b ) The modulated part of the FTS signal, without the overall damping leakage through the Landau-Zener region are present. Detection of free Na gives the population time constant(s), and in fact, as shown by Cong et the build-up of population is not a single exponential, but can be fitted to two exponentials.This non-exponentiality indicates that the packet is inhomogeneous in its level structure" (see below). In some sense, this is reminiscent of T1- and T,-type relaxations, an analogy which has been made clearly by Beswick and Jortner.16 Can isolated molecular systems dephase and then rephase again to give an echo? Because the wave packet executes the different resonances of the motion (or equivalently spans the different quasi-bound levels) owing to the avoided crossing, there are different timescales for the motion: the packet first oscillates between the covalent and ionic curves, and spreads on the picosecond, not femtosecond, timescale.In the process of breaking the bond, the packet spreads significantly, and at ca. 15 ps our results indicate that it becomes so-called 'chaotic', spreading in all regions of R. Calculations of snapshots at these times confirm this picture. By accident, we discovered that if we wait long enough (30-40ps), this so-called 'chaotic' packet appearance starts to take on a coherent appearance, and recurrence echo of the initial resonance oscillations (with the same period!) occurs (Fig. 6). These recurrences are very sensitive to the total available energy, and reflect the nature of the PES caused by the avoided crossing. The observations represented our first example of seeing the wavefunction of an isolated molecular system, in the course of the reaction, spreading and rephasing again.This brings to focus another point. Even though the wave packet spreads and appears 'chaotic', the system is actually non-chaotic; the waveA. I-€. Zewail 215 Fig. 7 Simulation of the wave packet motion in 2-D space of R and t. The lower plot shows the snapshots of the wavepacket motion at different internuclear separations. Note the time evolution of the splittings as R increases nature and the phases of the individual wavefunctions constituting the packet are still well defined, up to 40 ps; otherwise recurrences would not have occurred! 2.4. Observation of the Trajectories in R and i Fig. 7 displays trajectories in the R us. t domain. As shown in the figure, the wave packet changes direction as R and t change, starting from the initial time zero at R = 2.7 A.After half a period, the packet has reached the ionic turning point, and after a complete period, it has returned to the covalent turning point. At or near the ionic-covalent crossing, the packet bifurcates; some of it continues to move in the direction of increasing R, becoming Na and I, and the rest remains as [Na..-I]$*, oscillating between the covalent and ionic curves (see also Fig. 1). To observe the motion of the trajectories, a window in R ( t ) must be opened with sufficient distance resolution AR to allow us to view the directionality of the packet at different times. If the window is stepped continuously along R, then we can map out the motion and characteristics of the PES. For a given distance resolution, the temporal motion represents a snapshot of the PES at this particular R.For example, a window at R = 3 A will give the snapshot shown at the bottom of Fig. 7, which is basically the oscillatory motion displayed in Fig. 2. On the other hand, if a snapshot is taken at R = 4.5 A, the oscillatory motion displays a splitting because at this distance the packet is going in and out of the probing AR window. At longer R, the splitting increases in time, because the distance the trajectory travels is longer. The observation of such216 Femtosecond Transition-state Dynamics time delay/fs Fig. 8 Experimental femtosecond snapshots of the NaI reaction. ( a ) shows the snapshots taken at different h 2 , while maintaining the total energy fixed. ( b ) shows the reverse splitting would indicate two important points.First, it would mean that the window opened in R is sufficiently narrow to resolve the nuclear motion in and out of that region of the PES. Secondly, the splitting gives a time (at each R ) that is directly related to the clocking time, defined by the distance travelled from time zero to the probing point on the PES, as discussed before. Fig. 8 shows the experimental observations by Mokhtari et a1.l' for the NaI reaction. The packet was prepared by a femtosecond pulse at a wavelength A l corresponding to E = 2570 cm-' above the Na+ I threshold. To probe at different R, we used another femtosecond pulse of a different wavelength A Z . For a given total energy in the bond, both the time and A 2 can be changed systematically to obtain the snapshots at different values of R.Three snapshots in Fig. 8 are shown as examples of the many results obtained. The evolution of the splitting as A, decreases ( i e . as R increases) is evident. The splitting at A2 = 620 nm, for example, is 350 fs. This gives a clocking time for the packet to reach the probe on the PES of 175 fs. The distance being probed is 5.6 A, and this is consistent with theory, as discussed above. The window resolution is very appropriate for studying the dynamical motion of chemical reactions: the temporal splitting observed gives an experimental AR = 0.5 A on the PES. The potential for these types of reactions is quite flat (non-bonding type) at intermediate R (Fig. l ) , and therefore even better resolution may be achieved in other systems.As E is decreased, we expect the velocity to decrease and the distance travelled by the wave packet, to a given R, to decrease also. Depending on the PES, these two effects determine whether or not the splitting will increase or decrease with E (Fig. 4). Fig. 8 shows three snapshots at different A l . We observe an increase in the splitting as E isA. H. Zewail 217 lowered. We also observe a decrease in the period (Fig. 3). The latter is consistent with the potential ‘narrowing’ in R at lower E (Fig. 5 ) . The former indicates that the covalent side of the potential is very repulsive at short R and is dominated by velocity (not distance) effects (Fig. 4), as deduced in Fig. 5, and discussed above. 2.5.Theory Since the early report of these experiments, all major features have been understood using an intuitive classical mechanical description. Because the system is relatively heavy and we are interested in the early time motion, the centre of the wave packet is described as particles moving according to the laws of classical mechanics. Relying on these ideas makes the visualization of the experiments very simple. However, the wave properties of the particle are manifested in several ways. First, the spreading of the wave packet, which as shown above for NaI, is beginning to be appreciable at ca. 6 ps (for an electron, in contrast, this time is ca. s). Secondly, the uncertainty principle for a free wave packet -- AR2 AP2? h2/4 indicates that a wave packet broad in P-space is narrow in R-space. For heavy particles, the de Broglie wavelength is sufficiently small that wave properties may appear to be unimportant; for NaI, the de Broglie wavelength is ca.0.2 A, compared to a distance motion of 2 7 A. Thirdly, the wave packet at t = 0 is not the simple ‘classical mechanical packet’ projected from the ground state. The packet shape must take into account the question of the preparation by a finite pulse width: the classical picture is equivalent to a preparation by a pulse of zero duration (such pulses have been discussed’* recently!). Finally, classical mechanics fails to describe the spread and the (non-chaotic) rephasing of coherence particularly at long times, up to 40 ps, unless one designs different initial trajectories for simulations.Classical mechanical theory’,’’ has reproduced the oscillatory motion6”’ using the known PES and the equation of motion of R ( t ) . It also shows the salient features of many experimental observations, as discussed by Rosker et al.,617 Bersohn et al.” and Lee et al.” Semiclassical treatments by Marcus2’ and by Lin and Fain2’ have also been successful in obtaining the early-time oscillatory motion and damping. Metiu and co-workers22 have shown that rigorous quantum calculations are able to describe the FTS observations from t = 0 to ca. 8 ps. These studies are important in showing that quantum calculations, involving all known (not adjustable) parameters of the PES and the preparation process, are in accord with experiments. The calculations also illustrate the presence of spreading (less than observed, however) and show splittings on the peaks which were not identified with the clocking of the reaction.Snapshots of the packet at different times indicate the motion between the covalent and ionic regions. The quantum calculation of Choi and Light23 has successfully reproduced the oscillatory behaviour of the motion. All of these calculations describe the global dynamics in the region 0- 10 ps. Chapman and Child,24 in a beautiful paper, showed that the recurrences at long times are manifestations of the distribution of the level structure and resonance lifetimes (caused by the avoided crossing), and hence obtained the timescale for rephasing. Their calculations are in good agreement with experimental observations at long times, 30- 40 ps.In ref. 15 we discuss this in relation to the dynamics of the packet in the adiabatic well and its interaction with the ground state. Very recently, Fujimura and K 0 n 0 ~ ~ have computed the motion in the R and t domain and showed the trajectory of the motion at different total energies. They obtained splittings in the FTS resonance, similar to those shown in Fig. 7. Quantification of the218 Fern t osecond Trans it ion -s t a te Dynamics theoretical results with the PES derived from FTS experiments will be given in detail in ref. 68. 2.6. Summary The results reported here illustrate the concepts and methodology involved in probing the dynamics on the femtosecond timescale. The motion of the nuclear wave packet during the breaking of the NaI bond can be observed with an experimental resolution of ca.0.5 A of internuclear separation. The total energy and the position of the probing ‘window’ can be varied to map the trajectories R ( t ) and the shape of the potentials involved. The range of internuclear distances probed is up to 6.5 A on the covalent and 12A on the ionic curves. The dynamics probed in real time include motion of the activated complex, its damping by the avoided crossing between covalent and ionic potentials, and quantum spreading and rephasing of the wave packet as the complex decays to final fragments. Theory is quite advanced for these systems, and provides, successfully, the global picture. Because of their 1-D nature, these alkali halide reactions serve as prototype systems for studying simple elementary reactions and they help in understanding the concepts involved.But what about motion in two (or more) dimensions? 3. Probing the Transition-state and Dynamical Resonances In the case of alkali halides, the activated complex’ spans a configuration defined by the separation of atoms in the R-region (one coordinate). In the full collision along the covalent curve, reaction (11), Na+I ---* [Na..-I]$* - Na+I (11) the complex path is continuous along a repulsive curve. However, when the activated complex is prepared at a specified configuration in a half-collision, [ Na- .I]$* is estab- lished at a given R, and its dynamics can be followed. There is, of course, no saddle point in this case. If the reaction dynamics involve more than one coordinate, an interesting question arises: can one observe in real time the reactive evolution from the TS at the saddle point to final products on the global PES? The simplest system for addressing the question is of the type ABA- AB+A.This system is the half-collision of the full- collision A+BA - [ABA]$ ---* AB+A (111) It involves one symmetrical stretch ( Q1), one antisymmetrical stretch (QJ, and one bend (4). We have chosen the system [ 1. - -Hg. - -I]$*, for which the antisymmetric (translational) motion gives rise to vibrationally cold (or hot) nascent HgI. The symmetric motion is bound and may give rise to a dynamical resonance. The idea of the experiments was to excite directly the collision complex from the ground state to the transition state, [I...Hg...I]S*, and to follow the real-time dynamics of the complex as the motion proceeds from t = 0 (transition state) to long times (free fragments). The energetics are shown in Fig.9. One advantage of exciting the complex directly is the possibility of observing the dynamics with minimum-impact parameter averaging. In the full collision case, this averaging may ‘smear out’ dynamical resonance effects. The concept of transition-state detection along symmetric and antisymmetric coordinates is illustrated using the PES of Fig. 10 in these types of reactions. The dynamics of the complex in this case is fundamental to the understanding of the TS of reactions involving more than one degree of freedom, and, as pointed out byA. H. Zewail 219 4 *- I c ca.1000 cm' cu.1800 cm' Fig. 9 Energetics for the reaction of Hg+I,, and excitation of the TS, [I--.Hg-..I]$* (for the ground state surface, see ref. 69). The star indicates an arbitrary excitation where both channels are open Bernstein,26 it is directly connected to the bimolecular case of Hg + 12. In t h e ~ r y , ~ ' one projects the initial wavefunction onto the final product-state wavefunction and obtains expressions for product-state distributions. If, however, the wave-packet motion is described along Q1 and Q2, one considers the structural and vibrational frequency changes on going from the transition-state region to the final products. It is therefore of great interest to attempt probing such motion in this class of reactions in real time, and to relate the observables to the nature of the force field along the reaction coordinate.There are a number of interesting features for this reaction. First, the equivalence of the two bonds makes the PES symmetrical with respect to the I, HgI coordinate and the reaction path is well defined along the antisymmetric coordinate (Fig. 11). Secondly, because of the large change in structure, one expects changes in the vibrational frequen- cies on going from the transition-state region to the final products. The A-B bond in the upper state of ABA corresponds to a vibrationally excited A-B fragment. The bend gives rise to rotations. Thus, the dissociation impulse produces HgI in different vibra- tional/rotational states allowing one to monitor different sets of reaction trajectories.3.1. Observation of the TS and Nascent Fragments The TS was prepared by a laser pulse at A , = 310 nm. This amounts to ca. 12 500 cm-' of energy available for vibration and translation in the HgI+I channel, as discussed by Dantus et aL2' and shown in Fig. 9 and 12. As the HgI and I/I* (or Hg+21) fragments separate, they are probed by a second laser pulse at a different A 2 , e.g. 620 or 390 nm. At short interfra ment distances, the separation between the PE surfaces leading to HgI product in its X C+ and B 'X+ states is smaller than in the asymptotic limit. The 620 nm pulse thus probes early times, and 390 nm the long-time behaviour of the reaction. Bowman et al. and Dantus et ~ 1 . ~ ' studied FTS of the reaction and observed the femtosecond transients of the TS and the nascent fragments. Fig.12 shows transients probed at 390 nm, differing only in the detection wavelength Adet, which probes different (u") levels in the X state of HgI (Fig. 13). They are very dissimilar in characteristics, F220 Femtosecond Transition-state Dynamics Fig. 10 ( a ) The PES and the transition state for the [I-..Hg..-I]S* system. ( b ) A (schematic) cut along the symmetric and antisymmetric coordinates even when detected at nearby wavelengths (e.g. hdet = 427.5 and 432.5 nm). Fig. 12( a) shows rapid oscillations (with a period of 300 fs at longer delay times) observed at Adet = 427.5 nm, corresponding to HgI vibrational motion near the bottom of the anhar- monk potential well, while Fig. 12(6) shows an initial sharp peak followed by slow oscillations (with a period of ca.1 ps), corresponding to highly excited vibrational motion of HgI near the dissociation limit (Fig. 13).A. H. Zewail 22 1 7 5 ? c 3 3 5 7 Fig. 11 The two types of PES [(a) and ( b ) ] used in the theoretical calculations of wave-packet propagation from the TS to free fragments (for the parameters, see ref. 35) Fig. 12 Experimental FTS displaying the transitory behaviour observed in the detection of nascent HgI in different U" states as it evolves from the TS: ( a ) E,,,,, =4900cm-', (u'fig1)=7; (b) EHgl,l = 12 500 cm-', (uL,~) = 29. The total available energy for product vibration and translation was the same (12 500 cm '). The detection method identifies the I and I* channels, and hence the energy available in (a) (the I" channel) is less by 7600 cm-' (see text and ref.28). Note the drastic change in the oscillatory behaviour with time and energy In the I* channel, relatively less energy is available for vibrational and translational excitation, having mostly been taken up by spin-orbit excitation of I atoms. Ground-state HgI(X'Z+) is formed in low vibrational levels, then probed to the B2Z+ state. The resulting levels fluoresce strongly at 427.5 nm, less at 400 nm, and very little at 432.5 or 360nm compared with the I channel. In the I channel, highly vibrationally excited X 'E+ product is formed and probed to a different set of B 'X+ state vibrational levels; these fluoresce strongly at 432.5 and 360 nm, less at 440 nm, and little at 427.5 nm, relative to the I* channel.These fluorescence spectra thus allow a selection of the dynamics to be probed. For TS detection, we kept the total energy constant and changed the probe wavelength to a region where there is no absorption by free fragments (at h2 = 620 nm). The transients are shown in Fig. 14. We observe only two peaks, separated by 200 fs, and a fast damping imaging the ultrafast motion of the packet away from the saddle point toward final products. The transients of the TS and nascent fragments in real time reflect the dynamics quite well. Vibrationally excited HgI is coherently formed in the decay of the complex,222 Femtosecond Transition-state Dynamics 281 27 v’= 24 2 ~ * 2 5 1 0 (I 2 3 4 2 3 4 R I A Fig. 13 The scheme used in the LIF to detect different u” states of nascent product, HgI( u”) and the experiments probe different trajectories of the reaction to various final v” states of HgI, spanning the v” distribution.This is evident in the change of the vibrational period observed for HgI with (v”) = 7 vs. (v”) = 29 in Fig. 12. The periods (at long delay times) are in good agreement with the spectroscopic analysis for stable HgI,29t and the delay of the signal gives the dissociation time, describing the change of the complex from Ro ( t = 0 ) to the distance projected by the window of the probe. The observation of the TS describes the early-time motion in the symmetric-stretch direction, as discussed below. 3.2. Time-dependent Anisotropy and the Geometry of the TS The above results give the temporal picture imaging the vibrational dynamics of the complex and fragment, and the electronic excitation of iodine (spin-orbit states).The bend motion is on a longer timescale, and has important consequences for the alignment. From time-integrated alignment experiments3’ one knows the importance of the anisotropy in understanding the vectorial properties of the dissociation. Alignment in real time provides information on r o t a t i o n ~ , ~ ~ ~ ’ and more recently we have used it to study rotational (torque) dynamics in dissociation reactions.32 Here the experiments probe the relative alignment of the fragment transition moment and the initial alignment of the complex as a function of time. As shown in Fig. 15, the transients observed for the pump and probe in parallel polarization are very different, in their decay and buildup, from that of pump and probe in perpendicular polarization.Yet the vibrational periods observed in both transients are identical. The experiments indicate that while HgI is executing the vibrational motion, the torque on HgI is inducing rotations, and as a function of time the anisotropy changes. From these experiments, one obtains, in a simple description, the (J) produced as a result of the torque, the coherence time and t For other references on the spectroscopy, see ref. 28 and references therein.A. H. Zewail 223 100 -1 fs R,,,,, Fig. 14 (A) Transition-state femtosecond transients, exciting [I. - -Hg--.I]S* at A , = 310 nm and detecting at 620 nm. The transients in ( a ) and ( b ) are the same, but for ( a ) parallel and ( b ) perpendicular polarization.The three transients in each panel are for different detection wavelength (thin line, 440 nm; medium line, 390 nm; and heavy line, 360 nm). Note the ca. 200 fs time spacing between the peaks, independent of polarization and emission detection wavelength. (B) A cut along the translational coordinate, together with the absorption cross-section, showing the idea for detection of the TS and nascent fragments the geometry of the TS. There is a finite time for J to become well defined, and this has been discussed elsewhere.32 The alignment3' is related to rotational angular momenta by32 I ( t ) = C [ 1 + ar( ?)]A( t ) (7) where C and (Y are well defined constants, A(?) is the scalar dissociation temporal function and r(J, t ) is the anisotropy function: r(J, t ) = 0.4 ( P2[cos T-/( t ) ] ) (8) where T-/ is the time-dependent angle between the transition dipole of the pump transition at t = 0 and that of the probe at time t.The theoretical fits in Fig. 15 were obtained when J,,, = 80. The rotational distribution ( A J ) gives rise to the early time decay (and buildup) and defines a coherence time for rotational dephasing, measured to be ca. 1 ps.224 Femtosecond Transition-state Dynamics 2.0 1.6 2 1.2 2 0.8 .C( c1 $ z ._ N .C( - c“ 0.4 0.0 -0.4 -500 0 500 1000 1500 2000 2500 3000 3500 t/fs Fig. 15 The polarization anisotropy in real time. Note the build-up and decay, and persistence of the vibrational oscillation with the same phase in both ‘parallel’ and ‘perpendicular’ FTS experiments. The solid lines are the theoretical curves (see text) The coherence time is longer than the time constant for scalar dynamics (dissociation of the complex). The HgI fragment rotates relatively slowly, wo=O.O1 ps-’.The dip observed in the transient of Fig. 15 reflects the shift of the rotational distribution from J = O , as detailed in Ref. 32. These polarization experiments complement the ‘scalar experiments’ in that r ( t ) has signatures of the rotational and torque dynamics. It is interesting to note that we can now define r $ (complex dissociation time) and rR (rotational), and these are the same quantities used by Herschbach to define direct and complex-mode reactions.33 3.3. TS and the Dynamical Resonance Even without detailed theoretical calculations, the above understanding of the dynamics is intuitive, and is based on simple models for rotational and vibrational excitation, and on Polanyi’s general concepts re arding the position of the TS on the PES.34 The analysis was verified in our earlier work by a two-dimensional classical trajectory calculation, which yielded dissociation times and vibrational distributions in agreement with experi- ment.The quantum simulation of the dynamics allowed a more detailed comparison with the FTS transients, as well as pointing to a number of interesting features of the reaction dynamics and PES, including the early-time motion along the symmetric coordinate. The theory has been detailed for the case of [I.-.Hg...I]S* elsewhere,35 and the approach is that of a wave-packet analysis.36 Gruebele et ~ 1 .~ ~ have studied the wave- packet dynamics, product state distributions, and FTS by performing 2-D wave-packet calculations to compare with experiments. The PES we used is that of a damped Morse oscillator with parameters based on spectroscopic data, photofragmentation, I and I* yield, and some a6 initio calculations made on analogous systems. The explicit form is given in ref. 35. $8A. H. Zewail 225 Wave-packet propagations were done at energies of -1000,1350 and 8950 cm-’ with respect to dissociation to Hg+I+I atoms on two surfaces, labelled ( a ) and (6) in Fig. 11. Fig. 16(A)-(C) show some examples of the dynamics at different excess energies. Fig. 16(A) corresponds to an energy of -1000 cm-’ with respect to the full (Hg+21) dissociation limit on surface (6).The narrow-channel surface confines the dissociating wave packet, which essentially flows along equipotential contours. Fig. 16( B) corre- sponds to an energy of 1350cm-’ on surface ( a ) , and represents the simplest picture of I* channel dissociation. Here there is considerably more motion in the symmetric coordinate, until the expanding wave packet diffuses back into the walls of the HgI potential well at t > 300 fs. At 800 fs, well developed ‘clouds’ of Hg + I*, I* + HgI and I* + Hg+ I have formed. The early-time symmetric stretching behaviour becomes even more dramatic in the case of ca. 8950 cm-’ excitation energy on surface ( b ) , correspond- ing to the simplest picture of I channel dissociation. The wave packet proceeds along the symmetric coordinate before beginning to separate into three sections.Clearly, the most important motions during the initial phase of the dissociation reaction are not required to be along the natural reaction coordinate (path of steepest descent leading to products) in the present case. While at low energies the steepest descent path is good for parametrization of the reaction, at higher energies motion proceeds along it only at very early times (symmetric coordinate) and very long times (along rl). In the asymptotic limit one can obtain approximate vibrational product distributions by taking sections of the wave packet perpendicular to the translational coordinate rl , projecting onto the HgI(X *X+) bound eigenstates, and summing the weighted distribu- tion of all sections at different rl to obtain a translationally averaged vibrational distribution (with all coherent effects averaged out).Generally, the average vibrational quantum number decreases with increasing rl of the sections, as shown in Fig. 17, and discussed in more detail in ref. 35. Vibrational distributions for potentials ( a ) and (6) at the three energies studied were obtained using these calculations. The wider-channel PES generally causes a marked increase in the vibrational excitation. This is to be expected, since it results in wider ranging initial motion along the symmetric coordinate, which is partially transferred into a larger vibrational amplitude. On both surfaces, as the excess energy is increased, the vibrational distribution broadens considerably and moves to higher average v”.In addition to the calculations of product-state distributions (Fig. 10 of ref. 35), several quantities, such as emission spectra (Fig. 11 of ref. 35) of the probed HgI and oscillatory effects in the FTS transients (Fig. 18 here) due to wave packet motion, were obtained. The simplest parameter for comparison with experiment is the reaction time. A long-lived transition state would be reflected in a delay of the experimental transient rise time. In our calculations, the I-channel wave packets reach the asymptotic (>4.5 A) region in ca. 200 fs, while the I*-channel packet requires ca. 350 fs, comparing well with the experimental times for a prompt reaction. Fig. 18 shows FTS transients for the I and I* channels on surface ( b ) , calculated for a probe wavelength of 390nm.The periods for both reaction paths correspond closely to the experimental observations. Two features deserve special mention. Because the calculated transients correspond to detection of all the LIF signal (rather than hdet* 5 nm as in the experiments), and are not convoluted with a ‘monochromator response function’, they show more structure than experimentally observed. It is also notable that even the fairly broad vibrational distribution at 8950 cm-’ on surface (6) yields sharp, well defined FTS maxima with a 1 ps period. The width of the distribution does lead to some irregularities in the period at long times; indeed, some weak features have been observed28 in the experimental transients (Fig.12) which may correspond to this behaviour. Finally, the Fourier-transform spectra of the experimental transients reflect the expected time-integrated spectra. In the transition state, the spectra would be ca.226 Fern tosecond Transition-sta te Dynamics ? I F t f- t i 3 r 3 5 7 3 5 7 L 6 8 10 12 12 1 1 8 6 L L 6 8 10 12 lo 8 I 4 6 8 10 12 G 6 8 10 12 rJA Fig. 16 (A) Snapshots of the wave packet on surface ( b ) at different times; ( a ) = 155, ( b ) = 233, ( c ) = 389 and ( d ) = 467 fs. The total energy is -1000 cm-' with respect to total dissociation (Fig. 9). (B) The dynamics on surface ( a ) at 1350 cm-' with respect to total dissociation, and times ( a ) 160, ( b ) 320, ( c ) 400 fs and ( d ) = 800 fs. ( C ) The dynamics on surface ( b ) at 8950 cm-' with respect to total dissociation, and times ( a ) 58, ( 6 ) 233, ( c ) 400 and ( d ) =6OOfsA.H. Zewail 227 Fig. 17 Slices at three distances along the reaction coordinate rl through the asymptotic region of the packet in Fig. 16(A)(d) at 467 fs lOOcm-' broad, aside from any resonance effect. On the other hand, as the complex evolves to HgI, the Fourier transform indicates a sharp resonance (at 111 cm-') on a broad background. In the ion photodetachment work, N e ~ m a r k ~ ~ has shown characteris- tics of broad and sharp spectra, and related them to the ultrafast dynamics by wave-packet simulations. The 3-D quantum-scattering calculations by Schatz3* elucidate these points. 3.4. Surface Crossings and Initial Alignment The experiments of Hofmann and have determined the cross-section for the 1 and I* channels.These experiments can be discussed in terms of excitation to the I* channel surface followed by partial Landau-Zener crossing at a conical intersection228 Femtosecond Transition-state Dynamics I I - I 300 fs 0 1 2 3 4 5 6 t l PS Fig. 18 FTS transients obtained theoretically from the wavepacket propagation on surface (b) at the corresponding total energies (see text) with the I surface, or in terms of separate excitation to the I and I* surfaces. The I* cross-section reaches a peak at ca. 4300 cm-' higher photolysis energy than the I cross- section. Alignment experiments in the TS region help establish the nature of crossing (or lack of) between the PESs. In Fig. 14 the FTS display a strong polarization effect in the first 400fs.If the two PE surfaces of I and I* channels are non-interacting, then an extinction of the polarization is expected. This is because the I* asymptote correlates with a parallel transition, while the I asymptote with a perpendicular tran~ition.~' On the other hand, if there is a Landau-Zener interaction, then the states are mixed and the polarization anisotropy of the two channels becomes less pronounced, reaching a limiting value when the mixing is very strong. Our results therefore indicate that the two PE surfaces do not cross at the probe region. There may be a crossing at shorter R, but R should be (3.5 %i to insure that the surfaces are free of interaction at the probing region. These results are consistent with the fact that the second peak (at later time) is the one to achieve enhancement in the (11, 11) polarization experiment.The behaviour at different detection wavelengths (Fig. 14) requires knowledge of V, (with also possible crossing), and the 2-D calculation of the absorption in the TS region. These experiments, when completed at different energies and different h 2 , should provide the nature of the coupling between PE surfaces in the short-R region. It should be noted that on this timescale of the TS, the rotation of the complex is negligible, as evidenced by the measured long coherence time, 1 ps, discussed before. 3.5. Summary and Future Studies As discussed above, the uniqueness of this reaction is in showing characteristics of TS dynamics, from a saddle-point region to the asymptotic region (nascent fragment).The early-time transients arise from wave packets moving along the symmetric stretch coordinate (towards total dissociation). At longer times, diffusion into the potential wells sets in, and the vibrational motion of the wave packets gives rise to oscillationsA. H. Zewail 229 of the FTS signal. Classical and quantum calculations produce results that are close to experimental observations. These observations include: vibrational oscillations as the complex gives birth to free fragments in different v” states; TS decay, and motion along the symmetric coordinate; the decay (and buildup) of polarization anisotropy, in real time, as bending motion converges to rotations; and the initial alignment ( t < 400 fs), which reflects the symmetry of and coupling between the PESs.However, the case of this class of reactions is clearly still far from closed. Experiments at different total energies and different h2 would probe the PES at new regions, hopefully for complete characterization, as in the case of alkali halides. The study should also allow us to probe the validity of adiabatic correlation between TS vibrational excitation and coherent formation of vibrational excitation in the product. Characterization of the resonance in the symmetric stretch at different E would be of great interest. Careful alignment studies at several energies should pinpoint the location of surface crossings and the role of the bending vibration in the reaction, starting at different points within the TS region.Product-state distributions will yield valuable information and allow us to compare the coherent dynamical v” distribution at early times with the distribution for t --* 00. In parallel, ab initio surfaces would be very desirable as a basis for further quantum and classical dynamics studies and more quantitative comparisons between theory and experiments. In particular, three-dimensional calculations, including the bending motion, will then become useful in comparing with the longer-time behaviour of the FTS signal. Recently, two types of studies have been initiated. On the experimental side, Janssen et aL4* have studied the same system (IHgI), but at hl = 335 and 275 nm. Both the TS and the fragments were detected. The observed oscillations at these energies show some interesting new features, and when these experiments are completed we may learn about the question of adiabatic correlation.Theoretically’F there is hope for obtaining the calculation of the PES. When available for the IHgI system, we will study the wave- packet dynamics to compare with experiments. Other related systems in the ABA family of reactions are also under experimental investigation. 4. How Can a Broad-energy Pulse Probe a Sharp Resonance? With femtosecond pulses, one immediately thinks of the time resolution dictated by the ultrashort duration. However, according to the uncertainty principle, the pulse will have a broad-energy spectrum, and one might think that if the energy width is much broader than vibrational energy spacings of a resonance (e.g.the symmetric-stretch direction of the PES in section 3), then all the spectroscopic information will be lost. This is not true, provided one can exploit the coherence in the preparation of the complex, as has been observed in the context of vibrational and rotational dynamics of isolated molecules.2 Consider a one-dimensional system that can be treated rigorously by classical and quantum mechanics. If a femtosecond laser pulse excites a diatomic molecule, such as 12, to the bound region of an excited electronic state, a superposition of vibrational states is formed and then propagates back and forth in the bound well as a wave packet. Probing with a second laser pulse at successive time delays At should reveal the vibrational and rotational motion; this is possible because the bandwidth of the pump laser is larger than the separation of energy levels.Thus the uncertainty principle works t Progress in this direction has been made for systems of interest (CH,I,42a ICN,42b Na142C etc.) by Morokuma’s group. For HgI, , Rosmus’ group in Frankfurt (personal communication) is initiating studies of the PES.230 Femtosecond Transition-state Dynamics I Rotational I * , 1 1 , 20 600 640 delay time/ps 2 3 G 5 6 bond distance/ A Fig. 19 Experimental FTS results on iodine, showing the transients for both the vibrational and rotational motions ( a ) . In ( b ) the potential inverted from the FTS data together with that from high-resolution data are compared in our favour, because the short pulse’s finite energy width allows for this coherent superposition! The wave packet moves in and out of resonance with the probe laser absorption window located at a particular internuclear separation.The measured intensity I ( A t , A ) images the motion and gives the eigenstate frequencies of which the wave packet is composed. Fourier transformation of the intensity I ( A t , A ) gives spectro- scopic data about the bound vibrational states, recovering all the information that one might have thought was lost owing to the broad energy bandwidth of the ultrashort pulses. If polarized femtosecond pulses are used, the molecules can be aligned, and that alignment can be probed as the molecules rotate in real time, as discussed above for other systems2 The initial alignment decays as the rotational motion of molecules in different angular momentum states dephase, but at longer times the molecules rephase at a time determined precisely by the fundamental rotational period.Such observations of vibrational and rotational motions have been made for molecular iodine in various excited states by Dantus et al. and Bowman et aZ.43 From these results (Fig. 19) direct inversion to the potential-energy curve governing the 1-1 vibration has been obtained by Gruebele et al.,44 Bernstein et al.,45 and Janssen et al.46 The FTS results are in excellent agreement with results from high-resolution techniques. This approach demonstrates two points. First, even though the light pulses are very short and energy resolution is therefore poor, coherent superposition can recover the spectroscopic information, as observed in NaI, I2 and even in such large molecules asA.H. Zewail 23 1 50 r I 1 290 300 310 A/nm Fig. 20 Recent experimental FTS results on Biz with A, = 308 nm and A2 = 298.9 nm. (a)-(c) A schematic of the potentials (a), and the spectral and temporal evolution of atomic Bi resonance [(b)-(d)]; (6) shows the LIF signal taken when the delay time is t < 250 fs, while ( c ) is at t > 1 ps. Note the absence of one of the sharp lines in ( 6 ) and its appearance in ( c ) as time increases. (The broad bands are the pump and probe spectra on the same scale.) ( d ) The temporal evolution as [Bi...Bi]S* (top) dissociates to Bi+Bi (bottom). Because Bi2 is heavier than, e.g. ICN, the Bi fragment takes a long time to appear, ca.1 ps. The results are in agreement with recent quantum and classical calculations, and show the characteristic behaviour for dissociation on a repulsive PES (ref. 2 and 7), but with a long dissociation time [ref. 8(6)] anthracene.* Secondly because of the different time scales (and polarization effects) involved in vibrational and rotational motions, the temporal data separate the two, and this separation simplifies the analysis considerably; in these femtosecond experiments, we used only six measurements to obtain the potential shown in Fig. 19. Finally, in simple bound systems, the equivalence of energy- and time-resolved techniques is clear. The situation is different for transition states, however, owing to their ultrashort lifetimes and broad background spectra.It is therefore evident that resonance effects in the TS dynamics can be detected using ultrashort pulses. 5. Other Studies and Future Directions Since the early development of this field, a number of reactions have been studied. In ref. 2 the progress made was recently reviewed. The concepts and methodology have been illustrated with examples drawn on increasingly complex potential-energy surfaces, from bound diatomics, to 1-D direct reactions, to reactions involving potentials with avoided crossings, to 2-D half-collision reactions and finally to a special class of bimolecular reactions: (i) bound systems: I2 ,"3-45 ICl;46 (ii) 1-D repulsive systems: 12,43 ICN7 and Bi; (Fig. 20); (iii) systems with avoided crossing: NaI and NaBr;69'5-17 (iv)232 Femtosecond Transition-state Dynamics 2-D (or more) systems: HgI?8935 and CH31;47948 (v) a special class of bimolecular species: IH.C02 .49 The IBM group has provided experimental and theoretical studies of time-resolved absorption, on the sub-picosecond timescale, which illustrate the direct dissociation dynamics in Bi2 and Tl I.8a950 In Freiburg, the femtosecond dynamics of autoionization has been demonstrated on Na2.5’ On the theory side, a large number of contributions have been made, and ref. 2 gives a recent review of the work done by many groups. There are other directions that promise to be important. Experimentally, the use of multiphoton probing or excitation should allow one to reach different PE surfaces (see ref. 48, 51 and 52). Very recently, using molecular beam mass-spectrometry, M.Janssen and M. Dantus (this laboratory) have observed the femtosecond predissociation dynamics of molecules in Rydberg states (ca. 8-9 eV energy), using a total of two UV photons and one red. This study48 extends FTS to a new direction for probing the dynamics of highly excited molecules, and so far CH31, CD31, (CH3)3CI and I2 have been studied in molecular beams. With the use of depletion and stimulated emission techniques, one should be able to reach ground state PESs. Double-resonance methods in the preparation may help in reaching a well defined and different initial state. To date, LIF? ionization2 and mass-spe~trometric~~~~~~~ detection techniques have all been employed. The use of Raman and IR techniques is another advance that would complement these techniques.To obtain direct structural information on the fem- tosecond timescale, it is proposed to extend FTS by ‘replacing’ the probe optical pulse with an electron pulse so that femtosecond transition-state diffraction (FTD) can be obtained. The trajectories R ( t ) will then per se be observed for all atoms. The technique promises to be general for recording elementary and complex reactions and for studying molecular rearrangements. Such an FTD ‘machine’ is currently under construction at Caltech to cover the PS to FS time domains. Extension of this concept to X-rays may also be possible in the future. There are a number of systems, small and large, to be studied using these tech- niques, and in the coming years we anticipate extensions to new areas: reactions on surfaces; large organics, and ionic systems; other van der Waals impacted bimolecular reactions (and even ‘honest’ bimolecular reactions).The class of bimolecular reactions light-heavy-heavy versus heavy-light-heavy (HXeY andX-. .H-Y, where X and Y are atoms and diatoms, e.g. halogens) are of particular interest to us. We hope to be able to observe the oscillatory motion of the activated complex (Fig. 21), similar to the case of alkali halides and Hg12, but now on the ground-state PES of a bimolecular reaction. One significant advance here is the ability to study the bimolecular collision for systems like HBr.12, where the light H atom is ca. 20 A away from the force field of the reactants within 100 fs. These studies will be made using state-of-the-art femtosecond pulses and molecular beams.The same apparatus is currently used to resolve the femtosecond dynamics of the XH.C02 system (see ref. 49 for discussion), which so far has been studied in the ps regime. Studies of the inelastic scattering would also be of great interest. Control of wave-packet motion may be at the moment an academic curiosity; however, it is of great interest. In the iodine experiments by Gerdy et al.53 the control of the packet in the preparation process was made using two pulses of well defined relative phases. This sequence of pulses changes the amplitudes and hence the apparent simple oscillatory behaviour observed earlier using conventional FTS on I2 .43 Wave- packet theory54 is in agreement with experiments.Femtosecond phase controlled pulses by Scherer et al.55 have been demonstrated on 12, also in the gas phase, and wave-packet theory is in accord with experiments. Weiner et al.56 have reported on phase-controlled impulses in crystals, and M ~ k a m e l ~ ~ has discussed the theory under these conditions. The iodine experiments indicate that both the amplitude and phase of the motion are controllable. In this area, theory57 has been very enlightening and different proposals have been introduced by Brumer and Shapiro, Tannor and Rice, Rabitz, Manz and others.A. H. Zewail 233 ? LN Fig. 21 Femtosecond dynamics of a bimolecular reaction: Br + I2 + IBr + I. The calculations were made by M. Gruebele (this laboratory) and they demonstrate the oscillatory motion of the complex [Br.-.I-.-I].$ In real time, analogy with the results of Fig.2 should be made. The lifetime of the complex resonance in this case is ca. 6 ps at the translational energy of interest for this potential Fig. 22 The idea of TS spectroscopy of H/D2 system, courtesy of John Polanyi’s group (ref. 70); the ‘inverse case’ of IHgI (see text)234 Femtosecond Transition-state Dynamics The experiments, although shown to be d i f f i c ~ l t , ~ ~ are important for a number of theoretical and experimental reasons. We hope to be able to carry out such experiments (F+H, and H+ D2) now with FTS (Fig. 22) when the required sensitivity and temporal resolution are attained. The experiments will be similar to the HI:C02 but with ca. 6 fs time resolution.We will compare the results with those made by photodetachment in real-time by using FTS and invoking Neumark’s idea of going from the anion to the TS. Much remains to be studied in femtosecond transition-state dynamics and the femtochemistry of reactions. Have the experiments reached the so-called ‘chemistry timescale’? In 6 fs, the nuclear motions are indeed those which characterize chemical reactions and molecular dynamics.2 For reactions, this time corresponds, typically, to a motion of ca. 0.1 A, and it is shorter than any TS lifetime (deduced by classical and quantum calculations).2 The 6 fs duration represents the state of the art in laser pulse generation achieved by Shank and colleague^.^^ The energy uncertainty AE, although not a problem for the preparation even in bound systems (see section 4), should be compared with bond energies; AE is 0.7 kcal mol-’ for a 60 fs pulse and 7 kcal mol-’ for a 6 fs pulse.? So does it help to shorten the pulse further? One may say not, only because the energy uncertainty of sub-femtosecond pulses (attosecond regime) is very large (100 as = 420 kcal mol-*) compared to bond energies, as pointed out by Porter6’.$ As illustrated here (section 4), despite the broadening, the pulse can still be used for coherent preparation, and this ‘avoids’ the issue of the uncertainty principle.While sub-femtosecond pulses’ resolution may be considered outside the ‘limit of chemistry’,61 they may prove useful for electron motion and valency. For example, based on Pauling’s4 simple description of the bonding in HZ, the electron will hop between the two nuclei in a time of 2 fs (about an order of magnitude longer than the orbital motion about the nucleus of the electron in the hydrogen atom) because of the 50 kcal mol-’ resonance energy.The localization length of the initial packet must be on the atomic or molecular scale, still orders of magnitude larger than the scale of femtophysics (1 fm).62 Perhaps attosecond pulses would allow us to see such the process of electron valency (in H l , benzene structures etc.) in real time, just as femtosecond pulses make it possible to expose63 the (nuclear) dynamics of the chemical bond. This research was supported by the Air Force Office of Scientific Research and by the National Science Foundation. It is with pleasure that I thank members of my group for all their help and discussions during the writing of the manuscript.I would particularly like to thank Gareth Roberts for his help and thorough reading of the manuscript. I also thank Peijun Cong, Martin Gruebele, Bob Bowman and Jim Gerdy for all their efforts. In discussing the current work on bimolecular reactions with Prof. John Polanyi during a recent visit to Caltech, he suggested the extension of the studies to include inelastic scattering of the products; we hope to be able to study both the reactive and inelastic collisions. Finally, I thank Professor John Simons for his patience and kindness; E-mail did help in getting the manuscript over the barrier (transition-state) to overseas! Finally, the TS spectroscopy of the H + D2 system was pioneered by Polanyi’s Dedication Richard B.Bernstein, a dear friend and colleague, was scheduled to give the Spiers Memorial Lecture of this Discussion. Dick was planning to talk about the dynamics of t 1 cal = 4.184 J. $ Ref. 60 indicates that a 1 fs pulse has a broadening of 400 k J mol-‘ ( = 95.6 kcal mol-‘), simply by using ArAv = 1. In our calculation, we use experimental transform-limited pulses, and for gaussian pulses this relationship is actually AtAv = 0.441. Thus, 1 fs = 42 kcal mol-’ or 176 W mol-’. For sech2-pulses, AtAv = 0.315.A. H. Zewail 235 bimolecular reactions in real time, mentioned in the text, for work completed during two sabbatical leaves at Caltech. This article is dedicated to the memory of Dick; his friendship, excitement about femtochemistry, and the joy he brought in discussing science will never be forgotten.References 1 H. Eyring, J. Chem. Phys., 1935,3, 107; M. G. Evans and M. Polanyi, Trans. Faraday Soc., 1935,31, 875; for recent reviews see D. G. Truhlar, W. L. Hase and J. T. Hynes, J. Phys. Chem., 1983 87, 2664 and K. J. Laidler and M. C. King, J. Phys. Chem., 1983, 87, 2657. 2 For recent reviews see L. R. Khundkar and A. H. Zewail, Ann. Rev. Phys. Chem., 1990, 41, 15; A. H. Zewail and R. B. Bernstein, Chem. Eng. News, 1988 66, 24; A. H. Zewail, Science, 1988 242, 1645. 3 R. S. Berry, in Alkali Halide Vapors, ed. P. Davidovits and D. L. McFadden, Academic Press, New York, 1979 and references therein. 4 L. Pauling, The Nature ofthe Chemical Bond, Cornell University Press, Ithaca, NY, 3rd edn., 1960.5 P. W. Atkins, Physical Chemistry, Oxford University Press, Oxford, 4th edn., p. 856. 6 T. S. Rose, M. J. Rosker and A. H. Zewail, J. Chem. Phys., 1988, 88, 6672; M. J. Rosker, T. S. Rose and A. H. Zewail, Chem. Phys. Lett., 1988,146, 175; T. S. Rose, M. J. Rosker and A. H. Zewail, J. Chem. Phys., 1989, 91, 7415. 7 M. Dantus, M. J. Rosker and A. H. Zewail, J. Chem. Phys., 1987, 87, 2395; M. J. Rosker, M. Dantus and A. H. Zewail, J. Chem. Phys., 1988,89,6113; M. Dantus, M. J. Rosker and A. H. Zewail, J. Chem. Phys., 1988, 89, 6128; G. Roberts and A. H. Zewail, J. Phys. Chem., 1991, 95, 7973. 8 ( a ) J. H. Glownia, J. A. Misewich and P. P. Sorokin, J. Chem. Phys., 1990,92, 2335; J. A. Misewich, J. H. Glownia, R.E. Walkup and P. P. Sorokin, in Ultrafast Phenomena VZZ, Springer Series in Chemical Physics, vol. 53, ed., C. B. Harris, E. P. Ippen, G. A. Mourou and A. H. Zewail, Springer-Verlag, New York, 1990, p. 426; ( b ) R. M. Bowman, J. J. Gerdy, G. Roberts and A. H. Zewail, J. Phys. Chem., 1991, 95, 4635. 9 R. B. Bernstein and A. H. Zewail, J. Chem. Phys., 1989, 90, 829. 10 M. J. Rosker, M. Dantus and A. H. Zewail, Science, 1988, 241, 1200. 11 R. Bersohn and A. H. Zewail, Ber. Bunsenges. Phys. Chem., 1988, 92, 373. 12 R. D. Bower, P. Chevrier, P. Das, H. J. Foth, J. C. Polanyi, M. G. Prisant and J. P. Visticot, J. Chem. Phys., 1988, 89, 4478. 13 H. Bluhm, J. Lindner and E. Tiemann, J. Chem. Phys., 1990, 93, 4556; S. H. Schaefer, D. Bender and E. Tiemann, Chem.Phys., 1984,89, 65; Chem. Phys. Lett., 1982, 92, 273. 14 R. Grice and D. R. Herschbach, Mol. Phys., 1974,27,159; see also S. A. Adelman and D. R. Herschbach, Mol. Phys., 1977, 33, 793. 15 P. Cong, A. Mokhtari and A. H. Zewail, Chem. Phys. Lett., 1990, 172, 109. 16 J. A. Beswick and J. Jortner, Chem. Phys. Lett., 1990, 168, 246. 17 A. Mokhtari, P. Cong, J. L. Herek and A. H. Zewail, Nuture (London), 1990, 348, 225. 18 W. H. Knox, R. S. Knox, J. F. Hoose and R. N. Zare, Opt. Photonics News, 1990, April. 44. 19 S.-Y. Lee, W. T. Pollard and R. A. Mathies, J. Chem. Phys., 1989, 90, 6146. 20 R. A. Marcus, Chem. Phys. Lett., 1988, 152, 8. 21 S. H. Lin and B. Fain, Chem. Phys. Lett., 1989 155, 216; S. H. Lin, B. Fain and C. Y. Yeh, Phys. Rev. A, 1990, 41, 2718; S. H. Lin, B.Fain and N. Hamer, Adu. Chem. Phys., 1990, 79, 133. 22 V. Engel and H. Metiu, Chem. Phys. Lett., 1989 155,77; J. Chem. Phys., 1989,90,6116; J. Chem. Phys., 1989, 91, 1596; V. Engel, M. Metiu, R. Almeida, R. A. Marcus and A. H. Zewail, Chem. Phys. Lett., 1988, 152, 1. 23 S. E. Choi and J. C. Light, J. Chem. Phys., 1989, 90, 2593. 24 S. Chapman and M. S. Child, J. Phys. Chem. 1991, 95, 578. 25 H. Kono and Y. Fujimura, Chem. Phys. Lett., 1991, 184, 497. 26 R. B. Bernstein, in Proc. The Robert A . Welch Conference on Chemical Research, XXXZZ Valency, Texas, 1988, p. 221. 27 G. G. Balint-Kurti and M. Shapiro, in Photodissociation and Photoionization, ed. K. P. Lawley, Wiley, New York, 1985, p. 403; K. F. Freed and Y. B. Band, in Excited States, ed. E. C. Lim, Academic Press, New York, 1978, vol.3, p. 109; K. C. Kulander and E. J. Heller, J. Chem. Phys., 1978, 69, 2439; J. P. Simons and P. W. Tasker, Mol. Phys., 1973,26, 1267; 1974,27, 1691; R. T. Pack, J. Chem. Phys., 1976, 65, 4765; R. Schinke, J. Phys. Chem., 1988, 92, 3195 and references therein; R. D. Coalson and M. Karplus, J. Chem. Phys., 1990, 93, 3919; J. Jiang and J. S. Hutchinson, J. Chem. Phys., 1987, 87, 6973; R. Marquardt and M. Quack, J. Chem. Phys., 1989, 90, 6320. 28 R. M. Bowman, M. Dantus and A. H. Zewail, Chem. Phys. Lett., 1989, 156, 131; M. Dantus, R. M. Bowman, M. Gruebele and A. H. Zewail, J. Chem. Phys. 1989,91, 7437.236 Femtosecond Transition-state Dynamics 29 N.-H. Cheung and T. A. Cool, J. Quant. Spectrosc. Radiat. Transfer, 1979,21, 397; J.A. McGarvey Jr., N.-H. Cheung, A. C. Erlandson and T. A. Cool, J. Chem. Phys., 1981, 74, 5133. 30 C. H. Greene and R. N. Zare, Ann. Rev. Phys. Chem., 1982,33, 119; G. E. Hall and P. Houston, Ann. Reu. Phys. Chem., 1989,40,375; R. B. Bernstein, D. R. Herschbach and R. D. Levine, J. Phys. Chem., 1987, 91, 5365; J. P. Simons, J. Phys. Chem., 1987, 91, 5378. 31 P. M. Felker and A. H. Zewail, J. Chem. Phys., 1987, 80, 2460. 32 A. H. Zewail, J. Chem. SOC., Faraday Trans. 2, 1989,85, 1221; M. Dantus, R. M. Bowman, J. S. Baskin 33 D. R. Herschbach, Faraday Discuss. Chem. SOC., 1973, 55, 233; D. R. Herschbach, Angew. Chem., Int. 34 J. C . Polanyi, Science, 1987, 236, 680. 35 M. Gruebele, G. Roberts and A. H. Zewail, Philos. Trans. R. SOC. London, Ser. A , 1990, 332, 223.36 E. J. Heller, Acc. Chem. Res., 1981, 14, 368; S. 0. Williams and D. G. imre, J. Phys. Chem., 1988,92, 6636; 6648; V. Engel and H. Metiu, J. Chem. Phys., 1990, 92, 2317; H. Metiu and V. Engel, J. Chem. Phys., 1990, 93, 5693. 37 A. Weaver and D. M. Neumark, Faraday Discuss. Chem. SOC., 1991, 91, 5 and references therein; see also D. M. Neumark, Adu. Chem. Phys., in the press; S. E. Bradforth, A. Weaver, D. W. Arnold, R. B. Metz and D. M. Neumark, J. Chem. Phys., 92, 1990, 7205. and A. H. Zewail, Chem. Phys. Lett., 1989, 159, 406. Ed. Engl., 1987, 26, 1221. 38 G. C. Schatz, J. Phys. Chem., 1990,94, 6157. 39 H. Hofmann and S. R. Leone, J. Chem. Phys., 1978,69, 3819. 40 See e.g., M. Kawasaki, S. J. Lee and R. Bersohn, J. Chem. Phys., 1979,71, 1235, and references therein. 41 M.H. M. Janssen and M. Dantus, unpublished work from this laboratory. 42 ( a ) S. Yabushita and K. Morokuma, Chem. Phys, Lett., 1988, 153, 517; ( b ) Chem. Phys. Lett., 1990 43 R. M. Bowman, M. Dantus and A. H. Zewail, Chem. Phys. Lett., 1989, 161, 297; M. Dantus, R. M. 44 M. Gruebele, G. Roberts, M. Dantus, R. M. Bowman and A. H. Zewail, Chem. Phys. Lett., 1990, 166, 45 R. B. Bernstein and A. H. Zewail, Chem. Phys. Lett., 1990, 170, 321. 46 M. H. M. Janssen, R. M. Bowman and A. H. Zewail, Chem. Phys. Lett., 1990,172,99; M. H. M. Janssen 47 L. R. Khundkar and A. H. Zewail, Chem. Phys. Lett., 1987, 142, 426. 48 M. Dantus, M. H. M. Janssen and A. H. Zewail, Chem. Phys. Lett., 1991, 181, 281. 49 N. F. Scherer, L. R. Khundkar, R. B. Bernstein and A. H. Zewail, J. Chem. Phys., 1987,87, 1451; N. F. Scherer, C. Sipes, R. B. Bernstein and A. H. Zewail, J. Chem. Phys., 1990,92, 5239. 50 R. E. Walkup, J. A. Misewich, J. H. Glownia and P. P. Sorokin, Phys. Reu. Lett., 1990, 65, 2366 and references therein. 51 T. Baumert, B. Buhler, R. Thalweiser and G. Gerber, Phys. Rev. Lett., 1990,64,733; G. Gerber, Faraday Discuss. Chem. SOC., 1991, 91, 358. 52 R. M. Bowman, M. Dantus and A. H. Zewail, Chem. Phys. Lett., 1990, 174, 546. 53 J. J. Gerdy, M. Dantus, R. M. Bowman and A. H. Zewail, Chem. Phys. Lett., 1990, 171, 1. 54 B. Hartke, Chem. Phys. Lett., 1990, 175, 322. 55 N. F. Scherer, A. J. Ruggiero, M. Du, and G. R. Fleming, J. Chem. Phys., 1990, 93, 856; N. Scherer, R. Carlson, A. Matro, M. Du, A. Ruggiero, V. Romero-Rochin, J. Cina, G. Fleming and S. Rice, to be published. 56 A. M. Weiner, D. E. Leaird, G. P. Wiederrecht and K. A. Nelson, Science, 1990,247,1317; S. Mukamel and Y.-J. Yan, J. Phys. Chem., 1991, 95, 1015. 57 P. Brumer and M. Shapiro, Acc. Chern. Res., 1989, 22, 407; D. J. Tannor and S. A. Rice, J. Chem. Phys., 1985, 83, 5013; H. Rabitz, in Atomic and Molecular Processes with Short Intense Laser Pulses, ed. A. Bandrank, Plenum Press, New York, 1988; B. Hartke, J. Manz and J. Mathis, Chem. Phys. Lett., 1989, 139, 123; B. Hartke, E. Kolba, J. Manz and H. H. R. Schor, Ber. Bunsenges. Phys. Chem., 1990, 94, 1312 and references therein. 58 B. A. Collins, J. C. Polanyi, M. A. Smith, A. Stolow and A. W. Tarr, Phys. Rev. Letr., 1987, 59, 2551; 1988, 60, 383; 1989, 63, 2160; 1990, 64, 238; see also H. R. Mayne, R. A. Poirier and J. C. Polanyi, J. Chem. Phys., 1984, 80,4025. 175, 518; (c) Faraday Discuss. Chem. SOC., 1991, 91, 47. Bowman and A. H. Zewail, Nature (London), 1990,343, 737. 459. and A. H. Zewail, to be published. 59 C. V. Shank, Science, 1986, 233, 1276 and references therein. 60 G. Porter, in Plcosecond Chemistry and Biology, ed. T. A. M. Doust and M. A. West, Science Reviews, 61 P. C. Jordan, Chemical Kinetics and Transport, Plenum Press, New York, 1979, p. 82. 62 M. G. Bowler, Femtophysics, Pergamon Press, Oxford, 1990. 63 I. W. M. Smith, Nature (London), 1990, 343, 691. 64 G. A. L. Delvigne and J. Los, Physica, 1973, 67, 166; G. A. L. Delvigne and J. Los, Physica, 1972, 59, 65 N. J. A. van Veen, M. S. de Vries, J. D. Sokol, T. Baller and A. E. de Vries, Chem. Phys., 1981, Northwood, UK. 61; A. M. C. Moutinho, J. A. Aten and J. Los, Physica, 1971, 53, 471. 56, 81.A. H. Zewail 237 66 J. Wang, A. J. Blake, D. G. McCoy and L. Torop, Chem. Phys. Lett., 1990, 175, 225. 67 M. B. Faist and R. D. Levine, J. Chem. Phys., 1976,64, 2953. 68 Work to be published from this laboratory. 69 R. B. Bernstein, Chemical Dynamics via Molecular Beam and Laser Techniques Oxford University Press, 70 The graphics are taken from P. J. Andrews, Mosaic, 1989, 20 ( 2 ) , 36. Oxford, 1982. Paper 1/00399B; Received 29th January, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100207

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年代:1991

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Faraday Discuss. Chem. SOC., 1991, 91, 239-247 Non-adiabatic Reactive Routes and the Applicability of Multiconfiguration Time-dependent Self-consistent Field Approximations Ronnie Kosloff" and Audrey Dell Hammerich Department of Physical Chemistry and The Fritz Haber Research Center for Molecular Dynamics, The Hebrew University of Jerusalem, Jerusalem 91 904, Israel A time-dependent non-adiabatic formulation is considered for chemical reactions. Basic algorithms are presented for the photodissociation of CH31 under the influence of strong short laser pulses. Detailed insight into the dynamics of this process is demonstrated. A time-dependent self-consistent field approach is suggested when many degrees of freedom have to be considered simultaneously. The derivation is based on a Liouville space description for which quantum and classical mechanics are treated on equal grounds.A multiconfiguration approach is formulated for explicitly includ- ing correlation due to splitting of the probability density and for non- adiabatic motion. 1. Introduction It is apparent that the naive adiabatic picture of a chemical reaction proceeding on only one Born-Oppenheimer potential-energy surface is an oversimplification. The nature of a chemical reaction, in which large changes in the electronic configuration occur within small distances, leads to a non-adiabatic formulation. Photochemical reactions commonly involve more than one potential-energy surface. A typical example is the photoisomerization of rhodopsin, for which at least three potential surfaces can be identified.' A similar phenomenon arises in the interaction of molecules with metal surfaces.For the dissociation of nitrogen on catalytic surfaces, an important step in ammonia synthesis, at least two stable chemical species have been found to participate in the reactiom2 Also for the dissociation of oxygen on silver the different electronic species 02, 0, and 0- have been ide~~tified.~ The adiabatic picture fails completely for hyperthermal surface ionization processes in which a continuum of electronic states has to be considered, owing to the proximity of the ionization process to the s ~ r f a c e . ~ In this paper a strategy is proposed based on a time-dependent quantum-dynamical framework in which the molecular dynamics are studied. The traditional approach to this problem starts with the work of Landau and Zener.' Their approach preserves the Born-Oppenheimer potential-energy picture and corrects for isolated breakdown of the approximation.This is basically a one-dimensional scheme, suitable for isolated curve- crossing events. An extensive review of this approach and related developments can be found in the work of Nikitim6 The one-dimensional model for non-adiabatic processes, however, is not adequate for multidimensional cases. In particular, the LZ approximation fails when the motion is parallel to the crossing seam between the electronic surfaces. For large-scale realistic simulations, practical procedures have to be developed to overcome the above difficulty. The semiclassical method of Tully and Preston' is such a procedure.Basically it is a classical trajectory method which includes surface hopping calculated by the LZ formula or by some other improved non-adiabatic method. Its main disadvantage is that phase coherence is lost on each crossing event. Full quantum- mechanical calculations of multidimensional non-adiabatic scattering events have been 239240 Non-adiabatic Reactive Routes performed, as in the work of Baer on the HT system and the H l + H2 reaction.' The problem becomes far more complicated when the dimensionality increases further, as is found in full 3D calculations or for chemical reactions in a solvent or on a surface for which infinitely many degrees of freedom participate. In the next sections a procedure based on a time-dependent quantum-mechanical approach is presented.Section 2 presents the basic procedures of a non-adiabatic process by the example of the photodissociation of CH31. Section 3 summarizes the time- dependent self-consistent field (TDSCF) approximation which is the main tool used to reduce the dimensionality of the problem. Section 4 considers correlated motion by a multiconfiguration approach in Liouville space. 2. Time-dependent Quantum-mechanical Approach It is best to review the basic time-dependent methods through a specific example. The photodissociation of CHJ will serve this purpose. It is a system well studied both experimentally and theoretically.' In this process two electronically different iodine atoms are produced. This means that the photodissociation proceeds on at least three electronic surfaces.The time-dependent Schrodinger equation of the system has the form: where t,bulv is the projection of the w$vefunction onto the upper surfaces. +, isjhe Rrojeztion onto the ground surface. Hi is the upper/lower surf%ce Hamiltonian: Hi = T, + V, where T, = P2/2p the kiTetic energy operator and V, is the upper/lower potential-energy surface. V,, and Vvg are the interaction potentials: Vig = -pi,E( t ) , where pig is the dipole operator to each syrface, and E ( t ) represents the amplitude of a semiclassical electromagnetic field. The Vu, term represents the non-adiabatic coupling between the two upper surfaces. It is customary to treat the system within a limited dimensionality configuration space, including the dissociative I -CH3 coordinate and the umbrella CH3 vibrational motion.The time-dependent approach solves the dynamics, including the radiative coupling, starting at t = 0 with the system in the ground state of the lower electronic surface." The calculation is discretized on a spatial grid with evenly distributed sampling points. Each electronic surface has its own grid. It should be noted that the electromagnetic field is included directly in a time-dependent Hamiltonian operator allowing the simula- tion of strong field effects and pulse shaping." The kinetic energy term in the Hamiltonian is calculated by transforming to momentum space by the fast Fourier transform (FFT) algorithm, multiplying by ( k 2 / 2 ) p and then back-transforming by an inverse FFT to configuration space.Using this method the Hamiltonian is represented with very high accuracy owing to exponential convergence with respect to grid spacing. The computa- tional effort scales as N log N, where N is the total number of grid points needed to represent the problem." The initial ground-state wavefunction is foynd by propagating the Schrodinger equation in imaginary time with the Hamiltonian H, until the ground state is ~onverged.'~ The dynamics of the dissociation are obtained by solving eqn. (2.1) subject to the initial conditions. Because the Hamiltonian is time dependent, the total propagation time is divided into small segments Af in which the variation of the Hamiltonian is small. A short-time propagator is used to advance + one interval of time.+ ( t + A t ) =eo+(t) (2.2)R. Koslofl and A. D. Hammerich where the operator d is obtained from the Magnus series: 241 t+At s H ( s ) d s - l I t 2h2 t [ I ; l ( s ) , I j ( s ’ ) ] d s d s ’ + . . . The propagator e0 in eqn. ( 2 . 2 ) is expanded as a polynomial allowing a recursive algorithm. It has been found14 that an optimal way to represent this polynomial is by the Newton interpolation formula: e 0 = a,i + a, ( O - z o i ) + a,( O - z& d - z , i > + - * where zi are sampling points located within the energy spectrum of the operator 6 and ai are the divided difference coefficients. For example a, =f( z,) = ezo, a , = (ezl - e’o)/(z, - zo). The sampling points zi are optimized so that there will be a mjnimum residuum from the approximation with respect to the operator function f(0).The familiar Chebyshev expan~ion’~ can be obtained by choosing the sampling points z, as zzros of the Chebyshev polynomial of degree M + 1 which spans the energy range of 0. This time propagation method has been shown to have accuracy matching the convergence characteristics of the Hamiltonian representation. l4 A typical encounter of the photodissociation of CHJ induced by a short pulse of 10 fs is displayed in Fig. 1. The field intensity is 1 x 1014 W cm-*, leading to 85% excitation. The three panels exhibit the wavefunction density on the ground, radiatively coupled and non-adiabatically coupled surfaces with irradiation by a 10 fs resonant Gaussian pulse. The x axis is the dissociative coordinate and the y axis the CH3 umbrella vibration.Stimulated emission is evidenced by the loss of symmetry and structure apparent in the ground-state wavefunction. The dynamics are highly non-linear as the 17 7~ pulse employed cycles density many times between the two strongly coupled electronic surfaces. The non-adiabatic coupling is also strong resulting in a branching ratio of 3/1 between the two exit channels. The product in the I channel resulting from the curve crossing is vibrationally hotter than that in the I* channel, attributing to the greater width along the y axis (umbrella motion) in the uppermost panel of the figure. A more detailed examination of the dynamics reveals that the non-adiabatic coupling cycles density between the coupled surfaces even far into the dissociative channel.The richness of the photodissociation dynamics can be better illuminated by compar- ing the diabatic potential-energy surfaces with their ‘adiabatic’ counterparts formed by diagonalizing the potential matrix which includes the off-diagonal radiative and non-adiabatic coupling terms. As these potentials include the field they are time depen- dent. Fig. 2 shows the minimum-energy path (reaction coordinate) along the diabatic curves and their ‘adiabatic’ analogues, the latter at 30fs, the peak field intensity. The upper field dressed potential exhibits a shallow well capable of supporting a metastable state that can undergo several cycles of absorption and emission. The lowering of the ground-state potential and raising of the excited-state potential (for instance around 8 a.u.) implies that the energy gap between the two surfaces is closer to the laser central frequency over a long distance, offering an efficient mechanism for the transfer of amplitude between the two surfaces.Recent calculations by Morokuma and co-workers’6 have shown that the validity of the limited dimensionality calculation is questionable due to breaking of the C,, sym- metry. As a result at least a four-dimensional calculation has to be performed in order to include the symmetry-breaking degree of freedom. Although a 4D calculation is feasible on modern computers, a 9D calculation which includes the C-H stretch coordinates or a simulation of the photochemical reaction in a condensed medium is beyond the performance of current computers and therefore requires a new strategy.The next section will outline the TDSCF approach.242 Non-adiabatic Reactive Routes Fig. 1 Simulation of the photodissociation of CH31 induced by a resonant 1Ofs Gaussian laser pulse. From bottom to top are displayed the square modulus of the wavefunction at 44 fs on the ground, radiatively coupled and non-adiabatically coupled electronic potential-energy surfaces. The x axis represents the dissociative I-CH3 coordinate and the y axis the CH3 umbrella vibrational motion 3. TDSCF Formulation The goal of this section is to outline a consistent procedure for modelling a quantum system in contact with a larger system which can serve as a heat bath. The physical system under investigation is very demanding. The main problem relates to its multiple bodied aspect so that a full quantum-mechanical description of all degrees of freedom is beyond current computational capabilities.A practical modelling of the processes, therefore, requires a hierarchical procedure in which only the relevant degrees of freedom are treated in a full quantum-mechanical fashion. Other degrees of freedom are described by a classical or semiclassical approximation. Mixed quantum/classical calculations have been tried by many authors.” Owing to the difference in formulation of the quantum and classical mechanics, mixing the theories often leads to conflicts with questionable interpretation. A consistent treatment has to be formulated on a common denominator. A density description in Liouville space can serve such a purpose.This approach overcomes the difficulty that a single trajectory has no direct analogue in quantum me ch an i cs.R. Koslofland A. D. Hammerich Oa20 n 243 0.03 - I_- Fig. 2 Reaction coordinates on the diabatic CH31 potential-energy surfaces and their ‘adiabatic’ analogues which include the radiative and non-adiabatic couplings. The upper panel portrays the diabatic surfaces’ with the two horizontal lines denoting the energy of the ground state before and after full resonant excitation. In the lower panel are the corresponding ‘adiabatic’ curves at 30 fs. Since the electric field is time dependent the ‘adiabatic’ potentials are also The correct many-bodied solution is formally solved by the Liouville-von Neumann equation for the density operator: dP&& at where the Liouville operator can be separated into individual contributions: 9 = zs + 9 b + z s b (3.2) where the subscript s indicates the primary system and b the bath.A numerical scheme to solve the Liouville-von Neumann equation under dissipative conditions which result from contact with a heat bath has been developed.** The method is based on a direct expansion of the density operator on a grid and a propagation scheme able to incorporate complex eigenvalues of the evolution operator for dissipative systems. Despite the appealing aspect of a direct solution to eqn. (3.1), the procedure is numerically expensive and therefore limited to model systems. For realistic simulations, further approximations are required, the main one being the use of a mean-field approach which expresses the full density operator as a tensor product of the density operators of the primary system s and of the bath degree of freedom b: p^‘p^s@p^b (3.3)244 Non-adiabatic Reactive Routes Such a separation replaces the full multiple bodied correlated motion with a mean-field interaction with the equations of motion: (3.4a) (3.4b) Once a partition of the density has been made, each of the two parts can be treated in a different fashion.For example, the nuclear motion of the bath can be described classically or semiclassically. A further approximation is to specify that the initial state be a pure state (zero temperature). In the mean-field approach of eqn. (3.4) this reduces eqn. (3.4~2) to a Schrodinger-type equation: (3.5a) where and is is the primary system Hamiltonian, psb(&) is the system-bath interaction potential, and R b is the bath nuclear coordinate.The effective potentials in eqn. ( 3 . 5 ~ ) assume a semiclassical approximation in which the averaged potential over the nuclear wavefunction can be replaced by the potential of the mean position. Similarly eqn. (3.4b) is replaced by Hamilton’s equations for the mean position and momentum: a: - (a::)s (3.5b) 6 s = l ~ s ) ( ~ s l -- - dPRb= -(..EJs at where H is the averaged classical Hamiltonian function and (-)s represents an average over the primary system’s degrees of freedom. A generalized Langevin (GLE) approach’’ can be used to describe the influence of the rest of the heat bath. Explicitly, the primary part exerts a force on the ith bath nuclei which is calculated by the matrix element: Mixed quantum/ classical calculations of this type have been applied successfully to many but in view of the non-adiabatic reactions considered in this work this approximation is bound to fail due to the omission of important correlations in eqn.(3.2). First, the bath subsystem has to know on which electronic surface the primary system resides in order to feel the correct force. Secondly, in reactive scattering, an important correlation is built up which is the result of the density splitting into the reactive and non-reactive parts.2’ These important correlations imply a modification of the simple mean-field approach. The method described below, a multiconfiguration approach, addresses this problem.4. MC-TDSCF Formulation For simplicity the formulation is developed for three configurations. Extension to more configurations follows the same lines. Define a projection operator P in Liouville space: P2 = P. (4.1)R. Koslof and A. L3. Hammerich 245 The projection operator P is defined in the s space and separates the system into two parts 1 and 2. These two parts for example could be the two electronic surfaces: PP: = P: Pp,2 = 0. Using the projection operator P in the s space the projection Q is defined for the other surface: P + Q + W = I (4.3) where the projection operator W selects the parts that are not included in the projections P and Q. These parts of the density operator are off-diagonal and represent correlation between the 1 and 2 parts.The tensor product density operator (3.3) is replaced by a correlated density operator: The bath density operator Pb is chosen to be normalized: tr {p:} = tr {p:} = tr {p;} = I b b b The total normalization leads to: tr {p: + p:} = 1 tr {p:} = o S S (4.5) because, by construction, the projection W selects off-diagonal terms of the density operator. The time derivative of eqn. (4.4) becomes: (4.7) now: PQ = 0 then: p = p,'Op:+p:Op;+ p,3op;+p;Op:+p,2op:+ p:op: Pdp=P2(P+Q+ W ) p at dp- QX(P+ Q+ W ) p Qdt- (4.8) Wdp= WX(P+Q+ W)p Combining eqn. (4.8) with the definition of the projection operators, and taking partial traces the following equation is obtained: at (4-9) Similar equations are derived for the other parts.246 Non-adiabatic Reactive Routes (4.10) which represents couple$ motio$ on two electronic surf5ces.Combining eqn. (4.9) with (4.10) and using PX = I1)( 11x1 1)( 1 I for any operator X one obtains: (4.1 1 ) where the [ , ]+ symbol represents the anticommutator, v: 1( r,) = tr{ Vll( r, , Rb)pi} and v;2( r,) = tr{ V12( r,, Rb)p:} are potentials averaged over the bath density operators p: and p:. The equation of motion for the bath mode becomes: (4.12) where v:l(Rb) =tr{Vll(rs, Rb)p:} and v;2(Rb) =tr{V12(rs, Rb)p?} A similar equation is obtained for p2. It should be noted that there is no direct coupling between the equations of motion of pi and pf. Owing to coupling to the bath and the fact that each surface bath moves under different conditions, the equations of motion are able to create statistical mixing in the individual components p:.Examining the structure of eqn. (4.12) it can be found that a semiclassical approximation for the bath will contain three coupled bath coordinates. Each of these coordinates will move under a different average force. 5. Discussion Time-dependent quantum-mechanical methods for molecular dynamics have evolved considerably. Calculations of realistic molecular encounters are able to shed light on fundamental processes. The purpose of this work is to gain insight into non-adiabatic molecular processes. The photodissociation of CHJ was brought as a demonstration of how one can elucidate a molecular process induced by a short and strong laser pulse. This type of intimate understanding, in particular the dynamical picture displayed by the instantaneous dipole, can lead to control of the chemical outcome.The coherent evolution is a key factor in achieving such control. Considering reactions with many degrees of freedom such as in condensed phases the main issue is whether the phase coherence is maintained long enough in order to achieve chemical control of the process. The surface-hopping approximation of Preston and Tully represents the other extreme view in which phase coherence is only maintained for a very short period. The density formulation presented in sections 3 and 4 has been constructed with this issue in mind. Simulation of ionization processes in strong fields22 has shown that phase coherence is preserved for very long times. It was found that extremely accurate integration schemes are therefore required in order to follow long-time interference effects.It is therefore expected that coherent chemical manipulations are possible in condensed phases. The time-dependent quantum-mechanical formulation, in particular eqn. (4.9)- (4.12) is a rich source of physical approximations. The possibilities range from a full quantum-mechanical calculation to a mixed quantum and semiclassical approach.R. Koslofl and A. D. Hammerich 247 Multiconfi uration time-dependent self-consistent field approximations have been tried before.*l* ' 3-26 . Their derivation was based on a wavefunction representation. The work of Kotler et u Z . * ~ directly addresses multisurface dynamics. For such cases, the choice of the projection operator is obvious. Other work2' emphasizes the correlation produced in reactive scattering.The work of Meyer et al.26 is a generalization to many configurations. The density operator formulation described here differs in major aspects from previous work. In quantum mechanics it is possible that a projection of a combined pure state on a local one-particle description of state leads to a mixed state. The influence of the bath degrees of freedom in eqn. (4.12) will lead to this effect. This research was supported by a grant from the G.I.F., the German-Israeli Foundation for Scientific Research and Development. The Fritz Haber Research Center for Molecular Dynamics is supported by the Minerva Gesellschaft fur die Forschung, GmbH Munchen, Germany. References 1 I. Ohmine, personal communication. 2 G.Haase, M. Asscher and R. Kosloff, J. Chem. Phys., 1989, 90, 3346. 3 M. E. M. Spruit, PhD Thesis, University of Amsterdam, 1989; M. Rocca and U. Valbusa, Phys. Rev. 4 A. Dannon, E. Kolodney and A. Amirav, Surf: Sci., 1988, 193, 132; A. Amirav and M. J. Cardillo, 5 L. D. Landau, Phys. 2. Sow., 1932, 2, 46; C. Zener, Roc. R. SOC. London, Ser. A, 1932, 137, 696. 6 E. E. Nikitin, Chemische Elementarprozesse, ed. Hermann Hartman, Springer-Verlag, Berlin, 1968. 7 R. K. Preston and J. C. Tully, J. Chem. Phys., 1971, 54, 4297. 8 Z. Top and M. Baer, Chem. Phys., 1977, 25, 1; M. Baer and C. Y. Ng, J. Chem. Phys., 1990,93, 7787. 9 H. Guo and G. C. Schatz, J. Chem. Phys., 1990, 93, 393; M. Shapiro, J. Phys. Chem., 1986, 90, 3644. Lett., 1990, 63, 2398. Phys. Rev. Lett., 1986, 57, 2299. 10 A. D. Hammerich, R. Kosloff, H. Guo and M. Ratner, in preparation. 1 1 R. Kosloff, S. A. Rice, P. Gaspard, S. Tersigni and D. Tannor, Chem. Phys., 1989, 139, 201. 12 R. Kosloff, J. Phys. Chem., 1988, 92, 2087. 13 R. Koslop and H. Tal-Ezer, Chem. Phys. Lett., 1986, 127, 223. 14 H. Tal-Ezer, R. Kosloff and C. Cerjan, J. Comput. Phys., to be published. 15 H. Tal-Ezer and R. Kosloff, J. Chem. Phys., 1984,81, 2967. 16 Y. Amatatsu, K. Morokuma and S. Yabushita, J. Chem. Phys., in the press. 17 See e.g. G. D. Billing, Comput. Phys. Rep., 1990, 12, 383. 18 M. Berman, R. Kosloff and H. Tal-Ezer, submitted. 19 See e.g. B. J. Garrison and S. A. Adelman, Sur$ Sci., 1977, 66, 253; J. C. Tully, J. Chem. Phys., 1980, 20 Y. Zeiri and R. Kosloff, J. Chem. Phys., 1990, 93, 6890. 21 A. D. Hammerich, R. Kosloff and M. A. Ratner, Chem. Phys. Lett., 1990, 171, 97. 22 C. Cerjan, R. Kosloff, N. Bar-Tal, in preparation. 23 R. Kosloff, A. D. Hammerich and M. A. Ratner, in Large Finife Systems, 20th Jerusalem Symposium, 24 Z. Kotler, A. Nitzan and R. Kosloff, Chem. Phys. Lett., 1988, 153, 483. 25 N. Makri and W. H. Miller, J. Chem. Phys., 1987, 87, 5781. 26 H.-D. Meyer, U. Manthe and L. S. Cederbaum, Chem. Phys. Lett., 1990, 165, 73. 73, 1975; R. R. Lucchese and J. C. Tully, Surf: Sci., 1983, 137, 570. ed. J. Jortner, A. Pullman and B. Pullman, Reidel, Dordrecht, 1987, p. 53. Paper 1/00263E; Received 18th January, 1991.

ISSN:0301-7249    

DOI:10.1039/DC9919100239

出版商:RSC    

年代:1991

数据来源: RSC

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Faraday Discuss. Chem. SOC., 1991, 91, 249-258 Coherence and Transients in Photodissociation with Short Pulses Horia Metiu Department of Chemistry and Physics, University of California, Santa Barbara, CA 93106, USA The time evolution of the product energy distribution and product state coherence following the one photon excitation of a dissociating state of a molecule with one or two short pulses is discussed qualitatively and illustrated with exact quantum calculations. In this paper the opportunity is taken to present some simple ideas in a very qualitative way. Two general questions are addressed: what can we do with short pulses that cannot be done with long ones? and which cw experiments most resemble those performed with short pulses? Fourier-transform theory shows that a short pulse is a linear superposition of cw beams.The probability that the pulse acting on a molecule induces a transition from a state i to a state f is proportional to Here cri -. is the cw cross-section for the transition i -+f, f(o) is the Fourier transform of the electric field of the pulse and ofi is the transition frequency from the initial state i to the final state f. In a cw experiment f(ofi) is replaced by S(o -of), where o is the laser frequency. Thus, eqn. (1) suggests that a short pulse is just a low-resolution laser, which excites more than one final state. Of course saying this misses a most important point: eqn. (1) is valid only at a sufficiently long time r,, after the pulse started acting on the molecule. Many of the things that make the use of short pulses worthwhile happen at t < T,,; moreover, the ability of simultaneously exciting more than one state allows us to enhance the information regarding the excited-state dynamics.1. Transient Final-state Distribution Let us consider a molecule that predissociates, after being excited by a laser pulse, to form the atom A and the molecule B. The state of the fragments is described by (k, n), where Ak is their relative momentum (in the centre-of-mass system) and n labels the internal states of B. What would one see if one measured the product distribution before r,,? We can solve the time-dependent Schrodinger equation and monitor the wavefunction in the asymptotic region (i.e. where the interaction between fragments is negligible) at discrete, regular and small time intervals t,, , A = 0, 1,2, .. . ; to is the time when the laser and the molecule begin interacting. At t l there is no product wavefunction in the asymptotic region; the pulse has created an excited-state wavefunction but the molecule did not have time to dissociate and it still lingers in the ‘transition state’ (to qualify as a topic of discussion at this meeting). At t2 a small wavepacket x ( R , r; t 2 ) appears in the asymptotic region; ( x ( R , r ; t,)12 is the probability that the molecule has dissociated at some time between t l and t Z . Here r represents the internal coordinates of B and R is 249250 Coherence and Transients in Photodissociation the distance between A and B. We can expand this packet in the basis set lk, n), which is appropriate for the asymptotic region, and obtain la,(k; t2)I2 is the probability that at t2 the fragments have relative momentum Zlk and B is in the internal state n.If we look at the product energy very early ( i e . at t 2 ) , the distance R between the fragments A and B is known fairly accurately and is close to the distance Ro, where the fragments stop interacting with a small uncertainty proportional to ( t2 - tl). There- fore, the momentum uncertainty in x ( R , r; t 2 ) is considerable. This means that, for every n, lar,(k; f2)I2 has a large width as a function of k. The width of Ia,(k; t2)I2 (at given n) can exceed all the energy scales in the system: the widths of the predissociation resonances (in the absorption cross-section) excited by the pulse, as well as the width of the pulse in the frequency domain.Energy conservation is ‘violated’. The energy distribution Ia,(k; t2)I2 is very different from eqn. ( l ) , which has peaks for all the predissociation resonances excited by the pulse. How does quantum mechanics go from the shapeless structure of the early measure- ment to the structure present when the measurement is late? Let us imagine again that we watch the asymptotic region as the time-dependent Schrodinger equation is being solved. At every time t A a new wavepacket x ( R , r; t A ) appears in the asymptotic region. It represents the probability amplitude that the molecule predissociated in the time interval between tA-* and t A . Since we refrain from performing any measurement until the time t > t,, we do not know when the predissociation took place.Because of this, to obtain the wavefunction at the time t when the measurement is made, we must add the amplitudes representing all possible predissociation times: The packet Ix, t A ) is the amplitude for the predissociation at tA and the operator U ( t - ?A) propagates the packet from tA to t. Since we call (R, r l x , t A ) = x ( R , r; tA) wavepackets, we call (R, r I $, t ) = $(R, r ; t) a wavetrain. If t exceeds the dissociation lifetime all wavepackets have reached the asymptotic region and the construction of the wavetrain, by the predissociation process, is completed. From now on the time dependence of the train is trivial: it shows that the fragments fly further and further apart from each other; since no forces act on them in the asymptotic region the wavetrain no longer changes its energy distribution; this means that (n, k I $, t) becomes independent of time.In fact one can show that (n, k I $, t ) 2 gives eqn. (1). The transition from a featureless energy distribution at early time to one rich in resonance peaks at later time takes place through the interference between the packets composing the train. To see how this comes about we use (4) U ( t - tA ) I k, n ) = exp { -i ( t - t, ) E ( k, n ) } 1 k, rz ) together with eqn. (2) and (3) to write (k, n l + , t)=Cexp{-i(t-fA)~(k, n ) } a , ( k ; t,)=exp{-itE(k, n)}a,(k; t ) ( 5 ) A with a,(k; t ) = C exp{+itAE(k, n ) } a , ( k ; tA). A Here E(k, n ) = [ ( h k ) 2 / 2 r n + ~ , ] / h and E,, is the internal energy of B.Eqn. (6) shows that the amplitude a,(k; t ) of the wavetrain in the energy representation at time t, is a coherent superposition of the wavepacket amplitudes ar,(k; t h ) , each weighted by aH. Metiu 25 1 c, .* P 4 -2 1200 fs 1300 fs I ( x 11 loo fs I 300 fs I cx 21 2.4 2.6 2.8 2.6 2.8 energy/ eV Fig. 1 The time evolution of the final-state distribution lank(t)12 at 100, 200, 300 and 1300fs, respectively, after the laser pulse started acting on the molecule. (-) n = 0, (- - -) n = 1. The curves corresponding to the vibrational states n = 0 and n = 1 are shown as a function of total energy E = fi2k2/2p+ en. Different scales are used, as indicated. The laser puke has an FWHM of 30 fs. The peak frequency 2.5523 eV is tuned to excite the (1,l) resonance in the absorption cross-section phase factor exp {+itAE(k, n ) } .The probability that at time t the fragments have the cnergy ~ ( k , n) is W k ; t) = I(k n I *, ?>I2 = l a n ( k 111' = C Ia,(k; tA)l*++C +C exp {-i(tp-tA)~(k, n ) ) a , ( k ; t,i>*a,(k, tp)+cc (7) A A P where cc means the complex conjugate of the preceding term. The single sum (the incoherent contribution) adds, as in classical physics, the probabilities that each wavepacket has the energy E ( k, n). Since each term la,( k ; ?,)I2 has a broad, featureless dependence on k, the incoherent contribution to the product energy distribution is broad and featureless. The structure in the distribution must be built by the double sums (the coherent contributions), which represent quantum interfer- ence.These terms must diminish the incoherent one at some values of k and add to it at others. The time t seems to have disappeared from eqn. (6), but that is not true: t determines the number of packets included in the wavetrain, since th must be less than t. The more packets the train has, the finer the interference pattern can be. En el and Metiu' have calculated the product state distribution for a two-dimensional model of the CH30N0 photodissociation into CH30 and NO. CH30 was treated as an atom and NO was allowed to vibrate, but not to rotate. The absorption cross-section for the model has sharp predissociation resonances* whose lifetimes are of the order of 1 ps. The molecule was excited by a Gaussian laser pulse with an FWHM of 30fs, whose peak frequency was tuned to excite the ( 1 , l ) resonance2 in the absorption cross-section.The pulse width, in the frequency domain, is sufficiently large to excite the ( 1 , O ) and the (2,O) resonances. Fig. 1 shows the product-state distribution I(k, n I $, t)12 = la,(k; ?)I2 at several times t after the pump pulse started acting on the molecule. When t is a hundred femtoseconds F252 Coherence and Transients in Photodissociation the product-state distribution is broad and featureless. After 200 fs the peaks are already defined and they are roughly at the energies corresponding to a long-time cw measure- ment;2 the peak heights at 300fs still differ from the final ones, which are established at 1300 fs. The distribution at 1300 fs is exactly that given by eqn.(1). 2. Coherence of the Product Wavefunction The most obvious way of detecting the transient final-state distribution is a pump-probe (PP) experiment that excites the product^.^ Let us assume first, for simplicity, that the probe pulse is extremely short and excites the fragment B to an electronic state B*. The states of the fragments after the excitation are denoted by Ik,, n,); hkf is the relative momentum and nf the internal state of B". Let us further assume that we measure how much light is emitted by a specific state n, of B". If the probe pulse was fired at the time t after the pump, the amplitude giving this signal is proportional to The matrix element (kf, nfl k, n ) satisfies the propensity rule (kf, nfl k, 4 = m - kf)(nfl n> (9) where (nfl n ) is the Franck-Condon factor for the transition from the internal state In) of B to the internal state Inf) of B".The physics behind the propensity rule is simple. The photon momentum being practically zero the excitation by the probe cannot change the relative momentum of the fragments, therefore, kf must be practically equal to k. Using eqn. (5) and (9) in eqn. (8) gives The probability that B" is in the state n f regardless of the final relative momentum kf is P b f ; t ) = dkfl(kf, %I+, t>12 n n m I =C I(nfln>12Pn(t)+CC (nfln>(mInf) exp{--it(~n -Ern))On,(t)+CC ( 1 1 ) The first term in eqn. (1 1) is the sum of the probabilities r that at time t the fragment B is in the state In), multiplied with the Franck-Condon factors I(n,l n)12. We must sum over all states n because we have used a delta function probe pulse; otherwise, the number of states n included in the sum will depend on the width of the probe pulse.The time dependence of this incoherent term is that of the product distributions Pn ( t), which we discussed earlier. The double sums in eqn. (1 1) represent coherent contributions. They oscillate as a function of the delay time of the probe, with the frequencies ( E, - E,) determined by the gaps between the internal states of B. One interesting feature of the coherent contribution to the signal is the presence of the overlap integral o n m ( t ) dkf an(kf; t)am(k,; t)* (13) I If a,( k,; t ) and a,( k,; t ) * do not overlap, as functions of k f , then the states In) and }m)H. Metiu 253 30 fs I- 0 200 400 t/fs Fig.2 The pump-probe LIF signal for the case when a &function probe excites the photodissoci- ation products. The pump FWHM is 10, 20 and 30 fs and the peak frequency is 2.5523 eV. The state populated by the pump is repulsive and the absorption cross-section is broad of B cannot contribute coherently to the LIF-PP signal; they cannot pair up to give an oscillating contribution (i.e. beats) to the signal. More precisely, if the dissociation dynamics is such that both ‘reactions’ AB -+ A+ B( n) and AB --* A+ B( rn) take place, the probe cannot excite coherently B(n) and B(m) unless there is a finite probability that A+ B( n) and A+ B( rn) have the same relative velocity. This translational overlap condition is a propensity rule because its derivation used eqn. (9).To test the rule we have performed4 exact calculations on a two-dimensional system that dissociates into A and NO. The NO molecule is allowed to vibrate but not to rotate. The excited state potential is repulsive. The probe excites NO to NO* and the total emission from one state of NO* is plotted as a function of the delay time between the pump and the probe (Fig. 2). The oscillations characteristic of coherence are seen for the shorter pulses only. In Fig. 3 we show the final-state distributions la,( kf, ?)I’ for the excitation by the three pulses. We note that all three pulses excite coherently the vibrational states n = 0, n = 1 and n = 2 of NO. However, coherent beats are not seen in the LIF signal of the longest pump pulse, because the overlap integral is zero. Furthermore, when beats are seen (for the shorter pump pulses), the frequency E ~ - E ~ is not present in the signal because the overlap integral 0,, is zero.This is why even though three internal degrees of freedom are excited coherently we observe only two level beats. Exact calculations4 with the two-dimensional model of CH,ONO predissociation lead to similar conclusions. We note that, as discussed earlier, the final state distribution varies in time and its dependence on momentum is broader at early times. Thus, we expect that the overlap integral On, ( t ) becomes smaller in time. Since On, ( t ) modulates the exponential time dependence in eqn. ( l l ) , the decay in the amplitude of the coherent signal in Fig. 3 reflects the decay of the overlap integral.The coherent signal due to the rotational states is simpler’ because of the selection rules for the excitation by the probe. If we monitor emission from the state n f = j of B* then this state can be excited by absorption from either the state j - 1 of B or from j + 1. This means that the emission from n, will show two level beats. Exact calculations with a simplified model of ICN,’show that this is the case. Because the ICN excited state is repulsive and the rotational energy is small, the translational requirement discussed above is always satisfied for rotations.254 Coherence and Transients in Photodissociation 1 I .5 2.0 2.5 3.0 translational energy/eV n = O 1 1.5 2.0 2.5 3.0 translational energy/eV n = O I I .5 2.0 2.5 3.0 translational energy/ eV Fig.3 The product energy distribution P,, ( k ; t ) = I(k, n 1 4, t)I2 = la, ( k ; ?)I2, for the model used in Fig. 2, as a function of the relative translational energy of the fragments, for n = 0, 1 and 2 and for the pump FWHM: ( a ) 30 fs; ( b ) 20 fs and (c) 10 fs It is often assumed that the laser-induced fluorescence signal in the pump-probe experiments is proportional to the product concentration. This is obviously not true when the working conditions are such that the coherent contribution to the signal [the double sums in eqn. ( 1 l)] is not negligible. One can hardly interpret the signal oscillations in Fig. 3 to mean that some of the fragments recombine and dissociate periodically. The coherence effects influence the total PP-LIF signal whether or not the total emissionH. Metiu 255 is frequency resolved.Several exact calculations596 have provided examples where the time evolution of the PP-LIF signal is not proportional to that of the population of the wave train created by the pump. Many research groups7-” have used a pump pulse to excite coherently more than one eigenstate of a molecule, and a probe pulse to induce beats in the dependence of the LIF-PP signal on the delay time between the pump and the probe. In these the pump excited coherently molecular bound states, while we are here with the transient coherence of the wavetrain describing the products of photodissoci- ation’ or prediss~ciation.~ The connection between coherence and photodissociation has also been discussed in the context of different experimental arrangements by Brumer and Shapiro.12 3.Transients caused by Laser Excitation The above discussion was confined to the transient properties of the wavetrains created by predissociation. The same concepts can be used to examine the wavetrain prepared by the excitation of a molecule by a laser. Instead of adding coherently the wavepackets representing the probability amplitude that the molecule dissociates at the time t A , we add the wavepackets representing the probability amplitude that the molecule has adsorbed the pump photon at the time t A . At the level of abstraction used here there is hardly any difference between these processes; they are both described by eqn. (3) and only the physical interpretation given to the wavepackets and the wavetrain differs.In the case of laser excitation I$, t) is the wavetrain describing the nuclear motion induced by photon absorption on the upper electronic energy surface. The states lk, n) used in the above equations are now the nuclear eigenstates of the excited electronic state. The excited state population created by the laser is given by eqn. (7). It is worthwhile to examine this analogy closely. To do this we calculate exactly the state created by one-photon absorption from a laser pulse and monitor its evolution at discrete, evenly spaced and ‘infinitesimally’ close times t A . The pulse makes contact with the molecule for the first time at to=O. At time t , the algorithm creates a small wavepacket Ix, t , ) , on the upper electronic state, representing the probability amplitude that the photon has been adsorbed in the time interval T = t l - t o .Ix, tl) is the ground state at time tl multiplied with the electric field at t , and the transition dipole between the ground and the excited electronic states. Let us examine what happens if we make an energy measurement at t , . Since we have initiated the absorption process at to = 0 and terminated it (by performing a measurement) at t , the molecule interacts with the pulse only for a time T ; the effect of this interaction is equivalent to that of a delta-function laser pulse, whose spectrum includes all frequencies; thus, at tl all the nuclear energy eigenstates that have a non-zero Franck-Condon factor with the initial state are excited. This includes all electronic states, all photoionization states, and, to dramatize a little, even those states in which the 1s orbitals of the atoms are ionized! This excitation process is independent of laser frequency or the temporal width of the laser pulse; both parameters are made irrelevant by the shortness of the time between the beginning of the laser-molecule interaction and the energy measurement.If we have a little more patience and allow the computer to go on for three time increments the algorithm will construct a wavetrain I$, t) composed of three wavepackets, created at the times t l , t2 and t , . An energy measurement at the time t = tl + f2 + t3 = 37 interrupts the excitation process and is equivalent to an excitation of the molecule by a pulse of temporal width 37.The spectrum of this equivalent pulse is narrower than that of the pulse equivalent to a measurement performed at t , ; we may still observe that several electronic states are excited, but the 1s orbitals of the atoms are no longer ionized. The peak frequency of the equivalent pulse does matter, since the states that are excited are grouped around the energy reached by the laser frequency.256 Coherence and Transients in Photodissociation Let us emphasize how intriguing this is: the train is composed of three wavepackets; each packet represents a state in which the 1s orbital is excited, but their sum is a state in which this excitation is absent! This behaviour has a simple explanation: the wavepackets have been created at different times t A with different phases exp (--hatA), where w is the peak pulse frequency; because of nuclear dynamics, their phases change during their brief lifetimes t - t h .These phase differences cause the destructive interfer- ence that makes the energy eigenstates which differ most from the laser frequency to disappear from the wavetrain, and the constructive interference that builds up the population of the states close to the laser peak frequency. As eqn. (7) indicates, without the coherent contribution made by the double sums the probability that the off-resonance states are excited will build up with each wavepacket. The state created by the pulse, at a long time after the pulse is extinguished, depends on how many molecular eigenstates Ef satisfy the equation f( Ef - ci) = 0. Here f( o) is the power spectrum of the pulse, E~ is the initial energy of the molecule and Ef represents the energy eigenvalues of the molecule.If the equation is satisfied for one eigenvalue Ef only, then we are performing a cw experiment which prepares the pure state I&f). If it is satisfied for several eigenvalues Ef, then a coherent superposition of these energies is prepared. If no eigenvalue satisfies the condition (Le. off-resonance excitation) then in the long-time limit the excited-state population is zero. In all cases, at the early times when the pulse acts on the molecule, many nuclear and even electronic states are excited. The lifetime of these transient excitations is the time needed by interference to destroy the states that do not resonate with the laser.This is of the order A/Ae, where Ae is the smallest difference between the laser peak frequency and the optically active eigen- states that satisfy f( Ef - ei) # 0. The off -resonance transients can be maintained indefinitely by exciting the molecule with a semi-infinite ‘pulse’. This happens because it takes a time A/Ae to destroy, by interference, the wavepackets forming the wavetrain. Thus, if we make a population measurement at a time t, the packets promoted on the upper surface at a short time prior to the measurement (i.e. between t - A/Ae and t ) are still in existence. The closer the laser is to resonance (i.e. the smaller is Ae), the longer is the survival time, and the transient wavetrain contains more packets. If the upper potential surface is repulsive, the off-resonance semi-infinite pulse creates a finite wavetrain whose length can be tuned by choosing the appropriate off-resonance parameter Ae.If the pulse is suddenly extinguished this train disppears on a timescale A/Ae. During its brief life on the upper electronic surface each wavepacket has a chance to either emit a photon and give a spontaneous Raman signal, or to absorb a photon from a second laser, which leads to two-photon absorption. Thus, the transients are the intermediate states from which off -resonance Raman and two-photon absorption spectroscopy proceeds. This observation, first made and extensively exploited by Heller,I2 indicates that by tuning the pump off resonance and performing Raman or two-photon spectroscopy we can study, with long pulses, the dynamics of short wavetrains on the excited potential-energy surface. These short wavetrains are similar to those excited by ultrashort or resonance pulses.Thus one can do femtosecond chemistry with a cw set up. Experiment~l~ and exact calculations on model systems14 justified these insights of Heller. 4. Interference between Wavetrains We have discussed so far how the interference of the wavepackets forming a wavetrain affects the results of the various measurements. We can also ask whether the interference between two wavetrains might lead to something interesting. Let us monitor one-photon absorption by a molecule exposed to two laser pulses; the photon will be absorbed from one of the pulses, but we do not perform any measurement to find out from which.AsH. Metiu I 257 600 1000 1400 delay time/fs Fig. 4 The total population [eqn. (14)] created by the two laser pulses, as a function of the delay time between them. Both pulses are Gaussian, with an FWHM of 1Ofs and a peak wavelength of 328 nm. The two curves correspond to a phase difference S between pulses of S = 0 and S = T a consequence, the amplitude I+, t ) = l + , t ; 1 ) t ; 2) ( 1 4 ) describing the state of the excited molecule at the time t, is a linear superposition of the amplitudes I+, t ; 1) and I+, t ; 2) describing the probability of absorption from the pulse 1 or from the pulse 2, respectively. The excited-state population is P ( t ) = ( + , t l + , t ) = ( + , t ; l l + , t ; l)+(+,t;21+,t;2)+2Re(+,t; 1 l + , t ; 2 ) ( 1 5 ) The first two terms represent the excited-state populations PI( t ) and P2( t ) created in two separate one-pulse experiments; P( t ) # PI( t ) + P2( t ) whenever the interference term PI2( t ) = 2 Re (+, t ; 11 +, t ; 2) # 0.Because the excited molecule dissociates, the reaction yield is modified by interference; in a two-pulse experiment in which we do not determine from which pulse the photon was absorbed the yield is different from the sum of the yields obtained in two separate one-pulse experiments. We have studied quantitatively the interference process discussed above by solving exactly4 the time-dependent Schrodinger equation for an NaI molecule interacting with two laser pulses. For simplicity we took the pulses to be identical except for an overall phase factor.The peak frequency was tuned to excite the molecule, through one-photon absorption, to a state from which predissociation occurs. The model and the method of calculation were described in ref. 1 5 . In Fig. 4 we show the excited-state population created by one-photon absorption after the molecule interacted with both pulses. The abscissa is the delay time between the pulses. For delay times <900 fs and > 1100 fs the total population is equal to the sum of the populations created if each pulse acted on the molecule alone. Interference takes place only for delay times between 900 and 1100 fs. This is the time it takes the wavetrain I+, t ; 1 ) to return to the Franck-Condon region of the upper potential-energy surface.The interference takes place only when the wavepackets being created by the second pulse overlap with the wavetrain created by the first pulse.258 Coherence and Transients in Photodissociation Such train-interference experiments complement the information generated by pump-probe experiments; furthermore, if performed on a molecule whose dynamics are well understood, they could be used to study the properties of laser pulses. Obviously other multiple pulse sequences could induce interesting behaviour, as demonstrated in numerous multiple-pulse NMR experiments. The general question of the relationship between pulse shape and excitation outcome has been studied extensively by Rabitz.16 The example used here is much simpler and in particular does not require strong pulses.This work was supported by NSF and AFOSR. I express my gratitude to V. Engel, R. Heather, K. Haug, D. Imre and E. Heller for many useful discussions and interesting insights. References 1 V. Engel and H. Metiu, J. Chem. Phys., 1990, 92, 2317. 2 ( a ) S. Hennig, V. Engel, R. Schinke, M. Nonella and J. R. Huber, J. Chem. Phys., 1987, 87, 3522; R. Schinke, S. Iiennig, A. Untch, M. Nonella and J. R. Huber, J. Chem. Phys., 1989, 91, 2016; M. Nonella, J. R. Huber, A. Untch and R. Schinke, J. Chem. Phys., 1989, 91, 194; M. Nonella and J. R. Huber, Chem. Phys. Lett., 1986, 131, 376; ( b ) V. Engel, R. Schinke, S. Hennig and H. Metiu, J. Chem. Phys., 1990, 92, 1. 3 This is an extremely active field and we quote only the more recent reviews: A. H. Zewail, Science, 1988, 242, 1645; A.H. Zewail and R. B. Bernstein, Chem. Eng. News, 1988, 66, 24; for the work of Eisenthal, Fleming, Nelson, Sorokin Tang and others see the current literature. 4 V. Engel and H. Metiu, unpublished. 5 R. Heather and H. Metiu, Chem. Phys. Lett., 1989, 157, 505. 6 V. Engel and H. Metiu, J. Chem. Phys., 1989, 91, 1596. 7 Y. S. Yan, E. B. Gamble and K. A. Nelson, J. Chem. Phys., 1985, 83, 5391; K. A. Nelson and L. R. Williams, Phys. Rev. Lett., 1987, 58, 745; J. M. Ha, H. J. Harris, W. Risen, J. Tauc, C. Thomsen and Z. Vardeny, Phys. Rev. Lett., 1987,57,3302; Y. X . Yan, L. T. Cheng and K. A. Nelson, Adu. Nonlinear Spectrosc., 1987, 16, 299. 8 M. Mitsunaga and C. L. Tang, Phys. Reu. A , 1987, 35, 1720; I. A. Wamsley, M. Mitsunaga and C. L. Tang, Phys.Rev. A, 1988, 38, 4681; M J. Rosker, F. Wise and C. L. Tang, Phys. Rev. Lett., 1986, 57, 321; F. W. Wise, M. J. Rosker and C. L. Tang, J. Chem. Phys., 1987, 86, 2827. 9 J. N. Dodd and G. W. Series, in Progress in Atomic Spectroscopy, ed. W. Hanle and H. Kleinpoppen, Plenum Press, New York, 1978; S. Haroche in High Resolution Laser Spectroscopy, ed. K. Shimoda, Springer-Verlag, Berlin, 1976; Laser and Coherence Spectroscopy, ed. J. I. Steinfeld, Plenum, New York, 1978. 10 ( a ) P. M. Felker arid A. H. Zewail, Adu. Chem. Phys., 1988, LXX, 256; ( b ) J. S. Baskin, P. M. Felker and A. H. Zewail, J. Chem. Phys., 1986,84,4708; P. M. Felker and A. H. Zewail, J. Chem. Phys., 1989, 86, 2460; P. M. Felker, J. S. Baskin and A. H. Zewail, J. Phys. Chem., 1987, 90, 5701. 1 1 P. Brumer and M. Shapiro, Chem. Phys. Lett., 1986, 126, 541; P. Brumer and M. Shapiro, Furaduy Discuss. Chem. SOC., 1986, 82, 177; P. Brumer and M. Shapiro, Acc. Chem. Res., 1989, 22, 407; T. Seideman, M. Shapiro and P. Brumer, J. Chem. Phys., 1989, 90, 7132; M. Shapiro, J. W. Hepburn and P. Brumer, Chem. Phys, Lett., 1988, 149, 451; P. Brumer and M. Shapiro, Chem. Phys., 1989, 139, 221; C . Asaro, P. Brumer and M. Shapiro, Phys. Rev. Lett., 1988, 60, 1634. 12 S-Y. Lee and E. J. Heller, J. Chem. Phys., 1979, 71, 4777; E. J. Heller, R. L. Sundberg and D. Tannor, J. Phys. Chem., 1982, 86, 1822. 13 D. G. Imre, J. L. Kinsey, A. Sinha and J. Krenos, J. Phys. Chem.. 1984, 88, 3956; D. G. Imre, J. L. Kinsey, R. W. Field and D. H. Katayama, J. Phys. Chem., 1982, 86, 2564; M. 0. Hale, G. E. Galica, S. G. Glogover and J. L. Kinsey, J. Phys. Chem., 1986, 90, 4997; J. Zhang and D. G. Imre, J. Chem. Phys., 1989, 90, 1666; K. Q. Lao, M. D. Person, P. Xayariboun and L. J. Butler, J. Chem. Phys., 1990, 92, 823; K. Q. Lao. E. Hensen, P. W. Kash and L. J. Butler, J. Chem. Phys., 1990, 93, 3958. 14 R. Heather, X-P. Jiang and H. Metiu, Chem. Phys. Lett., 1987, 142, 303; R. Heather and H. Metiu, 1. Chem. Phys., 1989,90,6903; S. 0. Williams and D. G. Imre, J. Phys. Chem., 1988,92, 6636; M. Jacon, 0. Atabek and C. Leforestier, J. Chem. Phys., 1989, 91, 1585; S. Das and D. Tannor, J. Chem. Phys., 1989, 91, 2324. 15 V. Engel and H. Metiu, J. Chem. Phys., 1989, 90, 6116. 16 See e.g. H. Rabitz, in Atomic and Molecular Processes with Short Intense Laser Pulses, ed. A. D. Bandrauk, Plenum, New York, 1988, p.389 Paper 1/00171J; Received 14th January, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100249

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Famday Discuss. Chem. SOC., 1991, 91, 259-269 Hydrogen Exchange Reaction H + D, in Crossed Beams L. Schnieder, K. Seekamp-Rahn, F. Liedeker, H. Steuwe and K. H. Welge* Fakultat fur Physik, Universitat Bielefeld, 4800 Bielefeld 1, Germany Despite its fundamental importance as the prototypical bimolecular reaction, the hydrogen exchange reaction still remains a challenging and open prob- lem, both experimentally and theoretically. Theory has now developed to a stage much superior to that of experiment. Nowhere is this more true than, for example, in the determination of differential scattering cross- sections, state-to-state specific with respect to the vibrational and rotational degrees of freedom of the molecular products. In this paper we describe a new experimental approach to such measurements, and present first results from crossed-beam studies of the H + D2 reaction (at relative translational energies of I .29 and 0.54 eV)t using the novel technique of hydrogen Rydberg atom time-of-flight spectroscopy to monitor the velocity and angular distribu- tions of the D atom product. As the most fundamental system of elementary chemical kinetics, the hydrogen exchange reaction and its isotopic variants and H+D2 --* HD+D (Id have been a subject of much theoretical and experimental research.However, although begun more than 60 years ago with the fundamental work of London,’ the theoretical investigation of this reaction has only recently reached the point at which the problem has been treated quantitatively in three dimensions by exact quantum-mechanical2 and also quasi-classical trajectory calculations3 for the case in which the energy necessary to overcome the activation barrier (ca.0.42 eV for the linear H3 ~ o m p l e x ) ~ is provided as kinetic energy of the collision partners. The results are multiply differential cross- sections that are quantum-state specific with respect to the internal (vibration and rotation) degrees of freedom of the product molecules, as a function of the collision energy in the electronvolt range. The experimental investigation, also begun more than 60 years ago (by Farkas)’ is, in comparison, much less advanced. Significant progress has been achieved in recent years by studies with laser-based techniques under bulk conditions by Wolfrum,6 Valen- tini’ and Zare.s These experiments have yielded detailed, i.e.quantum-state specific, reaction rate constants (or total cross-sections) for reactions wirh kinetically hot H( D) atoms at energies in the range of 1 eV (produced photolytically by photodissociation of hydrogen iodide molecules). Most recently, experiments have also been reported involv- ing internally hot molecular reactant^.^ -7 i eV= 1.602 18 x lo-.” J. 259260 H + D2 Exchange in Crossed Beams Measurements of the dependence of the quantum-state specific total cross-sections, by Nieh and Valentini," on the relative translational energy appear to show pronounced structures. These have been interpreted in terms of quantum resonances of the transition complex and have attracted particular attention. However, these observations have not been corroborated by the theoretical calculations," which, although they do indeed predict energy-dependent resonance-like structures, suggest that such features will appear in a pronounced fashion only in the multiply differential state selective cross- sections.The calculations indicate that when measurements are made under the integral bulk conditions the structures are smoothed and averaged out. This has been confirmed by detailed experiments by Kliner et aL12 Cross-beam experiments which, in principle, can be expected to yield the most detailed quantum-state specific differential cross-sections have been carried out since 196313 with reaction ( l b ) . Most notable in this regard are recent investigations of this system by Gotting et aZ.,14 Buntin et all5 and by Continetti and Lee16 with kinetically hot reactants ( i e .with fast atoms). Common to all crossed-beam experiments is the detection of the HD product molecules by mass spectroscopy and analysis of their velocity (speed and angle) distribution by time-of-flight (TOF) spectroscopy. One important requirement for such experiments is that the collision conditions be energeti- cally monochromatic. Gotting et ~ 2 . ' ~ have produced fast D atoms by adiabatic expansion of gas from an electric discharge in deuterium, Buntin et all5 have employed the photodissociation of D2S at 193 nm, and Continetti and Lee16 have used DI photolysis at 248 nm. However, the goal of quantum-state specific differential cross-section measurement has not been achieved.It appears that with these experiments the conven- tional crossed-beam TOF technique has reached its practical limits of sensitivity and energy resolution. In this paper we present a new experimental approach to investigating the hydrogen exchange reaction in a crossed-beam configuration. The technique is based on a new kind of TOF spectroscopy for hydrogen atoms which we have developed previously for the investigation of photodissociation processes and which is distinguished by high sensitivity and kinetic energy resolution. 17-22 In its present state the TOF technique itself has a resolution of the order of A E / E = 0.003, i.e. 3 meV for H atoms with 1 eV of kinetic energy. In the experiments presented in this paper the overall resolution achieved was much lower because of the less accurately defined kinematics of the collision conditions.Nevertheless the studies indicate that the technique has sufficient potential to achieve rotational state resolution of the HD product molecules. In these first experiments we have concentrated upon reaction ( 1 c). We have chosen this reaction instead of reaction (16) for the simple reason that the precursor HI was available for the generation of fast reactant H atoms and because the main purpose of the work was to study the feasibility of the technique. Reaction (1 6) could, of course, be studied with the present technique equally well, and such experiments will be done. In this paper we describe the technique in some detail and report the first results so obtained.Experimental Fig. 1 shows schematically the experimental set-up, consisting essentially of a vacuum chamber separated into two parts: the photolysis chamber, where fast hydrogen atoms are generated, and the reaction-detection chamber. In the photolysis chamber a pulsed beam of HI in Ar cooled by adiabatic expansion and with its axis 15 mm away from the separating wall is crossed perpendicularly by a pulsed photolysis laser beam of 1 mm diameter (pulse duration ca. 5 ns). Atoms from the intersection volume enter the reaction-detection chamber through an orifice (ca. 2 mm diameter) and cross a pulsed D2 beam at a distance of 15 mm behind the wall. D atoms generated in the reactionL. Schnieder et al. 261 H I / A r I l a s e r p r o b e , Laser (121 6nm) 0 \ Fig.1 Schematic view of the experimental geometry. Two parallel pulsed molecular beams (HI-Ar and DZ, respectively) are crossed by pulsed lasers for dissociation ( A = 266 nm) and D-atom excitation ( A = 121.6 and ca. 365 nm) zone are selectively excited by two-photon absorption with tunable (VUV and UV)-laser light (ca. 15 ns pulse duration). In the first step atoms are excited from the ground state, D( Is), to the first excited state, D(2p), at the Lyman-a wavelength (121.6 nm), and from there to either ionization [reaction (2a)l or to high Rydberg D*(n) states [reaction ( 2 b ) ] , i e . D(ls)+VUV -+ D(2p)+UV -+ D'+e- (2a 1 -+ D(2p)+UV --+ D*(n) (2b) The velocity distribution of the nascent D(1s) atoms is then obtained by a TOF measurement of the ions or the Rydberg atoms, since momentum and kinetic energy remain practically unchanged in the excitation process.We have developed and employed first the D+ TOF technique, and subsequently also the D*( n ) TOF technique. In photofragment spectroscopy experiments we have achieved 17-20 an energy resolution of A E / E ~ 0 . 0 1 with the ion TOF technique and A E / E =0.003 with the Rydberg TOF technique.2"22 The drift path length, given by the distance between the (VUV and UV)-laser beams and a fine-mesh metal grid, was 24.3 cm in these experiments. In the case of ion TOF measurement the drift region was maintained, as much as possible, free of electric fields. Ions arriving at the grid are accelerated beyond the grid and detected by a multiplier. In the more recent variant Rydberg atoms are field-ionized upon passing through the grid, and ions (or electrons) are detected by the multiplier.The detector can be rotated around the (VUV and UV)-laser beam axis through angles ranging from OLAB = 5" to 6 L A B = -135", with @LAB = 0" defined by the reactant H-beam direction. The application of the Rydberg TOF technique depends crucially on the radiative lifetime of the Rydberg levels, since the radiative lifetime T,,d must be long compared with the flight time T. According to the two-photon selection rules, levels with orbital angular momentum quantum numbers Z = O and 2 can be excited under field-free conditions. Following the excitation scheme (2b) levels with Z=2 are most probably populated. Even for rather high principal quantum numbers such as 80 the radiative lifetime only reaches 268 ps [Fig.2(a)], a value which is comparable with the flight times occurring in the present measurements (see below). In order to achieve longer262 H+D, Exchange in Crossed Beams I I ' I 1 10 30 50 70 90 n -80 -60 -40 -20 0 20 40 60 80 "1 - n2 Fig. 2 (a) Lifetime of excited states in atomic hydrogen as a function of the principal quantum number, n, for angular momentum I = 0,2 and n = I - 1. ( b ) Lifetime of parabolic states as functions of the parabolic quantum number n, - n2 for different values of the principal quantum number, n, and magnetic quantum number rn = 0 lifetimes the excitation has been carried out with a DC electric field (of the order of 10 V cm-') applied to the excitation region. In the field, parabolic states are prepared with lifetimes shown in Fig.2 ( b ) . We have tested the effects of this measure, which was originally introduced as a means of removing ions from the excitation volume, by observing flight-time distributions as a function of the principal quantum number of the Rydberg level: no significant change of the TOF distribution was observed when levels ranging from n = 30 to n = 90 were excited. The explanation for these surprisingly high lifetimes is the production of Rydberg atoms in high orbital angular momentum states, I, produced adiabatically as the atoms leave the electric field. Resu 1 t s We have carried out experiments at various H atom kinetic energies with photolysis light at 266, 193 and 280 nm using, respectively, the fourth harmonic of the Nd : YAG laser, the radiation of an ArF laser (oscillator-amplifier arrangement), and tunable light from a frequency-doubled dye laser.Here we report results obtained at 266 nm. At thisL. Schnieder et al. 263 3.0 2.5 2 . 0 % > u- 1.5 1 . 0 0 . 5 0 2.68 ,/ 6 / - 193 nm 4 - H + D,( v = 0 I HD (V=O) +D O142eV - 3.0 - 2 . 5 - 2.0 2 q!! \ - 1.5 - 1 . 0 - 0 . 5 - 0 Fig. 3 Energy diagram for the reaction H + D2 with different energy scales for total energy and relative translational energy. Indicated are the experimental values for the relative translational energy and the accessible vibrational states of the HD molecule laser delay/ps Fig. 4 Plot of the time dependence of the H-atom density at the intersection volume obtained by varying the delay between the dissociation laser (193 nm in this case) and the probe lasers for H-atom detection.Results are shown for two different orientations of the polarization vector of the dissociation laser laser relative to the direction of detection for two different velocity groups of H atoms264 H+D, Exchange in Crossed Beams time of flightlps I 1 ' 1 I I 1 II 30 35 40 45 50 55 time of flight/ps Fig. 5 D-Atom TOF spectra for ( a ) Ere, = 1.29 eV and ( b ) Ere, = 0.54 eV. The length of the drift path is 243.5 mm energy the HI dissociation yields atoms with kinetic energies in the laboratory frame of Eki,(H) = 1.59 and 0.66 eV associated with, respectively, the lower and upper spin-orbit states of the iodine atom. The D2 beam, obtained from a pulsed valve and collimated by a skimmer to 3 mm diameter at the intersection with the H-atom beam, had an average speed of ca.1950 ms-' with a speed distribution corresponding to a translational temperature of ca. 35 K and a rotational temperature of ca. 200 K. At this D2 beam kinetic energy the two laboratory energies of the H atoms correspond to relative kinetic energies in the centre-of-mass (CM) frame of Eg& = 1.29 and 0.54 eV. (For photolysis at 193 and 280 nm the corre- sponding CM collision energies are EL% = 2.68 and 1.93 eV and E$E = 1.11 eV.) The vibrational states of the HD product molecules that are thermodynamically accessible at these energies are indicated in Fig. 3, together with the potential barrier for reaction via the linear collision c~mplex.~L.Schnieder et al. 265 Fig. 6 Vector diagrams for ( a ) V, = 17 641 ms-' and ( b ) V, = 11 216 ms-' and right-angle intersec- tion of the two beams 1.50 1.25 1:OO 0.75 0.50 0.25 kinetic energy of D atoms/eV 0.65 0.50 0.35 0.20 kinetic energy of D atons/eV Fig. 7 D-Atom kinetic energy distributions obtained from the TOF spectra shown in Fig. 5. Indicated are the calculated D-atom kinetic energies in combination with product molecules in different quantum states266 H -k D2 Exchange in Crossed Beams Ere, = 1.29 eV 1.5 1.0 0.5 1.5 1.0 0.5 kinetic energy/eV Fig. 8 D-Atom kinetic energy distributions recorded under different laboratory scattering angles for ( a ) Erel = 1.29 eV and ( b ) Erel = 0.54 eV. The solid angle of detection was 0.0053 sr The H atoms produced in the HI photodissociation are rather well defined in kinetic energy; the uncertainty due to kinematic smearing is small in comparison with other effects limiting the resolution.Fig. 4 shows pulses of the H atoms as they pass the reaction-detection zone determined in its extensions by the width of the narrower of the VUV and UV laser beams (the respective diameters of which were 0.5 and 0.8 mm). As can be seen, depending on the polarization of the photolysis light (which was of wavelength 193 nm in this particular illustration), clean pulses of either fast or slower H atoms reach the reaction zone, the length of which (ca. 200 ns) is determined by, aside from the speed of the atoms, essentially the photolysis laser beam diameter, which was ca. 1.5 mm. Fig.5 shows TOF spectra measured at EgL = 1.29 and 0.54 eV. These raw-data signals are accumulated from 20 000 laser shots (10 Hz repetition rate). From these spectra the corresponding kinetic-energy distribution of the atoms is straightforwardly derived from the time-to-energy transformation. In order to obtain the energy distribu- tion (kinetic and internal) of the HD+ D products, the collision kinematics must be taken into account. From the Newton diagrams (Fig. 6) we see that only forward scattered D atoms can be observed. Fig. 7 gives the signals converted to D-atom kinetic energy. Indicated are the vibrational-rotational energies of the HD products. Obviously, the structure of the signal distribution reflects the distribution of the HD molecules inL. Schnieder et al.267 Ere, = 0.54 eV kinetic energy/eV Fig. 8 (continued) the vibrational states, i.e. v1 = 0, 1 and 2 at EP& = 1.29 eV and v1 = 0 at EgE = 0.54 eV. Qualitatively, it is seen that in the OLAB = 0" direction the rotation of the HD molecules is only relatively weakly excited. Since the vibrational structure is clearly resolved, a more detailed analysis of the rotational distribution should, in principle, be feasible. We refrain from doing this at present, however, since better results with resolved rotational structure are anticipated in the near future. Fig. 8 shows spectra measured at various scattering angles from eLAB=O to 75". Although rotational structure is not resolved, we observe qualitatively that the rotational excitation of the DH product molecules increases with the scattering angle.Fig. 9 shows the result of a measurement of the simple differential cross-section, i e . the total signal as a function of the scattering angle, integrated over the speed of the products and thus over all internal states of the HD products. In these measurements, made with the Rydberg TOF technique, the total resolution is limited principally by kinematic smearing effects and not by the TOF measurement itself, i.e. by contributions from the collision geometry (solid angles) and energetics as well as from the rotational energy spread in the D2 reagent beam. Unfortunately, the H + D2 reaction has not yet been treated theoretically to anything like the same detail as the D+ H, reaction, with the result that a quantitative evaluation of the experimental results is not possible at this time.However, the decrease of the differential reaction cross-section with the scattering angle is as one would expect, qualitatively, from comparisons with theory.23 Also, the relative shift of the rotational268 H+D, Exchange in Crossed Beams I I I 0 30 60 90 %A,/ O 0 30 60 90 k 4 B / " Fig. 9 Total D-atom flux as a function of laboratory scattering angle for ( a ) Ere, = 1.29 eV and ( b ) Ere, = 0.54 eV distribution of the HD product to higher rotational levels with increasing scattering angle agrees qualitatively with the theoretical predictions for the reaction D + H2.2 We thank the Deutsche Forschungsgemeinschaft for the support of this work. References 1 F. London, Z. Elektrochem., 1929, 35, 552.2 J. 2. H. Zhang and W. H. Miller, J. Chem. Phys., 1989, 91, 1528. 3 N. C. Blais and D. G. Truhlar, J. Chem. Phys., 1988, 88, 5457. 4 D. G. Truhlar and C. J. Horowitz, J. Chem. Phys., 1978, 68, 2466. 5 A. Farkas, 2. Phys. Chem., Teil B, 1930, 10, 419. 6 T. Dreier and J. Wolfrum, Inr. J. Chem. Kine?., 1986, 18, 919. 7 D. P. Gerrity and J. J. Valentini, J. Chem. Phys., 1984, 81, 1298. 8 E. E. Marinero, C. T. Rettner and R. N. Zare, J. Chem. Phys., 1984, 80, 4142. 9 D. A. V. Miner and R. N. Zare, J. Chem. Phys., 1990,92, 2107. 10 J.-C. Nieh and J. J. Valentini, Phys. Rev. Let?., 1988, 60, 519. 11 J. 2. H. Zhang and W. H. Miller, Chem. Phys. Ler?., 1988, 153, 465.L. Schnieder et al. 269 12 D. A. V. Kliner, D. E. Adelman and R. N. Zare, to be published. 13 S. Datz and E. H. Taylor, J. Chem. Phys., 1963,39, 1896. 14 R. Gotting, H. R. Mayne and J. P. Toennies, J. Chem. Phys., 1986, 85, 6396. 15 S. A. Buntin, C. F. Giese and W. R. Gentry, J. Chem. Phys., 1987, 87, 1443. 16 R. E. Continetti, B. A. Balko and Y. T. Lee, J. Chem. Phys., 1990,93, 5719. 17 H. J. Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold, Faraday Discuss. Chem. SOC., 1986, 18 J. Biesner, L. Schnieder, J. Schmeer, G. Ahlers, Xiaoxiang Xie, K. H. Welge, M. N. R. Ashfold and 19 J. Biesner, L. Schnieder, G. Ahlers, Xiaoxiang Xie, K. H. Welge, M. N. R. Ashfold and R. N. Dixon, 20 Xiaoxiang Xie, L. Schnieder, H. Wallmeier, R. Boettner, K. H. Welge and M. N. R. Ashfold, J. Chem. 21. L. Schnieder, W. Meier, K. H. Welge, M. N. R. Ashfold and C. M. Western, J. Chem. Phys., 1990, 92, 22 M. N. R. Ashfold, R. N. Dixon, S. J. Irving, H.-M. Koeppe, W. Meier, J. R. Nightingale, L. Schnieder 23 N. C. Blais and D. G. Truhlar, Chem. Phys. Lett., 1989, 162, 503. S. A. Buntin, C. F. Giese and W. R. Gentry, Chem. Phys. Lett., 1990, 168, 517. 82, 99. R. N. Dixon, J. Chem. Phys., 1988,88, 3607. J. Chem. Phys., 1989,91, 2901. Phys., 1990, 92, 1608. 7027. and K. H. Welge, Philos. Trans. R. SOC. London, Ser. A, 1990, 332, 375. Paper 1/00751C; Received 18th February, 1991

ISSN:0301-7249    

DOI:10.1039/DC9919100259

出版商:RSC    

年代:1991

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1991, 91, 271-288 Quantum Theory of Laser Catalysis in One and Three Dimensions Tamar Seideman,? Jeffrey L. Krause$ and Moshe Shapiro" Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, 761 00 Israel A theory of the laser catalysis of the H + H2 exchange reaction in the collinear configuration and in three dimensions is presented. The collinear H + H2 system in a strong laser field is treated by a method composed of a converged coupled channels expansion for the non-radiative processes, coupled with an exact partitioning technique for the interaction with the radiation. The method enables computations to be performed for an arbitrary number of field-intensities with very little effort beyond that required for a single- intensity computation.By studying the optical reactive line-shapes as a function of the scattering energy, the signature of the scattering resonances on the optically induced reaction is unravelled. It is shown that when the collision energy is tuned to a resonance, laser catalysis results in selective vibrational excitation of the product H2 molecule. Implications of this effect for past and future experiments are discussed. A three-dimensional theory based on the same exact partitioning tech- nique is then presented. In this case, the bound-free scattering amplitudes, which serve as input to the theory, are obtained by assuming separability in terms of a hindered-rotor vibrationally adiabatic basis. We use the theory to compute reactive differential and integral laser-catalysis cross-sections.We study the laser intensity dependence of the reactivity, the role played by isolated and overlapping power-broadened resonances and how the angle of the relative velocities of the reagents affects the reactivity. I. Introduction The application of lasers to chemical species during the reactive act holds the potential for increasing our understanding of chemical reaction dynamics. A variety of theoretical methods have been proposed to study how lasers can be used to assist'-6 or modify7 the natural outcome of reactive collisions. Encouraging attempts at realizing such ideas in the laboratory have also been reported.'-13 Recently we suggested a so-called 'laser catalysis' scheme in which an energetically forbidden exchange reaction is initiated by transitions to an electronically excited bound state.14-16 The basic principles are illustrated schematically in Fig.1 for the H + H2(v) -+ H,(u')+H reaction. As the H projectile collides with the H2 target, the H3 adduct absorbs a photon to a bound level of H f , an excited electronic state of the collision complex. In the excited state the system shuttles back and forth between the reagent and product configurations and can, via stimulated emission of a photon, end up on the product side of the ground-state barrier. We showed that if the process is performed coherently, the probability of product formation can approach unity, by tuning the laser frequency about the optical resonance. We also showed that the power requirements for laser catalysis are not as demanding as initially expected.T Present address: Dept. of Chemistry, University of California Berkeley, Berkeley CA 94720, USA. t Present address: Theoretical Atomic and Molecular Physics Group, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA. 27 1272 Quantum Theory of Laser Catalysis \ f T I I T -/ \ H+H, -4.5 -3.0 -1.5 0.0 1.5 3.0 4.5 S/a.u. Fig. 1 Schematic illustration of the laser catalysed H + H2 reaction In this paper we present ‘exact’ collinear computations and a three-dimensional formulation supplemented by approximate calculations of differential and integral laser catalysis cross-sections. The collinear computations are based on a method we developed previously, in which we showed how to generate quantum-mechanical bound-free transition dipole amplitudes for reactive systems in the weak-field domain.” The numerical technique used is a ‘hyperspherical’ version of the artificial channel method.18 It avoids the explicit generation of scattering wavefunctions, and is particularly suitable for applications which require the dipole elements for a large number of bound (resonant) states.Coupled with an exact partitioning theory,I4 this method yields ‘numerically exact’ quantum mechanical probabilities for the collinear H + H2 laser-catalysed exchange reaction. One interesting off-shoot of these computations is their possible relevance to the observations by Valentini and co-worker~~~ of narrow scattering resonances in the d = 1 product-state distribution of the H + H2 reaction.These resonances were observed at total energies very near the predicted positions of reactive scattering resonances. The widths of the observed peaks were, however, in substantial disagreement with those obtained from converged 3 D quantum calculations.20-22 In what follows we shall show that laser catalysis is especially sensitive to the existence of scattering resonances and that it gives rise to substantial excitation of the v ’ = 1 product H2. Thus, the observations by Valentini and co-workers may be related to events which were catalysed by the strong photolysis laser used in their experiment^^^ (intensities reaching 10” W cm-2). We also show in this work how to calculate three-dimensional differential and integral laser catalysis cross-sections, and address ourselves to the important issue of the power requirements necessary for laser catalysis.The hope is that, because our scheme is based on free- bound transitions, which in contrast to free-free transitions are quite strong, the power demands will be within the realm of practical laser systems. In the present study we give quantitative estimates of the power dependance of laser catalysis. The organization of this paper is as follows: In section 2 we briefly review the partitioning theory for collinear laser catalysis. Our collinear computations are presented in section 3. In section 4 we derive the form of the full 3 D optical reactive amplitudes and in section 5 we present and discuss results for laser catalysis differential and integral cross-sections.T.Seideman, J. L. Krause and M. Shapiro 273 2. Collinear Field-Matter Partitioning Theory In order to treat optical reactions for arbitrary field strengths we partition the complete system Hamiltonian into two parts, H = H i + H , ( 1 ) where HI is the matter Hamiltonian and H2 is the sum of Hrad, the free radiation Hamiltonian and Hint, the radiation-matter interaction term. Hi,,, is given in the dipole approximate as where oj is the frequency of thejth mode, u: and uj are the creation and annihilation operators of that mode and V is the cavity volume. The full transition matrix for any scattering process in the presence of the field may be formally partitioned as T = TI + T2 (3) The partitioning of T is accomplished by first considering the partitioning of IE, V, y+), the scattering eigenstates of the total Hamiltonian, ( E - H)IE, V , y+)=O (4) where E is the total energy, y is the asymptotic arrangement channel index, z, is the vibrational quantum number, and the + indicates an 'outgoing' scattering state, into two electronic-radiation components.Defining P and Q as complementary projection operators, respectively projecting out the ground electronic state diessed by n photons and the first-excited electronic state dressed by n - 1 photons, we obtain that C?'(V'I o)=(E7 ~ ' 7 PTI PHintQGQHintPI ~7 ~ 9 ~ 3 (7) (E-PHP)IE, V , y t > = O (8) (9) In the above, IE, V, 7;) are scattering states of the (field-free) ground state Hamiltonian The projected Greens operator is given as QG( E ) Q = { E + i E - QHQ - QHintP(E + i E - PHP)-' PHinto)-' Using I&), the eigenstates of QHQ, ( Ee - QHQ) I Ee) = 0 as a basis for G, the matrix representation of QGQ, and identifying the light intensity as I = cwn/ V, we have, in matrix notation, that EI - h - ( 2 mI/ c) dE ' Ft ( E ') F( E ')/ ( E + i E - E ') I-' (11)274 Quantum Theory of Laser Catalysis In eqn.( 1 l ) , h is a diagonal matrix composed of the excited-state eigenvalues of eqn. ( l o ) , and F is a free-bound interaction matrix defined by with Ft denoting its Hermitian adjoint. Eqn. ( 7 ) now reads T2=(27r1/c)Fi(E) G ( E ) * F ( E ) ( 1 3 ) T2, obtained from eqn. ( 1 3 ) , together with Tl , obtained uia the IE, u, y:) solutions of the field-free scattering process, allow for the construction of the full S matrix which is related in the usual way to the T (= Tl + T2) matrix S = I-27ri{T,+ T2} (14) The absolute-squares of the S matrix elements, (Spy( u’l u)12 give directly the probability to undergo a laser-mediated reactive transition. The above formulation enables the calculation of the probability of an optical reaction at an arbitrary field strength.The field intensity enters as a multiplicative factor into the basic free-bound matrix of eqn. (12), which, as shown in eqn. ( 1 1 ) and ( 1 3 ) , is all that is needed to obtain T2. Thus, optical reaction probabilities can be calculated for all field strengths without additional work [save for the simple matrix inversion of eqn. (1 l ) ] . Some of the most important aspects of the theory are the properties of the so-called optical resonances.They are simply the power-bmadened bound states of the H3 complex in an excited electronic (e.g. the 2pA”) state. The general theory developed here allows for the case of overlapping resonances which, as shown below, occur in 3D at intensities exceeding 400 MW cm-2 and excitation frequencies above 66 000 cm-’. For these para- meters the density of states is sufficiently high that the spacings between adjacent levels become comparable to the power-broadened resonance widths. At lower excitation frequencies, or at lower laser powers, the optical resonances are found to be isolated, i.e. a situation in which the resonance widths are much narrower than the spacings between neighbouring resonances. Under these circumstances, we can write a considerably simplified expression for T2 , where I is the laser intensity and Ae and re denote the shift and the total width of the resonance and re(v, p ) is a partial width, 3.Collinear Results We have calculated previously numerically converged free-bound F matrices using the hyperspherical artificial channel method’7,24 for the collinear H + H2 reaction. The electronic potential-energy surfaces used in these calculations were the Porter-Karplus surface25 for the ground state, and the GI potential surface of Mayne et a1.26 for the excited A” surface. Contrary to our earlier work on laser catalysis we did not use theT. Seideman, J. L. Krause and M. Shapiro 0 5 00 -0 275 I 0 015 0 0 2 l o k w / cm- ' .:Ix_ -0003 w/cm-' 0000 0 003 0 5 00 -0003 0000 0003 1.0 ( a ) O 5 u o 3 w / cm- ' 0.003 0.0 0 003 0 .o 0.000 w/cm-' 0 0 ~ , 5 -0.15 0.00 w/cm-' 1.0- ( 6 ) 0.5 - w/cm-' Fig.2 Total exchange probability (Spy(O 10; E, u)l2 at scattering energies of ( a ) , (6) E = 0.38 eV; ( c ) , ( d ) E = 0.46 eV; ( e ) , (f) E = 0.53 eV. ( a ) , ( c ) and ( e ) show the coupled-channels results and ( b ) , ( d ) and (f) the reactive-WKB results of ref. 14(a). The photon frequency is measured with respect to the (shifted) energy of the excited level. The laser intensity is 400 MW cm-* in all cases SLTH ground-state surface2' because of difficulties in the Truhlar-Horowitz fit at large internuclear distances. As outlined above, given the F matrix, the vibrational levels of the excited state surface ( E J , and the non-radiative reactive TI matrix (all of which are obtained automatically as part of the artificial channel procedure), we can calculated exactly the laser catalysis probabilities.In Fig. 2 we present the total reactive probability as a function of the photon energy for three collision energies. The field intensity is 400 MW cm-* and the photon frequency is centred about the second even parity level of the G1 surface. The exact quantum- mechanical calculations are shown in Fig. 2(a), ( c ) and ( e ) while the corresponding reactive-WKB results of ref. 14 are given in Fig. 2 ( b ) , ( d ) and (f). Evidently, at low [Fig. 2( a ) and ( b ) ] and moderate [Fig. 2( c ) and ( d ) ] collision energies, the agreement between the two methods is satisfactory. As expected, when the collision energy nears the top of the reaction barrier [Fig.2 ( e ) and (f)] the WKB results begin to differ from the exact results. We note the extreme sensitivity of the reactive lineshapes to the precise location of the reaction threshold and therefore to the quality of the potential surface. At low collision energies, the lineshapes are nearly pure Lorentzians, but as the collision energy increases, the non-radiative amplitude increases (owing to tunnelling) and begins to interfere with the optical amplitude. This coherent interference results in the typical Fano-like dependence of the reactive probability shown in Fig. 2( c ) - ( f ) . As noted before,14 the asymmetric frequency dependence of the reactive line allows, in principle, significant control over the ratio of products to reactants in the reaction.276 '0 ( c ) Quantum Theory of Laser Catalysis 1:r-f- 0 I -0 004 0 000 0.004 h w/cm-' a -0.004 0: 0 000 0.004 o/cm-' Upon examining Fig.2( c ) and ( d ) in detail, for example, we see that tuning the photon frequency to slightly below the optical resonance affects a complete conversion of reactants to products, while tuning to the blue completely inhibits the reaction. The reverse occurs at the collision energy of Fig. 2(e) and (f). Of prime interest for the present work is the regime of higher collision energies, where reactive scattering resonances are found. The signatures of the scattering reson- ances on the (weak field) transition-state spectroscopy of the H + H2 reaction have been illustrated previously. 17,18728 We now show that the interaction of the scattering reson- ances with the optical resonances in the strong-field regime is even more interesting.In Fig. 3 we present the laser-induced probabilities for the v = O + v' = 0 and v = 0- v'= 1 hydrogen exchange process at two collision energies. Fig. 3 ( a ) and ( b ) correspond to collision energy of 0.87 eV, the energy of the first scattering resonance of the collinear H + H2 reaction, and Fig. 3( c) and ( d ) depict the exchange probabilities at an energy slightly below that resonance. It is immediately obvious that the combined radiative and non-radiative transition probability to the v = 1 level ( P l 0 of Fig. 3) is greatly enhanced as the collision energy sweeps through a scattering resonance, and that the peaks are very narrow.This is precisely the effect observed by Valentini and co-workers. However, we should point out that the centerline frequency of the laser used in the Valentini experiments was not on-resonance with any excited state of H3. The photolysis wavelength was 266 nm and the collision energy was 0.87 eV, so the total energy was still substantially below resonance with even the lowest-lying 2pA" or 2sA' levels. Further studies at the exact photon energy of observation are necessary to verify that laser catalysis has indeed been observed by Valentini. The vibrational selectivity noted here may be traced to the interference which gives rise to the asymmetric optical lineshape. As shown in Fig. 3, as the collision energy is tuned to the scattering resonance, each of the optical Fano lineshapes undergoes aT.Seidernan, J. L. Krause and M. Shapiro 277 strong structural variation and can, in some cases, completely invert. This behaviour is a result of the change in phase of the non-radiative process induced by the scattering resonance. As a result, it is possible, by fine tuning the laser frequency in the vicinity of the optical resonance, to achieve selective catalysis of essentially any product vibration. 4. Field-Matter Partitioning Theory in Three Dimensions In order to extend the formulation of section 2 to the 3D regime we define two field-free 3D basis sets, one for the ground (scattering) state and one for the excited (bound) manifold. We express both bases in the same (Jacobi) set of coordinates, consisting of the three Euler angles of overall rotation, 4, 6, Y and the three triangular shape variables R, r, 6.Defining J as the total angular momentum, M as its projection on a space-fixed z axis, A (the 'helicity') as its projection on a (moving) body-fixed z axis (usually taken to be R, the atom-diatom centre-of-mass displacement vector) and p a5 the parity quantum number, where the parity under inversion is given as ~ ( - 1 ) ~ , we write the eigenstates of the non-radiative Hamilton in either electronic state as (18) y / J , M , P = DJ9P A , M ( 4 7 6, Y)*i(R, r, 6> In eqn. ( 1 8 ) we have assumed that the helicity ( A ) is a good quantum number. This ('helicity decoupling' or 'centrifugal decoupling') approximation and its many variations are known to work well for many molecular systems." The D:,$ functions of the above are parity-adapted rotation matrices, We next assume adiabaticity of the bending coordinate 6, qJh(R, r, 6)=@,?(6JR, r ) $ y ( R , r ) / R r ( 2 0 ) where @;(a I R, r ) are 'hindered rotor' states which are solutions of the bending part of the non-radiative Hamilt~nian.~' The hindered rotor states are obtained by expanding them in terms of the spherical harmonics, @;( 6 1 R, r ) = 1 cy( R, r ) Y9,*( 6, 0) 9 Each hindered-rotor state correlates asymptotically with a free-rotor state, hence our use of the same notation, j , for the hindered-rotor and the free-rotor quantum numbers.As shown in ref. 30, the helicity decoupling and adiabatic approximations reduce the set of coupled Schrodinger equations in three variables to a set of decoupled two-variable equations, each completely analogous to the collinear case of section 2 .A full bound state, denoted [by analogy with IE,) in eqn. ( l o ) ] as JE,), is specified by e = { M 2 , J2 , v 2 , j 2 , h 2 , i}, where i is the vibrational quantum number in the v 2 , j 2 , A2 channel. For the bound manifold the above is all that we need to define the basis set. For the scattering manifold, our basis wavefunctions are denoted [by analogy with the collinear IE, v, y:) states of eqn. ( S ) ] as IE, k, g, yt), where g is a collective index for the { v, j , mj} quantum numbers, with j and mj being, respectively, the diatomic rotational angular momentum and its z-projection, and k is a unit vector along the direction of relative motion of the colliding partners.These functions satisfy the non-radiative Schrodinger equation, ( E - PHP) 145, r;, g, y;) = 0 ( 2 2 )270 Quantum Theory of Laser Catalysis and must also correlate to the appropriate asymptotic states, IE, i, g, yo), defined as the eigenstates of Ho , the non-interacting Hamiltmian, (E-Ho)IE,i,g, Yo)=O (23) We therefore expand IE, i, g, y:) in terms of the ‘partial waves’ of eqn. (18) to obtain ( R ~ , W , @ . I E , i , g , y : ) We are now in a position to write explicit expressions for the radiative and non- radiative T matrices. The non-radiative part, given in standard scattering theory3’ as CY(i, g’I i, g ) = ( E , 2, g’, Pol VlP, i, g, 7 0 (25) is computed approximately using the adiabatic hindered rotor basis of eqn.(20) and (21). The radiative T2 matrix is given, by complete analogy to the collinear expression reqn. (13)1, as where G+(e’l e; E) is the 3D generaliz2tion of the resolvent matrix of eqn. (9), (its explicit form is given below) and F(E, k, g, y ) is a rectangular matrix composed of the 3D free-bound (photorecombination) amplitudes, F(el E, i, g, Y ) = (EeIP tIE, i, g, 3 4 (27) Since our wavefunctions are expressed in terms of the body-fixed variables, we also wish to express p E^ in terms of these coordinates. Fixing the space-fixed z axis to lie along the direction of the electric-field vector of the laser, we have that where pk(R, r, 6) are the components of the dipole in the body-fixed frame. (For A’+ A’’ transitions only the k = *I components of p k exist.) Combining eqn.(IS), (24) and (28), and confining our treatment to the initial h = 0 case, we obtain for the free-bound amplitudes Wl E, c;, g, Y) where n2 stands for the ( J , , v2, j , , A,) bound-state quantum numbers. T(n,, iI v, j, y>, the ‘shape’ amplitudes, are defined as T(n,, il v,j, y ) = R2 dR r2 dr d6 sin S!P;z*(R, r, 6)pA2(R, r, 6)!P+‘J* ‘A ’) ( R , r, 8) (30)T. Seideman, J. L. Krause and M. Shapiro 279 with the angular integrals X(J21 J; A 2 , p , M ) given as = (-1)'"~[3(2J2+ l)]'l2 (--A2 J2 A2 ')( 0 -M J2 0 M J)[l+p(-1)J2+1+J] (31) In order to single out the M dependence of F it is advantageous to define a t matrix, The full free-bound amplitudes can now be written in terms of f as F(el E, i, g, Y ) = (-1)jDi,rni(+k, 8k, O ) Defining A(e'1 e; E ) = 2 dffF(e'1 E, k, g, P)F*(el E, i, g, P ) P& I (34) we obtain from eqn. (9) and ( 1 1 ) that Using eqn.(32) and (33), we can perform the mj summation and the k^ integration of eqn. (34) by exploiting the orthogonality of the rotation matrices. We obtain that It follows from eqn. (36) that the only non-vanishing off-diagonal G matrix elements are those satisfying the selection rules This structure of the G matrix, which is a direct result of the electronic transition selection rules, reduces significantly the computational effort. The above equations describe the laser mediated reaction to all powers of the radiation intensity, incorporating implicitly the ladder of transitions to the entire manifold of angular momenta. In contrast to the weak field case, transitions from a single angular- momentum state to all other angular momentum states are in principle allowed in strong fields.280 Quantum Theory of Laser Catalysis Finally, we combine eqn.(26) and (35) to obtain a compact expression for T2. In order to simplify the equations we define auxiliary M- dependent free-bound amplitudes, ~ ( e l J , v,j, 7) as in terms of which = (-l)j+j‘Dj;*.,(+; 0 mi 7 6 I 7 o)Di,rn,(+,c7 6 k 7 0 ) x 1 YF,,-M(2)T*(e’lJ’, ~ ’ , j ‘ , P)G+(e’le)~(elJ, ~ , j , Y ) Y , - M ( i ) (39) e‘,e, J ‘. J Given eqn. (24) and (25) for TI and eqn. (39) for t 2 , the differential cross-section for the entire (radiative + non-radiative) process may be computed as As in ref. 30, we will be primarily interested in the experimentally measurable, unpolarized quantities rather than the polarized cross-sections of eqn.(40). The unpolar- ized cross-section (for the h = 0 case) is given as 5. 3D Results and Discussion Eqn. (25) and (30)-(41) constitute the essence of our theory and form the basis for the compytatioFs of all crpss-sections of interest. The practical evaluation of either a P y ( k ’ , g’( k, g) or cFPY(k’, v ’ , j ’ l k, v , j ) , if based directly on these equations, is however a lengthy task. This is because, as shown in ref. 30, as many as 33 J partial waves, for as many as nine excited-state bending channels ( 1 S j , S 9, assuming j , = 0, l ) , and three vibrational channels ( v2 = 0,1,2) are typically involved in any given transition. In addition, the reactive process may be aided by transitions at different wavelengths owing to the existence of many optical resonances (i.e.the intermediate bound excited states broadened by the interaction with the radiation field). Typically, as many as 25 reson- ances (differing by their i quantum number) may be supported by a single { J 2 , j z , v2} adiabatic channel potential. The large number of quantum states involved suggests simplifying our procedure whenever possible. This may be achieved with essentially no loss of accuracy, when the resonance widths are much smaller than their spacings. Our computations show that for most intensities considered here and for most of the resonances, the line-strengths (which give widths to the free-bound spectral lines), are 3-4 orders of magnitude smaller than the nearest-neighbour separations. Under these circumstances, we may assume that each resonance is isolated and equations analogous to eqn.(15)-(17) may be used. The isolated resonance approximation was found to agree to better than five significantT. Seideman, J. L. Krause and M. Shapiro 281 -0. I4 Fig. 4 Differential cross-section for the 1 v = 0, j = 0, y} -+ I v = 0, j = 0, p } exchange, mediated via the {J2 = 11, j , = 1, u2 = 0, i = 4) resonance figures with the exact procedure based on eqn. (35) for all E ( = ho + E,,,,,) d 0.3 a.u., and laser intensities of 100-500 MW cmP2. For E a 0.3 a.u., where the level separations between neighbouring states become appreciably smaller, or at laser intensities which broaden the resonances to a degree comparable with the nearest-neighbour spacing, the isolated resonance approximation is not assumed.(Below we discuss the interesting interferences which occur when substantial overlap between neighbouring resonances exists.) In Fig. 4 we display the photon frequency and angular dependence of the (mj- summed, mi-averaged) differential cross-section for the reactive process with the laser frequency tuned to the vicinity of the transition to the IJ2 = 11, j , = 1, u2 = 0, i = 4) bound state. Because of the presence of the external field, the observed cross-sections depend on both Ok and 0;. In Fig. 4 we have set Ok, the incident polar angle (with respect to the light’s electric field vector) of H relative to the centre of mass of H2, to ~ / 2 . As shown in Fig.4, the cross-section changes from a backward-peaked non-radiative shape to a backward-forward symmetric shape as o is tuned to the centre of the line. The interference between the radiative and non-radiative processes, which is made explicit in eqn. (41), results in a loss of the backward-forward symmetry at slightly off-line-centre frequencies. In the backward direction, to the red of the resonance frequency, the lineshape drops sharply to zero and then increases, whereas in the forward direction (0; = -7r/2) the cross-section retains its Lorentzian shape. The above phenomenon is the three-dimensional analogue of the Fano-type interfer- ence noted in ref. 14 and in section 3 for collinear reactions. The interference between the radiative and non-radiative terms of eqn.(41) can be either constructive or destructive. It is only noticeable in the backward direction where the non-radiative process is sizeable. Much of the observed structure, and in particular the above interference effects, strongly depends on which J and J’ contribute to eqn. (41). Altogether, five J, J’ ( = J 2 , J2 f 1 ) A = 0 states contribute to an isolated J2 resonance. (If the resonance is not isolated, many more partial waves may contribute.) lu=O,j=O,P) + (u=O,j=O, 7 )282 Quantum Theory of Laser Catalysis Fig. 5 Differential cross-section for the 12, = 0 , j = 2, y ) ---+ 1zi = 0 , j = 2, p ) exchange, plotted as a function of Ok and el, at the resonance frequency of the radiative transition to the {J2 = 14, j , = 7, 21, = 0, i = 5 ) excited level In Fig.5 we examine the effect of changing both 0; aed &. The (constant) frequency is chosen to coincide with the centre of the lu = 0 , j = 2) ---* IJ2 = 14,j2 = 7, u2 = 0, i = 5 ) optical resonance. The effect of the laser is clearly a strong function of the direction of the relative velocity of the two incident beams in the laser field. We see that the laser will most effectively catalyse molecules with incident angle close to Ok = ~ / 2 . This perpendicular preference is a result of the A’+ A” electronic transition considered here. In order to explore this effect f\lly, we have compAuted the (incident-angle-dependent) integral cross-sections, apr(g’ I g; k ) , defined as the k’ (= &, &) integrated cross-section for a fixed value of the incident angle Ok.We obtain that where the first term represents the non-radiative contribution, (42) (43) the second term describes the pure radiative process, and the third term results from the interference between the radiative and non-radiativeT. Seideman, J. L. Krause and M. Shapiro 283 I .70 i I73 I I5 58 0 1.35 - .84 32 .80 0. -0.14 w/cm-’ -157 0k / rad Fig. 6 Integral cross-section for the I u = 0 , j = 0, y ) - 1 u = 0, j = 0, p ) exchange; ( a ) mediated uiu the {J2 = l,j2 = 1, u2 = 0, i = 8) resonance; ( b ) mediated uiu the {J2 = 1 1 , j 2 = 1, u2 = 0, i = 4) resonance routes, In Fig. 6 ( b ) we show the incident angle dependence of the integral cross-section for an exchange mediated via the same IJ2 = 1 1 , j 2 = 1, v2 = 0, i = 4) resonance studied in284 Fig.4. This is contrasted in Fig. 6(a) with a reaction preceeding via a low angular momentum state. Very clearly the reaction probability shows a typical ‘Fano-type’ dependence on frequency which varies with the incident polar angle. We now turn our attention to the computation of the overall enhancement of the reaction by the laser (reaction-enhancement factor), most conveniently defined as Quantum Theory of Laser Catalysis do [ dad + 2iRe( uinterf)] F = unonrad In order to perform the o integration we need to know I ( o ) , the laser intensity per unit frequency, which, for a pulsed laser, replaces the fixed intensity appearing in eqn. (35) and (38). In practice this is usually not necessary because, unless the intensity is very high, most pulsed lasers have much larger bandwidths than those of the H + H2 power-broadened lines.This means that I is practically constant over the o integration range we need to consider. Integrating eqn. (44) and (45) over o we obtain, by substituting the explicit definition of T ( e I J, v, j , y ) in eqn. (38), expanding the product of spherical harmonics [ref. 32, eqn. (4.6.5)] and employing the properties of the 6 - j symbols [ref. 32, eqn. (6.2.8)], for isolated resonances, I d o { orad + 2Be( uinterf)} where I-&’, j ’ , p ) and re are the partial and total widths, analogous to the collinear widths defined in eqn. (17). We see that the isolated resonance approximation and the assumption that the laser bandwidth is much larger than re has two important consequences: A linear dependence of the reaction-enhancement factor on the intensity and a 1 + PP2(cos 6,) dependence on the incident angle.The p parameter, which may be called the reaction-enhancement anisotropy, is defined as the ratio of the anisotropic term [i.e. the term multiplying P2(c0s 0,) in eqn. (47)] to the isotropic term. As in weak-field photodissociation e ~ p e r i r n e n t s , ~ ~ , ~ ~ p varies from +2 (a pure cos2 t)k distribution) to -1 (a pure sin2 6 k distribution). The above expression works well as long as resonances do not overlap. In Fig.7 we show the intensity and the beam orientation dependences of the reaction-enhancement factor, for a number of transitions of varying line strengths. As shown in Fig. 7A, the linear dependence of the enhancement factor on the intensity is realized over a wide range of intensities.Depending on the transition, we see enhancements (at sub-barrier energies) of orders of magnitudes at intensities up to 1000 MW cm-2 (which was the highest we examined). This behaviour is maintained even for graph (e), where the isolated resonance approximation is inapplicable. Apparently the non-linear depen- dence on the laser intensity and saturation of the enhancement factor must occur at much higher intensities.T. Seideman, J. L. Krause and M. Shapiro 285 1 . 6 1.4 1 . 2 1 . 0 0 200 400 600 800 1000 -1 0 1 I / M W cm-* Blrad Fig. 7 The enhancement factor as a function of A, the radiation intensity, and B, the relative orientation of the incident molecular beams with respect to the electric field axis.The laser-induced process is mediated via ( a ) the {J2= 5, j 2 = 1, u2 =0, i = 7) level, ( b ) the {J2 = 9 , j2=3, u2 =0, i = 2) level, (c) the (5, = 4, j , = 1, u2 = 0, i = 3) level, ( d ) the {J2 = 5, j , = 3, u2 = 0, i = 3) level, ( e ) the coupled {J2 = 19, j2 = 5, u2 = 0, i = 11) and {J2 = 29, j , = 3, u2 = 0, i = 9) levels, and S, the sum of four levels in the 0.31-0.33 a.u. energy range In Fig. 7B we show that the 1 +pP,(cos 0,) dependence is obeyed by the majority of transitions. The value of p varies considerably, though, for different transitions. For most of the transitions [trace (a) is an exception] the enhancement factor peaks at Ok = n / 2 , Le. p is negative. This type of behaviour is expected if the step of photon absorption is dominated by a Q branch, for which, using classical terms, the transition- dipole is perpendicular to R.The somewhat surprising aspect of eqn. (47) and Fig. 7 is that the reaction-enhance- ment factor exhibits the type of behaviour usually associated with first-order-type processes. This is contrary to expectations based on perturbation theory, in which laser catalysis is a second-order process. The key element that gives rise to the first-order behaviour is the bandwidth of the laser, which was assumed to be greater than the power-broadened resonance widths. The integration over the resonance lineshapes has reduced the dynamics to those of excitation and de-excitation of a quickly decaying intermediate level. Under such circumstances the process merely depends on the rate of populating the intermediate state, which is linear in the laser intensity.The situation is quite different if the power-broadened lines are wider than the laser bandwidth ( i e . laser catalysis with a CW source). In that case the non-linear dependence of G on I [see eqn. (35)] will not be masked by the o integration and higher power dependences may be observed. At higher energies the level spacings gradually decrease and we reach a situation in which resonances begin to interact. In this case the full (2x2) resolvent matrix of eqn. (35) must be computed. The resulting differential cross-section and its intensity dependence at a fixed scattering angle are shown respectively in Fig. 8 and 9. We have also evaluated the reaction-enhancement factor in this congested region, by numerically integrating over w.The results for the intensity dependence and incident angle depen- dence are given as graph (e) of Fig. 7. We see that even in this case the enhancement286 Quantum Theory of Laser Catalysis Fig. 8 Differential cross-section for the 1 v = 0, j = 0, y ) - 1 u = 0,j = 0, p ) exchange, mediated via the coupled {J2 = 19,jz = 5 , v2 = 0, i = 11) and {Jz = 29,jz = 3, vz = 0, i = 9) resonances 1.25 1 . 5 1.75 2 2 . 2 5 1 w - 75 840/cm-’ A 1 . 1 5 1 . 2 1 . 2 5 1 . 3 w - 75 840/cm-’ Fig. 9 The differential cross-section of Fig. 8 at el, = 7r/2, subject to radiation intensities of 100, 200,300,400 and 500 MW ern-'. The inset shows the four nearest lying levels in the H3 spectrum at 100 M W ern--*T. Seideman, J.L. Krause and M. Shapiro 287 factor is linear with the laser intensity. The dependence on the incident angle appears, however, to be much sharper than the 1 + /3P2(cos 0,) form. 6. Conclusion In this paper we presented collinear and 3D analyses of the laser-catalysed H + H2 reaction. The most important outcome of the collinear results is that laser catalysis can cause large enhancements of vibrationally excited H2 product molecules at scattering- resonance collision energies. We indicated that this effect may be related to the peaks observed in the experiments of Valentini and co-worker~,'~ but obviously further studies concerning the effects of the finite laser bandwidth, the distribution of kinetic energies of the incident hydrogen atoms, and the mixture of initial states present in the target are needed.Work is also in progress to generalize these calculations to 3D, on more accurate potential-energy surfaces. The two most important aspects of our sub-barrier 3D computations and theory are the demonstration of the existence of interferences between the non-radiative and radiative processes and the linear dependence of the frequency-integrated reaction- enhancement factor on the laser intensity. We were able to trace this linear dependence to the existence of isolated resonances and to the fact that the laser bandwidth is usually much greater than that of the power-broadened lines. This work was supported by the Minerva Foundation, Munich, Germany, and by the US-Israel Bi-National Science Foundation grant no.89-00397/ 1. References 1 ( a ) T. F. George, I. H. Zimmerman, J-M. Yuan, J. R. Laing and P. L. DeVries, Acc. Chem. Res., 1977, 2 A. E. Orel and W. H. Miller, Chem. Pbys. Left., 1978, 57, 362; J. Chem. Phys., 1979, 70, 4393; 1980, 3 J. C. Light and A. Altenberger-Siczek, J. Chem. Phys., 1979, 70, 4109. 4 M. Mohan, K. F. Milfeld and R. E. Wyatt, Chem. Pbys. Left., 1983, 99, 411. 5 ( a ) I. Last, M. Baer, I. H. Zimmerman and T. F. George, Chem. Pbys. Lett., 1983, 101, 163; (b) M. Baer, I. Last and Y. Shima, Chem. Phys. Lett., 1984, 110, 163; (c) I. Last and M. Baer, J. Chem. Phys., 1985,82, 4954. 10, 449; ( b ) P. L. DeVries and T. F. George, Faraday Discuss. Chem. SOC., 1979, 67, 129. 73, 241. 6 J. C. Peploski and L. Eno, J. Chem. Pbys., 1985, 83, 2948; 1988, 88, 6303. 7 J.L. Krause, M. Shapiro and P. Brumer, J. Chem. Phys., 1990, 92, 1126. 8 P. Hering, P. R. Brooks, R. F. Curl, R. S. Judson and R. S. Lowe, Phys. Rev. Left., 1980,44, 687; Phys. 9 B. E. Wilcomb and R. Burnham, J. Cbem. Phys., 1981, 74, 6784. 10 ( a ) H. P. Grieneisen, K. Hohla and K. L. Kompa, Opt. Commun., 1981, 37, 97; (b) H. P. Grieneisen, H. Xue-Jing and K. L. Kompa, Chem. Phys. Lett., 1981, 82, 421. 11 (a) P. R. Brooks, R. F. Curl and T. G. Maguire, Ber. Bunsenges. Pbys. Cbem., 1982, 86, 401; ( b ) T. C. Maguire, P. R. Brooks and R. F. Curl, Pbys. Rev. Lett., 1983, 50, 1918. 12 ( a ) P. D. Kleiber, A. M. Lyyra, K. M. Sando, S. P. Heneghan and W. C. Stwalley, Phys. Rev. Lett., 1985, 54, 2003; ( b ) P. D. Kleiber, A. M. Lyyra, K. M. Sando, V. Zafiropulos and W. C.Stwalley, J. Chem. Ph*vs., 1986, 85, 5493. Rev., 1980, 44, 687. 13 G. A. Raiche and J. J. Belbruno, Chem. Phys. Lett., 1988, 146, 52. 14 T. Seideman and M. Shapiro, J. Chem. Phys., 1988, 88, 5525. 15 M. Shapiro and T. Seideman, Large Finite Systems, ed. J. Jortner and B. Pullman, Reidel, Dordrecht, 16 T. Seideman and M. Shapiro, J. Cbem. Phys., 1991, 94, 7910. 17 J. L. Krause and M. Shapiro, J. Chem. Phys., 1989, 90, 6401. 18 M. Shapiro, J. Chem. Phys., 1972, 56, 2582. 19 J-C. Nieh and J. J. Valentini, Pbys. Rev. Lerr., 1988, 60, 519; D. L. Phillips, H. B. Levene and J. J. Valentini, J. Cbem. Phys., 1989, 90, 1600; J-C. Nieh and J. J. Valentini, J. Chem. Phys., 1990, 92, 1083. 20 J. Z. H. Zhang and W. H. Miller, Chem. Pbys. Lett., 1988, 153, 465; J. Chem. Phys., 1989,91, 1528. 21 D. E. Manolopoulos and R. E. Wyatt, Cbem. Pbys. Lett., 1989, 159, 123. 22 M. Zhao, D. G. Truhlar, D. J. Kouri, Y. Sun and D. W. Schwenke, Chem. Phys. Lett., 1989, 156, 281. 1987, p. 361.288 Quantum Theory of Laser Catalysis 23 J. J. Valentini, submitted. 24 J. L. Krause and M. Shapiro, Israel J. Chem., 1989, 29, 427. 25 R. N. Porter and M. Karplus, J. Chem. Phys., 1964,40, 1105. 26 H. R. Mayne, R. A. Poirier and J. C. Polanyi, J. Chem. Phys., 1985, 80, 4025. 27 ( a ) P. Siegbahn and B. Liu, J. Chem. Phys., 1978, 68, 2457; ( b ) D. G. Truhlar and C. J. Horowitz, 28 V. Engel and R. Schinke, Chem. Phys. Lett., 1985, 122, 103. 29 ( a ) M. Tamir and M. Shapiro, Chem. Phys. Lett., 1975, 31, 166; M. Shapiro and M. Tamir, Chem. Phys., 1976, 13, 215; ( 6 ) R. T. Pack, J. Chem. Phys., 1974, 60, 633; ( c ) P. McGuire and D. J. Kouri, J. Chem. Phys., 1974, 60, 2057; D. J. Kouri and P. McGuire, Chem. Phys. Lett., 1974, 29, 410; (d) G. C. Schatz and A. Kuppermann, J. Chem. Phys., 1976, 65, 4642. 30 T. Seideman and M. Shapiro J. Chem. Phys., 1990, 92, 2328. 31 See for instance R. D. Levine, Quantum Mechanics of Molecular Rate Processes, Clarendon Press, Oxford, 1969. 32 A. R. Edmonds, Angular Momentum in Quantum Mechanics, Princeton University Press, Princeton, 2nd edn., 1960. 33 ( a ) J. Solomon, C. Jonah, P. Chandra and R. Bersohn, J. Chem. Phys., 1971,55, 1908; ( b ) G. E. Busch and K. R. Wilson, J. Chem. Phys., 1972, 56, 3638; ( c ) M. J. Dzvonik, S. C. Yang and R. Bersohn, J. Chem. Phys., 1974, 61, 4408. J. Chem. Phys., 1978, 68, 2566; 1979, 71, 1514(E). 34 G. G. Balint-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137. Paper 0/05692H; Received 14th December, 1990

ISSN:0301-7249    

DOI:10.1039/DC9919100271

出版商:RSC    

年代:1991

数据来源: RSC