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. 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