摘要:

Faraday Discuss. Chem. SOC., 1986,82, 125-148 Photofragmentation: Understanding the Influence of Potential Surfaces and Exit-channel Dynamics B. Koplitz, Z. Xu, D. Baugh,? S. Buelow,$ D. Hausler, J. Rice, H. Reisler, C. X. W. Qian,O M. Noble7 and C. Wittig" Chemistry Department, University of Southern California, Los Angeles, California 90089-0484, U.S.A. Photoexcitation is used to prepare species whose subsequent fragmentation can be exploited for the purposes of studying, controlling and manipulating different kinds of molecular processes. First, we show how a form of sub-Doppler resolution spectroscopy can be used to determine centre-of- mass kinetic energy distributions, thereby enabling internal energy distribu- tions to be obtained for elementary processes which occur at a fixed total energy.We present data for H atoms monitored at the Lyman-a wavelength. Secondly, we show how such processes can be used to study binary interac- tions by preparing van der Waals complexes (e.g. C0,HBr) and then photo- dissociating one constituent of the complex (HBr + hv --* H + Br), thereby propelling the H atom toward the other constituent with well defined initial conditions. Finally, we turn from such direct fragmentation processes to those in which radiationless decay of S1 leads to reaction via T1 and/or So surfaces. For the case of Bu'NO, we study both channels, and find a barrier of ca. 650 cm-' on TI. Reaction via So is 'statistical', while the T, path leads to dynamical bias. Below the T1 barrier, reaction is slow (>3.5 ps) compared to radiationless decay (<50 ns), thus allowing metastable species to be prepared. In studying the dynamics of molecular photofragmentation, attention is usually paid to the relevant potential-energy surfaces (PES) and their associated couplings, as well as exit channel interactions of the separating fragments. The development of a quantitative and predictive understanding of molecular photo fragmentation has been the unifying theme of both experiment and theory in this area for many years.Theoretical progress has been rapid and impressive, thus stimulating researchers to devise more sophisticated experiments. Fortunately, the environments in which photodissociation measurements are typically conducted are agreeable for precise measurements ( e.g. nascent fragment distributions, their associated spatial anisotropies and occasionally reaction rates), and this compatibility has led to a rather thorough perusal of many dissociation phenomena.An implicit assumption in this research has often been that the knowledge thus obtained can be used to further our understanding of chemical dynamics in general, since photodissociation is like any other molecular encounter, except that the initial conditions are very well specified. Drawbacks to this strategy are (i) that dissociation dynamics are often dominated by exit-channel interactions on excited PESs, thus biasing observations in favor of energies and mechanisms which are not truly representative of the majority of systems undergoing chemical change in the gaseous phase (e.g.t With the Electrical Engineering Department. $ Present address: Los Alamos National Laboratory, Division Chem-4, Mail Stop 5567, Los Alamos, New § With the Physics Department. ll Present address: Melles Griot, 1770 Kettering St, Irvine, California 92714, U.S.A. Mexico 87545, U.S.A. 125126 Injluence of Potential Surfaces and Exit-channel Dynamics bimolecular reactions), (ii) the dissociating surface is not always known, since the state accessed initially may couple to one or more electronic surfaces from which dissociation occurs and (iii) inferences are usually drawn on the basis of measurements made on a single species and only a few of the available degrees of freedom. This limitation can leave unanswered important questions concerning the species and degrees of freedom not probed, such as internal state distributions of ‘dark’ fragments and correlations between the excitations of the different fragments.Very often, it is not possible to probe both fragments, and therefore this problem cannot be solved easily. In this paper we address issues (i)-(iii) experimentally and show that the precision which characterizes photodissociation experiments with small molecular systems can be carried forward to the realm of large molecules, more than one PES, binary encounters and complete energy mapping of nascent products. Nascent state distributions alone are often insufficient for characterizing the PESs and the associated molecular dynamics, and it is important to measure complementary features which provide critical tests of the proposed models. For example, in the case of A -P B + C at a specific total energy, determining the centre-of-mass (c.m.) kinetic energy distribution for a particular quantum state of species B automatically provides the internal energies of species C which are associated with the specified state of B.In the special case when one of the products is produced only in a single state (e.g. RH + R+ H, where H is always in its ground state), knowledge of the c.m. kinetic energy distribution gives the entire internal energy distribution of R. In cases where reaction rates can be measured in real time, it is possible to use temporal discrimination to establish the participating surfaces and to obtain the nascent product excitations associated with the individual PESs.Thus, we can separate ‘statistical’ from ‘non-statistical’ pathways, distinguish large molecule radiationless decay channels [intersystem crossing (ISC) and internal conversion (IC)], and obtain qualitative information about So, S, , and T1 PESs such as mode-specific couplings, energies, barriers etc. Finally, we can exploit this precise knowledge of the fragmentation process by combining the production of well defined product excitations with the interactions of such species with other molecules under conditions of high orientation and alignment. These conditions are achieved by preparing van der Waals type precursors which serve to arrange reactant geometries rather precisely. Here, the electronically excited PES which dissociates one component of the binary complex yields a product which can go on to react via a ground-state PES in a way that has no simple counterpart in the homogeneous gas phase.We start with the very simple case of HBr in which 193.3 nm photodissociation prepares H atoms having ca. 256 kJ mol-’ of kinetic energy in the c.m. system. In the case of ground-state products, the predominant reaction is: * HBr(X ‘C+) + hv( 193.3 nm) + H(2S) + Br(2P,,2) hv - Do = 21 430 cm-’. (1) For this system we show not only that sub-Doppler resolution spectroscopy of the nascent H atoms leads to the usual form factors,* but also how a special form of sub-Doppler resolution spectroscopy can provide profiles which can be easily read and interpreted. In these experiments, contributions which arise from velocities not parallel to the wavevector of the probing radiation are eliminated.Since atomic hydrogen has no energy states of concern, these data enable one to infer the internal energy distribution of the ‘dark’ product using the relation G(Eint) = P(E,in>S(E,in = E’ - Eint) where Et = hv - Do, and G ( E ) and P ( E ) are probabilities per unit energy. This technique can be applied to many interesting systems, particularly cases where poly- atomic molecules are dissociated. H atoms are unique in the sense that once the repulsive portion of the exit channel is reached, the subsequent dynamics favour product kinetic energy because of the mass differences. This characteristic enables reasonable qualitativeB. Koplitz et al. 127 interpretations to be made.In several cases, the internal energy distributions are quite revealing and could not have been obtained using LIF or other conventional spectro- scopic techniqup. For ezample, with the Grqup-V hydrides, 193 nm photodissociation occurs via-the A 'Al + X 'A, system, with A 'Al predissociating from geometries far from the X 'Al equilibrium ge~rnetry.~ In the case of PH3(E' = 21 970 cm-'), we find the PH, product to be very highly excited. Few fragments are formed with internal energy below 10 000 cm-', and the distribution peaks at 18 000-20 000 cm-'. The case of NH3 is qualitatively similar. Data acquisition is very rapid, and we should soon be able to resolve product vibrations in several small molecular systems using this method. Next, attachment of CO, to the HBr makes a hydrogen-bonded species of the form C0,HBr.Dissociation of HBr now propels the H atom toward CO,, thereby enabling the reaction: (2) to be studied under circumstances where the initial conditions are severely restricted relative to the homogeneous gas phase.4 Nascent OH(X 211) is measured using laser- induced fluorescence (LIF). In this case, the HOCO intermediate is bound relative to the products, and one wonders if the PES can erase or lessen the system's memory of any entrance channel specificity. This technique can be extended to other systems in which binary complexes are used as precursors, and we are presently doing experiments with H+OCS in order to discern the competitive OH+CS and SH+CO pathways. Here, the OH+CS and SH+CO channels have markedly different AH values (230 and -4 kJmol-', respectively).If we are able to make the H atom approach and attack OCS from the oxygen side, we will establish the ability of this reaction to proceed via a steep uphill path and test the influence exerted on reactivity by the careful arrangement of the initial conditions. Finally, we turn from fragmentation processes dominated by entrance- or exit- channel dynamics to unimolecular reactions initiated by electronic excitation followed by radiationless transitions. Unimolecular reactions involving simple bond fission usually give rise to statistical fragment energy distributions, and consequently do not yield information regarding the PESs involved. We show, however, that with a combina- tion of time-resolved rate measurements and fragment energy disposal, the participating PESs can be unravelled. We choose the specific case of 2-methyl-2-nitrosopropane (Bu'NO) where initial excitation is via a v* +- n transition and the S1 state decays non-radiatively. Just above Do, products accrue via So and nascent NO excitations are characterized by 'statistical' distributions.However, at higher energies, reaction shifts rapidly to the triplet (T,) channel, and the characteristic reaction times for So and T1 differ by three orders of magnitude, allowing NO state distributions to be determined for each pathway. TI is characterized by exit-channel bias, which is likely to favour Etrans, and the internal degrees of freedom of product NO are actually colder than those at the lower Et, where dissociation on So proceeds without a barrier.Such experiments, in which reaction time discrimination can be used to isolate particular channels, enable us to compare bond-fission reactions with and without a barrier. H(*S)+CO,(X 'Z) + OH(X ,II)+CO(X 'X) AH = +lo7 kJ mol-' H-Atom Doppler Profiles from 193.3 nm Photodissociation: HBr and PH3 The 193.3 nm photodissociation of HBr is initiated via a transition to a repulsive PES,' and the ensuing reaction is rapid. This process can be monitored via the Lyman-a transitions (121.6 nm) using the tripled output from a dye laser to excite the H atoms and a fourth photon to ionize H(22P) atoms efficiently, thereby producing protons which are detected with a time-of-flight mass spectrometer. A schematic drawing of a typical experimental arrangement is shown in fig.1. Scanning the dye laser creates a tunable vacuum ultraviolet (v.u.v.) probe with which a Doppler profile for the H atoms128 Influence of Potential Surfaces and Exit-channel Dynamics Fig. 1. Schematic diagram of the experimental apparatus. can be obtained. By combining the counter-propagating laser configuration with the strategy of varying the delay between the firing of the photolysis and probe lasers (td), a new twist on conventional Doppler spectroscopy is realized. For the case of HBr, simply increasing t d drastically alters the observed H-atom Doppler profile. In effect, the probe beam discriminates against H atoms with velocity components perpendicular to the laser propagation axis, and as a result the Doppler profile changes. To understand the nature of what is occuring, a simple model is helpful.Although fig. 2( a ) shows (in cross-sectional form) the present geometry for the photolysis/probe arrangement, a qualitative understanding of the role that delay plays can be gained by examining fig. 2( b). This highly idealized case allows one to focus on the salient features of the method. Photodissociation produces H atoms uniformly throughout the shaded photolysis region (H-atom speed = 2.25 x lo6 cm s-’),’ and we consider the effect which t d has on the Doppler shift spectrum observed at the detection region. The concentric circles represent the spatial regions from which H atoms travelling at 2.25 x lo6 cm s-’ must originate if they are to arrive at the detection point at the indicated delays. For short td, e.g.50 ns, a complete distribution of H-atom velocity components along kprobe is observed, since the entire ‘circle of origin’ is contained within the photolysis region. At longer delays, e.g. 100 ns, the situation becomes different because the photolysis region does not completely contain the ‘circle of origin’. As depicted in fig. 2(6), those spatial regions which would produce H atoms possessing significant velocity components perpendicular to &robe yield no signals, since no photolysis occurs in those regions. Therefore, the Doppler profile will exhibit a large reduction of intensity at frequencies corresponding to little or no Doppler shift, and this reduction will become more pronounced as td increases.A comparison of the places where the 100 and 150 ns circles intersect the photolysis region reveals that the maximum velocity component perpen- dicular to &robe decreases as td goes from 100 to 150 ns, and as a result a wider hole develops in the observed Doppler profile. The geometry shown schematically in fig. 2( a ) is used to model the actual experiment, although the essential character of fig. 2( 6) remains. To accommodate the more realistic129 Fig. 2. Two-dimensional schematic representations of the photolysis/probe region. The shaded areas indicate where photolysis occurs, while the dark areas mark the probe detection regions. In ( a ) , the photolysis beam is a collimated Gaussian (uph = 2.8 mm) and the probe beam is a focused Gaussian ( upr = 0.1 mm).In (b) the concentric circles identify the positions in space from which H atoms travelling at 2.25 x lo6 cm s-’ must originate in order to amve at the detection region at the indicated delay, t,. (a) is close to the experimental geometry, while (b) is simply illustrative. geometry and the spatially anisotropic velocity distributions,2 numerical simulations are done. Taking the photolysis and probe beams as collimated and focused Gaussians, respectively, yields @ph(p> = Kph exp ( - 2 p 2 / u i h ) (3) where aph(p) and Qpr(z, p ) are the fluences of the photolysis and probe lasers, respec- tively, p is the distance from the z-axis, Wph = 2.8 mm is the photolysis beam waist, upr = 0.1 mm is the probe beam waist, Kph and Kpr are constants and zo = ( T ~ & ) / A .The observed signal in the laboratory frame at time t corresponds to S( u,, t) convoluted with the probe laser frequency profile, where S ( vz, t ) is given by where v, is the component of the c.m. velocity in the directioi-: of the probe, v = Iul is the speed, v is the velocity in the laboratory frame (u = c+ v, where c is the thermal velocity of the parent molecule), and u, and vp are the cylindrical components of u. It is assumed that the lasers act as delta functions in time. R,( v,, v ) is the Doppler profile for a particular choice of photolysis and probe polarizations and wavevector orientations,130 Influence of Pot en t ial Surfaces and Exit -cha nnel Dynamics T(v,,-u,) represents the thermal motion of the parent along the z-axis, T[v,- ( u2 - u:)"~] accounts for the thermal motion of the parent in the direction perpendicular to the z-axis, @( v,, v,, t) describes the spatial distributions of the probe and photolysis lasers, and P ( u ) is the desired speed distribution, including the u2 weighting factor for three-dimensional space.The integration over z spans the physical opening to the drift tube, and the integration limits for u, u,,, v, and p are (0, a), (-u,+ u ) , (0, a) and (0, a), respectively. This model provides calculated Doppler profiles at specific delays, which can be compared to the present experiments and used to estimate the signal-to-noise ratio and resolution. It predicts that for sufficiently long delays and a sensible choice of laser polarizations, that the Doppler profile associated with a specific value of kinetic energy will have two peaks, corresponding to molecules traveling parallel and antiparallel When fitting the calculations to the experimental results, there are several parameters which must be adjusted.Spatial anisotropies deriving from the p E electric dipole interaction are introduced through factors such as the R,(u,, u ) of eqn (9, which have especially simple forms for the dissociation of diatomics and many linear molecules.2 However, for a polyatomic, this factor takes into account the number and location of the equivalent H atoms as well as the location of p relative to the molecular frame. This complexity can be lessened if dissociation is nearly isotropic, which is often the case (e.g. predissociation on a timescale that allows the parent to rotate and/or vibrate will smear the anisotropy resulting from the p E interaction).Having chosen a form for R,(v,, u ) , we then choose P ( u ) and calculate the Doppler profile at the different delays. P ( u ) is adjusted until the fit is reasonable, and we also estimate the range of P ( v ) which provides satisfactory fits. This stage is qualitative; we do not yet have a quantitative criterion for what constitutes an acceptable fit. The distribution for Eint is obtained using to kprobe- The effect of probe delay on both experimental and calculated Doppler profiles is presented in fig. 3 for the case of HBr photodissociation. The photolysis of HBr should not lead to spatially isotropic fragment velocities, and the observed Doppler lineshape for td = 30 ns is, in fact, characteristic of a perpendicular electronic transition followed by rapid dissocation.* As expected, the profile changes dramatically with increasing td, and with sufficient delay, the lineshape evolves into two peaks corresponding to H atoms whose velocities are nearly parallel to kprobes At t d = 280 ns, the resolution is limited by the present dye laser system (ca.0.6 ern--' at 121.6 nm). As shown, the calculated Doppler profiles for HBr are in fairly good agreement with the data. In these calculations, P ( u ) consists of a single speed, and the asymmetry parameter used in R,(v,, u ) is for a perpendicular transition with kprobe parallel to kphotolysis, an unpolarized photolysis beam. The asymmetries and random fluctuations in the spectra are due to inexact spatial alignment of the laser beams and timing jitter.Despite these (temporary) technical difficulties, the signal-to-noise ratio is high, even at long delays. The case of HBr photolysis is special since the H atoms are nearly monoenergetic. The Br spin-orbit states (2P1/2 lies 3685 cm-' above 2P3/2) result in two speeds, with dissociation leading predominantly (85%) to the Br ground state.' For the purposes of the present discussion, the difference between the two speeds is not significant (2.25 x lo6 and 2.05 x lo6 cm s-'), and the point we wish to emphasize concerns using this technique to obtain kinetic energy (and thus internal energy) distributions. Examination of the t d = 30 ns spectrum in fig. 3 reveals a Doppler width of ca. 12 cm-', in accord with the maximum possible H atom speed.However, in general the lineshape alone does not prove that the speed distribution is narrow. On the other hand, the t d = 280 ns spectrum yields not only the maximum speed, but also illustrates the narrowness of the distribution. This finding, of course, is consistent with what one would expect for the trivial exampleB. Koplitz et al. 131 I 1 I I I I 1 1 1 1 I 1 v, - 5 I 1 I l I I I I I I 1 I I 1 1 +5 -5 VO V.U.V. probe frequencylcm-‘ Fig. 3. (A) Experimental and (B) calculated Doppler profiles for H atoms (Lyman-a) produced by 193.3 nm HBr photolysis. Td = ( a ) 30, ( b ) 100, (c) 220 and ( d ) 280 ns. The experimental td values are uncertain by *50 ns. The calculated curves are from eqn (3)-(6).vo = 82 259.1 cm-’. of HBr photodissociation. However, when photolysing a larger molecule or a cluster, a priori knowledge of the H atom speed distribution is no longer possible, because of vibrational and rotational degrees of freedom in the remaining species. Yet the principle which led to the simplification of the Doppler profile in the case of HBr still applies when photolysing polyatomic molecules, where the speed distribution may be broad. The agreement between experiment and calculation at td = 280 ns is quite satisfactory, and eqn (3)-(6) predict that a reduction in the laser bandwidth by a factor of 10, while maintaining constant fluence, will increase the signal-to-noise ratio by ca. 2, suggesting that this method can be extended to much higher resolution (e.g.6 E / E < 0.01) without serious signal-to-noise problems. We now show how this method can be applied to the case of polyatomics. Measure- ments have been carried out for PH3, NH3, H2S, and C2H2, which all serve as reasonable examples.6 Here we elaborate on the case of PH3, since our LIF measurements on the PH2 fragment indicate that the 193.3 n,m photolysis of phosphine at sufficiently low fluence produces predominantly PH2(X * B , ) with 21”) 3.’ However, because of the complexity of the PH2 spectrum, it is nearly impossible to obtain the nascent internal energy distribution using conventional spectroscopic methods such as LIF. The 193.3 nm132 Influence of Potential Surfaces and Exit-channel Dynamics photodissociation of PH3 provides a large amount of excess energy (21 970 cm-') which must be distributed between product internal and c.m.kinetic energies: PH,(r? 'Al)+ hv( 193.3 nm) + PH,(A 'Al) -+ PH2(2 2Bl) + H(2S) ( 7 a ) + PH2(A 2Al) + H(*S). ( 7 6 ) Unless PH3( A 'Al) experiences v2 (umbrella-mode) vibrational motion prior to reaction, the PH2 nascent rotational excitation will be small, since repulsion between phosphorus and the departing H atom cannot exsite rotations effisiently. Also, the bond lengths and HPH angles are similar for PH3(X 'Al) and PH2(X 2Bl) (Re = 1.4195 and 1.418 A; HPH 93.2 and 91.7 O, re~pectively),~,' so that direct dissociation, which projects the PH3(X 'Al) bond lengths and angles onto the PH2 eigenstates, leads to little product vibrational exciiation for the dominant reaction channel, reaction ( 7 a ) .On the other hand, the PH3(A_'Al) equilibrium geometry is almost planar, with LHPH =r 115 0,3 while LHPH in PH2(X * B , ) is only 91.7 '. If the repulsive portioc of the PES is accessed from near this geometry, there will be a large amount of PH2(X 2B1) bendingexcitation, with 5tretching modes contributin less, since the bond lengths of PH3(A and PH2(X *B1) differ by only 0.007 1 (1.425 and 1.418 A, respectively). In addition, dissociation from a nesr-planar PH, geometry requires that the nuclei move from the djstinctly non-planar X 'Al equilibrium position, and since the barrier to inversion on A 'A, is small compared to Ei? PH2 rotations may also be ezcited. Thus, there is good reason to expect vibrationally and rotationally excited PH2(X 2Bl), a? is deduced (very qualitatively) from LIF meas~rgments.~ It is also known that PH2(A 2Al) is a nascent product, albeit minor, and the A 2Al equilibcum bond lengths and angles (1.389 A and 123.2 o)8 are close enough to those of PH3(A 'Al) so that Lovibrational excitation will be modest if this exit channel is accessed from near the PH3( A 'A,) equilibrium geometry.By measuring the H atom kinetic-energy distribution, it should be possible to distin- guish between several of the possibilities listed above. For example, if excitation is to a repulsive PES and dissociation is rapid, the H atom will carry away nearly all of the available energy, and the PH2 will contain modest internal excitation. At the other extreme, if the product c.m.kinetic energy is low, the system must have attempted a severe geometry change before entering the exit channel. In between, it will be possible to fit distributions using simple geometric arguments as described below. Data for the case of PH, are shown in fig. 4. The most striking feature is the narrowness of the Doppler profile for td = 50 ns. The maximum shift allowed by energy conservation is k6.2 cm-', corresponding to E' = pu2/2, and the distribution is clearly peaked at much lower values. The distribution of c.m. kinetic energies corresponds directly to the PH2 internal energy distribution, and it is obvious that PH2 contains a great deal of internal excitation. The entries corresponding to td = 50, 300 and 500 ns are used to obtain the shape of the H-atom kinetic-energy distribution, as discussed above.When only an isotropic distribution of H-atom velocities is assumed, the fits at the longer delays are not good, as shown in the upper entries of fig. 4. However, when spatial anisotropy is introduced by making the fractional contribution of low kinetic energies increase with time, the fit becomes reasonable. In fitting the data at 50, 300 and 500ns, it was necessary to assume that ca. 4, 10 and 15%, respectively, of the H ajoms have low kinetic energy, corresponding to PH2 internal energies in excess of the A 2A, origin. This is shown in the lower entries of fig. 2, and these low kinetic energies may correspond in part to the channel producing PH2(A 2A1) + H. More refined experi- ments will probably resolve this.The kinetic-energy distributions shown in fig. 5 ( a ) are narrow, peaking at low energies. The solid and dashed curves correspond to two different fits which are on the edge of acceptability ( i e . the best fit would lie between these curves). The speed distribution obtained by fitting eqn ( 5 ) , while not unique, cannot depart significantlyB. Koplitz et al. P * (D * N 0 N I U I u) I 133134 Influence of Po tent ial Surfaces and Exit-cha n n el Dynamics 0.04 0 0 10000 Ei,,/ cm- ' 20000 Fig. 5. ( a ) H-atom kinetic energy distributions from PH3 photolysis; PH,(g ' A ) + Av( 193.3 nm) + PH,+ H; E' = hv - D,(PH,-H) = Ekin + Eint. The solid and dashed lines define the range of acceptable fits. ( b ) PH, internal energy distribution corresponding to the curves shown in ( a ) .from the curves shown in fig. 5 ( a ) and still provide a reasonable fit to the data. Fig. 5( b) shows the corresponding PH2 internal energy distributions associated with the distributions shown in fig. 5( a ) . The P( Eint) distribution is narrow and 'inverted', with a most probable Eint of 18 000-20 000 cm '. Clearly, PH2 formed by 193.3 nm photodis- sociation is very excited, with few fragments having Eint < 10 000 5m-l. The results show why the LIF measurements cannot resolve the nascent PH,(X 2B,) internal energy di~tribution.~ LIF spectra from such highly excited molecules would involve many states, and for high vibrational excitation, the Franck-Condon factors would be spread over a number of vibronic bands. Presently, our measurements cannot discern the relative amounts of PH2 rotational and vibrational excitation, and it is possible that both rotations and vibrations are excited. For example, the PH3 v2 umbrella mode correl?tes with rotation about the a-axis of PH2, while the equilibriym geometry of free PH2(X 2Bl) differs markedly frcm that of the PH2 part of a PH3(A 'Al) molecule.Electronically excited PH2(A 2Al) is energetically accessible, as shown in fig. 5, and is known to be formed directly via 193.3 nm photoly_sis. Sam and Yardley' estimated that <2% of the dissociation events result in_PH2(A2Al), and for these cases the H atoms will be relatively cold. They find an A2Al vibrational distribution, which isB. Koplitz et al. 135 curious, but on average the vibrational excitation decreases monotonic?lly with I$.Our measurements indicate that the majority of the PH2 is formed in the X 2B, state, since over half of the PH2 molecules have internal energies lying below the A2Al origin. From our results it is also clear that dissociation does not occur via a, unimolecular reaction mechanism on a PE? that correlates without a barrier to PH2(X 2B1) + H(2S). Were this the case, the PH2(X 2Bl) V, R distribution would be more statistical than it is. Muller et aL3 have carried out a6 initio calculations at the HF and CI level, yhich provide insight into the possible dissociation mechanisms. They find that tbe PH3( A-'A,) state is very weakly bound, in accord with the continuous nature of the A 'Al + X 'Al absorption spectr?m, and the lowest triplet, a" 3A1, is dissociative for all reasonable geometries.The A 'Al state is-barely pyramidal, while a" 3A1 is planar CA;), and in a planar C2" symmetry both the A 'Al and a" 3A1 states correlate with PH2(X 2Bl) + H(2S). However, when the symmetry is lowercd, there is an avo-ided crossing which results in adiabatic surfaces w@ch connect PH3(X 'Al) with PH2(X 2Bl) + H(2S), and PH3(A 'A, or a" 3A1) with PH2(A 2B1) + H(2S). Although a reaction coordinate was not deterqined in the a6 initio calculations, enough geometries were sampled to insure that the A 'Al surfacehas shallow minima which may not support bound eigenstates. From the shape of the A 'A, surface, it follows that dissociation could be veryJast, and we believe that the i3A1 surface will not be strongly enough coupled to A 'Al that singlet-triplet transitions would be competitive with dissociation. Since the PH3 transition moment lies parallel to the C3, axis," there should be a bias in favour of H atom velocities which lie parallel rather than perpendicular to kprobe.This prejudice will be especially true for molecules which have moved toward planarity before the H atoms are expelled. It should be noted that near-planar species which develop repulsion along a PH2-H coordinate _will lead t,o high PH2 internal excitation regardless 9f whether PH2 is formed in the X 2B1 or A 2A1 state. In the case of the latter, the A 2A, state requires so much energy (18 300 cm")" that little is left over for c.m. kinetic energy. With the forqer, the HPH angle of ca.115 " deriving from the near-planar configuration of PH3(A 'Al) is quite different thsn the PH2(X 2Bl) equili- brium angle of 91" 42'. This disparity should encourage PH2(X 2B1) bending excitation. Thus there will be a tendency for the detection of species with low kinetic energies to be favoured by the anisotropy at long td, since planarity is associated with (i) maximum spatial anisotropy, (ii) more efficient detection of H atoms using the present experimental geometry and (iii) high PH2 internal excitation. This is in accord with our observations. At short fd, we find that several percent (e.g. 4% at fd = 50 ns) of cold H atoms improve the fit over what could be obtained from an isotropic distribution. This percentage increases to 10 and 15% at td=300 and 500ns, and this may be due to the spatial anisotropy.In a separate paper, we will discuss the procedures used to fit the experi- mental resu~ts.~ Rough Frangk-Condon factors were calculated for several PH2 geometries projected onto the PH2(X 2Bl) eigenstates. For an HPH angle of 120" and using PH3(A 'Al) bond lengths, the PH2(X *B,) vibrational energy distribution peaks near 6000 cm-: when assuming minimum uncertainty Gaussian packets with the same widths as PH2(X 2B1). Narrower widths and better vibrational wavefunctions move Evib to higher energy, and we are in the midst of these calculations. It will also be necessary to estimate E r o t , and this can only be done after understanding the motions which transpire on the PH3( A 'Al) PES. For now, we note that the data can be reconciled qualitatively using a model in which initial PH3 excitation is followed by motion toward a planar geometry, and the repulsive part of the PES is accessed from the near-planar configuration. H Atoms approaching Molecules with Entrance Channel Geometric Specificity We now turn to cases where H atoms are prepared by HBr photodissociation for the specific purpose of studying bimolecular encounters with alignment, orientation andh 2 5 3 E 4 c .3 * 1 3 - 2 2 2 1 2 a a 0 .d Y 1 5 10 15 rotational quantum number, N Fig.6. (a) SD and (b) OD rotational distributions from the bulk D + OCS reaction; Eki,(c.m.) = 244 kJ mol-'. (a)O, Rii, Q i i ; 0, R22, 4 2 2 ; ( b ) 0, Rii; @, R22; 0, Q i i ; a, 4 2 2 - $3 3 aB. Koplitz et al. 137 impact parameters carefully arranged.As mentioned in the introduction, we have already used the C02HBr van der Waals precursor in order to locate the H atom relative to the C02. HBr photodissociation propels the H atom toward the C02 with a set of initial conditions which is quite restricted relative to unbiased encounters. The results of these experiments have been published: and H + D substitution produces no significant diff erences.12 The technique can be applied to many cases in which the precursor geometry of the complex under consideration (or similar complexes) is known from experiments (e.g. SCOHF13 and HFHX, where X = F,14Cl16) or a6 initio calculations (e.g. 02HF),16 and we are presently working on the reaction: D+OCS + OD+CS AH=230kJmol-' ( 8 4 + SD+CO AH = -47 kJ mol-'.( 8 6 ) The two paths differ markedly in energy, and with Ekin = 244 kJ mol-', reaction ( 8 a ) is barely possible. Deuterium is used rather than hydrogen simply because SD can be detected by LIF (SH is quite difficult because of prediss~ciation).'~*'~ With the D atom approaching the oxygen end, it may be possible for reaction ( 8 a ) to be favoured, despite the large energy difference, and we wish to determine the role of the initial conditions (geometry and velocity) in this and similar systems. In preliminary experiments, we have studied reaction ( 8 ) under bulk conditions and the most important results are shown in fig. 6. These data were obtained using low pressure samples and short fd (i.e. single-collision conditions), and the nascent distributions are independent of fd .For the OD channel, E' == 14 kJ mol-', and the distribution is characteristic of the statistical regime [( E,,,( OD)) = 3 kJ mol-'1. This is not surprising, since small E provides ample time for the nuclear motions to erase or lessen the system's memory of the initial conditions. On the other hand, the very large Et associated with reaction ( 8 6 ) can encourage non-statistical behaviour, since the reaction time will be very short.'' The SD distribution is quite non-statistical, since (E,,,) == 4 kJ mol-', while E ' == 290 kJ mol-'. While not unique, one explanation of this coldness is that the entrance channel D-SCO motion evolves very rapidly to a classical turning point at a region of the PES in which the SD bond is formed and the S-C coordinate is repulsive.Subsequently, it is hard to make SD rotate because the repulsive force against the S atom is toward the SD c.m. Further discussion awaits more detailed experimental studies. In the bulk experiments, g g a =r 0.1 n 8 b . This is hardly surprising considering the energetics. If we are able to study reaction ( 8 ) using an SCODBr precursor, as with the analogous C02HBr system, the results should prove most enlightening. This is an example of how many of the virtues and methods of photofragmentation studies can be used to advantage in studying processes which are essentially bimolecular in chracter. The Photodissociation of Expansion-cooled Bu'NO Finally we look at unimolecular processes which are carried out using photoexcitation to prepare an electronically excited state which undergoes radiationless decay to dissocia- tive states.These cases are distinct from the HBr and PH3 examples given above, in that the dissociative PES is not steeply repulsive at the point of access. Thus, dissociation has little direct character other than that deriving from a small exit channel barrier which is approached after considerable nuclear motion. We will concentrate on nitroso molecules, but the principles apply to numerous molecular systems. The predissociation of nitroso compounds has been examined previously, yielding information about mechanisms ( HN0),20 overall rates (CF3N0),2'722 and energy par- titioning among fragments ( CF3NOT NCN023-25); fig. 7 shows schematic potential curves for the low-lying So, S, and TI surfaces.For HNO and NCNO, near threshold reaction proceeds via radiationless decay o f S1, followed by intramolecular vibrational138 Infruence of Potential Surfaces and Exit-channel Dynamics Fig. 7. A schematic diagram of the three lowest potential surfaces of a typical nitroso compound: RNO + R+ NO. redistribution (IVR) and reaction on So. Nascent CN from NCNO is very cold at threshold ( Eint < 0.4 ~ m - l ) , ~ ~ and for all E t studied (=a000 cm-I) the fragment distribu- tions can be fitted accurately using a statistical model which assumes a loose transition state and no exit-channel In the case of HNO with E t ~ 9 0 0 c m - ' , predissociation occurs from levels which cannot couple directly to So because of sym- metry,20 and T, is therefore implicated. Unlike NCNO, CF3N0 yields NO on a con- venient timescale ( ~ 2 0 0 ns), but unfortunately the rate-limiting step is the radiationless transition out of S, .22 Nascent NO populations deviate from statistical predictions at E t a 1000 cm-*, and the role of TI is unclear.22 There are several reasons for studying the predissociation of Bu'NO.It is structurally similar to CF3N0, but with more vibrational degrees of freedom (39 us. 12), and consequently the So and TI surfaces have much higher densities of states. This results in faster S1 radiationless decay than for CF,NO, while RRKM theory predicts that reaction via So will be much slower than for CF3N0 (e-g. several ps with E' = 500 cm-'). In principle, this permits temporal separation of the radiationless decay process( es) from unimolecular reaction on So.Earlier work with 300 K Bu'NO failed to uncover a slow reaction rate (Tdiss < 10 n ~ ) , * ~ but it was not clear whether this was due to incomplete IVR, dissociation on TI, or the fact that hot bands can dominate the 300 K observations, particularly near dissociation threshold.27 There was also a sudden drop in the S, fluorescence quantum yield (af) at exciting wavelengths (A,) below 695 nm, which was manifest as a dramatic signal decrease in the 300 K LIF spectrum.27 Thus, we decided to examine Bu'NO predissociation using a free-jet expansion in order to (i) measure reaction and radiationless transition rates, (ii) investigate the role of TI , (iii) compare the reaction rates to statistical theory and (iv) compare the results of theories of fragment energy disposal.and only details specific to the present measurements are given here. Helium carrier was used to minimize clustering of Bu'NO. The terminal expansion velocity in the molecular beam (ca. 2 mm ps-') makes it difficult to use focused laser beams at values of td in the ps regime. Thus one-photon LIF was used to probe NO, and tunable U.V. was generated using a Nd:YAG An account of the experiment can be foundB. Koplitz et al. 139 pumped dye laser, frequency doubler and Raman shifting device. Approximately 50 p J was obtained from the 2nd anti-Stokes shift in H2. The photolysis source was an excimer pumped dye laser (3 mJ, f.w.h.m. = 0.4 cm-', 15 ns duration). The beams counter- propagated collinearly, perpendicular to the expansion, and focusing the photolysis beam with a 1 m lens produced optimum signals without causing two-photon Bu'NO excitation.The experiment was controlled by a computer and programmable eight- channel pulse/delay generator. Five types of data were collected: (i) LIF spectra of Bu'NO, (ii) Bu'NO fluorescence lifetimes ( Tf), (iii) NO yield spectra (i.e. photodissoci- ation spectra), (iv) NO appearance rates and (v) LIF spectra of nascent NO. With (i)-(iii) the experimental methods are by now routine, and details can be found in the NO appearance times were hard to measure accurately, because of the high expansion velocities and long fragment appearance times. The procedure was tedious and will be described fully in a separate publication.28 NO LIF spectra were recordzd by tuning A, to the desired Bu'NO peak, setting td, and scanning the A 2E+( v' = 0) t X 2rI( zl" = 0) spectral region.24y28 The low-J region was recorded in the 'on/off mode',24 since background NO proved impossible to eliminate.Bu'NO monomer was prepared from the dime^-,^' and all sample preparation was done in a glass vacuum line. A Teflon-coated pulsed nozzle minimized the background NO which accompanies sample degradation. Typical Bu'NO LIF spectra are shown in fig. 8(a). The most striking feature is a convergent progression extending from the red, with rapidly increasing intensity to higher energy, which is very similar to the one observed for CF3N0.31 Without doubt, this is v39, the t-butyl torsion. The longest wavelength peak shown in fig.8( a ) is a weak feature at 713.46nm which is barely discernible above the noise, and may still not be the electronic origin. Making no assumptions about the origin, the torsional progression was fitted using a three-fold sinusoidal potential and tabulated solutions of the Mathieu equation.32 This fit indicates that the weak feature at 713.46nm is the second member of the torsional progression (39;). By scanning very slowly, with our highest signal-to- noise ratio, a weak feature was observed at 718.64 nm and is tentatively assigned as the electronic origin (13 91 1 cm-'). We were also able to identify the CNO bending pro- gression, and a detailed account of the spectroscopy will be published separatelyS2* Thus most of the absorption peaks used in the present study can be definitely assigned to torsional and/or CNO bending modes in S1, and these modes are known to be efficient in promoting radiationless transitions in nitroso corn pound^.^^^^^ The S, -So transition is orbitally forbidden, and both HNO and CF3N0 have rf= 30 ps.33-35 In the case of jet-cooled CF3N0, rf values are G200 ns near the S1 origin,22 and the small Of (<lo-*) are due to efficient radiationless decay. Although Bu'NO is similar to CF3N0 in many ways, the larger number of normal modes results in much larger So and T1 densities of vibrational states.Using the Whitten-Rabinovitch method,36 we estimate that at 14 000 cm-' above So the densities of states for CF,NO are p(So) = 106/cm-' and p(T,) = 5 x 103/cm-', whereas for Bu'NO, p(So) = 2 x 10'2/cm-1 and p(T1) = 2 x 108/cm-', assuming TI is 7000 cm-' above So.The increased densities of states of Bu'NO relative to CF3N0 leads to increased radiationless transition rates. For A, > 685 nm, there is little dependence of the Tf values on S, level for the narrow range of Et studied (300-500 cm-'), and T~ = 40 ns for all levels for which meaningful measurements could be made. This is indicative of the large molecule limit for radiation- less decay into a state with a near continuous level density. At A,=685 nm there is an increase in the radiationless decay rate, suggesting the opening of another channel, and for A,<685 nm there are a few levels with Tf=30 ns, but generally T f d 15 ns, the experimental resolution. The LIF spectra shown in fig.8( a ) show that Of drops at 685 nm by at least an order of magnitude. The Bu'NO dissociation spectra were recorded by setting the probe at the NO P,, bandhead while scanning and fig. 8 ( 6 ) shows such a spectrum obtained with140 Injluence of Potential Surfaces and Exit-channel Dynamics 39; + CNO bending 3 9 3 I I ( b ) I I I 1 I I I I I 710 700 690 680 670 excitation wavelength/nm Fig. 8. Bu'NO LIF and NO yield spectra as a function of A,. ( a ) is Bu'NO LIF with spectro- scopic assignments indicated where known. ( b ) and ( c ) are the NO photodissociation yield spectra recorded with the probe laser set to the PI, bandhead of NO at 226.3 nm, with laser delays of 60 ns and 3.2 ps, respectively. All the spectra are corrected for laser energy. td = 60 ns, compared to the LIF spectrum for the same region.A striking feature is the onset of NO production at ca. 685nm. However, dissociation spectra recorded with td = 3.2 ps [fig. 8(c)] show a significant production of NO at A,> 685 nm as well, indicating long appearance times for NO produced at A,> 685 nm. There is good correspondence between the LIF spectrum and the NO yield spectrum, and at A,< 685 nm there is a similar correspondence between the 60 ns and 3.2 ps yield spectra.B. Koplitz et al. 141 NO "fast" appearance times t - 40ns 679.66nm **p* - *-• . t = 35ns 676.73 nm . 0 100 delay (ns) 0 ' ..* *... * * * * * . t > 6 0 n s am.,.* 683.53nm 0 100 I I I I delay (ns) T < 20ns 675.96nm u 0 100 delay (ns) NO yield spectrum pump-probe delay = 60 ns monitoring NO P,, bandhead " I I 1 I I 690 680 670 excitation wavelength/nm Fig.9. NO appearance rates following excitation near the onset of the 'fast' process at ca. 685 nm (see text). These data show that NO production results from predissociation of Bu'NO following S , excitation, and that for A, > 685 nm the NO appearance rates are considerably slower than the S, decay rates. As seen from fig. 9, once the 'fast' channel opens, NO appearance is rapid ( s 6 0 ns). The rate increases with photon energy, and for A, <670 nm the NO appearance times are s 1 5 ns. There are peak to peak variations in the rates, probably due to variations in the ISC and/or IC couplings. This is supported by the fact that the peaks with small mf in the LIF spectrum are those with the most rapid production of NO.Most of the peaks shown in fig. 9 have biexponential NO appearance rates. Although the > 1 ps part of the appearance time could not be studied quantitatively (both amplitude and rate), the amplitude of the fast component definitely increases with E' relative to that of the slow component, and the fast component is dominant at A,<675 nm. Because of experimental difficulties, only two slow NO appearance rates could be confidently studied (A, = 693.67 and 696.95 nm, T = 3.4 f 0.5 and 3.7 * 0.5 ps, respectively), but all other dissociation times at A,> 685 nm are longer than 1 ps. These measurements demonstrate quite definitely that radiationless decay (ca. 40 ns) and unimolecular reaction (>3.5 ps) can be separated temporally. Nascent NO distributions were measured for two reasons.Owing to the opening of a rapid dissociation channel at A, < 685 nm, So dissociation rates could not be followed142 Influence of Potential Surfaces and Exit-channel Dynamics r i i i i i i I I I I I I I 1 1 1 1 I I I I I 227.00 226.50 226.00 225.00 wavelength/ nm Fig. 10. ( a ) The nascent one-photon A 'Z+ t X 211 LIF spectrum of NO following Bu'NO photolysis in the 3 9 r band at 693.67 nm, recorded with fd = 2.5 ps; ( 6 ) A simulated spectrum assuming Et = 487 cm-' and statistical partitioning of Et (prior distribution). to high Et and compared with RRKM theory. However, by measuring the nascent states of NO and comparing the distributions to calculations, conclusions regarding the statistical nature of the dissociation process can still be drawn.Also, since Do is below the S, origin, it is not possible to directly determine Do from the onset of predissociation. However, Do can be measured indirectly by observing the highest NO rotational level populated at several A, values or (if the populations are statistical) by fitting several populations to find their Et values and hence Do, The ButNO absorption peaks were divided into two groups, A,> 685 nm and A, < 685 nm. NO LIF spectra were obtained for A, > 685 nm using td = 2.5 ps, and fig. 10( a) shows a typical spectrum obtained with A, = 693.67 nm. The rotational and spin-orbit distributions correspond roughly to a temperature. In contrast, both NCN024 and CF3N02* yield NO with cold spin-orbit populations. Unfortunately, the Boltzmann-like distributions make it hard to derive a consistent value of Do by finding J,,, for various A,, as the high-/ signals are lost in the noise.Statistical theories can be used to calculate nascent distributions, e.g. phase-space theory,37i38 and modifications such as the separate statistical ensembles method26 and the statistical adiabatic channel However, calculations using these models are time-consuming for large molecules, and therefore we chose to use prior While these calculations do not conserve angular momentum, this omission is not significant for large r n o l e c ~ l e s . ~ ~ ~ ~ ~ Nascent NO populations were fitted with Et being the only adjustable parameter,28 and for A, > 685 nm the calculated and experimental distributions match very well for all levels for which rotational populations were available. Do was estimated using Do = hv - Et.There is good agreement between the various values obtained in this way (k20cm-'), and we assign Do the value 13 930*30 cm-'. In fig. 10 and 11, the experimental NO spectra and populations for A, = 693.67 nm (Et = 487 cm-') are compared to calculations using Do = 13 930 cm-'. The simulation has been described for two-photon e~citation,~~ and the only modification here is the use of one-photon selection rules and line strengths.44 The agreement between theory and experiment is excellent, despite a few deviations at high-J, due to digitizing small signals. Our value of Do is very close to that for CF3N0 (13 856 * 79 cm-1)22 and143 Fig.11. Nascent NO rotational state distributions [II,,,(O) and I13/2(a)] following photolysis at 693.67 nm (39p transition) compared to a prior distribution using Et = 487 cm-' (-). Note that the curves for the two spin states of NO coincide. The populations can be described by a temperature of 470 K. 227.00 226.50 226.00 wavelength/nm Fig. 12. Nascent NO LIF spectrum following photolysis at 679.71 nm; (a) td = 70 ns; ( b ) td = 2.5 ps. NO(A 2C t X 211), Et = 782 cm-'. confirms the value obtained from thermal measurements by Benson and coworkers (13 800 f 500 ~ m - ' ) . ~ ~ Nascent NO LIF spectra were recorded for several A,< 685 nm using td values <lo0 ns, and the case of A, = 679.71 nm is shown in fig. 12(a). The most striking feature is the large difference between the populations of the two NO spin-orbit states.This cold spin-orbit ratio is typical of spectra obtained with A,<685 nm (ie. much colder than expected from statistical theory). Fig. 13 shows a comparison of the population144 Influ en ce of Poten t ia 1 Surfaces and Exit- c h a n n el Dynamics I 8 -31 - 0 8 1 1 I I I8 Einternal/Cm-' Fig. 13. Nascent NO rotational state distributions [II,,,(U) and I13,,(H)] following photolysis at 673.09 nm compared to a prior distribution using Et = 927 cm-' (-). Notice that the NO spin states are anomalously populated (re. [I13,J<< [II,,,]) and that the distribution cannot be fit to a temperature. derived following excitation with A, = 673.09 nm compared to a prior distribution, and it is clear that the experimental rotational distribution is colder than the calculated one.As mentioned above, most of the lines excited with A,<685 nm show various degrees of biexponential behaviour in their NO appearance rates, and fig. 12 shows spectra taken with td = 70 ns and 2.5 ~s for a line (679.71 nm) that shows marked biexponential behaviour. At long t d , the spin-orbit ratio is definitely changing towards a more statistical value. We find that lines which do not exhibit a biexponential behaviour do not show any changes in the spin-orbit and rotational populations with delay time, confirming that collisions in the jet are insignificant. The experiments indicate that there are two processes producing NO, each with a different rate and NO( E, R) distribution.We propose that with A, > 685 nm dissociation proceeds via So. but when A, < 685 nm (Et > 650 cm-') the barrier to dissociation via T, is exceeded, and this channel opens (see fig. 7). The only nitroso molecule for which the PESs are accurately known is HN0,20 but the basic form of the potentials in the R-NO coordinate should be common to all. So has no barrier to dissociation in the absence of rotation, and values of Do range from 13 856+79 cm-' for CF3NOZ2 to 17 085 f 10 cm-' for NCN0.35 Threshold dissociation of NCNO via So leads to cold product^,^' and the S , origin lies ca. 14000cm-' above So, with a barrier on S1 to dissociation to ground-state fragment^.^' Little is known about T,, although its origin has been determined for HNO and is at 6280~m-',~' which agrees with ab initio calculation^.^^ The calculations suggest a small barrier to dissociation via T,, but this could not be accurately estimated.,' However, in HNO, which predissociates near threshold via So,'' a second channel opens ca.900 cm-' above Do and is thought to be dissociation via T, .20 In Bu'NO, Do is below the S, origin. Excitation near the S, origin results in dissociation via So, and in general radiationless transitions may occur via IC ( S , -+ So) and/or through successive ISC (S, --+ So). At these energies, dissociation on So occursB. Koplitz et al. 145 hr, ~ IT,t - Bu' + NO - But+ NO - 51 SO Fig. 14. The proposed mechanism explaining the predissociation of Bu'NO following electronic excitation to a vibrational level of S1.on the microsecond timescale, as expected from RRKM calculation^,^^ indicating com- plete IVR. Although reaction rates could not be measured accurately, nascent NO populations are predicted rather well using simple statistical models.41742 Assuming that the barrier on T, is ca. 650 cm-', then with A, < 685 nm (14 600 cm-l) the molecule has two dissociative pathways available, as shown in fig. 14. At 14 600 cm-' molecules which have undergone ISC into vibrational levels of T1 may undergo either ISC to So or direct unimolecular dissociation. The results indicate that the two processes occur at comparable rates near the top of the T, barrier. This causes the observed biexponential NO appearance rates, since some molecules dissociate on T, very quickly (<20 ns) whereas others remain trapped on So for up to several ps.Variations in the relative amplitudes of the fast and slow components probably reflect variations in the S, -+ T, and/or T, -+ So crossing rates. As they pass the top of the T1 barrier, the NO fragments will be relatively cold due to the small excess energy above the barrier, as opposed to reaction via So. However, the products gain energy in the exit channel, and this is principally in the form of translation (plus some rotation) and will be partitioned between the fragments according to conservation of momentum rather than densities of states. Thus, the distributions no longer conform to a model which statistically partitions E t. The 'cold' NO rotational distributions observed at A, < 685 nm suggest that the energy available for partitioning amongst product internal degrees of freedom is lower than that calculated by Et = hv - Do.In order to gain insight into the release of energy upon crossing the T, barrier, we calculated the rotational and spin-orbit distributions that correspond to Et = hv - Do- Eb, where Eb is the barrier height for dissociation on T1. We find much better agreement with the experimental distributions when the rotational distributions are calculated in this manner, suggesting that much of the potential energy released beyond the barrier is channeled into translation. However, the spin-orbit populations still do not match the experimental ones. A qualitative picture that may be used to describe the NO spin-orbit populations is similar to that used to explain the relaxation and reactivity of atomic spin-orbit ~ t a t e s .~ ~ - ~ ~ At infinite separation, two separate surfaces exist for But+ NO(X 2113,2), while at short interfragment distances the system is described by the electronic surfaces of Bu'NO. The evolution of the system from the surfaces of the separate radicals to the molecular system is governed by spin-orbit coupling, electrostatic interactions and rotation of the nuclei, and these cannot be simultaneously diagonalized at short dis- t a n c e ~ . ~ ~ At large separations, the spin and electronic orbital angular momenta of NO couple to form the total (electronic) angular momentum, which is weakly coupled to the interparticle axis. At small separations, coupling to the internuclear axis is stronger than spin-orbit coupling, and the electrostatic interactions dominate. The transition between the two coupling schemes occurs at intermediate separations, and non-adiabatic transitions between the surfaces are thought to occur mainly at internuclear distances where the electrostatic interactions and the spin-orbit separation are similar ( 123 cm-' in the case of NO).53 Thus each molecular surface contains admixtures of the two spin-orbit states, but their final ratio at infinite separation depends on the couplings and interactions between the surfaces of the dissociating molecule.If the coupling between the electronic surfaces and the nuclear degrees of freedom is weak and/or the146 Influence of Potential Surfaces and Exit-channel Dynamics interaction time is short, the population of the spin-orbit states may be non-statistical, and will vary with the dissociative surface.Thus, the spin-orbit populations may be non-statistical, even when other degrees of freedom are statistical. In Bu'NO and other predissociating molecules, the situation is particulary compli- cated because radiationless transitions indicate coupling between the molecular elec- tronic surfaces as well. The statistical spin-orbit ratio associated with dissociation on So may be due to efficient coupling between 111/2 and 113/2 in the exit channel. For dissociation on T,, if the NO spin is uncoupled from the nuclear motions that evolve beyond the T1 barrier, and the electronic surfaces correlating with N0(2111/2) and NO( 2113/2) are already separated, the NO spin-orbit distributions may be determined by the excess energy at the top of the T1 barrier, and thus be 'colder' than the ones obtained on So.This mechanism is in accord with the results obtained with A,= 679.71 nm, which exhibit a biexponential NO appearance rate and a [2111/2]/[2113/2] ratio that chaiges with delay time. Above the T1 barrier, competition between dissociation on T1 and T1 + So ISC explains the biexponential nature of the NO appearance rate, and in the same region the Qf values decrease dramatically. However, we see no direct relationship between these two processes. Molecules which reach T, do not fluoresce, and their fate is governed by the relative reaction and ISC rates. Conversely, molecules which decay non-radiatively from S, are not influenced by the subsequent dynamics on the TI and/or So PESs.Thus, we conclude that the decrease in Qf with increasing Et is due to enhanced S,-T1 coupling. The torsional modes, which facilitate S1-So coupling, do not seem as important for S1-T, coupling, since these states have the same dihedral angle. Apparently, bending motions, which are excited with h,<685 nm, are much more efficient in promoting ISC, thus accounting for the decrease in Well above the T, barrier, most molecules that have undergone ISC into T1 will dissociate on T, instead of undergoing ISC to S,, since T, ---* products becomes faster than T, --* So. RRKM calculations yield T1 dissociation rates < 10 ns when the T1 origin is > 5000 cm-' above the So origin.49 [we assumed identical transition-state frequencies for dissociation on So and To (see ref (27).] This is consistent with the HNO results, which suggest that the T, origin is about halfway between So and S1.47 In principle, the branching ratio of the two processes out of T, could be determined from accurate measurement of the two amplitudes in the biexponential appearance rates.This is not possible in the present experiments, as described above, and in any case the extent of direct IC (S, + So) cannot be estimated at these energies. Even so, data taken at shorter A, suggest that the 'slow' appearance rate accounts for <lo% of the fragmentation, and it is safe to assume that S, + T, + products dominates at higher energies. The variation of Tf values for A, < 685 nm indicates some mode specificity in the S1 + T1 crossing rates.In addition, the peak at 696.14 nm has a small, anomalously fast component in its NO appearance rate, but it is difficult to tell whether this is due to mode specificity in the radiationless transition or unimolecular reaction steps in this complex system. In summarizing the results of these experiments, we note that Bu'NO is the largest aliphatic nitroso molecule whose predissociation has been studied in detail. It presents not merely another test of statistical theories, but also a case for which the radiationless decay and unimolecular reaction rates can be separated in time. In the interesting region just above Do, Bu'NO definitely conforms to the large-molecule case.It has proved possible to observe ISC and/or IC, and competitive dissociation on two surfaces (So and T,), in addition to assigning some of the S, vibrational structure, which is similar to that of CF,N0.31 As expected for ButNO, radiationless decay is fast ( s 4 5 ns) relative to near-threshold dissociation on So ( T 3 3.5 ps). Dissociation on So leads to nascent NO distributions which can be matched using a statistical partitioning of the excess energy, with a loose transition state and no exit channel barrier. Even the spin-orbit states are populated statistically. Conversely, above a small barrier (cu. 650 cm-') to dissociationB. Koplitz et al. 147 on TI, non-statistical behaviour is observed. S1 ---* T1 + products rapidly becomes the dominant reaction mechanism as the T1 reaction rate increases, and consequently simple bond fission above a barrier can be studied in detail.NO is produced with a rate three orders of magnitude larger than that for reaction on So at the same energy, as expected on the basis of RRKM calculations. The T1 barrier causes non-statistical NO distribu- tions and much of the barrier energy is channelled into relative translation. Also, the [rI3,J/[II1,J ratio is much smaller than statistical, which could be due to the fact that the electron spin is uncoupled from the nuclear motions at the top of the TI barrier. Other angular momentum coupling effects may also be contributing to the cold spin-orbit temperature, seen also in NCNO and CF3N0 predis~ociation.~~’~~ It can be inferred that for large nitroso molecules, predissociation will be dominated by dissociation on T1. Indeed, in CF3N0 it was found that the nascent NO rovibrational populations were non-statistical for Et > 1000 cm-’, and this could be a result of T1 exit-channel interac- tions.In the small energy region above Do and below the T1 barrier, large nitroso compounds offer the possibility of studying isolated activated complexes. These species could have long lifetimes and would make interesting collision partners both for bimolecular reactions and surface scattering. We have benefitted greatly from discussions with R. A. Beaudet, G. A. Segal and P. D. Dapkus. This research was supported by the U.S. Office of Naval Research, contract no. N00014-84-K-033 1. References 1 F. Magnotta, D.J. Nesbitt and S. R. Leone, Chem. Phys. Lett., 1981, 83, 21. 2 R. N. Zare and D. R. Herschbach, Proc. IEEE, 1963, 51, 173. 3 J. Muller, H. Agren and S. Canuto, J. Chem. Phys., 1982, 76, 5060. 4 G. Radhakrishnan, S. Buelow and C. Wittig, J. Chem. Phys., 1986,84,727. 5 C . F. Goodeve and A. W. C. Taylor, Proc. R. SOC. London, 1935, 152, 221. 6 Z. Xu, B. Koplitz, S. Buelow, D. Baugh and C. Wittig, Chem. Phys. Lett., 1986, in press. 7 D. Baugh, B. Koplitz, Z. Xu and C. Wittig, unpublished work. 8 J. M. Berthou, B. Pascat, H. Guenebaut and D. A. Ramsey, Can. J. Chem., 1972, 50, 2265. 9 C. L. Sam and J. T. Yardley, J. Chem. Phys., 1978, 69, 4621. 10 (a) A. D. Walsh and P. A. Worsop, 4th In?. Conf Mol. Spectrosc., Bologna, 1959 (Pergamon, Oxford, 11 D. A. Ramsey, Nature (London), 1956, 178, 374.12 S. Buelow, G. Radhakrishnan and C. Wittig, unpublished work. 13 F. A. Baiocchi, T. A. Dixon, C. H. Joyner and W. Klemperer, J. Chem. Phys., 1981, 74, 6544. 14 T. R. Dyke, B. J. Howard and W. Klemperer, J. Chem. Phys., 1972, 56, 2442. 15 K. C. Janda, J. M. Steed, S. E. Novick and W. Klemperer, J. Chem. Phys., 1977,67, 5162. 16 A. E. Reed, F. Weinhold, L. A. Curtiss and D. J. Pachatko, J. Chem. Phys., 1986, in press. 17 R. R. Friedl, W. H. Brune and J. G. Anderson, J. Chem. Phys., 1983, 79, 4227. 18 J. J. Tiee, M. J. Ferris and F. B. Wampler, J. Chem. Phys., 1983, 79, 130. 19 K. Kleinermanns and R. Schinke, J. Chem. Phys., 1984, 80, 1440. 20 R. N. Dixon, K. B. Jones, M. Noble and S. Carter, Mol. Phys., 1981, 42, 455. 21 K. G. Spears and L. Hoffland, J. Chem. Phys., 1977, 66, 1755; 1982, 74, 4765. 22 R. D. Bower, R. W. Jones and P. L. Houston, J. Chem. Phys., 1983,79, 2799. 23 I. Nadler, M. Noble, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 82, 2608. 24 C. X. W. Qian, M. Noble, I. Nadler, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 83, 5573. 25 I. Nadler, H. Reisler, M. Noble and C. Wittig, Chem. Phys. Lett., 1984, 108, 115. 26 C. Wittig, I. Nadler, H. Reisler, M. Noble, J. Catanzarite and G. Radhakrishnan, J. Chem. Phys., 1985, 27 H. Reisler, F. B. T. Pessine, Y. Haas and C. Wittig, J. Chem. Phys., 1983, 78, 3785. 28 M. Noble, C. X. W. Qian, H. Reisler and C. Wittig, J. Chem. Phys., submitted for publication. 29 M. Noble, C . X. W. Qian, H. Reisler and C. Wittig, J. Chem. Phys., 1986, 84, 3573. 30 M. Noble, I. Nadler, H. Reisler and C. Wittig, J. Chem. Phys., 1984, 81, 4333. 31 B. M. DeKoven, K. H. Fung, D. H. Levy, L. D. Hoffland and K. G. Spears, J. Chem. Phys., 1981,74, 1962); (b) A. D. Walsh, J. Chem. SOC., 1953, 2296. 83, 5581. 4755.148 Influence of Potential Surfaces and Exit-channel Dynamics 32 Tables relating to Mathieu Functions, US. Nut1 Bur. Stand, Appl. Math. Ser. 1967, 59. 33 R. D. Gordon, S. C. Dass, J. R. Robins, H. F. Shurvell and D. R. F. Whitlock, Can. J. Chem., 1976, 34 R. N. Dixon, M. Noble, C. A. Taylor and M. Delhoume, Faraday Discuss. Chem. SOC., 1981,71, 125. 35 K. Obi, Y. Matsumi, Y. Takeda, S. Mayama, H. Watanabe and S. Tsuchiya, Chem. Phys. Lett., 1983, 36 P. J. Robinson and K. H. Holbrook, Unimolecular Reactions (Wiley, London, 1972). 37 P. Pechukas and J. C. Light, J. Chem. Phys., 1965, 42, 3281. 38 P. Pechukas, C. Rankin and J. C. Light, J. Chem. Phys., 1966, 44, 794. 39 M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem., 1974, 78, 240. 40 M. Quack and J. Troe, Ber. Bunsenges., Phys. Chem., 1974, 78, 1240. 41 R. D. Levine and J. Kinsey, in Atom- Molecule Collision Theory-A Guide for the Experimentalist, ed. 42 E. Zamir and R. D. Levine, Chem. Phys., 1980, 52, 253. 43 D. J. Nesbitt, H. Petek, M. F. Foltz, S. V. Filseth, D. J. Bamford and C. B. Moore, J. Chem. Phys., 44 L. T. Earles, Phys. Rev., 1935, 48, 423. 45 K. Y. Choo, G. D. Mendenhall, D. M. Golden and S. W. Benson, Int. J. Chem. Kine?., 1974, 6, 813. 46 V. Marudarajan and G. A. Segal, Chem. Phys. Lett., 1986, in press. 47 H. B. Elk Jr and G. B. Ellison, J. Chem Phys., 1983, 78, 6541. 48 A. W. Salotto and L. Burnelle, Chem. Phys., Lett., 1969, 3, 80. 49 W. L. Hase and D. L. Bunker, Prog. 234, Quantum Chem. Prog. Exchange (Chem. Dept., Indiana 50 F. H. Mies, Phys. Rev. A, 1973, 7, 942. 51 V. Aquilanti and G. Grossi, .I. Chem. Phys., 1980, 73, 1165. 52 V. Aquilanti, P. Casavecchia, G. Grossi and A. Lagana, J. Chem. Phys., 1980,77, 1173. 53 M. H. Alexander, T. Orlikowski and J. E. Straub, Phys. Rev. A, 1983,28, 73. 54 H-J. Yuh and P. J. Dagdigian, J. Chem. Phys., 1984, 81, 2375. 55 N. Furio, M. L. Campbell and P. J. Dagdigian, J. Chew. Phys., 1986, 84, 4432. 54, 2658. 95, 520. R. B. Bernstein (Plenum, New York, 1979), chap. 22. 1985, 83, 223. University). Received 25th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200125

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986,82, 149-161 Dissociation on Ground-state Potential-energy Surfaces Herbert Bitto,? Dean R. Guyer,$ William F. Polik, and C. Bradley Moore" Department of Chemistry, University of California, Berkeley, California 94720, U. S. A. Two new techniques allowing for the resolved spectral study of dissociation on ground-state potential-energy surfaces are presented. First, Stark level- crossing spectra of highly vibrationally excited ground-state formaldehyde ( S ; ) characterize the initial rovibrational wavefunctions of dissociative for- maldehyde states. Individual S,* D2C0 states are resolved near the barrier to dissociation but broaden and overlap at higher energies. Neighbouring resolvable states possess enough individual vibrational character to vary by over one order of magnitude in lifetime.A potential barrier height of 78.0-81.1 kcal mol-' has been determined for H2C0 + H,+ CO dissociation. Second, photofragment excitation (PHOFEX) spectra probe the production of correlated fragment states from ketene photodissociation. Molecular- beam PHOFEX spectra show that ketene possesses no observable rotational structure and only weak vibrational structure. The PHOFEX spectrum of an individual rotational state of the lowest vibronic state of singlet methylene gives the energetic threshold for formation of that state along with ground- state CO. The threshold for the combination with each successive CO( u" = 0, J") channel is clearly resolved. A statistical calculation reproduces the main features of the PHOFEX spectra.Analysis of the PHOFEX spectra gives a H2CC0 --* 'CH2 + CO dissociation threshold of 30 102 f 15 cm-'. Finally, the effect of a potential barrier in the dissociation coordinate on statistical us. dynamical control of dissociation is discussed. Photofragment spectroscopy and dynamics on ground-state potential surfaces are of particular importance to chemists.' Nearly all thermal unimolecular reactions occur on ground electronic state potential-energy surfaces. Molecules react when they have sufficient energy above threshold for reaction to compete with collision-induced energy transfer. Most unimolecular reaction rate theories postulate that anharmonic and Coriolis couplings cause intramolecular rovibrational energy transfer to be rapid on the timescale of reaction. These theories yield unimolecular reaction rates that are fully described by rate constants, k(E, J ) , depending only on the rigorously conserved quan- tities total energy, E, and total angular momentum, J.The fragments produced by dissociation are necessarily smaller molecules and are often less highly excited. Thus description of the product states often requires a full set of quantum numbers. For the case of rapid intramolecular energy transfer within the dissociating molecule, the most detailed microscopic rate constant is then where nA and n B stand for the full set of vibrational and rotational quantum numbers of fragments A and B. The translational energy and orbital angular momentum are T Present address: Physikalisch-Chemisches Institut der Universitat Zurich, Winterthurerstrasse 190, CH- t Present address: Spectra Technology, Inc., 2755 Northup Way, Bellevue, Washington 98004-1495, U.S.A.8057 Zurich, Switzerland. 1 49150 Dissociation on Ground-sta te Pot en tial-energy Surfaces defined for each E, J, nA, nB by conservation of energy and angular momentum. Thermal experiments produce data which are averaged over broad distributions of E and J and over many, if not all, of the quantum numbers nA and nB. It is therefore of great interest to obtain detailed photofragment energy distributions (resolved nA and/or n,) and absolute rate constants, znA, ng k,,,,(E, J ) , for well defined values of E and J. Although full knowledge and understanding of k,,,,(E, J ) would seem to provide more than an ample supply of information, there are circumstances for which the quantum-state structure and excitation of the reactant must be considered in more detail.When the density of rovibronic levels is less than their average inverse linewidth, individual resolvable quantum states exist. Even if these states are 'ergodic' or 'com- pletely mixed', their properties can be expected to vary from state to state.2 An index ni for the rovibrational quantum numbers of the initial state must be added, For molecules with low dissociation thresholds, e.g. van der Waals molecules, the initial-state wavefunctions for excitation of high-frequency vibrations may be reasonably well approximated by rigid-rotor- harmonic-oscillator basis wavefunctions. Each ni level is well described by a set of quantum numbers. For typical chemical bond-breaking energies, couplings are strong and vibrational quantum numbers impossible to assign; E, J and M (the projection of J on an external axis) are probably the only good quantum n~mbers.~ The nature of individual vibrational wavefunctions may be described only in terms of matrix elements for radiative and non-radiative transitions.Such resolvable states can only exist near the threshold for reaction. At higher energies the rate of dissociation broadens individual levels so that they are overlapping; level-by-level changes therefore are smoothed out. As energy is increased above threshold for reaction, dissociation rates increase and may become comparable to or faster than intramolecular energy transfer rates.Mode specificity depending on preparation of the initial state might be observable. Even in the region of resolvable quantum states close to threshold, coherent superpositions of these states (perhaps even a zero-order state for an uncoupled oscillator basis) may be prepared using short pulses so as to excite preferentially some particular vibrational mode( s ) . ~ Two sets of experiments are described here which probe dissociation of small polyatomic molecules on electronic ground-state potential surfaces. Each experiment attempts to come closer to the goal of determining state-to-state photofragmentation rates. First, molecular eigenstate spectra of dissociative So formaldehyde energy levels (S,") are presented. These spectra yield the dependence of the unimolecular decay rate on the initially prepared S," quantum state.They also illustrate the extent to which it is possible to prepare well defined initial quantum states and explore the nature of these states. Second, photofragment excitation spectra of ketene explore the production of single fragment states at and near the threshold for unimolecular dissociation. The opening of individual product state channels nA, nB is clearly resolved in these spectra. A novel method is presented for accurate determination of the 'CH2 + CO dissociation threshold. The spectra are consistent with a statistical distribution of the available energy. Formaldehyde Dissociation Dynamics Experiment Molecular eigenstate spectra of S,* formaldehyde were obtained using a form of level- crossing spectroscopy.A J, K, IM(-resolved s, rovibronic state is prepared with a narrowband laser in a variable homogeneous d.c. electric field. Since S , and S," have different dipole moments, the S, state is Stark-shifted relative to the S," manifold as the40 30 -i- 20 E 2 m -. Q I C C H. Bitto, D. R. Guyer, W. F. Polik and C. B. Moore D2 + CO 151 30 80 60 I E 9 0 - 24 40 20 0 dissociation coordinate Fig. 1 Potential-energy surface diagram for D2C0. An initially prepared S1 rovibronic state can decay radiatively ( krad) and non-radiatively ( knr). Non-radiative decay consists of So + S1 internal conversion followed by unimolecular dissociation ( kuni) into molecular products D2 and CO. electric field is increased, thereby tuning individual S," states into and out of resonance.As an S," state passes through resonance, the S1 fluorescence lifetime decreases because of enhanced non-radiative decay through the resonant S," state. By monitoring S1 fluorescence lifetimes as a function of electric field, the highly vibrationally excited S," energy levels can be mapped out. Fig. 1 shows the So and S, potential-energy surfaces for D2C0 at zero field and the competing radiative and non-radiative decay pathways for an initially prepared S, state. The excitation light for these experiments was obtained by passing the output of a ring dye laser (Coherent 699-29) through a set of amplification stages pumped with a XeCl excimer laser (Lambda-Physik EMG 103 MSC) at 10 Hz. The resulting nearly fourier-limited pulses were frequency doubled with a KDP crystal to yield 10 ns, 0.2 mJ pulses with 80 MHz f.w.h.m.which were used to excite J, K, [MI-resolved states of various S1 formaldehyde vibrational states. In order to reduce spectral congestion and narrow the Doppler width, 20 TOKT of formaldehyde was seeded in 0.5 atmS of He and cooled in a pulsed, supersonic expansion ( T,,, = 8 K). The molecular beam was colli- mated with a skimmer before passing into a second differentially pumped chamber. The laser crossed the molecular beam at right angles in this chamber between two 2 in. square electrodes separated with a 0.9645 cm optical flat cut into quarters (electric field homogeneity ca. 0.005 '/o ). The laser polarization was either parallel or perpendicular to the electric field depending on whether AM = 0 or AM = * 1 excitation was desired.Flourescence was observed at right angles to both beams through a transparent electrode and appropriate filters were used to reduce scattered laser light. An Apple IIe computer t 1 atm = 101 325 Pa. * 1 Tom= 101 325/760 Pa.152 Dissociation on Ground-state Potential-energy Surfaces applied voltage/ kV 6 ' Y l 20 12 8 4O 4 u . -0.10 -0.20 S, energy/cm Fig. 2 Stark spectra of ll,(M = 1) in the four lowest vibrational levels of S, D2C0. Observed lifetime is plotted against the energy of the l,,(M = 1) state as Stark-tuned by the specified voltage. The dramatic lifetime variation results from the S, level passing through resonance with S;E' levels. O A ! I ' ! I ' ' ' I I simultaneously ramped the electric field, scanned the dye laser in accordance with the computed Stark tuning curve for the J, K, I MI rovibronic transition, and collected lifetime data points at equal voltage increments (4-10 V) over 20 kV scans.Results At fields greater than a few kV cm-', the Stark splitting of formaldehyde and the narrow laser bandwidth allow preparation of an individual J, K, IMI -resolved Sl rovibronic state. Fig. 2 presents the spectra for the rotational level lll(M = 1) in each of the four lowest vibrational states of S, D,CO. The observed S, lifetime is plotted against the energy Stark-tuned by the S1 state, resulting in a spectrum of the S," level structure. AtH. Bitto, D. R. Guyer, W. F. Polik and C. B. Moore 153 energies corresponding to the lowest vibrational states in S, D2C0, 4' and 4l, it is evident that the S," levels have linewidths narrower than the average linespacing.Thus individual molecular eigenstates are well resolved in the Stark level-crossing spectra. The lineshapes of these S,-S," resonances can be fitted using standard radiationless transition theory expression^,^ and it has been shown that the unimolecular decay rates of S," D2C0 levels (the linewidths of spectral features) in the vicinity of 4' S1 range from 2 x lo7 to 5 x 10' s-l, representing over one order of magnitude variation.6 The decay rates clearly do not increase monotonically with energy as predicted by statistical theories (e.g. RRKM). At higher energies corresponding to 42 and 43 S, D,CO, the S," levels begin to overlap one another.A few isolated S," levels appear to be resolved in the 42 spectrum; however, the individual structure is washed out in the 43 spectrum. Although most of the resolvable peaks appear to be Lorenzian, the spectra exhibit a few derivative-shaped features. The average S," decay rate as a function of energy has been used to calculate a potential barrier height (including zero-point energies) of 79.1-82.2 kcal mol-'? for D2C0 + D2+ CO, which corresponds to 78.0-81.1 kcal mol-' for H2C0 + H2 + C0.6 Discussion It is evident from the 4' and 4' Stark spectra that highly vibrationally excited quantum states of S," formaldehyde possess enough individual vibrational character to influence their decay rates. The unimolecular decay rate deduced from the linewidth gives the dissociation rate of a formaldehyde molecule in an individual rovibronic state dissociat- ing into unspecified product states, En,,", k,,,,( E, J).The parent state is characterized by rotational quantum numbers (J, M and perhaps K,, depending on the extent of Coriolis coupling) and by total energy. The vibrational character of each level is partially described by the S," linewidth, corresponding to vibrational energy in the reaction coordinate, and by the intensity (internal conversion matrix element) corresponding to Franck-Condon overlap with the optically prepared S1 state. It will be interesting to see if the rovibrational character of the parent state influences the fragment quantum numbers by measuring the dependence of the product state distribution on the initial state.These experiments are possible for formaldehyde in an electric field. At energies corresponding to 43 S, D2C0 and higher, it is not possible to prepare individually resolved S," parent states; a superposition of eigenstates is prepared which decays into products. However, this superposition is defined by the state preparation process.' 43 S, D2C0 is excited in the out-of-plane bending mode ( v4); the S1 equilibrium geometry is non-planar and its C-0 bond length is longer than in So. Thus the So + S, internal conversion process favours preparation of coherent superpositions of S," states with significant out-of-plane bend and C -0 stretch vibrational motion. S1 excitation in other coordinates will tend to be preserved in internal conversion to S,". S," states with different vibrational character will be prepared when a different S, vibrational band is excited.Product state distributions from different S1 vibrational states may reflect this initial vibrational excitation. Finally, the resolved Stark spectra should allow a statistical characterization of dissociative S," formaldehyde quantum states. The rovibrational nature of a parent molecule near the ground-state dissociation threshold is complicated by Coriolis coupling and potential surface anharmonicities. The extent of Coriolis coupling near the threshold may be determined by examining the J-dependence of the observed state density.8 Several types of analysis may aid in determining the ergodicity of rovibronic states at this level of vibrational excitation.Level spacing distributions have been successfully used in nuclear physics to characterize the extent of ergodicity? More recently, Heller and Sundberg have related quantum ergodicity to intensity fluctuations observed in spectra. lo Both of these techniques should be applicable to Stark level-crossing spectra. t 1 M I = 4.184 J.154 Dissociation on Ground-state Potential-energy Surfaces One potential limitation with these methods of analysis is that they both depend on measuring all lines in a spectrum. Thus practical signal-to-noise limits and overlapping lines may limit their usefulness. However, Leviandier et al. have shown that the Fourier transform of a complex spectrum can give a sound measurement of statistical properties of levels even for poorly resolved spectra." This method may therefore prove more suitable for statistical characterization of dissociative S,* quantum states.Ketene Photofragmentation Experiment Ketene photofragmentation experiments were performed in the molecular-beam apparatus which was used for the Stark spectroscopy described above but with the Stark electrodes removed. The molecular-beam gas mixture was prepared by passing 0.2- 0.8atm of He, Ne or Ar over ketene kept in a Pyrex U-tube at dry-ice temperature. When experihnents did not require narrowing of the parent molecule transverse velocity distribution, the skimmer between the two chambers was removed and the pulsed beam source moved closer to the interaction region to obtain higher particle density. The linearly polarized photolysis and probe laser beams were combined with a dielectric- coated mirror, and they crossed the free jet 2 cm downstream from the nozzle at right angles.The polarization vectors of both lasers were aligned parallel to the molecular beam. The probe laser pulse was delayed 100-200 ns with respect to the photolysis laser pulse. Laser-induced fluorescence (LIF) of the 'CH2(a" ' A , ) fragment was observed at mutual right angles to the laser and molecular beams with a red-sensitive photomultiplier tube. Straylight was suppressed with a suitable combination of cutoff filters. The relative probe and photolysis pulse energies were monitored by photodiodes which detected light scattered off a frosted glass plate after the beams passed through the exit port of the vacuum chamber.Three different laser systems were employed as probe and photolysis light sources. The output of a dye laser (Quanta Ray, PDL- 1) pumped by the second harmonic of a Nd:YAG (Quanta Ray DCR-2) was frequency-doubled with a KDP crystal (Inrad autotracking system). The U.V. pulses ( d 3 mJ per pulse, 1 cm-' bandwidth) were used for photolysis of ketene between 333 and 310 nm. The pulsed radiation of a second dye laser (Lambda Physik, FL2002, 0.2 cm-' bandwidth) pumped by the second harmonic of another Nd: YAG (Quanta Ray, DCR- 1) or the nearly Fourier-limited pulses (80 MHz) of the laser system described ic the formaldehyde experiments served for probing singlet methylene by LIF via the b 'B,(u;= 14,15) + a" ' A l ( $ = 0 ) absorption. Fig. 3 displays the potential-energy surfaces relavent to the dissociation process.The fluorescence signal was linearly dependent on the probe power at pulse energies below 1 mJ for the broader bandwidth laser, while the nearly Fourier-limited pulses easily saturated transitions at even lower pulse energies; linear dependence on the photolysis power was measured up to the highest pulse energies employed in this experiment. The experiment was performed under control of a DEC MicroPDPll/73 computer (RSX11M operating system) at either 10 or 20Hz repetition rate. Interfaces allowed for tuning the gratings of the PDL- 1 and FL2002 dye lasers, triggering the pump lasers, inhibiting the probe laser every other shot for background subtraction, and acquiring data with an eight channel 12 bit analogue-to-digital converter.For typical spectra the integrated fluorescence signal (4 ps gate, SRS integrator) and the integrated photodiode signals monitoring probe and photolysis energy were measured. The signals were averaged for a preset number of cycles and stored for each wavelength point. Normaliz- ation of the spectra to photolysis power and also to probe power in cases of non-saturating probe laser intensities as well as further data analysis could be performed separately.H. Bitto, D. R. Guyer, W. F. Polik and C. B. Moore 155 dissociation coordinate Fig. 3 Schematic potential surfaces of the three lowest electronic states of ketene. Light between 333 and 310 nm excites ketene via the 'A" + 'Al transition, but the subsequent fragmentation leading to 'CH2( a' 'A,) and CO(X 'x+) can only occur on the electronic ground-state potential surface.The bond fisson proceeds without a barrier through a C, out-of-plane-bent geometry to 'CHz + CO. For energies below the 'CH2 + CO threshold, dissociation occurs on the triplet surface over a small barrier. Results In photofragmentation spectroscopy based on fragment LIF probing it is possible to record two different kinds of spectra. Observation of fragment LIF at a fixed probe wavelength as a function of photolysis laser wavelength yields a photofragment excitation (PHOFEX) spectrum, which is the product of the parent molecule absorption spectrum and the quantum yield of the fragment rovibrational level probed. This spectroscopy has seldom been used for dynamical information concerning the dissociation process.The second kind of spectroscopy, sweeping through the fragment LIF spectrum while photolysing at a fixed absorption wavelength, is commonly used for determining product state distributions and for measuring recoil velocity and angular momentum anisotropies. 1712 In fig. 4 two portions of 'CH2 LIF spectra taken with 0.2 cm-' resolution at 330 nm, a wavelength close to the threshold of 'CH2 and CO formation, and at 320 nm photolysis demonstrate a remarkable difference in the relative line intensities and in the number of observed transitions. This indicates a dramatic change in the product rotational state distribution. However, the spectroscopy of singlet methylene is far from being completely understood. Only 5% of the transitions observed after 308 nm photoly- sis of gas-phase ketene are assigned.13 This is due to the difficult spectroscopy of a non-rigid bender which is further complicated by perturbations arising from extensive singlet-triplet coupling in the lowest and first excited singlet Thus to date, a complete rotational state distribution of 'CH2 has not been determined.The following presents what nonetheless can be learned about ketene dissociation dynamics by analys- ing PHOFEX spectra. For a selection of assigned singlet methylene vibrational ground states13 ranging from the rotationless state Ooo up to 818, the highest J rotational level so far identified, PHOFEX spectra have been recorded from below the threshold of singlet methylene156 I I I I ( b ) - - - 1 I I Dissociation on Ground-state Potential-energy Surfaces I I I I 1 1 .Fig. 4 Laser-induced fluorescence spectra of prompt 'CH2 excited via the b"B,(v; = 14, 15) + a' 'A,( vg = 0) absorption after ketene photolysis in a molecular beam. The two identical portions of the 'CH2 spectrum recorded ( a ) for 330nm photolysis, a wavelength close to the threshold of 'CH2 formation, and ( b ) for 320 nm photolysis, demonstrate a dramatic change in the product rotational state population by a remarkable difference in the relative line intensities and the number of observed lines. formation up to 2200 cm-' above the threshold. Their shape is characterized by a steep rise at the threshold of the particular 'CH2(J&K:) channel followed by a slower fall-off. The steepness of rise and fall decreases with increasing rotational energy of the methylene state probed.The spectra are smooth even at 100MHz photolysis laser resolution, indicating that the ketene absorption at the low temperature in a free jet where spectral congestion is greatly reduced remains diffuse and does not exhibit rotational structure. Some vibrational structure of 10% modulation depth and ca. 350cm-' spacing is observed on all of the PHOFEX spectra. The peaks occur at the same photolysis wavelengths for every methylene state probed. Thus the structure is in the excited electronic state of ketene. At a signal-to-noise level better than 50 : 1 some additional structure is clearly observed and is most pronounced within 300 cm-' of the threshold. PHOFEX spectra monitoring low rotational states are modulated around the maxima of the spectra, while the broader spectra of high rotational states exhibit these features on the rise.The undulation pattern is identical in all spectra; the spacing between the onsets of each lobe decreases linearly to zero at the threshold for the methylene state probed. One example with a sufficient signal-to-noise ratio is presented in fig. 5 ( a ) . The PHOFEX spectrum which extends over the first 300cm-' above the threshold monitoring the 312 state via the 4w4-312 transition shows undulations with 5% maximum depth. The onset of each lobe isH. Bitto, D. R. Guyer, W. F. Polik and C. B. Moore I CO( J") 157 Fig. 5 Photofragment excitation (PHOFEX) spectra of ketene. ( a ) the PHOFEX spectrum of ketene monitoring the fragment 'CH2 in the 312 state by LIF shows a steep rise, slower falloff and undulations.( b ) A phase-space theoretical prior calculation matches the shape of the PHOFEX spectrum including the undulations due to the onsets of single rovibronic fragment channels 1CH2(312) + CO( 0'' = 0, J"), J" = 0, 1,2, . . . . indicated with vertical lines. The spacing of those undulations coincides with that of CO rotational term values. A statistical calculation (vide infra) shows that the undula- tions must be interpreted as the onsets of single correlated-product channels 1CH2(312) + Finally, note that the overall behavior of PHOFEX spectra depends on the bandwidth of the probe laser. Spectra measured with 0.2cm-' bandwidth covering the whole methylene Doppler profile fall off more slowly than those recorded with 80MHz (0.003 cm-') resolution on line centre (fragments probed in the centre of the Doppler profile with zero-velocity component in the probe laser direction).Detection in the profile wing yields a spectrum which levels off more slowly. These phenomena are the result of the increase in fragment translational energy, and hence Doppler width, with increasing photolysis energy. CO( v" = 0, J"). Discussion PHOFEX spectra intensities are proportional to the product of the number of excited parent molecules (determined by the absorption cross-section) and the yield of the monitored fragment state. For ketene this cross-section is nearly constant; its absorption158 Dissociation on Ground-state Potential-energy Su faces decreases only 15% from 333 to 310nm, revealing little vibrational ~tructure.'~ A 350 cm-' progression contributes 10% to the total absorption at room temperature.Therefore the variation of the absorption spectrum influences PHOFEX spectra by only 15% and is neglected in the analysis. The yield of a specific rovibrational 'CH2 state is determined by the radiationless processes following electronic excitation as well as by competing pathways for formation of all accessible rovibrational fragment states. In the spectral region investigated ketene is excited via the 'A"- ' A , transition to the planar C-C-0 bent excited singlet The energy 5 sufficient to yield singlet and triplet methylene, but neither 3CH2(2 3B1) and CO(X '1') nor 'CH2(G 'Al) and CO(X 'Z+) correlate to the excited singlet state.17 Singlet methylene formation must proceed on the electronic ground-state potential surface reached via internal conversion while triplet methylene must be formed on the lowest triplet potential surface accessed via intersystem crossing and/or internal conversion to the electronic ground state with subsequent intersystem crossing.The yield of singlet methylene in a specific rovibrational state at an available energy E above the dissociation limit, @T0T['cH2(n)9 = @TOT['cH2, ElP['cH2(n), El can be factored into a total yield @TOT [ 'CH2, El and a relative frequency of the observed singlet methylene state, P"CH,(n), El = "CH,(n), E1/1 k"CH,(n), El in terms of chemical rates for formation of specific 'CH2 states with the summation extending over all accessible singlet methylene states.For brevity, a shorthand notation for the vector of the singlet methylene quantum numbers n = (vr, v,", vg, JlfC:p) is used. (PTOT['CH2, E l was found to be close to unity in previous experiments at 308 nm photoly~is,'~~'~ while at the threshold, E = 0, the yield must vanish. The steep rise of the J" = 0 methylene PHOFEX spectrum suggests that @TOT[ 'CH2, E l approaches unity within a few hundred cm-' above threshold.20 The following discussion concentrates therefore on P['CH2( n), E l for singlet methylene states exceeding 100 cm-' internal energy, which contains the dynamical information on the dissociation process. The rotational distribution of nascent CO from 308 nm gas-phase ketene photolysis has been successfully modelled by a phase-space theoretical prior calculation assuming only a total energy constraint and unit yield.18 Therefore the prior distribution Po[ 'CH2( n), E l which is defined as the reference for the information-theoretical analysis of the experimental data, suggests itself for comparison to the data.Po is calculated from the ratio of the number of states accessible to specified fragments states to the total number of accessible states, where the number of states scales with the square root of the fragment translational energy E~ = E - EINT[ 'cH2( n)] - E,NT[CO(V", J " ) ] , as does the translational state density of a particle in a three-dimensional box.21 For a single correlated fragment channel the prior distribution is Po[ 'CH2( n), co( u", J"), E] = gFET1"/Z 1 gFET1/2 n v",J" with the fragment state degeneracy gF = gv( 'CH2)gr( 'CH,)g,(CO)g,(CO) expressed with fragment vibrational and rotational degeneracies.The degeneracies g, are one, and g, = 2J"+ 1 for both products. The summation extends over all energetically accessible fragment states. Because total nuclear spin is conserved during the dissociation process (vide infra) the total accessible phase space and thus the summation over the methylene states is restricted to the nuclear spin species of the specified methylene state. The desired prior distribution for a specified singlet methylene state is obtained by addingH. Bitto, D. R. Guyer, W. F. PoZik and C. B. Moore 159 (summation over internal states of CO) all energetically allowed single rovibronic fragment channel prior distributions: Po['CH2(n), E l = C Po['CH2(n),CO(v",J"), E l .v,,,J" The only information required for the prior distribution calculation is the rovibra- tional energy levels of the fragments. The term values of CO are calculated from well known constants.,, Singlet methylene rotational levels are obtained from the experi- mental term values for J " a 514 and otherwise approximated by a symmetric top for J"> 5. The vibrational frequencies of singlet methylene (v, = 2806 cm-', v2 = 1352 cm-', v3 = 2864 ~ r n - ' ) ' ~ ? ~ ~ are treated harmonically, but the available energy in the recorded PHOFEX spectra never exceeds 2200 cm-', and therefore only the bending vibration v2 could be populated.The prior distribution calculated for the 312 state of methylene is depicted in fig. 5 ( 6 ) . It matches reasonably well the experimental PHOFEX spectrum above. The rise is predicted correctly while the fall-off is slightly too slow. The calculation also predicts the most interesting features, the undulations. The undulations are due to basic principles inherent in the prior phase-space theory. The shape of individual fragment channel distributions, i.e. the steep rise and the slow fall-off, is determined by the statistics of available product channels. The peak spacing of these distributions is governed by energy conservation, and therefore peaks are separated according to the term values of the successively accessible CO rotational states: 2B(J"+1). When the CO level spacing becomes comparable to the width of a single rovibronic fragment channel prior distribution, undulations appear in the PHOFEX spectrum.These undula- tions die away at ca. J" = 15 as the individual fragment channel distributions broaden. Note that undulation of PHOFEX spectra is a general effect and should be encoun- tered in all spectra of continuously or sufficiently smoothly absorbing parent molecules if fragments with relatively large rotational constants are generated in a statistically controlled dissociation. It would be interesting to know if undulations can be observed for dynamically constrained bond fission. In order to observe this subtle but important phenomenon, cooling of the parent molecules is necessary because thermal averaging would remove structure with a spacing kT. The undulations provide important insight into the dissociation process.They are due to the appearance of individual fragment channels and therefore the analysis of the spectra reveals product correlated populations. The valleys between the lobes mark the onsets of new channels, in this case 'CH,(n)+ CO( d', J"), J" = 0, 1, . . . . Extrapolation to J" = 0, where the undulations are not resolved, is straightforward, and the threshold of the specified channel 'CH2( n) defined by energy conservation can be unambiguously determined. Application of this method to the PHOFEX spectrum in fig. 5( a ) results in a threshold for 'CH2( u: = 0, v: = 0, u l = 0, 312) at 30 224 cm-'. Subtraction of the singlet-methylene internal energy yields the threshold for singlet-methylene formation at 30 092 cm-', which agrees within the quoted experimental uncertainty with the most accurate previous determination of the dissociation limit by Hayden et QZ." in a molecular-beam time-of- flight study (30 120k 175 cm-').The accuracy of the molecular-beam time-of-flight mass spectrometry results is impressive indeed ! The coincidence of the dissociation limit with the threshold determined from PHOFEX spectra shows that (neglecting tunnelling) dissociation occurs without a barrier (> 175 cm-') in the exit channel. For a correct threshold determination two more effects have to be considered. Ketene as well as methylene possesses two identical hydrogen atoms. Therefore ketene and methylene exist as two nuclear spin species, ortho and para, which do not freely interconvert.Because the nuclear spin species are conserved during supersonic cooling in the free jet,24 through optical excitation, and during the dissociation process,25 ortho-'CH, can only originate from ortho-ketene and similarly para-'CH, from para-ketene. The lowest160 Dissociation on Ground-sta t e Pot en t ia Len ergy Surfaces state ortho-ketene can exist in is the J" = 1, K" = 1 state. Therefore thresholds of all ortho-'CH, states are red-shifted by the internal energy of this ketene state ( A + B = 9.7 cm-')26 with respect to para states, and the threshold of rovibrational ground state 'CH2 given above has to be corrected accordingly. The residual thermal energy of the parent molecule gives rise to an additional red shift which is estimated to be < $kT = 5 cm-'.Including other uncertainties at this stage of analysis, the threshold for 'CH, formation can be located at 30 102* 15 cm-'. A further test of the prior distribution is provided by the LIF Doppler profile dependence on photolysis energy. The photolysis energy dependence of the profile is well matched by prior theory; e.g. the profile of the 404 + 312 transition exhibits a f.w.h.m. of 0.125*0.01 cm-' at 310 nm ketene photolysis compared to 0.121 cm-' from the calculated prior distribution. Dynamics of Fragmentation Photofragment spectroscopy of dissociation on ground electronic state potential-energy surfaces is beginning to yield some useful generalizations concerning the dynamics of unimolecular decomposition.Most experiments to date have been carried out within a few thousand cm-' of threshold, in the energy range relevant to thermal unimolecular decomposition.' For simple bond fission without a barrier, detailed measurements of rotational distributions are matched almost perfectly by simple phase-space theory (PST) statistical calculations. NCNO + CN + NO and CH2C0 + 'CH, + CO are excellent examples. These calculations assume only that all product states consistent with con- servation of total energy and angular momentum are equally probable. In the simplest case no adjustable parameters are included. Measurements of OH rotational distribu- tions from HOOH dissociation by Crim and coworkers27 appear to require the more detailed treatment of the statistical adiabatic channel model.Vibrational excitation of fragments for NCNO and perhaps singlet CH2C0 appears to be reliably predicted by excluding parent rotation from the degrees of freedom among which energy is shared, the separate statistical ensembles (SSE) method of Wittig et aL2' The usefulness of this theory has not been tested for a significant variety of conditions. As parent vibrational energies increase well above threshold it seems likely that some vibrational degrees of freedom will not be fully randomized on the timescale of fragmentation. Many experi- ments will be required to map out the competition between the dynamics of energy transfer and fragmentation and to explore the possibilities of mode selectivity for more highly excited systems. Nevertheless it is already clear that in the near-threshold region dissociation in the absence of a barrier is well described by straightforward statistical theories. Dissociation over a potential-energy barrier is qualitatively different. The release of energy under the control of repulsive forces in the exit valley is not statistical.As soon as the top of the barrier is crossed, fragments accelerate away from each other too rapidly for energy to be randomized among the product degrees of freedom. For dissociation just at threshold, the molecules must pass through the transition-state geometry with only zero-point vibrational energy. Rotational distributions reflect the geometry of this transition state and the shape of the exit valley. The high rotational excitation of CO (Jpeak = 42) from H2CO-+ H2+C0 with a 78-81 kcal mol-' barrier provides a striking example.29 Less than 1% of the available energy is released as CO vibration in this case.For triplet ketene fragmentation, CH2C0 + 3CH2+ CO, over a barrier < 4 kcal mol-', the rotational distribution is also distinctively non-thermal (Jpe.&= 13).30 In this case the value of Jpeak is well predicted by assuming a repulsive force directed along the breaking bond at the ab initio geometry of the transition state. The same impulsive model for formaldehyde predicts too small a value for Jpeak forH. Bitto, D. R. Guyer, W. E Polik and C. B. Moore 161 CO. In formaldehyde the H2 appears to push off from the p-orbital electrons outside of the carbon atom of C0.29,31 As energy is increased above a barrier it is likely that the excess will be randomly distributed among parent vibrations and possibly rotation.Neither experiments nor theoretical models for combining these energy distributions have progressed very far. Fragment state distributions for surfaces with barriers will provide severe tests of ab initio potential surfaces and dynamical theory for some time to come. This research has been supported by grant CHE83-04893 from the U.S. National Science Foundation and by the San Francisco Laser Centre through the loan of a pulsed dye laser system. H. B. acknowledges a NATO postdoctoral fellowship administered by Deutscher Akademischer Austauschdienst. W. F. P. thanks the U.S. National Science Foundation for a pre-doctoral fellowship.References 1 H. Reisler and C. Wittig, Annu. Rev. Phys. Chem., 1986, 37, 307. 2 E. J. Heller, Annu. Rev. Phys. Chem., 1984, 35, 563. 3 H. L. Dai, C. L. Korpa, J. L. Kinsey and R. W. Field, J. Phys. Chem., 1985, 82, 1688. 4 J. D. McDonald, Annu. Rev. n y s . Chem., 1979, 30, 29. 5 A. Nitzan, J. Jortner and P. M. Rentzepis, Proc. R. SOC. London, Ser. A, 1972, 327, 367; eq (3.15). 6 D. R. Guyer, W. F. Polik and C. B. Moore, J. Chem. Phys., 1986,84, 6519. 7 E. S. Yeung and C. B. Moore, J. Chem. Phys., 1974, 60, 2139. 8 H. L. Dai, R. W. Field and J. L. Kinsey, J. Chem. Phys., 1985, 82, 2161. 9 T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey and S. S. Wong, Rev. Mod. Phys., 1981, 10 E. J. Heller and R. L. Sundberg, in Chaotic Behavior in Quantum Systems, ed. Giulo Casati (Plenum 1 1 L. Leviandier, M. Lombardi, R. Jost and J. P. Pique, to be submitted. 12 R. Vasudev, R. N. Zare and R. N. Dixon, J. Chem. Phys., 1984,80,4863; W. M. Jackson and H. Okabe, 13 H. Petek, D. J. Nesbitt, D. C. Darwin and C. B. Moore, J. Chem. Phys., submitted. 14 H. Petek, D. J. Nesbitt, C. B. Moore, F. W. Birss and D. A. Ramsay, J. Chem. Phys., submitted. 15 J. W. Laufer, J. M. McDonald, V. Scherr and S. P. Mcglynn, Chem. Rev., 1971, 71, 73. 16 W. D. Allen and H. F. Schaefer 111, J. Chem. Phys., 1986, 84, 2212. 17 S. Yamabe and K. Morokuma, J. Am. Chem. SOC., 1978, 100, 7551. 18 D. J. Nesbitt, H. Petek, M. F. Foltz, S. V. Filseth, D. J. Bamford and C. B. Moore, J. Chem. Phys., 19 C. C. Hayden, D. M. Neumark, K. Shobatake, R. K. Sparks and Y. T. Lee, J. Chem. Phys., 1982,76,3607. 20 H. Bitto, D. R. Guyer, and C. B. Moore, in preparation. 21 R. D. Levine and J. L. Kinsey, Information-theoretic Approach: Application to Molecular Collisions, in Atom-Molecule Collision Theory A Guide for the Experimentalist, ed. R. B. Bernstein (Plenum Press, New York, 1979). 22 K. P. Huber and G. Herzberg, Constants ofDiatomic Molecules (Van Nostrand Reinhold, New York, 1979). 23 H. Petek, D. J. Nesbitt, P. R. Ogilby and C. B. Moore, J. Phys. Chem., 1983, 87, 5367. 24 H. L. Selzle and E. W. Schlag, Chem. Phys., 1979, 43, 111; J. Muhlbach and J. R. Huber, J. Chem. 25 B. Schramm, D. J. Banford and C. B. Moore, Chem. Phys. Lett., 1983, 98, 305. 26 G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand Reinhold, New York, 1966), 27 T. M. Ticich, T. R. Rizzo, H-R. Dubal and F. F. Crim, J. Chem. Phys., 1986, 84, 1508. 28 C. Wittig, L. Nadler, H. Reisler, M. Noble, J. Catanzarite, and G. Radhakrishnan, J. Chem. Phys., 29 D. J. Bamford, S. V. Filseth, M. F. Foltz, J. W. Hepburn and C. B. Moore, J. Chem. Phys., 1985,82,3032. 30 H. Bitto, I-C. Chen and C. B. Moore, J. Chem. Phys., 1986, 85, in press. 31 D. Debarre, M. Lefebvre, M. PCalat, J-P. Taran, D. J. Banford and C. B. Moore, J. Chem. Phys., 1985, 83, 4476. Received 12th June, 1986 53, 385. Press, New York, 1985), pp. 255-292. Adv. Photochem., 1985, 13, 1. 1985, 83, 223. Phys., 1986, 84, 3014. vol. 3. 1985,83, 5581.

ISSN:0301-7249    

DOI:10.1039/DC9868200149

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986,82, 163-175 Dissociation Dynamics of NH,( a lA;) Experiment and Theory Michael N. R. Ashfold, Clive L. Bennett and Richard N. Dixon" School of Chemistry, University of Bristol, Cantock's Close, Bristol BS8 1 TS The spectroscopy and predissociation of the vibroCicJeve1.s of the 'A; excited stctes ,Of NH3 and ND3 have been studied vta A,X dispersed emission spectra, C'-A dispersed emission spectra and C'-A stimulated emission pumping, in each case following two-photon excitation to a selected inter- mediate level. The predissociation lifetimes span more than two orders of magnitude. The lowest levels predissociate by H( D) atom quantum tunnel- ling, the higher levels by vibrational rearrangement. A model calcul?tion is presented to illustrate this mechanism for the u1 = 1 levels of the A state, which are very short-lived. Photofragmentation by predissociation is a phenomenon that affects most excited elec- tronic states of most polyatomic molecules, yet in very few cases is the detailed mechanism of this process fully understood.Frequently this is because the predissociation results from the non-adiabatic coupling of a zero-order bound electronic state to a state that possesses at least one coordinate in which nuclear motion is unbound: detailed under- standing of the process necessarily requires knowledge of at least two potential-energy surfaces and of the nuclear momentum operators that can cause coupling between them. Model systems which are more amenable to theoretical analysis are provided by molecules in which predissociation occurs on a single electronic potential-energy surface, such as the first excited (A 'A;) state of ammonia.In this work we present new experimental results concerning the vibronic level dependence of this predissociation, and introduce model calculations which suggest an explanation for these observed dependences. The full understanding of dissociation dynamics requires a detailed knowledge of the spectroscopic properties of the transient excited state of the parent molecule' and the monitoring of the excited species as it evolves from the initially prepared Franck- Condon region along the dissociation coordinate to the final products. Such studies are, in principle, possible for the ammonia molecule, but not all the necessary experiments have yet been performed.Kinsey's group' have shown how the wavelength resolved emission spectrum of a photoexcited molecule can provide a uniquely jetailed picture of its motion along the dissociation coordinate. However, in the case of A-state ammonia the excited state levels investigated to date (here and el~ewhere)~-~ predissociate at a sufficiently slow rate to ensure that the easily observed 'resonance Raman' spectrum is dominated by emission from the vertical Franck-Condon region. Photochemic_al studies7-'' have shown H atom loss to be the primary dissociation chpnel for NH,(A) molecules. The NH2 radical product is formed predominantly in its X 2Bl ground state with a high level of internal e~citation.'~ Unfortunately no quantitative measurements of the nascent internal quantum state population distributions have yet been derived, mainly- becauje of the incomplete state of spectroscopic knowledge relating to the NH2(A *A1-X ' B , ) band system.Thus the present work concentrates upon further studies of the spectroscopy of A-state ammonia molecules and the vibrational dependence of its dissociation dynamics. 163164 Dissociation Dynamics of NH3( 2 'A,") Ground-state ammonia has a pyramidal ( C3u) equilibrium geometry and the following electronic configuration: ( 1 ~ ~ ) ~ ( 2 a ~ ) ~ ( le)4(3a1)2; r? 'A,( C3J. All the known singlet states resulting from a one electron excitation out of the lone-pair ojbital (;al, or 1 a," in D3h) have planar equilibrium configurations. The lowest-energy A 'Ag-X 1Ai(D3h) transition (3sa: + la,") is dipole-allowed, and the one-photon absorption spectrum is dominated by a long progression in the excited state out of plane bending vibration, vb. In NH3 all these vibronic bands are predissociated to the extent that no rotational structure may be resolved by conventional absorption spectroscopy, even under the 'cold' condition: prevailing in a supersonic molecular beam.20 In ND3, however, bands involving the A-state levels 2' and, especially, 2l are sufficiently long-livsd to, show poorly resolved rotational structure.The equiyalenl two-photon ND3(A + X) spectra, obtained by monitoring the very weak A -+ X emission (quantum yield 4 -= 10-4)3y4 as a function of the laser excitation wavelength,21 show the same characteristics.The analyses of the rotational structure of these spectra show that the N-D equilibrium bond length is some 6% longer than in the ground state. 17921 The change in N-D bond length revealed by the rotational an_alxsis implies that the symmetric stretching mode, vl, should also be active in the A-X spectrum, yet neither absorption 16-20 nor electron impact22 measurements have succeeded in identifying any spectral features that might betray its presence. Early Franck-Condon calculation^^^ tried to explajn this apparent lack of any vibronic structure, other than that associated with the A-X 2," progression, by assuming an accidental dzgeneracy between vi and 3 vb. Attempts to reproduce the experimentally observed A-X absorption band contour using this model, however, met with only limited success.Much better agreement between experiment and theory was obtained in the more recent two-dimensional Franck-Condon calculations of Avouris et ~ 1 . ~ ~ This model retained the assumed near coincidence betwzen vi and 3 4 , but allowed for the possibility that spectral features associated with A state levels carrying one or more quanta of vi might show a much increased lifetime broadening. 2 emission spectrum. The C' 'A: Rydberg state was unknown from classical spectroscopy (it is one-photon forbidden), but has been thoroughly investigated since its detection by Nieman and Colson2' through resonance-enhanced multiphoton ionisation (MPI). The spectros~opy~~-~' and predisseciation d y n a r n i c ~ ~ ~ > ~ ~ - ~ l of its various 2" vibronic levels are well characterised.The C' state has a planar equilibrium geometry, with an N-H (N-D) bond length very similar to that of the ground electronic state.25 The lowest few vibronic levels are remarkakly sta>le with respect to predissociation and may be observed, with ease, via their C'+ A e m i ~ s i o n . ~ l - ~ ~ Both state? hale planar equilibrium geometries. Thus the spectrum of the wavelength-dispersed C'-+ A emission from a given 2" vibronic level is of very simple appearance, with a dominant band associated with the 2: transition, weak bands due to the transitions 2:+2 and (when allowed) 2:--2, and a broad feature attributable to the trpsition ly2:.31 Analysis of this latter band has allowed estimation of the reduction in A-state lifetime that results from excitation of one quantum of symmetric stretch.Stimulated emission pumping (SEP) provides an alternative, more direct, ro-ute to establishing the linewidths of transitions to individual rovibronic levels of the A state of intermediate lifetime, as recently demonstrated by Xie et ~ 1 . ~ ~ These workers used one tunable dye lase: and 3 + 1 MPI as a meaFs of populating and detecting selected rovibronic levels of C'-state NH3; individual C'-+A transitions revealed themselves as 'dips' in the total ion signal when a second, synchronous dye laser was tuned through the appropriate resonant frequencies. The success of this 'pump' and 'dump' form of Further information about the 2 state of ammonia can be obtained from theM. N. R. Ashfold, C.L. Bennett and R. N. Dixon 165 optical optical double resonance (OOQR) spectroscopy in the present case relies on the well established spectroscopy of the C’ level?, thei: stability with respect to predissoci- ation and the large dipole strength for the C’+ A transition. Dip techniques have undoubted merit as a means of probing the spectroscopy of heavily predissociated systems; the present work demonstrates the need for some caution in their use for linewidth measurements when one step in the double-resonance scheme involves a multiphoton excitation. The results of the present study confirm previous conclusions, and provide ne? data, regarding the marked vibronic level dependence of the predissociation rate of A-state NH3 and ND3 molecules. Rates measured for the levels 2’ and 2’ in both isotopic species have been interpreted in terms of H atom loss by quantum tunnelling through an exit channel barrier, the height of which increases with out-of-plane bending angle.*l Higher bending vibronic levels, and especially those in which the symmetric stretch is also excited, show much enhanced predissociation rates.For all such levels the gross anharmonicity of the A-state potential will provide the driving force for vibrationally non-adiabatic coupling from the initially prepared level into the dissociation mode, thereby reducing the effective height of, or even completely circumventing, the exit channel barrier. Experimental Much of the experimental procedure has been described previously; new features only are summarised below. A“ --* 2 Dispersed Emission Spectra Single vibroiiic levels of A-state NH3 and ND3 were populated by coherent two-photon excitation.*l The static gas samples were contained in a fluoryescecce cell, the design of which included a countersunk spectrosil port for viewing A+ X emission, along an axis orthogonal to the direction in which the laser beam propagates, close to the exit window. The emission was focussed (7.5 cm focal length f l l .5 biconvex CaF, lens) onto the entrance slit of a small scanning monochromator (Jobin Yvon HUV 20) equipped with a 1200 lines per mm holographic grating, and detected using a solar-blind photo- multiplier (Hamamatsu R166UH). The revised cell design is such that emission emanat- ing from the focal region has only to pass through ca. 2 mm column of unexcited parent molecules before reaching the observEtion _window. As a result even the most short- wavelength features appearing in the A + X emission spectrum (see fig.2 later) suffer little attenuation by reabsorption. e’ -+ A” Dispersed Emission Spectra cr+g tw_o-pho_ton excitation was achieved as before,31 but in the present studies dispersed C’ -+ A emission spectra were recorded using a 0.5 m monochromator (Spex 1870 equipped with a 1200 lines per mm grating) in which the exit slit assembly had been replaced by an optical multichannel analyser (PAR OMA 2 system with model 1420 intensified silicon diode array detector). e’ + A” Stimulated Emission Pumping The folded OODR scheme used for these studies is shown in fig. 1. Two dye lasers are pumped with the 532 nm output of a Quanta-Ray DCR-2A Nd-YAG laser.The ‘pump’ laser (1) is a Quanta-Ray PDL-2; its output is frequency doubled (Inrad model 5-12 ‘Autotracker’, KDP crystals) and then used to populate selected rovibronic levels of166 Dissociation Dynamics of NH,(i ‘A;) C’ 2”, JK Fig. 1. Schematic representation for the detection of fluorescence djps Jy stimulated emission pumping. The frequency of the pump laser is held fixed_on ,a known C’-X two-photon excitation while the frequency of the dump laser is tuned through C’-A transitions. A small monochromator transmits the fluorescence of the monitoring transition while rejecting scattered light from both lasers. c‘-state NH, or ND3 uia a coherent two-photon excitation process. The ‘dump’ dye laser (2) is a home-built oscillator-amplifier system of Hansch de~ign.3~ In the present arrangement it could provide an output of ca.1 mJ in the wavelength range of interest (550-600 nm) with a bandwidth of ca. 1 cm-’. This output was calibrated by splitting off a portion of the beam and simultaneously exciting optogalvanic signals of neon in a hollow-cathode discharge. The two dye-laser beams are counterpropagated through an externally blackened Pyrex fluorescence cell of standard design36 containing a static sample of ca. 50 Torrt NH3 or ND3. Both are focussed (fi = 20 cm, f2 = 14 cm) so as to overlap in space and time. Laser 1 is set at a frequency appropriate for excitation to the selected C’ rovilbronig level. Two different detection methods have been employed.In the first, C’+ A fluorescence from the focal region is collected (5 cm focal length f / l biconvex lens) and imaged onto the entrance slit of a 10cm monochromator (Jobin-Yvon H10 IR, bandwidth ca. 30 nm), the grating of which is set to pass only the red end of the emission [primarily that associated with the 2:+* band, see fig. 3 CJ ref. (31)], and detected with a photomultiplier (Hamamatsu R7 12). The resulting photocurrent is preamplified, pjocegsed using a boxcar and passed to an Apple I1 micro_c~mputer.~~ Individual C’+A 2: rovibronic transitions associated with the selected C’ level are observed by monitoring the reduction in this fluorescence (the ‘dip’) that occurs when laser 2 is tuned through resonance. As an alternative, the population of the selected C’ level is Eonitored via its resonance enhancement to the ionisation signal and the associated C’-* A rovibronic resonances detected via ‘ion dips’ in a manner analogous to that described by Xie et Results Fig.2 shows the dispersed emission spectrum obtained following two-photon exc_ita$on of ND3 at a laser wavelength of 422.16nm (the QQ branch maximum of the A-X 2; band).21 Short progressions in uy and I.’; (respectively the symmetric stretching and bending vibrations of the ground electronic state) are clearly apparent. The spectrum provides unequivocal support for previous spe~ulation~~’*~ that the u1 vibration must t 1 Tom = 101 325/760 Pa.M. N. R. Ashfold, C. L. Bennett and R. N. Dixon $2; q21, 4 3 2 1 0 4 3 2 1 m 13; R I 167 I I 1 I I 1 280 260 240 220 200 wavelength/nm Fig. 2.Wavelength dispersed A+r? emission spectrum following tFo-photon excitation of ND, at 422.16 nm (the ‘Q branch maximum of the A-X 2; band). be Franck-Condon-active in the ammonia A-2 transition even though it is indiscernible in the one-photon absorption spectrum.’*’ Levels of the A” State with u1 = 1 Previsus studies of the Cr-*A emission have identified weak, broad features involving the A-state symmetric 2tretcting ~ibration.~’ Fig. 3( 6) displays a dispersed emission spectrum of the ND3( C’ ---* A) lY2: band recorded with the OMA (instrumental resol- ution 0.037 nm/pixcel) following tEo-pJoton dye-laser excitation at 306.41 nm, on the peak of the QQ branch of the ND3( C’-X) 2; transition. Also ipludsd, for comparison, [fig.3 ( a ) ] is the OMA recording of the (much more intense) C’+ A 2: band following excitation at this same wavelength. Computer simulations of the full el-2 excitation spectrum show the effective two-photon bandwidth of the exciting laser to be well modelled by a gaussian of 2 cm-’ f.w.h.G. The energies and predissociation properties of the individual rotational levels of the C’ 22 vibronic state of ND3 are well e~tablished.~’ Knowing the appropriate two-photon line-strengths for these transitions it is_ thus possible to calculate the relative contributions each level makes to the total ND3( C’ 3 A) emission following excitation at 306.41 nm. Thisw enables the simulation of the contour of the wavelength-dispersed spectrum of the C’-+ A 2: vibronic band, given the Honl-London factors for the individual rotational transitions and the measured instrument respope function, when used in conjunction with the predissociation parameters for the A 22 state (derived below). The solid curve shown in fig.3 ( a ) is the result of this prediction. The good agreement with the experimental data encourages t.he use of this band contour simulation technique to extracJ a mcan linewidth for the individual rovibronic transitions associated with the ND3( C’ t A) 172% band, thereby obtaining a predis- sociation rate for the 1 122 state of ND3(A). The C’ + A emission spectrum involving168 Dissociation Dynamics of NH,(A ‘A;) 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t L 17 600 17 400 17 200 17000 wavenumber/cm-’ wavenumber/cm-’ Fig.3. Fluorescence band profiles of the ND,(e’-* A) spectrum recorded with an optical mult$ha_nnel analyser following two-photon excitation at 306.41 nm (the “Q branch mazimum of the C’-X 2; band), together with band-contour simulations (solid lines). (a) The C’+A 2; band, and simulatjon with a Lorentzian f.w.h.m. of 23 cm-’ for each transition (see table 1). (b) The (C’+ A) lY2; band. The two simulations have f.w.h.m. of 50 and 250 cm-’. this level [fig. 3 ( b ) ] is much weaker, but obviously broader. Any analysis of this band along the lines outlined above must recognise the possibility of two additional difficulties. First, the rotational term values for the A 1’22 leyel are not known: we approximate the B and C rotational constants to those of the A 22 level, recognising that these values are likely to be overestimates, but consider this to be an unimportant source of error in the band-contour simulation. Secondly, and potentially more seriously, the uncertaintyM.N. R. Ashfold, C. L. Bennett and R. N. Dixon 169 widths of individual P, Q and R transitions from a given e’ rovibronic level are likely to be such that they overlap in frequency. This raises the possibility of interference between the different transition amplitudes from the common upper level. When, as in the present experiment, the emission is detected along a third axis, orthogonal to both the laser propagation and polarisation directions, this interference could give rise to apparent modifications of the relative line-strengths of P, Q and R branch transitions (c.f the Hanle effect).Fortunately such effects will be of minimal importance in the present studx because the excitation to the C’ levels of interest occurs predominantly via the C(A) component of the two-photon transition tensor. The distribution of emitting molecules is therefore almost isotropic, thereby nullifying the possible interfer- ence modifications to the intensity distribution which could arise as a result of the anisotropic character of dipolar emission. The experimental band contour of fig. _3(6) i,s decidedly asymmetric. Although subject to less thorough investigation, other C’ + A lY2; bands of ND3, including that with n = 1, appear to show similar asymmetry and overall breadth. Two solid lines have been superimposed on the experimental data points in fig.3(6). These have been calculated using the normal Honl-London factors for the rotational transitions, and Lorentzian widths of either 50 or 250cm-’ for the individual rovibronic levels of the A 1’22 state. The narrower of these gives a reasonable account of the width of the major peak in the experimental profile, whereas the broader gives a better representation of the overall width. No sin le LoLentzian lineshape can reproduce the experimental profile. intensities are lower than those for ND,, as might be expected from Franck-Condon considerations, and the data are therefore of lower quality. These NH3 bands appear to be much more symmetrical than those of ND3, with full widths at half-maximum of ca. 500cm-’. The corresponding 8 ’+ A 1:2: bands of NH3 are even broader.Their relative Levels with only v2 excited In principle, double-resonance SEP techniques should be able to provide a more direct and absolute measure of individual rovibronic transition linewidths by virtue of the selection of a single resonant intermediate level. In practice, the low oscillator strength and wide spectral breadth of the 172; features prevented use of these methods in the study of Franck-Condon off -diagonal transitions. However, the results of Xie et al.34 and those shown here in fig. 4 provide ample illustraGon ofthe potential utility of such dip techniques in studies of the stronger, diagonal C ’ + A 2; transitions of NH3 and ND, . The extraction of true molecule-limited linewidths from double-resonance dip spectra of this kind requires some care.The dip will be distorted in just the same way as are peaks in a conventional absorption spectrum. As in order to obtain a true measure of the f.w.h.m. linewidth, we model the transition probability associated with each experimental lineshape as a Lorentzian function g ( v ) expressed in the form 1 - exp[ -g( v)] in order to allow for the non-linearity introduced by the Beer-Lambert law. Xie et al.34 discuss some other possible effects of saturation in double-resonance spectro_scopjes, but argue that power broadening should be unimportant-in the case of NH3( C‘+A) transitions because ammonia molecules ‘dumped’ into the A state dissoci- ate rapidly and irreversibly. Despite this assertion, we find it relatively easy to power broadcn these dip spectra, especially those involving the more long-lived levels of ND3(A).The level widths listed in table 1 were obtained from spectra recorded at the lowest laser powers compatible with an adequate signal to noise ratio. As such they must still be regarded as upper limits to the true lifetime limited widths, but the observation of dips with widths <2 cm-’ f.w.h.m. encourages belief that we can operate in an intensity regime where power broadening effects are minimal. Such would keem not to be the case in the work of Xie et al.,34 who report linewidths for the NH3(A) 2l1.0 0.9 0.8 Q) 8 2 0.7 E 3 G l . . ~ l . . . , . . l i 17 300 17 200 17300 17200 1 .o 0.9 0.8 0.7 0.6 I * r r . , . . , . , , , , , 17700 17600 17500 I " " 1 17700 17600 17500 'dump' laser frequency/crn-' Fig.4. Fluorescence dips observed by monitoring the e'+ 2"n2 tracsitions while down-pumping Av = 0 transitions from selected J,K levels of the 2l and 22 vibronic states of the C' states of NH, and ND3. The solid lines are least-squares fits to the experimental line profiles, and assume Lorentzian lineshapes suitably corrected for Beer-Lambert distortion. ( a ) ND3, 2l, J = 6, K = 6; ( b ) ND,, 22, J = 8, K = 8; ( c ) NH,, 2l, J = 6 , K = 6 ; ( d ) NH3, 2 2 , J = 6 , K = 6 .M. N. R. Ashfold, C. L. Bennett and R. N. Dixon 171 Table 1. Bandwidths and predissociation lifetimes for the vibronic levels of the A 'A; states of NH3 and ND3 our work other measurements vibronic level f.w.h.m./cm-' TIPS f.w.h.m./cm-' d P S ref. NH3 0.13 f 0.02 45*8 O.ll*O.O2 (19) 0.16 f 0.02 38f5 0.14f0.02 (19) O0 41f5 2l 33f5 22 43f5 1 r22 46f5 0.1 1 f 0.02 (34) 0.12 f 0.02 52* 5 0.10~0.01 (19) - - loo* 10 0.053 f 0.005 (19) - - 135 f 10 0.039 f 0.003 (19) 23 24 ca.500 ca. 0.01 - ND3 O0 4.5" 1.2 2.5 2.1 (17) 2' 1.1" 4.8 0.8 6.6 (17) 24 20* 10 0.27 f 0.13 (19) 22 2 3 f 4 0.23 f 0.04 23 35 f 10 0.15f0.04 40*5 0.13f0.02 (19) - - 40f5 0.13 f 0.02 (19) - 1 '2* =G 250 20.02 - " Ref. (21). level substantially greater than those found here. This almost certainly reflects the fact that bigher 'dump' laser powers are required in order to compete with the rate at which the C' molecules are ionised following c_oherent three- rather than two-photon excitation. Pjevi,ous analyses of the ND3( A-X) 2; two-photon excitation spectrum,21 and of the C'-A 2: dispersed emission spectrum,31 demonsirated that the efficiency of the weak predissociation from the 2l vibronic level of ND,( A) is rotational-level dependent. No such trends have been identified for the higher 2" levels investigated in the present work.Discussion F e present work and previous studies have shown that the rate of predissociation of A-state ammonia molecules varies with vibronic level by over two orders of magnitude. The available information is summarised below. (i) For both NH3 and ND, the 2l level of the i? state is more resistant to predissoci- ation than the zero point level.'7y21 (ii) The predissociation lifetime, r, for the 2l level of ND,(A) exceeds that for the corresponding level in NH, by more than an order of magnitude.(iii) This effect of isotopic substitution is less dramatic for the (more short-lived) zero-point levels, and even less marked for the 22 vibronic level. goyever, recent band-contour ~imulations'~ of the higher 2," vibronic features in the A-X absorption spectrum of NH, and ND, suggest that the ratio r(ND,)/7(NH3) gradually increases again for n > 2 . (iv) Excitation of the kstate symmetric stretching vibration results in a much enhanced predissociation rate for both isotopic species. However, the isotopic ratio of these rates is a factor of only about two [assuming the larger width of fig. 3 ( b ) as indicative for ND,] and, from a consideration of the overall widths of the various172 observed 6 + 172; bands, these rates appear to be relatively insenstive to the level of excitation of the out-of-plane bending vibration (n = 0-4 for ND3).Detailed interpretation of these findin2s requires knowledge of the full six- dimensional potential-energy surface for A-state ammonia, at least in the Franck- Condon accessible region and along the H2N- H (D2N-D) dissociation coordinate. Ab initio calculation^^^^^^ (for planar excited-state geometries) indicate the presence of a relatively low barrier in this dissociation coordinate. This barrier arises as a natural consequence of the evolving Rydberg (3sa :) + antibonding valence (a"4a i) nature of the excited orbital as one H(D) atom departs. For the lowest energy levels of the A state ( i e . the zero-point and 2' vibronic levels) predissociation can occur only as a result of H(D) atom tunnelling through this barrier. Hence the large deuterium effect on the lifetime of these levels, and the observation that the predissociation of these vibronic levels (in ND3 at least) occurs with a rotational-level-dependent efficiency21 as a con- sequence of centrifugal modification of the barrier height.The dissociation from the higher vibronic states exemplifies Herzberg's case I1 of predisso~iation,'~ namely predissociation by vibration. Since the excitation of one quantum of vl has the most dramatic effect on the dissociation rate we first consider the coupling of the stretching vibrations. The symmetry coordinates for small-amplitude motion are Dissociation Dynamics of NH3( L 'A;) s, = (Sr, + Sr, + Sr3)/3 1/2 s3,, = (6r2-6r3)/21/2.(1) S3, = (26r1- Sr2 - 6r3)/6 '', Hence dissociation to NH2 + H necessarily involves a concerted motion along both S , and S3. We have constructed a model potential for these three dimensions based on the extended Rydberg function approach of Murrell et aL40 V( rir2r3) is written as a sum of a potential for the fragments and an interaction potential: v( rl r2r3) = vNH2( r2r3) + Knt( rl r2r3) (2) with VNH~ = D{2 - 1 + b( r2 - r e ) J exp [ - b( r2 - re)] - [ 1 + b( r3 - re)] exP [ - b(r3 - r e ) ] ) (3) and The three parameters of eqn (3) are determined by the mean bond energy, mean harmonic force constant and equilibrium bond length re of NH2. Three constraints have been applied to the parameters of V,,, to ensure three-fold symmetry in its polynomial expan$on up to quadratic terms in ( ri - ro), where ro is the equilibrium bond length for NH3(A).For larger displacements the three-fold symmetry is ensured over the complete coordinate space by permuting the three bond lengths when calculating V from egn (2) such that rl always refers to the longest NH(ND) $stance. The minimum in the A-state potential lies ca. 10 600 cm-' above the H + NH2( X ,B1) asymptote, 16~17939 thereby fixing Vo. The three remaining free parameters in V,,, were chosen to control the height and location of the barrier in the exit channels and the harmonic force constant for S1. Preliminary dynamical calculations with this potential have used the semiclassical approach of Le Roy and Liu41 to compute the width of the v = 0 resonance for tunnel- ling along a one-dimensional local mode as a function of the barrier height. TheM.N. R. Ashfold, C. L. Bennett and R. N. Dixon 173 E ,a 0 - I -51 I I I 1 - 5 0 5 10 15 xlpm Fig. 5. A two-dimensional cross-section of a model potential for the 2 state of NH3(ND3). The x-coordinate is 6rl, while the z-coordinate is (6r2+ Sr3)/21'2, with Sr, = ( r, - ro). S1 and S3, are the symmetry coordinates of eqn (1). The contours are in units of 1000 cm-'-abovethe NH2+ N asymptote. The classical trajectory commences close to the r-centroid for the C' + A 1; transition with a total energy appropriate to the 1 level of NH3. Table 2. An extended Rydbag potential for the stretching coordinates of NH3 A 'A: [see eqn (2)-(4)] D/cm-' 30000 b / k ' 3.266 r,/A 1.024 10 000 3.266 - 1.464 13.333 -2.147 -0.782 4.000 1.08 observed widths lead to a barrier height of ca.2000cm-' at a bond extension of ca. 0.3 A. The cross-section of such a potential in the (Sl, S3x) plane is shown in fig. 5 , and the parameters given in table 2. Three-dimensional quantum calculations are in progress to determine whether this potential can quantitatively account for the widths and energies of the 0' and 1' vibronic states, and will be reported at a later date. In the meantime, classical trajectories throw light on the mechanism of dissociatio_n. ~ The trajectory of fig. 5 starts from a point close to the r-centroid for the C'-A 1: transition of NH3, but with rl shorter than r2 and r3 by 0.016 A. The resultant motion diverges sharply from the S1 direction after one half period of v,, and dissociation ensues following three periods of a complex motion in the ( S , , &) plane.The total energy for this trajectory is ca. 1800cm-' above the top of the barrier, appropriate to vl of NH3. Small changes in the starting conditions at the same total energy lead to widely different trajectories, but all have the characteristic of a complex short-lived resonance within the potential well, followed by a variable partition of the available energy between vibration of NH2 and the recoil of H from NH2. The mean lifetime of the resonance compares well with that determined experimentally (table 1). Substitution of H by D, with an appropriate lowering of the total energy, brings the energy of the 1' state closer to that of the barrier and increases the lifetime of the transient resonance.174 Dissociation Dynamics of NH3(i ‘A;) 1; transition must have Al vibronic symmetry, and can therefore interact with ‘2u3’ but not ‘u3’.The extent of this anharmonic interaction will depend on the isotopic masses as well as the detailed shape of the potential. We propose that the strongly asymmetric profile of the 1; band of ND, [fig. 3(b)] arises from the interaction of an initially prepared ‘ul’ state with a highly non-uniform continuum of ‘nu3’ states above the exit barrier. Similar asymmetric lifetime-broadened line profiles have been observed in the E 2E+-A 2C+ band system of NO,36 and attributed to an analogous two-step dissociation mechanism. The marked departure of the isotopic ratio for the ul interval (2300 * 50 cm-’ for NH, , 1790 f 50 cm-’ for ND3) from the harmonic ratio of is attributed to the changing mixing with nu,, rather than to gross anharmonicity along the S1 symmetry coordinate which is asymptotic to N + 3H with a high dissociation energy. The above discussion has ignored the inter-bond angles.An approximate adiabatic separation may be expected between the high-frequency stretching motions and the low-frequency bending motions. However, two bending force constants must vanish on dissociation to NH2+ H and the remaining HNH angle must relax at equilibrium from 120 to 103.4”, so that the potential cannot be separable into stretching and bending contributions. The anharmonic coupling between these motions provides the driving force for vibrational predissociation of the 2” vibronic states by the conversion of two or more quanta of u2 into stretching motion, in addition to the more direct mechanism of quantum tunnelling.The data of table 1 suggest that the non-adiabatic mechanism is dominant, with an efficiency in NH3 which rises systematically with n, for n > 2 . A more detailed interpretation of these dissociation rates must await accurate ab initio calculations of the six-dimensional potential-energy hypersurface. Quantum-mechanically the ‘vl’ state accessed in the c‘ + We are indebted to the S.E.R.C. for equipment grants and a studentship to one of us (C.L.B.). We also thank S . Calvert, A. Nixon, H. Rieley, K. N. Rosser, R. J. Stickland, B. Tutcher and Dr C . M. Western for assistance in some aspects of this work.References 1 See for example: M. N. R. Ashfold, J. M. Bayley, R. N. Dixon and J. D. Prince, Ber. Bunsenges, Phys. 2 D. Imre, J. L. Kinsey, A. Sinha and J. K. Krenos, J. Phys. Chem., 1984, 88, 3956. 3 P. A. Hackett, R. A. Back and S. Koda, J. Chem. Phys., 1977, 65, 5103. 4 T. A. Gregory and S. Lipsky, J. Chem. Phys., 1977, 65, 5469. 5 L. D. Ziegler and B. Hudson, J. Phys. Chem., 1984,88, 1110. 6 L. D. Ziegler, P. B. Kelly and B. Hudson, J. Chem. Phys., 1984, 81, 6399. 7 J. R. McNesby and H. Okabe, Adu. Photochem., 1964, 3, 157. 8 H. Okabe and M. Lenzi, J. Chem. Phys., 1967,47, 5241. 9 W. E. Groth, U. Schurath and R. N. Schindler, J. Phys. Chem., 1968, 72, 3914. 10 U. Schurath, P. Tiedemann and R. N. Schindler, J. Phys. Chem., 1969, 73, 456.11 R. A. Back and S. Koda, Can. J. Chem., 1977, 55, 1387. 12 G. DiStefano, M. Lenzi, A. Margani and C. Nguyen Xuan, J. Chem. Phys., 1977, 67, 3832. 13 C. Nguyen Xuan, G. DiStefano, M. Lenzi and A. Margani, J. Chem. Phys., 1981, 74, 6219. 14 V. M. Donnelly, A. P. Baronavski and J. R. McDonald, Chem. Phys., 1979,43, 271. 15 M. Suto and L. C. Lee, J. Chem. Phys., 1983, 78, 4515. 16 A. D. Walsh and P. A. Warsop, Trans. Furaduy SOC., 1961, 57, 345. 17 A. E. Douglas, Discuss. Furaduy SOC., 1963, 35, 158. 18 M. B. Robin, Higher Excited States of Polyatomic Molecules (Academic Press, New York), vol. 1 and 19 L. D. Ziegler, J. Chem. Phys., 1985, 82, 664. 20 V. Vaida, W. Hess and J. L. Roebber, J. Phys. Chem., 1984, 88, 3397. 21 M. N. R. Ashfold, C. L. Bennett and R. N. Dixon, Chem. Phys., 1985, 93, 293. 22 M. Furlan, M. J. Hubin-Franskin, J. Delwiche, D. Roy and J. E. Collin, J. Chem. Phys., 1985,82, 1797. 23 W. R. Harshbarger, J. Chem. Phys., 1970, 53, 903. 24 P. Avouris, A. R. Rossi and A. C. Albrecht, J. Chem. Phys., 1981,74, 5516. 25 G. C. Nieman and S. I). Colson, J. Chem. Phys., 1978, 68, 5656; 1979, 71, 571. Chem., 1985,89, 254. 2 (1974), vol. 3 (1985).M. N. R. Ashfold, C. L. Bennett and R. N. Dixon 175 26 J. H. Glownia, S. J. Riley, S. D. Colson and G. C. Nieman, J. Chem. Phys., 1980,72,5998; 1980,73,4296. 27 G. C. Nieman, J. Chem. Phys., 1981, 75, 584. 28 A. J. Grimley and B. D. Kay, Chem. Phys. Lett., 1983,98, 359. 29 M. N. R. Ashfold, R. N. Dixon and R. J. Stickland, Chem. Phys., 1984, 88, 463. 30 M. N. R. Ashfold, R. N. Dixon, K. N. Rosser, R. J. Stickland and C. M. Western, Chem. Phys., 1986, 31 M. N. R. Ashfold, C. L. Bennett, R. N. Dixon, P. Fielden, H. Rieley and R. J. Stickland, J. Mol. 32 J. H. Glownia, A. Hartford Jr, G. W. Loge, R. K. Sander, J. J. Tiee and F. B. Wampler, Ado. Laser 33 J. K. G. Watson, W. A. Majewski and J. H. Glownia, J. Mol. Spectrosc., 1986, 115, 82. 34 J. Xie, G. Sha, X. Zhang and C. Zhang, Chem. Phys. Lett., 1986, 124,99. 35 T. W. Hansch, Appl. Optics, 1975, 11, 895. 36 M. N. R. Ashfold, R. N. Dixon, J. D. Prince, B. Tutcher and C. M. Western, J. Chem. Soc., Faraday 37 R. Runau, S. D. Peyerimhoff and R. J. Buenker, J. Mol. Spectrosc., 1977, 68, 253. 38 E. M. Evleth, J. T. Cleghorn and E. Kassab, Chem. Phys. Lett., 1981, 80, 558. 39 G. Herzberg, Electronic Spectra of PoZyatomic Molecules (Van Nostrand, Princeton, 1966). 40 J. N. Murrell, S. Carter, S. C. Farantos, P. Huxley and A. J. C. Varandas, Molecular Potential Energy 41 R. J. LeRoy and W-K. Liu, J. Chem. Phys., 1978, 69, 3622. 101, 467. Spectrosc., 1986, 117, 216. Spectrosc., 1983, 2, 105. Trans. 2, 1986, 82, 1257. Functions (Wiley Interscience, New York, 1984). Received 18th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200163

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986, 82, 177-185 Coherent Radiative Control of Unimolecular Reactions Three-dimensional Results Paul Brumer* Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario, Canada M5S 1 A1 Moshe Shapiro Department of Chemical Physics, The Weizmann Institute of Science, Rehovot 761 00, Israel A method for controlling product yields in photodissociation using weak lasers is applied to CH31 dissociating to CH, + I(2P3/2) or CH3 + I*(2P1/2). Results, obtained in three dimensions, show substantial control over the 1*(2P1/2)/1(2P3,2) ratio for both M-selected and M-averaged initial states. The basis for the method in control of the continuum superposition state is emphasized. Much of Chemistry is dedicated to manipulating chemical reactions so as to produce new chemical species or to enhance the yield of desired chemical products.Traditional approaches rely upon gross thermodynamics-based methods, e.g. increases in pressure and temperature, to bias the equilibrium in favour of the desired species. With the advent of laser technology, interest was directed towards utilizing lasers to enhance reaction selectivity, but with little practical success. Many of the resultant suggestions' relied upon the laser's power to alter the system Hamiltonian (to that of the molecule+ radiation) in order to achieve this result. However, the extremely high powers required make these methods impractical. Recently, we developed a promising which relies upon laser phase coherence to achieve control of photon-initiated unimolecular decay; only weak laser powers are required. In addition we presented a number of quantum collinear computational examples to demonstrate the utility of the method.In this paper we extend these computations to three dimensions and discuss various selection rules which play a role in the allowed excitation routes. Further, we provide a more qualitative description of our method which allows a clear understanding of how this theory provides the basis for all weak-field approaches to influencing photon- initiated unimolecular product yields. This paper is organized as follows. The next section provides a partially pedagogical introduction to coherent radiative control of unimolecular reactions. Application is then made to CH31 dissociation to control the yield of CH3 + I(2P3/2) us.CH3+ I*(2P1/2). As in our previous control studies, the dissociation of methyl iodide, while an interesting system in its own right, is here regarded an example of the general method and is chosen because of the availability4 of reliable potential surfaces and photodissociation matrix elements. Extensions to other systems are in progress. Coherent Radiative Control of Unimolecular Reactions Consider photon-induced unimolecular decay ( i. e. photodissociation) of a molecule A in an initial stationary eigenstate Im) where rn designates the bound-state quantum numbers. The state energy is denoted Em. There are two ideal possibilities for the excitation: ( a ) a C.W. laser operating to produce a single photon frequency w or (6) a 177178 Control of Chemical Reactions transform-limited pulsed laser producing a coherent, frequency-broadened pulse.Since our interest is in the final product distributions, we are free to focus on the former case without any loss of generality. This results from our recent demonstration5 that product distributions associated with pulsed laser preparation are identical to those resulting from a related set of c.w. excitations. Specifically, the photodissociation product distribu- tion is independent of the coherence of a pulsed laser across its frequency bandwidth. Therefore, a set of independent C.W. experiments which have the same cumulative frequency envelope as the pulsed laser will produce the same product distribution. The process of interest is then D + F - A+ho -+ B+C where B+C etc.denote one of several possible chemically distinct product channels accessible at energy E = Em + Zzw. Below we distinguish these arrangement channels by the numerical label q ( q = 1,2,. . .). Adherence to a fixed initial energy and fixed excitation energy implies a time-independent picture of photodissociation; Le. the system is excited from an initial bound state at Em to total energy E; no dynamics takes place in the excited state. Rather, the resultant stationary-system wavefunction at energy E has plane-wave components in each arrangement channel whose magnitude gives the amount of product in that channel. The product yield, as well as distribution amongst the internal quantum states in each product channel, is dictated by two factors: the nature of the excitation lifting the system to energy E and the nature of the wavefunctions at energy E.Indeed it is an understanding of the system continuum stationary wavefunc- tions at energy E and the state created at this energy which is the key to identifying general requirements for yield control. Details are discussed in the following subsections. Eigenstates of the Hamiltonian Consider the Hamiltonian H of the molecule A which dissociates along relative coordin- ate R, ( q = 1,2, . . .) to form products in arrangement channel q. Specifically H = H i + V , where H: is the Hamiltonian of the products in asymptotic channel q and Vq + 0 as Rq-+w. We denote the eigenfunctions of H: at energy E by IE, n, 40) where the quantum number n defines the vibrational, rotational etc.state of the fragments as well as the scattering angle. Of the various methods for labelling the eigenstates of H at energy E in the continuum, incoming boundary conditions yield those most convenient for problems involving disso~iation.~~~ Specifically, we define eigenfunctions 1 E, n, q-) where the minus sign, denoting incoming boundary conditions, implies that 1 E, n, q - ) displays incoming spherical waves and an outgoing plane-wave component IE, n, qo) in the limit of large R,. A general wavefunction at energy E is then a linear superposition of degenerate eigenstates, i.e. R, -+ 00. Several important features are embodied in this description. First, the system is degener- ate at energy E, and this degeneracy is directly linked to the fact that a variety of diff erent product states are accessible at energy E.(Indeed the system is infinitely degenerateP. Brumer and M. Shapiro 179 since the n label includes the scattering angle.) Second, Preparation? of the system at energy E corresponds to the creation of a wavefunction with continuum component given by eqn(2). Third, the time independence of state populations is clear in that eqn (2) displays time dependence through one overall multiplicative phase factor. The Created Continuum State By virtue of eqn (3) the coefficient dq,, directly provides the probability of forming the product in final state IE, n, so). Further, the magnitude and phases of dq,, are directly determined by the nature of preparation. Thus, control of the resultant product distribu- tion is equivalent to the ability to experimentally manipulate the coefficients dq,n in the created continuum superposition state.To this end consider the extent of control over the reaction afforded by traditional photoexcitation from a single bound state Im). Standard photodissociation theory, applicable in the weak-field limit,' gives Here p8 is the component of the transition dipole moment operator along the electric-field vector whose magnitude, at frequency o, is E ( 0). Experimental control over the probabil- ity P(n, q, E) = ldq,n12/Cq,n )dq,n12 of forming the product in IE, n, qo), is clearly limited to varying the incident frequency and passively observing the consequences of the resultant change of E. It is, essentially 'nature' which dictates whether altering E will generate a variation of dq,, in accord with the desired reaction direction. What we seek, as an alternate, far more active, mode of operation, is a means of directly varying dq,, through experimental parameters.Any phase-incoherent method (re. methods which fail to maintain, and take advantage of, phase information) can be ruled out since it tends to give results which are linear combinations of similarly passively controlled yields. Thus we seek a coherent means of directly influencing the prepared wavefunction in the continuum. Multiple Frequency Coherent Preparation We have recently proposed a direct to achieving this goal. Specifically, we advocate a two-step process. First the system is prepared in a superposition of bound states Ij).Second, this superposition is simultaneously irradiated with a set of frequencies oEj = (E - E j ) / h. As a consequence, the energy E is accessed through several different routes, each of which maintains system phases. This phase-preserving multiple excitation route to energy E is the essence of coherent radiative control. The net result is that the system is formed at energy E with coefficients d,,,, which are functions of experimentally controllable phases and amplitudes. Here we cite the results of our published deriva- t i ~ n ~ ' ~ which is applied to three-dimensional CH31 dissociation below. Consider then initially forming a bound superposition state given by Ix( t = 0 ) ) = C . cjl Ej) and subsequently irradiating the system with frequencies wEj = (E - Ej)/ h with efectric fields given by E ( oEj) = E"( wEj) exp ( -i+Ej), where +Ej is the phase of the electric field. Application of standard weak-field photodissociation theory3 gives the relative yield P ( q , E) in arrangement channel q at energy E as with t We assume, in this section, a mode of preparation which yields a pure state rather than a mixture.180 Control of Chemical Reactions Here p i , j ( q ) contains only molecular attributes whereas Fi,j contains all aspects of the preparation, including the magnitudes and phases of the electric field and initially prepared coherent state Ix(0)).A similar result can be obtained2 for the probability of forming the system in product state IE, n, qo), leading to control over the formation of specific quantum states.The simplest case consists of an initial superposition comprised of two levels, i.e. Ix(0)) = c,ll)+ c212). In this case the relative yield can be written as R ( 1 : 2, E ) = P( q = 1, E ) / P ( q = 2, E ) exp (ie,) = F"(wEj)cj The experimental control parameters are Oi and x, which may be altered by either varying phases and amplitudes in the initial superposition state preparation step or in the subsequent application of the dissociating laser fields. The form of eqn (7) makes clear that the product yield is dictated by the interference between components of the continuum wavefunction which have arisen through independent, coherent, paths of excitation. It is clear that the degree of yield control depends upon the relative magnitudes of the i # jlpi,j( q)1 cumulative matrix elements and the i = j terms. Estimating these quantities will necessitate further studies of specific systems.One general class of uncontrollable photodissociation is worthy of Specifically, consider excitation from I i), ( i = 1 , 2 , . . .) to an energy E, such that a strict separable approximation holds, i. e. (Er, n, q-l~wEli>=AiX~(n)- (9) (10) Since P(q, E,) separates into one term involving preparation and one involving the product channels, the yield of any particular channel q, which is a probability ratio, will be independent of the control parameters. This loss of control requires eqn (9) to be satisfied for both phase and amplitude and hence is an extension of traditional assumptions at an isolated resonance." General interest in behaviour at a resonance warrants our ongoing studies to assess the effect of the phase of (E, n, q-lpE(i) on coherent control. Finally we note that a measurement is unable to isolate products of dissociation at fixed total energy E.Since the initial bound superposition (e.g. in the two level case) is being subjected to two frequencies, oE1 and wE2, excitation to energies (El + AmE2) and (E2+ zZoE1) also occurs if they lie within the absorption band. These serve as uncontrolled 'satellite' contributions to the photodissociation, diminishing the degree of observed control relative to the 'constant E' experiment. Nonetheless, the degree of observed control at E is often so large (see below) that the net overall variation in the yield is still substantial.This method is applied to the three-dimensional photodissociation of CH31 below. Then eqn ( 5 ) is of the form P ( q, E,) = (T/ A)'IXq( n)12 C Fi,jA,A,*. i . jP. Brumer and M. Shapiro 181 Coherent Radiative Control: A Three-dimensional Example The (single-frequency) photodissociation of CH31 to yield CH, + 1*(2P1,2) and CH3 + I(’P ) has been the subject of much recent study.t In addition, we have reported on control of yields in the collinear CH3I photodissociation. In this section we extend these computations to dissociation in three dimensions; the linear pseudo- triatomic model” of CH31 is maintained. In this case a bound CHJ state li) is defined by4 energy E i , angular momentum Ji and its z projection Mi; the product label n is composed of u, A and k, where k are the scattering angles, u denotes the final CH3 (umbrella) vibrational state and A is the electronic index.The label A = g denotes the ground CH31 state, A = 0 the ’QO state, and A = k l the doubly degenerate ‘Q1 states. The A index is also used to denote electronic states of the fragments because, in the diabatic representation, A = 0 (,QO) correlates with the I*(2P1,2) fragment and A = *1 with the I(2P3,2) fragment. Below we also use q = 1 to denote the (A = 0) I(2Pl!2) fragment and q = 2 to denote the (A = *l) I(2P3/2) fragment. Details of the potential surface and method of matrix-element computation are provided el~ewhere.~ Here it suffices to note the quality of the computation, which consists of a fully quantum treatment of photodissociation, involving three (the ground, Qo and ’ Q1) potential surfaces including the non-adiabatic coupling between the last two states.The primary quantity required in eqn (6) is the photodissociation amplitude (E, n, A-lpEIEi, Ji, Mi). For the case of linear pseudo-triatomic CH31 this is given in terms of4 (E, k u, A, Ip.sIEi, ~ i , Mi) (11) Here #k, t?k are the scattering angles, p is the reduced mass of the CH, and I, k,, is the relative product momentum in state u, A and t ( E, J, A, u I Ei, Ji) are the ( Mi-indepen- dent) reduced amplitudes, containing the essential dynamics of the photodissociation pro~ess.~ Given eqn (6) and (1 l), the general form of pi,,(A) = p$,;)(Ei, Ji, Mi; E’, 4; M,; E ) where the i, j quantum labels are now explicitly indicated as arguments, is given by X S(Mi, Mj)t(E, J, A, I Ei, Ji)t*( E, J, A, I Ej, 4).( 1 2 ) Here the Kronecker delta arises from the orthogonality of the D functions.12 Eqn (12) indicates that radiative control, which only occurs for non-zero p ( ” ) ( E i , Ji, Mi; Ej, 4, M,; E ) , requires that Mi = Mi. We note, for use later below, that symmetry properties of the 3j symbols12 imply p‘”’(Ei, Ji, Mi; Ej, Ji, Mj; E) = (-l)(’~+’j)/~‘”)(Ei, Ji, -Mi; Ej, Ji, -Mi; E ) . (13) t For a review of experimental and theoretical studies see ref (4).Control of Chemical Reactions 182 180 150 120 0 2 90 60 30 0. ( 0.17 0.33 0.50 0.67 0.83 ' M I , + 1 2 ) 160 150 120 0 \ CD 90 60 30 0 I Fig. 1. Contour plot of the yield of I*(2Pl,,) (i.e. percentage of I* as product) in the photodissoci- ation of CH31 from a polarized superposition state composed of V, = 0, J1 = 1, and V, = 0, J, = 2, where M, = M2 = I, at ( a ) uEI = 39 638 cm-' and ( b)uEl = 42 367 cm-'. V = 0 denotes the ground vibrational state of CH31.The abscissa is labelled by the relative amplitude parameter 12/( I , + I,) = ~f2~2/(~fl~z+ Ifil') and the ordinate by the relative phase parameter 8 = - 02. Two cases are of interest; the first, where the beam of molecules is M-selected, and the second where no such selection is assumed. Each of these cases is treated below. M-polarized Beams In this case the initial state is a single bound state 11) = I El, J1, M,) which is first irradiated to produce a superposition of two bound states: /El, J1, Ml) and I&, J2, M2 = Ml).Electric-dipole selection rules guarantee that M2 = Ml for a z-axis linearly polarized light. Subsequent two-colour irradiation raises the system to energy E as described above, and eqn (7) is directly applicable in conjunction with eqn (12). Note that eqn (13) indicates that the relative product yield R( 1,2; E) is identical for the case of )MII and -lMII if (Jl +J2) is even. In the case of odd (J1 + J2), the controlled yield (ie. yield us. x and O1 - 0,) is the same for the lMII and -lMll, but at relative phase ( O1 - 0,) shifted by T. Note also that eqn (13) implies that there is no control for MI = 0 and (J1 + J2) odd, Le. p ( * ) ( E j , Ji, Mi; Ej, 4, Mi; E) is zero. Fig. l(a) and 2(a) display the yield of I*(2P112) for two different M-selected initial bound-state superpositions.Results are shown at w1 = 39 638 cm-', which is near the absorption maximum. Fig. 1 (b) and 2( b) are for the same initial superpositions but at w1 = 42 367 cm-', near the absorption half-maximum. The three-dimensional results support our earlier claims,293 based on collinear calcula- tions, that phase control can lead to a dramatic enhancement of the quantum yields. Two features are worth noting. (a) The wavelength dependence of radiative control: different (phase and intensity) control parameters are needed to attain maximal quantum yields at the peak of the absorption as compared to irradiation at half maximum. ( b ) The dependence on relative parity: the equal-parity case [fig. 2(a) and ( 6 ) where J1 = J2 = 21 is strikingly different from the unequal parity case of fig.1( a) and (b) (J1 = 1 and J2=2). The equal-parity maps show a wider range of control as compared with the unequal parity results. In addition to the above, polarization of the initial beam plays a crucial role in radiative control. This is most severe in the unequal-parity case, where, contrary to theP. Brumer and M. Shapiro 183 Fig. 2. As in fig. 1 but for V, = 0, J , = 2, V2 = 1, J2 = 2, M1 = M2 = 0. (a) wEl = 39 638 cm-' and ( b ) wEl = 42 367 cm-'. V = 1 denotes the first vibrationally excited state of CH31 (essentially the first excitation of the C-I stretch). 120 5 7 90 0.75 I I I I I I I 0.35 I I Fig. 3. As in fig. 1 but for V, = 0, J1 = 1, V, = 0, J2 = 2, M , = M2 = 0. No phase control is seen since J1 + J2 is odd and Mi = 0.( a ) wEl = 39 638 cm-' and (b) wEl = 42 367 cm-'. M = 1 case [fig. l(a) and ( b ) ] , the M = 0 case (fig. 3) shows no phase control. This is in accordance with the selection rules discussed above. M-averaged Beams In this case the initial state is defined by the density matrix po= l/(J1 + 1) CM, I El , J1 , Ml)( El , J1, MII. Irradiation with frequency ( E2 - El)/ fi results in the formation of (2J1 + 1) independent superpositions of each [El, J1, MI) with an excited ( E 2 , J 2 , M2= M,). Each of these superpositions may be treated independently in the subsequent two-colour irradiation which lifts the system to E. The resultant P(q, E ) is184 Control of Chemical Reactions 0.0 0.17 0:33 0.'50 0.67 0.83 1.0 1*/(11+ 12) z2/ (11 + 1 2 ) Fig.4. I*(2Pl,,) yield in the photodissociation of CH31 starting from an M-averaged (unpolarized) ensemble of superposition states. The J and V are as in fig. 2. ( a ) wEl = 39 639 cm-' and (b) W E , = 42 367 cm-'. Fi, is assumed, for convenience, to be independent of M , . obtained then as an average over the (2J1 + 1) superpositions, i.e. P(q, E ) = ( ~ / f i ) ~ / ( 2 ~ 1 + 1) c c C F,,jp(")(Ei, J i , ~ 1 ; Ej, 4, ~ 1 ; E ) . (14) i=1,2 j = 1 , 2 MI From eqn (12) it follows that the M1 dependence of p(*)(Ei, J i , MI; Ej, 4, MI; E ) is entirely contained in the three-j product ( J 1 A ) ( J 1 4 ) -M1 0 M1 -MI 0 M1 Hence the M, summation can be performed separately. Defining we have that P(q, E ) = ( ~ / f i ) ~ C C p("(Ei, J i ; ~ j , 4; E ) (16) i=1,2 j=1,2 where P ( ~ ) ( E ~ , Ji; Ej, 4; E ) = C Ci,j(J)t(E, J, A, U I Ei, Ji)t*(E, J, A, ~1 Ej, 4).(17) J, v It follows immediately from the symmetry properties of the three-j symbols12 and eqn (15) that P ( ~ ) ( E , , J,; E2, J2; E) is zero if (J1 +J2) is odd; i.e. yield control in M-averaged situations requires even (J1 + J2). (This follows because, for odd J1 + J2, the positive M cancel out the negative M and MI = O term is identically zero.) As a result, for unpolarized initial states, state 2 must be created from state 1 by either a Q line absorption, which can be realized if states 1 and 2 belong to different electronic states, or Raman scattering, or any process involving an even number of photons. These limitations are lifted if the initial state is M-selected, as shown above.The yield R ( 1. 2; E ) now follows directly from eqn (7), where pi. i ( q ) is replaced by p(q)(Ei, J i ; Ej, 4; E). Fig. 4 shows the result for coherent radiative control of an initialP. Brumer and M. Shapiro 185 M-averaged pair of states at two different values of 0 , . The range of control demon- strated is very wide: at the peak of the absorption, [fig. 4(a)], the I*(2P1,2) quantum yield changes from 30%, for 12/( I , + 12) = 0.9 and - O2 = O", to 75% for 12/( II + 12) = 0.2 and - O2 = 140". A compariSon with'the even J1 + J2 polarized case, [fig. (2)], shows that the range of control degrades only slightly with M-averaging. This is to be contrasted (fig. 1 us. fig. 3) with the odd J , + J2 case. Summary This paper demonstrates that substantial yield control is possible in unimolecular decay processes using a set of phase controlled C.W.sources. The essential experimental requirement is the ability to alter the relative phase parameter - 02, which can be affected in either of the two sequential radiative steps. For example, the ability to vary the temporal duration of a transform limited pulsed source in the first step, and maintain fixed phase in the subsequent step, would suffice. Alternatively, laser phase-control methods may be of use13 as well as a number of alternate schemes under investigation. Such experimental efforts are well warranted, as evidenced by the results of the particular case examined in which population inversion of I*(2P,,2) could be created or eliminated both in M-polarized and unpolarized beams.References 1 See for example, A. Ben Shaul, Y. Haas, K. L. Kompa and R. D. Levine, Lasers and Chemical Change (Springer-Verlag, Berlin, 1981); R. L. Woodin and A. Kaldor, Adv. Chem. Phys., 1981,47(b), 3; R. W. Falcone, W. R. Green, J. C. White, J. F. Young and S. E. Hams, Phys. Rev. A, 1977, 15, 586; W. R. Freen, J. Lukasik, J. R. Wilson, M. D. Wright, J. F. Young and S. E. Hams, Phys. Rev. Lett., 1979,42, 970; T. F. George, I. H. Zimmermann, J. R. Laing and P. L. De Vries, Acc. Chem. Res., 1977, 10,449; T. F. George, J. Phys. Chem., 1982, 86, 10; A. M. F. Lau and C. K. Rhodes, Phys. Reu. A, 1977, 15, 1570; 1977, 16, 2392; K. C. Kulander and A. E. Orel, J. Chem. Phys., 1981, 74, 6529. 2 M. Shapiro and P. Brumer, J. Chem. Phys., 1986, 84, 4103. 3 P. Brumer and M. Shapiro, Chem. Phys. Lett., 1986, 126, 541. 4 M. Shapiro, J. Phys. Chem., in press. 5 P. Brumer and M. Shapiro, J. Chem. Phys., 1986, 84, 540. 6 See, e.g. R. D. Levine, Quantum Mechanics of Molecular Rate Processes (Oxford Univ. Press, Oxford, 7 M. Shapiro and R. Bersohn, Annu. Rev. Phys. Chem., 1982, 33,409. 8 See ref. 7 and P. Brumer and M. Shapiro, Adv. Chem. Phys., 1985,60, 371. 9 For an alternative separable case see M. Shapiro and P. Brumer, in Proc. Fritz Haber Symp. on Laser 1969). Spectroscopy, ed. Y. Prior (Plenum, New York, 1986). 10 P. Brumer and M. Shapiro, J. Chem. Phys., 1984, 80, 4567. 11 M. Bersohn and M. Shapiro, J. Chem. Phys., 1980, 73, 3810. 12 A. R. Edmonds, Angular Momentum in Quantum Mechanics 13 See, e.g. Y. Bai, A. Yodh and T. Mossberg, Phys. Rev. Lett., 2nd edn, 1960). (Princeton University Press, Princeton, 985, 55, 1277. Received 1 1 th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200177

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

GENERAL DISCUSSION Prof. K. F. Freed (University of Chicago, USA) said: Prof. Welge has shown some beautiful data on the photodissociation of H20. OH and a number of other photofrag- ments have the annoying feature of themselves predissociating, so that interrogation of vibrational populations by laser-induced fluorescence is hampered, and the vibrational distributions can often only be studied in some of these levels. We have, therefore, decided to study theoretically the predissociation in OH as a prototype for aiding in determining the mechanism of these types of predissociation. The A2Z+ state of OH is predissociated by curve-crossing with 4C-, 2Z- and 411 electronic states which all dissociate to the ground-state atomic limits. We have perfor- med close-coupled calculations of the predissociation dynamics in order to determine whether the final oxygen atom fine-structure state distributions reflect the nature of which of the three electronic states is inducing the predissociation.' This problem is not quite so obvious as it might appear since the 4C-, 2Cc- and 'II states all dissociate to a common limit, and therefore have large Coriolis and spin-orbit couplings which asymptotically mix these levels at large internuclear separations. Thus, even if a curve- crossing occurs to only one of these levels, the large-distance non-adiabatic couplings scramble the populations among these nominal electronic states.Our calculations include all the non-adiabatic couplings, use RKR potentials for the ground and 'Z+ state, ab initio potentials for the remaining states, and ab initio calcula- tions of the diagonal and off -diagonal spin-orbit coupling matrix elements.The calcula- tions have been made for the predissociation of the J = 7 , 1/2, N = 7 components of the A 2Zc+ state, and they indicate that for most vibrational levels predissociation occurs through crossing to only one of the three possible final electronic potentials, but in some instances there are contributions from more than one curve-crossing. The oxygen atom fine-structure distributions are thus predicted often to contain a signature of the predis- sociation mechanism in spite of the scrambling induced by the asymptotic non-adiabatic couplings. OH is a particularly good example because of the availability of experimental data and ab initio calculations, but it should be fairly typical of the behaviour expected in many other diatomic predissociations.Our calculations, therefore, indicate the utility of studying the atomic state fine structure distributions in order to elucidate the mechan- ism of the predissociation process as a function of the initial vibrational level. 1 S. Lee, C. J. Williams and K. F. Freed, Chem. Phys. Lett., 1986, 130, 271. Prof. J. C. Polanyi (University of Toronto) said: Prof. Welge has described a most attractive alternative to the more conventional procedure for determining time-of-flight distributions. By multi-photon ionization at the beginning of the flight path he makes it possible for the experimenter to record an entire speed-distribution with each MPI laser pulse.It would be interesting to learn what the actual gains are in signal-to-noise ratio, and where the limitations lie. Dr B. Koplitz, Mr Z. Xu, Mr D. Baugh and Prof. C. Wittig (University of Southern California, USA) said: Many of the sophisticated measurement techniques presently being employed in photo fragmentation studies allow very precise and elegant experi- ments to be carried out. Measurements of differential cross-sections allow experiment and theory to be compared at a high level, and the future looks bright for understanding molecular processes at an unprecedented level of precision. This promise is demonstrated clearly by the elegant experiments of Welge and coworkers. 187188 General Discussion A VO 0 n Fig. 1. A, Doppler profiles for monoenergetic, spatially isotropic velocities: (a) low kinetic energy, (b) high kinetic energy; and B, hypothetical V.U.V.spectral distribution of probe. However, we wish to emphasize that the price for such precision is that distributions of the differential cross-sections should be obtained. Take for example our sub-Doppler resolution studies. It is often thought that a Doppler signature is integral rather than differential because many different velocities can have the same projection on the direction of the probe wavevector. However, we have shown that species can be selected whose velocities are essentially parallel to kprobe, so that kinetic energy distributions along the direction of kprobe can be obtained. Now it becomes important to measure/de- duce the same information for different orientations of Ephotolysis, kprobe, Eprobe etc.Similarly, in the Bielefeld experiments one must deal with the issue of the velocity group which is selected by the probe. With hu - Do> 5 eV the maximum allowed Doppler shift is ca. 9cm-' and a spatially isotropic distribution of such velocities gives a rectangular Doppler profile of width 18 cm-'. Even the most callous of laser manufac- turers still provides dye laser bandwidths which result in V.U.V. linewidths of ca. 2 cm-', an order of magnitude smaller than the Doppler profile corresponding to the maximum allowed Doppler shift. Thus, there can be bias against detecting species having high kinetic energies. This situation is shown schematically in fig. 1. Note that if the laser is centred at v,, it will detect species having low kinetic energies much more efficiently than those having high kinetic energies.Thus, a velocity distribution obtained with the laser set at vo must be examined very carefully, lest one overestimate the low-kinetic- energy contribution. In general, there is a spatially anisotropic distribution of laboratory velocities and analyses must also account for this addition complication. On the other hand, the situation shown in fig. 1 does measure a differential cross- section and, in principle, an important body of information is available by scanning the laser frequency, albeit with added experimental complexity and the same uniqueness and deconvolution problems as with the sub-Doppler method. Nevertheless, one must be optimistic.We believe that two years from now, Doppler/TOF techniques will increase markedly in popularity and will significantly affect fragmentation and molecular dynamics studies of many systems. Dr M. Brouard, Mr M. P. Docker and Prof. J. P. Simons (University of Nottingham) said: One of the most difficult problems in a detailed analysis of photodissociation pathways is the estimation of branching ratios/quantum yieltds into alternative product states/channels. The photodissociation of H20 from the B *Al continuum, accessed either directly, as in Prof. Welge's characteristically elegant experiment,' or indirectlyGeneral Discussion 189 via predissociation pathways fro? higher Rydberg states: is an excellent case in point. The yield of OH(A) from the B 'A, continuum only accounts for 10% of the OH fragments; the time-of-flight measurement suggests that the remainder, OH( X), are generated viu the fi-+A transfer near linearity.The alternative route, via the fi+* transfer at the conical intersection discussed by Dunne and M ~ r r e l l , ~ is thought unimpor- tant, not least because the latter process is predicted to give OH(X) in high vibrational states, rather than the hjgh r2tational states experimentally demonstrated by Welge and coworkers.' Since the B-+A transfer is promoted by out-of-plane rotation about the a-inertial axis, cold water should generate much less OH(X) and also live much longer in the B state if (a) the long-lived resonances predicted by Segev and Shapiro4 are real, and ( b ) the 6.2 leakage path (which is not influenced by rotation) is unimportant. We have attempted to check ( a ) and (6) by measuring the excitation spectrum of OH(A) for a jet-cooled souLce o,f H20 using synchrotron radiation between 120 and 135 nm.I,f the-peaks in the B t X continuum narrow, or if sharper resonances appear, then the B t X paths-would-clearly b_e unimportant. The observations were as follows. X (0-0) features at 121 and 124 nm narrow, change their relative intensities from C : D = 1 :2.5 to 1 : 3 but do not shift in frequency. The absence of any shift established the generation of OH(A) from H20 monomers rather than clusters and the narr>wing confirms the rotational cooling; the decreased rate of predissociation from the C state follows the requirement ( J : ) # 0, for the generation of OH(A) via the heterogeneous pathway2 H20(c) -+ H20(6) -+ H+OH(A).(2) The peaks in the fi + 2 continuum centred at 133.25 and 131.8 nm in the excitation spectrum for OH(A) production at 300 K are shifted to shorter wavelengths, respectively 133.1 and 131.4 nm, by the jet expansion: these shifts correspond to ca. 100 and ca. 200 cm-'. Neither of the peaks is noticeably narrowed and no new features are observable (under 0.25 nm resolution). (3) Earlier experiments by Lee,5 which compared the OH(A) photofragment excita- tion spectrum at 300K with the absorption spectrum, also revealed a shift to shorter wavelengths with displacements of 70 and 140cm-' for the two peaks that we have monitored. Since jet-cooling promotes a further shift in the same sense, it suggests that dissociation of H,O(B *A,) to OH(A) proceeds though excitation of a cold sub-set of the Boltzmann rotational population at 300 K.The suggestion follows expectation-sincc H20(B) molecules with high rotation are much more likely f,o fall through the B -+ A 'trapdoor' than dissociate to OH(A). Dissociation on the A continuum leads to the ground-state fragments OH(X). So what conclusions can be drawn regarding the importmce (or otherwise) of the conical interszction? The answer depends on the reality of potentially long-lived reson- ances on the B-state continuum. If they are real, the!ack of any narrowing of the peaks in the ezpercmental spectrum implies that the 6- X 'leakage' is at least as important as the B-A. If they are not real, then the logic fails.The interpretation of Prof. Welge's experiments, therefore, casts some doubt on the quality of the resonances predicted by Prof. Shapiro. The best (but experimentally challenging) test would be to measure the quantum yield of OH(A) from jet-ccoled H,O. Under conditions where ( J : ) = 0, the yield should approach unity if P + X is unimportant. A final point: the absence of any evidence of OH(A) formation from water clusters, under conditions where they are likely to be present is striking. H20 is an excellent quencher of OH(A --+ X) fluorescence so the absence may not be surprising. ( 1 ) the D 'Al + X and C 'el 1 H. J. Krautwald, L. Schneider, K. H. Welge and M. N. R. Ashfold, Faraduy Discuss. Chem. SOC., 1986, 2 A. Hodgson, J. P.Simons, M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Mol. Phys., 1985,54, 351; 82, 99. M. P. Docker, A. Hodgson and J. P. Simons, Mol. Phys., 1986, 57, 129.190 General Discussion 3 L. J. Dunne and J. N. Murrell, Faruday Discuss. Chem. SOC., 1986, 82, 190; 191. 4 E. Segev and M. Shapiro, J. Chem. Phys., 1982, 77, 5604. 5 L. C. Lee, J. Chem. Phys., 1980, 72, 4334. Dr A. Hodgson (University of Notting@n) said: Of the two possible competing channels for removal of molecules from the B 'ALsurface (which correlated with OH/OD A 2E+),-viz. the Renner-Teller coupling to the A *B1 state in the linear configuration or to the X 'Al state near the conical intersection, there is strong experimental evidence for the former. Modelling of the OH/OD A 'E+ phojofragment fluorescence excitation spectrum following predissociation from H20/ D20 C B, (which has a geometry similar t? X 'Al) indicated a quantum yield for production of excited OH/OD A 2E+ on the B-state surface that was dependent on parent a-axis rotation (J',),' and-on product rotational leveL2 Such a J,-dependent coupling was predicted for B + A transfer by Dixon3 and clearly chis is a major pathway for trajectories starting near the Franck- Condon region on B 'A,.Evidence for the importance of B + -% cppling is more circumstantial. For OD(A 2E+) formed from predissociation of D20( c) on: may esti- mate2 that ca. 50% of a 300 K Boltzman? sample would be lost via B + A coupling. The quantum yield of OH(A 2Xt) from B 'Al is only 5-10%, and while the difference maxbe dye to deuteration or a different Franck-Condon region it may also be attributed to B -+ X transfer.Comparisons of the present experjmenis of Krautwald et al. with the calculations of Dunne and Murrel14 suggest that B --* X transfer is not important despite the efficiency of the process. 1 A. Hodgson, J. P. Simons, M. N. R. Ashfold, J. M. Bayley and R. N. Dixon, Chem. Phys. Lett., 1984, 2 M. P. Docker, A. Hodgson and J. P. Simons, Mol. Phys., 1986, 57, 129. 3 R. N. Dixon, Mol. Phys., 1985, 54, 333. 4 L. J. Dunne and J. N. Murrell, Furuday Discuss. Chem. SOC., 1986, 82, 190; 191. 107, 1; Mol. Phys., 1985, 54, 351. Dr L. J. Dunne (South Bank Polytechnic, London) said: The experimegtal observation by Krautwald et al.' that the OH(211) fragment produced in the B state selected photodissociation of water is remarkable.The rovibrational distribution is unusual for the fact that some 5 eV of disposable energy is available to cause vibrational excitation of the OH(211) fragment, yet it is produced rotationally hot but vibrationally very _cold. Ip the experiment of Krautwald et al. three states are important. These are X, A, B when placed in energetic ozder at the C2, equilibrium geometry. More generally, photon excitation from the X staie populates the B state either directlx or by a radiationless transition from the C state, which lies slightly abovs the B state at equiGbrium geometry. More generally, photon excitation from the ,X state populates the B state either djrectly or by a radiationless transition froe tbe C state, which lies slightly above the B state at equilibrium geometry.Both the A, < states correlate with the ground-state product channel OH(211) + H(2S), whereas the B state correlates with the excited OH(2X+) + H(2S) channel. The questign ,Of soFe jnterest is the relative significance of the non-adiabatic coupling of the B / X or B/A states leading to the above products. Dixon2 bas- produced a model based on the g / A non-adiabatic coupling, but the role of the B / X non-adiabatic coupling in the photochemical dynamics remains unclear. In collaboration with Murrell and Guo w,e have proceeded some way to confirm the inference of Dixon and coworkers that the B/A coupling is the dom!na_nt radiationless decay mechanism. A two-value potential-energy surface for the B / X state of H20 in a diabatic representation was derived some time ago3 and used for a theoretical study of the non-adiabatic photodissociation dynamics.Both a well established surface- hopping method and a density matrix495 method were used, and the results of both broadly agree. The majority of trajectories lead to the OH(211) channel, which is consistent with experimental findings. Ca. 10% of trajectories lead to O('D) + H2. TheGeneral Discussion 191 majority of OH (2E+) is produced in high rotational states of v=O, which is also confirmed by experiment. However, we find large populations of high vibrational states of OH(211), which disagrees very strongly with experime_nt._ For this reason it is likely that the OH(211) is mainly produced by the alternative B / A non-adiabatic process.One may speculate as to the physical situation producing the vibrationally cold OH(211) in the experiment of Krautwald et al. An exit pathway for a hydrogen atom perpendicular to the bond in the OH fragment and intersecting with its centre of gravity has a good chance of channelling the recoil required by linear momentum conservation into relative translational motion rather than OH vibrational excitation. 1 H. J. Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold, Faruduy Discuss. Chem. SOC., 1986, 2 R. N. Dixon, Mol. Phys., 1985, 54, 333. 3 J. N. Murrell, S. Carter, I. M. Mills and M. F. Guest, Mol. Phys., 1981, 42, 605. 4 L. J. Dunne, J. N. Murrell and J. G. Stamper, Chem. Phys. Lett., 1984, 112, 497. 5 J. P. Braga, L. J.Dunne and J. N. Murrell, Chem. Phys. Lett., 1985, 120, 147. 82, 99. Prof. J. N. Murrell (University of Sussex) said: Our interest in photodissociation is mainly on the question of how to calculate non-adiabatic transition probabilities for polyatomic systems. It is likely that the only models which can be applied generally will be based on classical motion of the nuclei. The accuracy of such models is, however, still to be established. In a poster presented at this Discussion we have compared the results of two such models with converged quantum-mechanical results for a collinear atom-diatomic col- lision involving charge transfer. The quantum-mechanical problem can be solved by the coupled-channel method as only few basis functions are needed. We find that the much used surface-hopping model,' which involves classical motion on adiabatic sur- faces and Landau-Zener transition probabilities at the avoided intersections (seams), overestimates the probability of charge transfer.We believe this is mainly due to the failure of this model to allow for interference between transition amplitudes on multiple crossing of the seams. An alternative classical path model2 in which Liouville's equations for the electronic density matrix are coupled to Hamilton's equations for the nuclei on an average potential, trace ( p V ) , gives better results. The latter model can also give rovibronic distributions if the density matrix is damped in the asymptotic region to give adiabatic states. This model, and the_surJface hopping model, have been applied to the H20 photodissociation through the B / X surfaces, as described in the contribution by Dr Dunne.In many respects the results are in good agreement with experimental observations. The only substantial disagreement is that the calculations predict high vibratio_nal_excitation of OH(211). Whilst our conclusion is that the B / A non-adiabatic process is likely to be dominant for this photodissociation, I will be surprised if the experimental observation that the OH(211) is vibrationally very cold turn out to be quite as conclusive as currently appears; to get rid of more than 5 eV of excess energy without a fair amount of this appearing in vibrations is a tall order. 1 J. C. Tully and P. K. Preston, J. Chem. Phys., 1971, 55, 562. 2 L. J. Dunne, J. N.Murrell and J. G. Stamper, Chem. Phys. Lett., 1984, 112, 497. Prof. K. H. Welge (University of Bielefeld, Federal Republic of Germany) said: I would offer the following comments in answer to the various questions raised concerning our new form of photofragment spectroscopy,' which I like to call 'resonant ionisation photofragment recoil spectroscopy'. The method combines many of the advantageous features of more conventional translational spectroscopy techniques with the high sensitivity associated with optical192 General Discussion 18 23 28 33 flight time/ps I I I I I I r I I I 1 5 4 3 I I I I I 1 2 3 kinetic energy/eV Fig. 2. ( a ) H+-ion TOF spectrum resulting from H2S photolysis at 193 nm, together with ( b ) the spectrum of the total kinetic energy.Individual peaks in ( b ) are labelled with the vibrational quantum number of the associated SH(X) fragments. detection methods. This is demonstrated by the fact that experiments can be carried out at photolysis laser fluxes as low as ca. 10" photons per pulse, many orders of magnitude less than required for more conventional photofragment recoil spectroscopy experiments (typically 2 1015 photons per pulse). The high sensitivity of the present technique results from (a) the high ionisation yield in the source volume (in the case of H-atom detection it can approach 100%) and (b) the high collection efficiency. Fig. 2(a), which shows the complete H+ ion TOF spectrum resulting from HZS photolysis at 193 nm, provides further illustration of the sensitivity of this technique.The general form of this TOF spectrum is discernable from a single-shot experiment. Signal averaging for just a few minutes (at 10 Hz repetition rate) yields the TOF spectrum shown in fig.General Discussion 193 2( a ) which, upon transformation, gives a total kinetic energy spectrum [fig. 2( b ) ] that compares very favourably with that reported previously by van Veen et a12 using more conventional photofragment translational spectroscopy methods and mass-spectrometric detection. In particular, it provides confirmation that a significant fraction (ca. 25%) of the nascent SH(X) fragments arising from H2S photolysis at this wavelength are formed vibrationally excited. This fact could not be established from earlier studies which attempted to monitor the nascent SH( X ) fragments via laser-induced fluorescence3 (as in the case of OH, predissociation in the excited A2Z+ state precludes the use of LIF detection methods for ground-state fragments with even modest levels of vibrational and/or rotational excitation); nor was it recognised in the more recent studies employing time-delayed Doppler-shift measurements on the H-atom ~artner.4’~ In common with other spectroscopies involving charged particles the energy resol- ution of our technique is ultimately determined by space charge, and by stray electric fields. In practice space charge also limits the ultimate sensitivity of the present arrange- ment.In principle, this limitation could be alleviated by exciting the atoms to a high Rydberg state with subsequent field ionisation after TOF separation, i.e.by employing (neutral) Rydberg atoms instead of ions as the probe. Inefficient detection of the slowest particles (i.e. most notably those with kinetic energies $0.3 eV in the present work) is a common problem in TOF experiments. However, the present apparatus has been designed so that translational spectroscopy of slow neutral fragments (H atoms in this case) can also be performed straightforwardly, simply by introducing a delay between the photolysing laser pulse and that from the ionising probe laser, extracting the resultant ions with a negative potential applied at grid Go, and measuring the integral signal as a function of time delay. Differentiation of the time-dependent integral signal yields the flight-time distribution of the nascent fragments. Of course, in observing all ions any information concerning the fragment angular distribution is sacrificed.Note, however, that such a procedure automatically incorporates measurement of the ‘zero kinetic energy’ fragments and thereby offers a route to study photofragmentation processes at threshold. Finally, it must be appreciated that the technique is not restricted to processes yielding H atoms but should be applicable to all atoms and, in principle at least, to molecular fragments also. This latter prospect is especially exciting since the use of resonant stepwise excitation offers the possibility of rotational state selective analysis with simultaneous velocity, v, and internal angular momentum J, determination. 1 H. J.Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold, Furuday Discuss Chem. SOC., 1986, 2 G. N. A. van Veen, K. A. Mohamed, T. Baller and A. E. de Vries, Chem. Phys., 1983,74, 261. 3 W. G. Hawkins and P. L. Houston, J. Chem. Phys., 1980, 73, 297; 1982, 76, 729. 4 B. Koplitz, Z. Xu, D. Baugh, S. Buelow, D. Hausler, J. Rice, H. Reisler, C. X. W. Qian, M Noble and 5 Z. Xu, B. Koplitz, S. Buelow, D. Baugh and C. Wittig, Chem Phys. Lett., 1986, 127, 534. 82, 99. C. Wittig, Furuday Discuss. Chem. SOC., 1986, 82, 125. Dr M. N. R. Ashfold and Prof. R. N. Dixon ( University of Bristol) (communicated): Unarguably many of the fine details regsrding the photodissociation dynamics of H20 molecules following excitation to the B *Al electronic state remain to be uncovered.However, we are confident that the results of the present experimental study’ demon- strate, unequivocally, that the nascent OH( X ) fragments resulting from H20 photolysis at 125.1 nm are formed predominantly in their ground vibrational state, with a very high level of rotational excitation. The observation of such clearly resolved structure in the H+-ion TOF spectrum (fig. 2) and the total kinetic energy spectrum (fig. 3) argues against there being significant formation of vibrationally excited OH( X ) fragments; their pres- ence [with, we assume, levels of rotational excitation comparable to that deduced for the OH(X, v = 0) product] would effectively wash out this structure.194 General Discussion H20( 6) molecules can disscciate- to the H + OH(X) asymptote only after non- adiabatic transfer to either the A or X potential-energy surface.The OH(X) product rotational state distributions deduced in the present experiment’ suggest a dominant role for the former fragmentation pathway. Murrel12 points to an entirely theoretical means of checking this conclusion given accurate potential-energy surfaces, namely the solution of the classical equations of motion fo_r the nuclei. Simons3 suggests a possible experimental test for the importance of B - X transfer. This requires identification of the spectral resonances predicted by Segev and Shapiro; and observation of the way in which their widths vary with parent temperature. However, the preliminary results from the synchrotron study reported here3 do not impinge directly on this problem.Rather they appear to provide furthgr evidence that the quantum yield for forming OH(A) following excitation to H20(B) does not fall to zero even at high (JE).5,6 Thus all parent rotational levels make some contribution to the OH( A) photofragment excita- tion spectrum. Jet-cooling relaxes the parent rotational state population distribution with the expected, and ob~erved,~ result that the peak in the excitation spectrum for forming OH( A) fragments shifts to shorter wavelength. However, such an interpretation necessarily implies that the spectral bandshape should narrow also; that this effect is not observed may be due to the limited spectral resolution available with the synchrotron source. 1 H. J. Krautwald, L. Schnieder, K. H. Welge and M.N. R. Ashfold, Faraday Discuss. Chem. SOC., 1986, 82, 99. 2 J. N. Murrell, Faraday Discuss. Chem. SOC., 1986, 82, 192. 3 M. Brouard, M. P. Docker and J. P. Simons, Faraday Discuss. Chem. SOC., 1986, 82, 188. 4 E. Segev and M. Shapiro, .I. Chem. Phys., 1982, 77, 5604. 5 R. N. Dixon, Mol. Phys., 1985, 54, 333. 6 M. P. Docker, A. Hodgson and J. P. Simons, Mol. Phys., 1986, 57, 129. Dr M. Shapiro ( Weizmann Institute, Israel) said: The reflection principle, as described by the paper of Schinke and Engel is a nice example of ‘mapping’ properties of fast dissociation processes. 172 Recently3 we have examined the concept of ‘photofragmenta- tion mapping’ for branching photochemical reactions. The process studied is the photodissociation of CH31 from various initial states CH3I + CH3( V ) + I(2P3/2) CHJ + CH3( v ) + I*(2P1/2) where v is the ‘umbrella-type’ bending vibration of the methyl radical.‘Exact’ detailed cross-sections for the linear pseudotriat~mic~ were calculated and plotted as a continuous function of hv (the photon energy) and v. The results are shown in fig. 3-5. The ‘mapping’ property is clearly demonstrated. For example, the photofragmenta- tion of the ground vibrational wavefunction results in a nodeless map (see fig. 3), whose topology is, therefore, identical to that of the original nuclear density. Note that the same type of mapping exists for the I* and I electronic channels. A comparison of fig. 4 ( a ) with 4(6) and fig. 5 ( a ) with 5 ( 6 ) shows that while the details of the maps are different, their topology is clearly that of the initial nuclear density.Thus when a given wavefunction has n nodes the nuclear density associated with it has n troughs and so does the photofragmentation map. The relative insensitivity of the map topology also applies to the parallel vis Ci vis perpendicular transitions. As shown in fig. 3(a) and ( 6 ) the maps differ in some details (owing to ‘final state interactions’), but their basic shape is the same. A comparison of fig. 4 with fig. 5 shows that even the relative sense of the nodal lines is maintained. The first excited state [fig. 4 ( a ) ] roughly corresponds to excitation of one quantum in the C-I stretching mode, whereas the third excited state [fig. 5 ( a ) and ( b ) ] corresponds to excitation of one quantum of the umbrella mode, with a nodeGeneral Discussion 195 c 0 Y196 General Discussion 1 1 I I I I 1 PI W ln * L- m (Y c 0 W ln 0General Discussion 197198 Genera 1 Discussion running (in the rcI, rC-H3 plane) perpendicular to the node of the first excited state.The same property is maintained in the photofragmentation maps. The behaviour outlined here for methyl iodide is typical of a classical Franck-Condon process, namely that in classical mechanics there is a direct correspondence between an internuclear configuration and an absorbed photon energy. Basically, at each configuration only one photon energy, that given by the stationary phase condition (which requires conservation of the instantaneous nuclear kinetic energy), can be absorbed. As a result, the probability of absorbing a photon at a given energy is proportional to the probability of finding the system in the configuration capable of absorbing the photon (i.e. satisfying the stationary phase condition for that photon energy).The classical picture is too simplistic, as no attempt is made to account for the fine details of the dissociation process on the excited surface( s). The final-state interaction (in this case the EVT coupling), although quite strong, maintains the topology imposed by the initial distribution. The main effect of the inelastic processes in the excited state is to shift and distort the distribution created in the initial photoabsorption process. The interest in the mapping, which requires performing photofragment spectroscopy at a number of photon energies, stems from the fact that it enables one to obtain information about nuclear densities of highly excited eigenstates, information not readily available by other methods.. 1 M. Shapiro, Chem. Phys. Lett., 1981, 81, 521. 2 M. S. Child and M. Shapiro, Mol. Phys., 1983, 48, 111. 3 M. Shapiro, J. Phys. Chem., 1986,90, 3644. 4 M. Shapiro and R. Bersohn, J. Chem. Phys., 1980, 73, 3810. Dr R. Schinke and Dr V . Engel (GGttingen, Federal Republic of Germany) said: Quantum-mechanically the photoabsorption cross-section is calculated from the golden rule expression (1) Since eqn ( 1 ) contains explicitly the initial nuclear wavefunction in the ground electronic state, +br, and the final nuclear wavefunction in the excited electronic state, +Lx, it is rather obvious that the cross-section aif( E ) reflects properties of both wavefunctions (or the corresponding multidimensional potential-energy surfaces Vgr and Vex, respec- tively). The interesting question is how this ‘reflection’ or ‘mapping’ appears for a particular system and what we can learn from its measurement? We find it helpful to distinguish two limiting cases depending on the strength of the so-called ‘final-state interaction’, which is nothing other than the interaction potential uif(E) - l(+Lrlp I + Z ~ ( E )>I2- VI( R, r ) = Vex( R, r ) - Vex( R = 00, r ) .(2) Here R is the dissociation coordinate of the unbound motion and r represents all internal bound coordinates of the fragments. In normal scattering VI controls the degree of rotational or vibrational excitation, for example, and it does exactly the same in a ‘half-collision’.(1) If V, depends very weakly on the internal coordinates r the final-state distribution of the fragments is primarily given by the expansion coefficients of the ground-state wavefunction in terms of final product wavefunctions according to aif(E ) - la)l2. (4) We assumed that $gr can be separated into R- and r-dependent parts which is usually fulfilled for low vibrational-rotational states. In view of eqn (4) the final-state distribu- tion is a direct reflection of the initial wavefunction. If the internal fragment energy EfGeneral Discussion 199 is small compared to the total available energy E (as is usually the case for rotation) the final-state distribution is roughly independent of E (an example is the dissociation of H20 in the first absorption band).If Ef is of the same order of magnitude as E (as is usually the case for vibration) the final-state distribution is energy dependent (an example is the model CH31 system studied by Shapiro). This energy dependence is induced by energy conservation rather than inelastic coupling due to V,. This is the Franck-Condon limit which has been amply discussed in the literature [see ref. ( 6 ) of our paper]. The cases studied by Shapiro (Chem. Phys. Lett., 1981, 81, 521) and Child and Shapiro (Mol. Phys., 1983, 48, 111) belong to this class of weak final-state interaction. In the paper of Child and Shapiro, final-state interaction is explicitly excluded. In the paper of Shapiro final-state interaction is included but is so weak that it has no significant effect on the results.(2) If V, depends strongly on the internal coordinates r the final distribution is, in classical mechanics, approximately given by where J ( ro) is the multidimensional excitation function determined by classical trajec- tories started at r,. It depends directly on the strength of the inelastic coupling induced by the interaction potential. The particular values rg’ in eqn ( 5 ) are determined by the important relation where j represents a set of quantum numbers. In view of eqn ( 5 ) and (6) the final-state distribution is in this case a reflection of the ground-state wavefunction and the excitation function J. Since the latter depends directly on VI the measured distributions reflect properties of the excited-state potential surface and can, in principle, be used for an inversion.In the Franck-Condon-limit J ( r,) is zero and eqn ( 5 ) and (6) are meaningless. We call this the mapping ‘inelastic reflection principle’. It has been observed, for the rotational degree of freedom, in many experiments and some classical studies. However, it has not been discussed or analysed before. In conclusion, in the weak-coupling limit the final distribution reflects directly and only the ground-state wavefunction. In the strong-coupling limit this reflection of the initial wavefunction is mediated by the classical excitation function which, in turn, reflects the inelastic coupling strength of the excited-state potential. Dr J. M.Hutson (Cambridge University) said: Drs Schinke and Engel have given us a very useful insight into the factors affecting rotational distributions in photo- dissociation processes. However, as presented here, their paper appears to be applicable only to direct photodissociation processes. Have they given any thought to generalizing their approach to handle indirect photodissociation processes, in which the photon initially prepares a well defined quantum state on the excited potential-energy surface? Under these circumstances, the excited-state wavefunction is not a simple reflection of the ground-state wavefunction. Another restriction in the present theory is that it deals only with the total angular momentum J = 0. Have the authors considered the effects of relaxing this restriction? Dr R.Schinke and Dr V. Engel (Gottingen, Federal Republic of Germany) said: The case of indirect photodissociation is certainly more complicated than the case of direct photodissociation discussed in our paper. The very direct relation between the initial state of the parent molecule, the potential anisotropy and the final rotational state distribution observed in direct photodissociation may be lost or replaced by some other correlation. We have already started to extend the rotational reflection principle to indirect processes but have not yet obtained a clear physical picture. J ( r g ) ) = j (6)200 General Discussion Under strong coupling conditions we expect that the details of the molecular wavefunction before dissociation are not important.The final rotational state distribution will be mainly determined in the break-up step. Important for the rotational reflection principle is the bending part of the initial bound-state wavefunction and this part will not be changed significantly by overall rotation ( J # 0). There are actually several experimental studies performed both in the bulk (300 K) and in the beam, and in both cases more or less the same final distributions were obtained. This indicates that details before the dissociation are not important. This statement is obviously true only for strong coupling but not in the Franck-Condon limit (dissociation of H 2 0 in the first band, for example). Prof. J. P. Simons (University of Nottingharn) said: One slight caveat which should be retained when analysing the rotation (or indeed vibrational) population distributions in primary photofragments is the possibility that they are modified by branching in the exit channel.For example, it is just possible that the highly inverted rotational population distributions in OH, OD ( A ) excited by photodissociation of water are _amplified by the rotationally dependent leakage from the dissociative continuum, B ' A , . If those molecules which suffer this fate are those whose dissociation would otherwise have generated OH(A) in low rotational levels, the final contribution in low rotational levels will be strongly depleted. Dr J. Halpern (Oxford University) said: We have been doing experiments on the photodissociation of ClCN and BrCN in the ultraviolet since 1982.'-3 Most of this work has concentrated on BrCN, which is somewhat unfortunate, as Waite and Dunlap have only calculated a potential-energy surface for ClCN.4 In a poster presentation of this discussion we displayed the CN nascent quantum-state distributions from the photolysis of BrCN at several different wavelengths between 193 and 248 nm.The details of this work have been submitted for publication el~ewhere.~ Here I should like to point out two things. First, the rotational distributions of the CN fragments are similar to those in Dr Schinke's paper for CN from the photolysis of ClCN. More importantly, when one accounts for the vibrational excitation of the CN fragment and the electronic excitation of the bromine atom, the CN rotational distributions all scale to one another as the amount of energy available to rotation.By this we mean the photon energy less the bond strength and any energy necessary for the vibrational excitation of the CN or electronic excitation of the bromine atom. The same general trend is noted by Fisher et ~ 1 . ~ This is as is predicted by the rotational reflection principal. The overlap of the scaled spectra with one another is excellent. Secondly, in a conversation with Dr Child, it was noted that the ratio of Fl and F2 components in the CN fragment distributions from the photolysis of BrCN seemed to have a similar sinusoidal variation as was observed from the photodissociation of ICN. Because our probing dye laser had a bandwidth five to ten times wider than that used in the experiments described by Dr Child, it is difficult to give a quantitative measure of this at present.1 J. B. Halpern and W. M. Jackson, J. Phys. Chem., 1982, 86, 3528. 2 R. Lu, V. McCrary, J. B. Halpern and W. M. Jackson, J. Phys. Chem., 1984, 88, 3419. 3 J. A. Russell, I. A. McLaren, W. M. Jackson and J. B. Halpern, J. Phys. Chem., in press. 4 B. A. Waite and B. I. Dunlap, J. Chem. Phys., 1986, 84, 1391. 5 W. H. Fisher, R. Eng, T. Carrington, C. H. Dugan, S. V. Filseth and C. M. Sadowski, Chem Phys., 1984, 89, 457. Mr C. J. Williams and Prof. K. F. Freed (University of Chicago, USA) said: We would like to mention some recent work,' done in collaboration with Dr H. Grinberg,General Discussion 201 on extending the analytical quantum theory of three-dimensional triatomic photodissoci- ation* to include the effects of anisotropic interactions on the repulsive potential surface. While accurate close-coupled calculations of product rotational energy distributions already exist for several triatomic photodissociations, the calculations are rather time- consuming and are currently limited to rather low total angular momenta J.Thus, in order to compare with experiments, which often involve high J, and in order to screen possible empirical potential surfaces for reproducing experimental data, it is useful to introduce computationally simple models which have been tested against more accurate close-coupled calculations. The model of Schinke and Engel is one such example, and our analytical theory is another. An important feature of the analytical quantum theory is the use of different coordinate systems appropriate to the initial bound and the final dissociative surfaces.This approach obviates the complication of expanding the initial bound-state wavefunc- tion in terms of a basis of functions involving scattering coordinates, as done in the work of Balint-Kurti and S h a p i r ~ . ~ However, our use of functions in different coordinate systems leads to the complexity of the emergence of three-dimensional non-separable integrals for the transition amplitudes (previously called multidimensional non-separable Franck-Condon factors2). This complexity had previously limited the theory2 to systems with isotropic atom-diatom potentials on the dissociative surface. We have successfully extended the theory to treat anisotropic potentials by using the following set of approximations: first, an infinite-order sudden (10s) approximation is employed for the continuum wavefunction that is then further simplified by using an Airy approximation, which has been shown to be accurate for purely repulsive potentials so long as the inter-fragment kinetic energy is not too The 10s approximation is formulated in an equivalent adiabatic representation,' which motivates the use of the diatomic fragment rotational quantum number j as the 10s j-variable.The 1 0 s I-variable is then assigned the 'democratic' value of I = max ( j , J ) . bound or quasibound state Ii > to the final dissociative state If> is written as Using the above described theory the golden rule transition rate from an initial where Vr is the coupling inducing the dissociation.The integrals over the diatomic internuclear separation r and the atom-diatom separation R, as well as those over Euler angles, are performed analytically, leaving a single angular integral in 8 to be calculated numerically. (This last integral is evaluated analytically with isotropic potentials.) Thus, our approach should be accurate so long as the 10s and Airy approximations are valid. In addition, our specific choice of the 10s 7 and Fig. 6-8 present our calculated rotational distributions for the CN( B *X+) frag_ment, produced in the direct photodissociation involving excitation into the ICN( C ' A ' ) continuum, where the results are compared with the close-coupled calculations of Heather and using the same potentials.Fig. 6 is for a purely isotropic potential to test the accuracy of the Airy approximation, while fig. 7 involves a mildly anisotropic potential. Fig. 8 applies to a highly anisotropic potential for which the 1 0 s approxima- tion is insufficient. 2Z+) state are compared with 10s and close-coupled calculations of Atabek et aL7 for the same potentials. The analytical quantum theory computations are in good agreement with the full 10s calculations when the same j and I variables are used, and this supports the Airy and qther approximations. However, our a priori adiabatic model choices of J = j and I = max (j, J ) are seen to yield model calculation which well reproduce the full close- coupled calculations better than the traditional choices (see fig.9) The adiabatic model choice works well also for ICN, and the degree to which it represents an optimal choice remains to be studied further. Fig. 10 presents calculations for predissociation from must be tested. Our calculations for the predissociation of the N20'(202 General Discussion diatomic rotational angular momentum, j Fig. 6. Comparison of analytical theory calculations of fragment rotational distributions with close-coupled calculations536 for ICN using an isotropic potential. The bending vibration is initially doubly excited; A, analytical quantum theory;' 0, close-coupled calculation^.^^^ 0.09L' " ' I " " I " " I " ' ' I ' ' I ' I " ' ' 4 b 0.08 3 0.07 2 a 0.06 -3 0.05 2 0.04 0.03 0.02 0.01 .- ._ - .- c.) 0 .- c) U N .- d 0 diatomic rotational angular momentum, j Fig.7. Same as fig. 6, but using a mildly anisotropic potential. levels with J = 20 to illustrate the applicability to arbitrary J. (Note that the thermal maximum at room temperature is J = 22 for the ground state of N,O'.) The calculations also have the initial state bending mode doubly excited. Our analytical quantum theory provides good agreement with close-coupled calcula- tions for isotropic and mildly anisotropic potentials for which the 10s approximation is valid. The method should, therefore, be useful for testing possible functional formsGeneral Discussion 203 0.09t' " ' I " ' ' I ' ' ' ' 1 ' ' " I 1 ' " I ' " ' j diatomic rotational angular momentum, j Fig. 8. Same as fig. 7, but using a highly anisotropic potential.diatomic rotational angular momentum, j Fig. 9. Comparison of analytical theory calculations of partial photodissoc_iation rates with both close coupled and 10s calculations7 for N,O+. A2 Analytic21 model' for j = 5 and 1 = 0 and an anisotropic potential; 0, 10s calculations7 with j =_5 and 1 = O and the same potential, 0 and 0, partial rates for the anisotropic potential with j = 1 = 5 for the analytical theory and 10s method, respectively. of repulsive potential to reproduce experimental data and for establishing general relationships between product energy distributions and features of the potential surfaces. 1 H. Grinberg, K. F. Freed and C. J. Williams, J. Chem. Phys., in press. 2 M. D. Morse, K. F. Freed and Y. B. Band, J. Chem. Phys., 1979,70, 3604; 3620; M.D. Morse and K. F. Freed, J. Chem. Phys., 1981, 74,4395; 1983, 78, 6045.204 Genera 1 Discussion 500 4 50 4 00 350 300 diatomic rotational angular momentum, j Fig. 10. N20+ calculations with J = 2 0 and the bend initially doubly excited. A, Isotropic potential; 0, anisotropic potential. 3 G. G. Baht-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137; E. Segev and M. Shapiro, J. Chem. 4 Y. B. Band, M. D. Morse and K. F. Freed, J. Chem. Phys., 1978,68, 2702. 5 R. W. Heather and J. C. Light, J. Chem. Phys., 1983,78, 5513. 6 R. W. Heather and J. C. Light, J. Chem. Phys., 1983, 79, 147. 7 0. Atabek, J. A. Beswick and G. Delgado-Barrio, J. Chem. Phys., 1985, 83, 2954. Phys., 1980, 73, 2001; 1982, 77, 5604. Dr J. Pfab (Heriot- Watt University) said: Prof.Wittig reported a beautifully detailed study of the photodissociation of Bu'NO in the second part of his paper. I wish to draw attention to the fact that that there is a near-coincidence of the n, T* electronic origin Too = 13 91 1 cm-' and the C-N dissociation energy Do = 13 930 f 30 cm-'. This remark- able coincidence appears to be general for aliphatic C-nitroso compounds. In CH3N0, we have deduced Too as 14410cm-' from spectral simulations' as compared to Do = 14 400 cm-'.* In CF3N0, where we have recently located the pre- viously unobserved origin in the fluorescence excitation spectrum of the jet-cooled molecule at 13 934 ~ m - ' , ~ rather than 14 031 cm-' reported in the literat~re,~ Do is 13 856 ~ m - ' . ~ For CClF,NO, Mr McCoustra and Miss Dyet in our laboratory have found Too = 14 187 cm-' and Do= 13 700*400 cm-' using the same approach, but a less-sensitive probe technique for NO, as in Prof.Wittig's study of Bu'NO.~ This coincidcnce of Too and Do can be explained by assuming that the potential surface for the A('A") n, n* state has no minimum or only a shallow minimum along the C-N dissociatio? c$ordinate. The lack of any activity of the corresponding vibra- tional mode in the A-X electronic spectra of these molecules also supports this con- clusion. 1 N. P. Ernsting, J. Pfab and J. Romelt, J. Chem. SOC., Furuduy Trans. 2, 1978, 74, 2286. 2 L. Batt and R. T. Milne, In?. J. Chem. Kine?., 1973, 5, 1067. 3 M. R. S. McCoustra, J. A. Dyet and J. Pfab, to be published. 4 B. M. DeKoven, K. H. Fung, D.H. Levy, L. D. Hoffland and K. G. Spears, J. Chem. Phys., 1981,74,4755. 5 R. D. Bower, R. W. Jones and P. L. Houston, J. Chem. Phys., 1983,79, 2799. Dr J. Pfab (Heriot- Watt University) then addecj: Miss Dyet, Mr McCoustra and I have found recently that the fluorescence of many A-state levels of jet-cooled CClF2N0General Discussion o~'or--- 205 J" Fig. 11. Rotational distributions of NO from the 641.8 nm photolysis of jet-cooled CCIF2N0. (0) 2111!2 and (0) 2113,2 states of NO. (-) The calculated Q priori distributions except for the spin-orbit ratio, which has been scaled to permit better comparison with experiment. decay biexponentially.' This prompted us to re-examine the fluorescence decay of jet-cooled CF3N02 and here too we have found evidence for biexponential decays.' c i s indicates directly that the T1 state plays an important role in the dynamics of the A state of these molecules.I wish to emphasise that in our cases the time-resolved fluorescence technique is a more sensitive probe for the involvement of TI than the rotational distributions of the NO photoproduct. Both jet-cooled CC1F2N0 ' and CF3N0 give rise to-statistical rotational distributions of NO in the photodissociation from levels of the A state that show biexponential fluorescence decay and are con- sequently coupled to T1 levels. 1 J. A. Dyet, M. R. S. McCoustra and J. Hab, to be published. 2 R. D. Bower, R. W. Jones and P. L. Houston, J. Chem. Phys., 1983, 79, 2799. Mr M. R. S. McCoustra and Dr J. Pfab (Heriot- Watt University) said: Prof.Wittig has suggested that non-statistical rotational distributions and spin-orbit distributions may be taken as evidence for the involvement of the triplet state in the predissociation of C-nitroso compounds, citing his own work on Bu'NO and that of Houston et al. on CF3N0.1 We would like to suggest that rotational distributions alone cannot be taken as proof of such involvement. Our own work on CClF2N0 highlights this, since we observe statistical rotational distributions at all excess energies up to ca. 2500 cm-'. In fig. 11 the experimental rotational state distributions for NO from the photolysis of jet-cooled CClF2N0 at 641.8 nm, ca. 2300 cm-' excess energy, are compared with a simple statistical model and the agreement is excellent. Note that the statistical distribu- tions have been scaled to account for the non-statistical spin-orbit distribution.The206 Genera 1 Discuss ion photophysical evidence we have commented on previously, suggests the involvement of the triplet state. As in the case of NCN02 and CF3N0,' we too observe non-statistical spin-orbit distributions. However, non-statistical spin-orbit distributions do not necessarily impli- cate the triplet state. King et aZ., for example, observed a spin-orbit temperature not in equilibrium with the rotational temperatures in NO from the IRMPD of jet-cooled methyl nitrite3 where it is very unlikely that any state other than the ground state is involved. 1 R. D. Bower, R. W. Jones and P. L. Houston, J. Chem. Phys., 1983, 79, 2799. 2 C. X. W. Qian, M. Noble, I.Nadler, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 83, 5573. 3 D. S. King and J. C. Stephenson, J. Chem. Phys., 1985,82, 2236. Dr M. S. Child (Oxford University) said: Prof. Moore has described some beautiful experiments, which provide a real challenge to the theoretician. It is interesting that the observed lifetimes ( 5 x 10-8-2 x s) are much longer than the RRKM expectation of 10-l2s but similar to those observed by Carrington and Kennedy for Hl.' Our conclusions with respect to the H; system2 are that lifetimes in this range for the predissociation of chemically bound species almost certainly arise from a classically forbidden process, of which quantum-mechanical tunnelling, through a real barrier or a centrifugal one, is the most obvious candidate.Even the internal V-T Feshbach process that can give immensely long lifetimes for van der Waals systems is expected to proceed much more rapidly in a chemically bound system in which the internal kinetic energy can reach several eV instead of a few hundred cm-'. 1 A. Carrington and R. A. Kennedy, J. Chem. Phys., 1984,81,91. 2 M . S. Child, J. Phys. Chem., 1986, 90, 3595. Prof. C. B. Moore (University of California) said: Indeed, the analysis in ref. ( 6 ) of our paper uses a quantitative treatment of tunnelling through the barrier between H2CO(So) and H2 + CO to deduce the height of this barrier from the H2CO(SO) lifetimes. Miss J. A. Dyet, Mr M. R. S. McCoustra and Dr J. Pfab (Heriot-Watt University) said: Prof. Moore reported a particularly informative example of the use of photofrag- ment yield spectroscopy using pulsed dissociation and synchronised delayed probing by laser-induced fluorescence.The potential of this new type of spectroscopy to yield dynamical as well as spectroscopic information has been recognised previously for example in the photodissociation of H202,1 N02,2 NCN0374 and (CH3)3CN0.5 We have ourselves similarily succeeded in recording NO yield spectra of nozzle-cooled CClF2N0 in the visible region, as shown in fig. 12. I-Jere the threshold for the production of NO (dl= 0) is lower than the origin of the A-X electronic transition (14 187 cm-') and was determined indirectly as 13 700 f 400 cm-' by fitting a priori statistical distribu- tions to the observed rotational distributions of NO (v" = 0).In our case, however, there is strong evidence from fluorescence-decay measurements that the triplet state of the parent molecule is involved and that dissociation does not proceed exclusively from the ground-state potential surface. 1 T. R. Rizzo, C. C. Hayden and F. F. Crim, J. Chem. Phys., 1984,81,4501. 2 U. Robra, H. Zacharias and K. H. Welge, unpublished results. 3 I. Nadler, J. Pfab, H. Reisler and C. Wittig, J. Chem. Phys., 1983, 79, 2088. 4 C. X. W. Qian,.M. Noble, I. Nadler, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 83, 5573. 5 B. Koplitz, Z. Xu, D. Baugh, S. Buelow, D. Hausler, J. Rice, H. Reisler, C. X. W. Qian, M. Noble and C. Wittig, Faraday Discuss. Chem. SOC., 1986, 82, 125.General Discussion 207 i 1 1 1 1 I I 1 1 I 1 660 710 640 680 A /nm A/nm Fig.12. NO fragment yield spectrum of jet-cooled CC1F2N0 obtained by tuning the dissociation laser while keeping the two-photon LIF probe laser fixed to the P,, + 021 bandhead. Mr C. X. W. Qian, Dr H. Reisler, Ms A. Ogai, Dr M. Noble and Prof. C. Wittig ( University of Southern California, USA) said: In the elegant ketene photodissociation experiments of Moore and coworkers, we saw clearly the correlation between the probability of producing a particular *CH2 ro-vibronic state and the opening of success- ively higher CO rotational states with increasing E t (see fig. 5 of their paper). Similarly, with E t fixed, the Doppler profile can sometimes be recorded for a specific state of one fragment, thereby obtaining the same kind of correlation. Here, we present very recent experimental results concerning such a correlation in the case of the photoinitiated unimolecular reaction of NCNO: NCNO+hv + NO(X’II)+CN(X’Z>, E t = h v - D o (1) E t = Ev(CN)+ER(CN)+Ev(NO)+E,(NO)+EE(NO)+E,(c.m.).(2) The photodissociation of cold (ca. 2 K) NCNO has been studied extensively in our laboratory, and is a textbook example of statistical predissociation.’ The V,R state distributions of both CN and NO have been measured for E t in the range 0-5000 ~m-’,’,~ and are predicted accurately using statistical rnethod~.~ However, questions still remain. For instance, is there dynamic bias which correlates high rotational states of CN with high rotational states of NO, or are the correlations the same as those predicted using the statistical models which reproduce the experimental internal state distributions? Such dynamic bias need not show up in state distributions, and separate measurements are generally required in order to detect such behaviour.In order to answer these questions, we recorded the LIF lineshapes of a number of CN transitions with sub-Doppler resolution, as displayed in fig. 13. The simulations (solid lines) are generated by convoluting the instrumental resolution [0.07 cm-’ f.w.h.m, determined from a threshold study of the R (0) line] with the Doppler profile constructed208 General Discussion from the statistical model used to fit the CN and NO internal-state distributions. In comparing the data to the calculations, we conclude that dissociation still looks very statistical, even at this more refined level of scrutiny.This experiment was done with a collinear geometry and the photolysis laser was unpolarized. In the future, we will carry out the usual checks with different laser polarizations and k values. However, it presently appears that the production of significant CN rotation is not simply associated with a counter-rotation of NO, but with a combination of orbital and NO rotational motions which is close to that predicted using statistic^.^ 1 H. Reisler and C. Wittig, Annu. Reu. Phys. Chem., in press. 2 I. Nadler, M. Noble, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 82, 2608. 3 C. X. W. Qian, M. Noble, I. Nadler, H. Reisler and C. Wittig, J. Chem. Phys., 1985, 83, 5573. 4 C. Wittig, I. Nadler, H. Reisler, M. Noble, J.Catanzarite and G. Radhakrishnan, J. Chem. Phys., 1985, 83, 5581. Prof. P. L. Houston (Cornell Uniuersity, USA) said: I would like to comment on fig. 5 of the paper by Bitto et al.,’ which displays the ‘CH2(312) signal as a function of photolysis energy. The undulations demonstrate the opening of CO( t~ = 0, J ) channels in coincidence with the selected level of ketene. These undulations could be more clearly resolved if the detection were arranged so that only the zero kinetic energy ketene fragments were monitored. We have heard in this Discussion about several methods for detecting fragments of a particular velocity. E.g. one could used sub-Doppler spectroscopy with a laser tuned to the center frequency of the ketene transition, as described by Koplitz et aL2 After a suitable delay between the pump and probe laser, nearly all of the ketene fragments absorbing at this frequency and recoiling with non-zero kinetic energy would have moved out of the probe beam. Alternatively, if multiphoton ionization were used as the detection scheme, one might use the time-of-flight technique described by Krautwald et aL3 or the pulsed extraction field technique described by Hall et aL4 to detect selectively only those ions with zero kinetic energy.The detection of zero-kinetic-energy fragments is strongly analogous to the work of Miiller-Dethlefs et a15 in which zero-kinetic-energy electrons are detected in ionization to determine the threshold energies for selected states of the positive ions. 1 H. Bitto, D. R. Guyer, W. F. Polik and C.B. Moore, Furuduy Discuss. Chem. SOC., 1986, 82, 149. 2 B. Koplitz, 2. Xu, D. Baugh, S. Buelow, D. Bausler, J. Rice, H. Reisler, C. X. W. Quian, M. Noble and 3 H. J. Krautwald, L. Schnieder and K. H . Welge, Furuduy Discuss. Chem. Soc., 1986, 82, 99. 4 G. E. Hall, N. Sivakumar, R. Ogorzalek, G. Chawla, H-P. Haem and P . L. Houston, Furuday Discuss. 5 K. Muller-Dethlefs, M. Sander and E. W. Schlag, Z. Nuturforsch. Teil A, 1984, 39, 1089. C . Wittig, Furaduy Discuss. Chem. SOC., 1986, 82, 125. Chem. SOC., 1986,82, 13. Dr H. Bitto (ETH Zurich, Switzerland) said: It is certainly feasible, although experimentally more elaborate, to increase the depth of the undulations in our PHOFEX spectra by selectively monitoring near-zero kinetic energy fragments. However, the important point is that observing the fragments ‘CHZ( n) of all kinetic energies collectively yields undulated PHOFEX spectra, that the undulations are clear enough to locate the thresholds of the product-correlated channels ‘CH2( n) + CO( 2)’’ = 0, J ” ) , J” = 0, 1,2, .. . , and that these spectra allow us to extract directly dynamical information on the dissoci- ation process. Monitoring zero-kinetic-energy fragments, instead, would result in a loss of this information. Mr R. Marquardt and Prof. M. Quack (ETH Zurich) said: In their paper on the dissociation on ground-state potential-energy surfaces, Bitto et al. present experimentalR ( 0 ) i 1 I I I I Fig. 13. CN LIF Doppler profiles following the photodissociation of expansion-cooled NCNO at three values of E t (i.e.three photolysis wavelengths). ( a ) 411.cm-', (b) 939 cm-', (c)2348 cm-'. Data are indicated by points, while SSE and PST simulations are indicated by solid and dashed curves, respectively. R(7) and P(10) splittings are due to spin-rotation coupling, and an isotropic spatial distribution of the recoil velocities was assumed in the simulations.210 General Discussion results on formaldehyde and ketene photofragmentation and discuss these in relation to some fundamental questions of unimolecular rate theory, which have been the subject of investigation by us over the last decade or so. (i) What are the (approximate) constants of the motion to be considered in a statistical theory of unimolecular fragmentati~n?'-~ As first proposed in ref.( 1 ) and now adapted by Bitto et al., owing to rovibronic coupling being presumably important at high excitation, these are first total rotational angular momentum quantum numbers J, M (but not any of the component quantum numbers such as K ) . With the principle of nuclear spin symmetry conservation* discussed in more detail in another comment further good quantum numbers are nuclear 'spin' angular momentum and nuclear spin symmetry I' and finally positive and negative parity ( i e . r*). Although it is gratifying that these concepts are being adapted now by a number of authors, this has to be done with appropriate care and we refer to the original papers and a review for detailed disc~ssion.'-~ In particular, concerning total angular momentum, one may note that the use of the usual 'prior' distribution6 has been shown to be inconsi~tent.~.~ Furthermore, with strong external fields, J is not a good quantum number. (ii) Under which conditions and for which quantities may one apply the statistical expressions for the unimolecular rate constants? Here, many one must note that k(E, J, I', .. .) is to be interpreted as a statistical average over resonances, if the resonances are isolated, in an energy range AE satisfying' LIE >> L ~ ( E , J, r, . . .)I-' with p(E, J, r, . . . .) being the density of metastable states for a set of good quantum numbers. k is not the decay constant of an isolated resonance and one should note the inequality in the expression, although the equality is commonly used.578 (iii) Which dynamical constraints have to be included in the calculation of accessible product channels W(E, J, r, .. .) in addition to the good quantum numbers? In this context we would predict that as in other a careful evaluation of the experiments of Bitto et al. will show significant improvements when using the statistical adiabatic channel model' instead of the prior distribution or phase-space theory (some features at low energy in fig. 5 of the paper may suggest this, but we would propose this also on more general physical grounds). (iv) When there are overlapping, decaying resonances, under which conditions can one expect quasi-classical coherent motion with non-exponential decay after coherent redistribution, and when will one have possibly intrinsically quantum-statistical behaviour with essentially exponential decay? This last question is perhaps the most interesting one, as it refers to current discussion on intramolecular kinetics preceding unimolecular fragmentation, of the global vibrational state,' ' statistical and microcanonical redi~tribution.'~ We have investigated the detailed dynamics of the CH chromophore on the basis of the Fermi resonance Hamiltonian discussed in detail in ref.(15) and (16), which was also used to provide new assignments of older spectra investigated by Wong and M00re.l~ The Hamiltonian was recently shown to be quantita- tively consistent with ab initio We summarize here only the most important conclusions from extensive quantum-dynamical ~ a l ~ ~ l a t i o n ~ . ~ ~ ~ ~ ' ( a ) For symmetric-top X3CH compounds, the local short-time CH dynamics corre- sponds to an effectively two-dimensional motion in the (r, 0) plane of the X3CH group with a good quantum number I for rotation of H about the symmetry axis (degree of freedom corresponding to angle 4, see fig.14.General Discussion 21 1 Fig. 14. Definition of coordinates for the CHX3 system with local CH dynamics. ( b ) Only for very short times of <lo0 fs can one find quasi-classical coherent oscillatory motion with i.r.-multiphoton excitation. (c) On longer timescales one finds spreading of the wavepacket leading to a quasi- microcanonical distribution of probability density over the available configuration space. Such a distribution is shown as an example in fig. 15 and many further results are given in ref.(14). ( d ) With narrow-band excitation one can prepare eigenstates of the stretch-bend Hamiltonian, some of which are of a special nature (hyperspherical Our findings on X3CH depend, of course, upon the dynamical system under consideration [see also ref. (22)]. However, they suggest quite generally certain possibilities to be considered also for systems such as formaldehyde and ketene. These possibilities include: ( a ) dynamically founded approximate good quantum numbers, in addition to the ones discussed under (i); ( b ) ‘mode selective’ coherent reaction behaviour with coherent i.r.-multiphoton excitation on very short timescales; ( c) intrinsically statistical behaviour due to quantum-mechanical spreading of the wavepacket on long timescales, an effect which would be absent for single classical trajectories, but would occur for a narrow classical ensemble with chaotic dynamics.These findings may be helpful in the planning and interpretation of future experiments on photofragmentation on ground-state electronic potential surfaces. 1 M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem., 1974, 78, 240; 1975, 79, 170; 1975, 79, 469. 2 M. Quack, Mol. Phys., 1977, 34, 477. 3 M. Quack, J. Phys. Chem., 1979, 83, 150. 4 M. Quack, Stud. Phys. Theor. Chem., 1983, 23, 355. 5 M. Quack and J. Troe, Theor. Chem. Adv. Persp., 1981, 6B, 199. 6 R. D. Levine and J. L. Kinsey, in Atom- Molecule Collision Theory, ed. R. B. Bernstein (Plenum Press, 7 M. Quack and J. Troe, Ber. Bunsenges. Phys. Chem., 1976,80, 1140. 8 M. Quack, Nuooo Cimento, 1981, 63B, 358.9 J. R. Beresford, G. Hancock, A. J. MacRobert, J. Catanzarite, G. Radhakrishnan, H. Reisler and C. New York, 1979). Wittig, Faraday Discuss. Chem. Soc., 1983, 75, 21 1. 10 T. M. Ticich, T. R. Rizzo, H. R. Dubal and F. Crim, J. Chem. Phys., 1986, 84, 1508. 11 M. Quack, Faraday Discuss. Chem. SOC., 1981, 71, 359. 12 M. Quack, Faraday Discuss. Chem. Soc., 1981, 71, 325. 13 E. Abramson, R. W. Field, D. Imre, K. K. Innes and J. L. Kinsey, J. Chem. Phys., 1984,80, 2298.212 General Discussion Fig. 15. Typical 'quasi-microcanonical' density distribution (evolving in time) for an excitation energy corresponding to six quanta of CH stretch excitation in a typical CHX, compound with a Fermi resonance Hamiltonian corresponding closely to the parameters of CHF,.The maps indicate lines of equal probability density. The triangular line indicates the classically allowed range on the potential surface. The dashed lines show the energy width of the N = 6 polyad [for details see ref. (14)]. 14 R. Marquardt, M. Quack, J. Stohner and E. Sutcliffe, J. Chem. SOC., Faraday Trans. 2, 1986,82, 1173; 15 H. R. Dubal and M. Quack, J. Chem. Phys., 1984,81,3779. 16 A. Amrein, H. R. Dubal and M. Quack, Mol. Phys., 1985, 56, 727. 17 J. S. Wong, Thesis (Berkeley 1981); J. S. Wong and C. B. Moore, in Proc. 28th Cong. Inr. Union Pure Appl. Chem., Vancouver 1981, ed. K. J. Laidler, p. 353. 18 S. Peyerimhoff, M. Lewerenz and M. Quack, Chem. Phys. Lett., 1984, 109, 563. 19 H. R. Dubal, M. Lewerenz and M. Quack, to be published.20 J. Segall, R. N. Zare, H. R. Dubal, M. Lewerenz and M. Quack, J. Chem. Phys., 1986,86, 634. 21 M. Quack, presented at the GDCh Hauptversammlung, Heidelberg 1985, appeared partly in Labor 22 A. Amrein, H. R. Diibal and M. Quack, to be published. 23 J. Manz and H. H. R. Schor, Chem. Phys. Letr., 1984, 107, 542. R. Marquardt and M. Quack, to be published. 2000 (1986). Dr P. Rosmus (University of Frankfurt), Dr P. Botschwina (University of Kaiser- slautern), Dr H-J. Werner (University of Frankfurt), Dr V. Vaida and Dr M. McCarthy (University of CoZorad_o) snd Dr P. Engelking (University of Oregon) said: Recently, we have calculated' the A-X absorption and emission spectra of NH3 and ND3 from ab initio potential-energy and electronic transition moment surfaces and two-dimensional anharmonic vibrational wavefunctions. In fjg.16 the purely theoretical spectrum of the emission from the v; = 1 level of the ND3 A-state is shown. This spectrum can be compared directly with the experimentalGeneral Discussion 213 2 50 240 230 220 210 200 Alnm Fig. 16. Theoretical 2-2 emission spectrum ND3 (vi = 1). Only the 1: 21, and 1h21, progressions are shown. The theoretical emission spectrum is represented by Gaussians with linewidths equivalent to those in the experimental spectrum of Ashfold, Bennett and Dixon. dispersed emission spectrum of Ashfold, Bennett and Dixon. The theoretical spectrum has been obtained from the calculated vibrational term values and vibrational transition moment matrix elements. The agreement for the 1: 2: and 1: 22, progressions is good.For wavelengths > ca. 235 nm it is difficult to make a unique assignment of the anhar- monic wavefunction. This part of the spectrum is therefore not showG in fig. 16. Ashfold et aL2 also suggested a qualitative shape of the ammonia A-state potential- energy surface along the NH2 + H dissociatioi coordinate. Our calculated surface3 for this process confirms their assumptions. The A-state dissociation proceeds via a planar barrier and thc minimal energy path for the NH2 + H Erocess collows planar geometries through the X-A conical intersection. Since the-A and-X states of NH2 form a Renner-Teller pair, the crossing distance of the X and A states of NH3 in planar structures depends strongly on the angle in the NH2 fragment. 1 P.Rosmus, P. Botschwina, H-J. Werner, V. Vaida, P. Engelking and M. McCarthy, J. Chem. Phys., 2 M. N. R. Ashfold, C. L. Bennett and R. N. Dixon, Chem. Phys., 1985, 93, 293. 3 M. McCarthy, P. Rosmus, H-J. Werner, P. Botschwina and V. Vaida, J. Chem. Phys., submitted. submitted. Dr M. N. R. Ashfold, Mr C. L. Bennett and Prof. R. N. Dixon (University of Bristol) said: We have heard plenty in this Discussion to entourage our belief that a much fuller description of the predissociation dynamics of A-state ammonia molecules lies just around the cornzr. Rospus has described the results of a6 initio calculations of large portions of the A- and X-state potential-energy surfaces and of the electronic transition moment surface connecting these states,' from which it has proved possible to reproduce214 General Discussion the overall form of the ammonia A + 2 absorption spectrum and of the A + 2 dispersed emission spectra involving low 2" vibronic levels such as that shown in our paper.This qualitative match of theory with experiment (both in band positions and relatije intensities) is further illustrated in fig. 17(a) and (b) for the zero-point level of ND,(A). It is to be hoped that analyses of the corresponding spectra originating from much higher 2" levels [e.g. fig. 17(c)] will enable a further refinement of the higher energy regions of these surfaces and, possibly, provide additional insight into the dissociation process itself. The technique of H-atom time-of-flight (TOF) spectroscopy2 has also been applied to a preliminary study of NH3 photolysis at 193 nm.The H+-ion TOF spectrum so obtained when using a short, 4 cm, flight path is shown in fig. 18 together with the total kinetic energy spectrum. The results confirm previou: qualitative conclusions regarding the high level of internal excitation in the NH2(X) fragments resulting from NH, photolysis at this wavelength; they also highlight, once again, the insensitivity of conventional TOF methods to near-zero kinetic energy particles. In future studies we plan to use a variably delayed, pulsed extraction field to quantify the yield of the slow H+ ions lost in the present field-free experiment, and to study the photofragmentaLio? of ammonia molecules following excitation at wavelengths much closer to the A-X electronic origin.In contrast to the 193 nm photodissociation studies reported to date3 it is to be hoped that, at longer photolysis wavelengths, the resulting product-state population distribution will be most sensitive to the detailed dissociation dynamics and less affected by the large amplitude bending motion of the photoexcited parent molecule. 1 P. Rosmus, P. Botschwina, H-J. Werner, V. Vaida, P. Engelking and M. McCarthy, J. Chem. Phys., 2 H. J. Krautwald, L. Schnieder, K. H. Welge and M. N. R. Ashfold, Furuduy Discuss. Chem. Soc., 1986, 3 V. M. Donnelly, A. P. Baronavski and J. R. McDonald, Chem. Phys., 1979, 43, 271. submitted. 82, 99. Prof. M. Quack (ETH Ziirich) said: Ashfold, Bennett and Dixon have obtained beautifully detailed data on the predissociation dynamics of ammonia (NH, and ND3) in the A('A;) state.This work would find a natural continuation by looking for state-to-state correlations between ro-vibronic states of ND, and ND2 (the latter being accessible via laser-excited fluorescence, for instance). In this particlar case, predictions have been put forward concerning state-to-state selection rules based upon the principle of nuclear-spin symmetry conservation.''2 For instance, it is predicted2 that A', and A: states of ND3 (in D3,,) will only dissociate into A, and A2 states of NH2 (in C2v), whereas A; and A; will dissociate into B1 and B2. E' and E" states of ND, can dissociate into any of the A,, A2, B, or B2 states of ND2. Although we have formulated the rules in terms of the point-group species of the molecules under consideration, the underlying symmetry principle is related to an approximate, dynamical constant of evolution C (time evolution operator U, Hamiltonian H ) uc == cu (1) H,C = CH, (2) H = H,+ H1 (small).(3) with In the present case the approximate good quantum numbers are the nuclear spin symmetry species and parity neglecting the small Hl , which couples channels of different nuclear-spin symmetry species. For the fast dissociation to be expected for NH, and ND3 from the results of Ashfold et al., one can conclude that the selection rules will hold to a high degree of approximation.I 4 3 2 1 --m-- 1202: I I 1 260 240 220 200 wavelength/nm I I I I 280 260 240 220 260 wavelength/nm Fig. 17. (a) Stick spectrum showing the ab initio calculated' band positions and relative intensities for the- 1E2: and 1y2: progressions in the spsctrum of the wavelength dispersed emission from ND3(A) 0'; and wavelength dispersed A --* X emission spectra following two-photon excitation of ND3 ?t (_b) 428.02 nm and (c) 394.28 nm, wavelengths that correspond to the qQ-branch maxima of the A-X 0: and 2: bands, respectively.Neither spectrum is corrected for the wavelength dependence of the detection response which has declined to ca. 60% (at 260 nm) relative to that at 230 nm, nor for the loss of intensity at A e m d 215 nm due to self-absorption.216 General Discussion 600 x 9 cu 0 0 5 10 15 20 time of flightlps 3 2 1 kinetic energy/eV 0 Fig. 18. ( a ) H’-ion TOF spectrum resulting from NH3 photolysis at 193 nm. E(bv) = 6.42 eV.( b ) Transformation of the TOF spectrum shown in ( a ) into a spectrum of total kinetic energy, Threshold energies for the producLchannels leading to formation of NH2 fragments in their X and A electronic states are indicated. Relevant information from such selection rules can also be derived for other photo- fragmentations presented at this Discussion, for example3 PH,(C,,) ---+ PH2+H (4) or4 CH20 --* CO+H2. ( 5 ) The latter system has been investigated experimentally and evaluated in terms of ‘ortho-para’ selection rules.’ The prediction, which had been communicated6 to the authors of ref. (5) and had been published prior2 to the experiment, is found to beGeneral Discussion 217 fulfilled in the experiments.' However, reaction (5) may also in the future be a candidate for investigations of the violation of nuclear-spin symmetry conservation, which we predict here for certain special conditions: violation of the 'ortho-para' nuclear-spin symmetry selection rule is potentially predicted for CH20 if (i) A*(A1,2) and B*(Bl,2) states in the S1 and So state are Stark-tuned into almost exact resonance; (ii) the predissociation is slow.The second factor determines to what extent, quantitatively, the nuclear-spin symmetry conservation law is violated. More generally, nuclear-spin symmetry will be violated prominently in large polyatomic molecules, which show very slow vibrational predissociation in the electronic ground state near threshold. The last point concerning nuclear-spin symmetry violation brings us to some interesting recent considerations on parity violation in chemical reactions including photofragmentations.As pointed out elsewhere: the parity-violating weak neutral current perturbation leads not only to energy differences between enantiomers but also to non-conservation of the parity quantum number ( * l ) in isolated chemical systems with densities of states p > 1015 cm on timescales of hours or days. This is relevant for the possibility of demonstrating experimentally parity violation in molecules and perhaps also for large polyatomic molecules in space occuring under conditions of near isolation. In relation to the large H/D isotope effect demonstrated for NH, predissociation, we may mention that the approximate analysis of linewidths by simulation of high- resolution spectra of CH, and CD3 near 216 nm gave a very similar isotope effect for the predissociation of the vibrational ground state of CH3 (2A',), namely r = 60 cm-' for CH, and r = 8 cm-' for CD3.* One may wonder whether the dynamics of this predissociation show similarities with NH, predissociation and perhaps Ashfold et al.have already considered this process? 1 M. Quack, Mol. Phys., 1977, 34, 477. 2 M. Quack, Stud. Phys. Theor. Chem., 23, 355 (Proc. Int. Symp. Symmetries and Properties of Non-rigid 3 B. Koplitz, Z. Xu, D. Baugh, S. Buelow, D. Bander, J. Rice, H. Reisler, C. X. W. Qian, M. Noble and 4 H. Bitto, D. R. Guyer, W. F. Polik and C. B. Moore, Furuduy Discuss. Chem. SOC., 1986, 82, 149. 5 B. Schramm, D. J. Banford and C. B. Moore, Chem.Phys. Lett., 1983,98, 305. 6 M. Quack, 1st Int. Formaldehyde Meeting, Eindhoven Veldhoven, 1979. 7 M. Quack, Chem. Phys. Lett., 1986, 132, 147. 8 K. Glanzer, M. Quack and J. Troe, 16th Symp. Int. Combustion (The Combustion Institute, Pittsburgh, Molecules, Paris, 1982). C. Wittig, Faraday Discuss. Chem. SOC., 1986, 82, 125. 1976), p. 949. Dr F. G. Godwin, Dr C. Paterson and Dr P. A. Gorry (University of Manchester) said: It is very gratifying to see the detailed quantum calculations of Shapiro' and Brunier and Shapiro on methyl iodide photodissociation using potential-energy curves which reproduce a variety of experimental quantities. Unfortunately, there is growing evidence2 that the magnetic circular dichroism decomposition of the A band into the 3Q0, ,Q1 and 'Q1 components by Gedanken and Rowe3 is in error at 248 nm.This would affect the 'Q1 surface used in the calculation and the 3Q0-1Q1 coupling parameter, which is set by the I/I* ratio. On the MCD decomposition the transition at 248 nm would be made up of ca. 70% ,QO +- N (parallel, p = 2) and 30% 'Q1 + N (perpendicular, p = -1). On a naive basis this would produce p = 1.1, as opposed to the experimental value of p = 1 .95.4 Recently Shapiro' has shown that the true p cannot be treated as an incoherent sum in this manner, but rather some coherent summation occurs. This results in some of the perpendicular transition producing parallel photofragmentation and hence a higher p value. It seems very unlikely that this can fully reconcile the TOF and MCD results since the TOF results clearly show that <3% of the iodine atoms recoil perpen- dicularly to the electric-field vector.Quite the opposite is observed for CH3Brr5 where the contributions from the 'Q, and 'Q1 states are clearly evident. Hopefully, quantum218 Genera 1 Discussion 1.0 - - I -40 -20 0 20 40 AE/kJ mol-' Fig. 19. The translational energy distributions (equivalent to the internal energy distribution in the radical) for various alkyl iodides. All distribution peaks have been referenced to a common point to illustrate their similarity in widths. (-) C2H,I, (- - -) CF3CH21, ( - - - .) n-C3H,I, and (0) CH31. ( a ) RI + R+ I*, ( b ) RI + R+ I. calculations of the coherent p value and photofragmentation experiments at more wavelengths in the A band can resolve the matter. The internal energy disposal calculated for CH31 on the basis of excitation of the CH, umbrella mode' agrees well with the experimental results.We would like to report here new results on the photodissociation of C2H51, CF3CH216 and n-C3H712 at 248 nm. Surprisingly, the widths of the energy distribution for the I and I* channels are remark- ably constant; with the I channel being approximately twice as wide as the I* channel (fig. 19). Thus although the actual energy disposed into internal excitation of the radical varies considerably, as shown in table 1, the width does not. Surprisingly, the distribu- tions from CH31 are also quite similar, even though this is alone in having three hydrogens attached to the a carbon rather than two hydrogens and a carbon atom.Hence dramatic changes in the radical mass, number of oscillators, oscillator frequencies and geometry determine only the partitioning between translation/internal excitation but leave the width unaltered. This is most easily understood in an impulsive framework in which the width is largely governed by absorption to the C-I chromophore, providing an initial spread of C-I momenta, followed by rapid dissociation which pushes the C atom into the radical, at which point the energy partitioning is determined. Simple impulse model calculations show the correct trend, but overestimate the internal energy contribution. We now have a picture in which initial excitation is to the 3Q0 state and the energy partitioning is determined on impulse considerations.On this basis the I atoms arise solely from curve crossing and the @* quantum yields for producing excited I* atoms are just the probability of not crossing to the 'Q1 state. This can be tested by a very simple two-part model. First, the translational energy of the fragments is obtained from the soft radical impulse model:'General Discussion 219 Table 1. Translational energy disposal and I* quantum yields for the alkyl iodides” molecule ( EJ ( E d @* @* soft-12 CH31 225 143 0.73 0.76 C2Hd 157 118 0.64 0.63 n-C3H,I 108 85 0.56 0.54 n-C,H,I - - 0.49 0.47 C F3 C HZI 90 62 0.82 - a (E,) and (I?,*) represent the average translational energies of the fragments determined by TOF experiments. The @* yields (except CF3CH21) are from ref. (8), but recalculated for a methyl iodide quantum yield of 0.73. where pa = rncrn,/( mc + m,) and pf = m,m,/( m,+ m,).This yields a fragment separa- tion velocity of ~ = ( 2 E J p ~ ) l ’ ~ which can then be used to calculate @* via a simple Landau-Zener expression for the curve-crossing probability @* = exp( - E / v ) . Any scaling of the soft-radical value for Et is absorbed in the empirical E parameter. The experimental and calculated a* values are given in table 1 using Eavl = 255 kJ mol-’ and E = 1430 ms-’. (The partially fluorinated molecule is omitted, since the introduction of F atoms has a significant perturbing effect.) The agreement is remarkably good and strongly suggests that the above description is broadly correct. 1 M. Shapiro, J. Phys. Chem., 1986,90, 3644. 2 F. G. Godwin, C.Paterson and P. A. Gorry, Mol. Phys., 1987, in press. 3 A. Gedanken and M. D. Rowe, Chem Phys. Lett., 1975,34, 39. 4 M. D. Barry and P. A. Gorry, Mol. Phys., 1984, 52, 461. 5 G. N. A. van Veen, T. Baller and A. E. de Vries, Chem. Phys., 1985,92, 59. 6 C. Paterson, F. G. Godwin and P. A. Gorry, Mol. Phys., 1986, in press. 7 S. J. Riley and K. R. Wilson, Furuduy Discuss. Chem. SOC., 1972, 53, 132. 8 P. Brewer, P. Das, G. Ondrey and R. Bersohn, J. Chem. Phys., 1983.79, 720. Prof. S . A. Rice (University of Chicago, USA) said: I believe the work of Brumer and Shapiro to be very important. In particular, this work defines a theoretical paradigm by showing that, without arbitrary assumptions concerning localization of energy or ‘where’ reaction occurs, it is possible to control the selectivity of product formation if one can control the phase of the evolution of the excited molecule.In the Brumer- Shapiro method that control is achieved, via interference effects, by use of two continuous lasers each having well defined and controllable phase. Tannor and Rice have also proposed a method for controlling the selectivity of product formation.”’ Whereas the Brumer-Shapiro scheme, as first put forward, uses continuous lasers and controls product formation on an excited-state electronic potential- energy surface, the Tannor-Rice scheme, as first put forward, uses pulsed lasers and controls product formation on the ground electronic state potential-energy surface. The Tannor-Rice scheme, and the elaboration by Tannor, Kosloff and Rice,’ also defines a theoretical paradigm in the sense that it shows how, without arbitrary assumptions, it is possible to influence (control) the selectivity of chemical reactivity.The central idea is that in a two-photon or multiphoton process that is resonant with an excited electronic state, the resonant excited-state potential-energy surface can be used to assist chemistry on the ground-state potential-energy surface. By controlling220 General Discussion Fig. 20. Model ground-state Born-Oppenheimer potential-energy surface. the delay between a pair of ultrashort (femtosecond) laser pulses, it is possible to control the propagation time on the excited-state potential-energy surface. Different propagation times, in turn, can be used to generate different products.There are many cases for which selectivity of product formation should be possible using this scheme. The examples studied to date show a variety of behaviour ranging from virtually 100% selectivity to poor selectivity, depending on the nature of the excited-state potential- energy surface. In particular, it is assumed that the ground electronic state Born-Oppenheimer potential-energy surface has two or more exit channels corresponding to the formation of two or more distinct chemical species. It is also assumed that there exists an excited-state potential-energy surface whose minimum is displaced from that of the ground-state surface and whose normal coordinates are rotated from those of the ground-state surface. This excited-state potential-energy surface is used to assist the chemistry on the ground-state potential-energy surface.The time spent on the excited- state surface is used to select the desired chemical species. It is easy to see how this works, with a classical mechanical description of the dynamics. Consider the hypothetical notential-energy surface shown in fig. 20; it has a central minimum and two inequivalent exit channels separated from the minimum by saddle points. The trajectory that begins at rest at the minimum of the ground-state surface is projected vertically up to the excited-state surface (fig. 21). It now evolves for some time on the excited-state surface, after which it projected vertically back down to the ground-state surface. The time spent on the excited-state surface is one of the controllable variables in the Tannor-Rice scheme.The trajectory is now propagated on the ground-Ftate surface long enough to determine its ultimate fate, i.e. whether it leads to A+ BC, AB + C or ABC. Fig. 22( a ) shows a trajectory that exists from channel 1 (A+ BC; excited-state propagation time is 600 a.u.). Fig. 22(b) shows a trajectory that exists from channel 2General Discussion I 22 1 Fig. 21. Harmonic excited-state Born-Oppenheimer potential-energy surface. The classical trajec- tory that originates at rest from the ground-state equilibrium geometry is shown superimposed. Fig. 22. Classical trajectories on the ground-state that arise from a vertical transition down (coordinates and momentum unchanged) after propagation time t2 - t , on the excited-state potential-energy surface.( a ) t2 - tl = 600 a.u., ( b ) t 2 - tl = 2100 a.u.222 General Discussion i I 1000 2000 3000 t (a.u.) Fig. 23. Probability (0 or 1 ) of exit from channel 1 as a function of excited-state potential-energy surface propagation time. (AB+ C; excited-state propagation time is 2100 a.u.). As may be seen in fig. 23 and 24, in the classical mechanical description there are windows of 50- 100 a.u. width for exit out of a desired channel. The quantum-mechanical description of the dynamics follows a very similar pattern. At the instant that the first photon is incident the ground-state wavefunction makes a vertical (Franck-Condon) transition to the excited-state surface. The ground-state wavefunction is not a stationary state on the excited-state potential-energy surface, so must evolve as t increases.There are some interesting analytical properties of this time evolution if the excited-state surface is harmonic. In that case a Gaussian wavepacket remains Gaussian for all time, the centre of the Gaussian wavepacket follows the classical trajectory for harmonic oscillation, both in coordinate and momentum space, and the Gaussian wavepacket develops a phase equal to the classical action integral for the same motion, namely += (Ptj--E)dt. I: These properties are retained to a good approximation for smooth, anharmonic potential- energy surfaces. Moreover, Ehrenfest’s theorem3 ensures that the centre of the wavepacket will obey the classical equations of motion for any potential surface, provided the wavepacket remains sufficiently localized.The duration of the propagation on the excited-state surface can be regulated by the delay of a second pulse relative to the initial pulse of light. The second pulse leads to a vertical (Franck-Condon) transition down to the ground-state surface. Note that the wavefunction amplitude is unchanged in the Franck-Condon transition. If the delay and width of the second pulse is chosen on the basis of the position and width of the windows in fig. 24 it is plausible to expect the wavepacket amplitude on the ground surface to select one channel over the other.General Discussion 223 0 1 2000 3000 t (a.u.) Fig. 24. Same as fig. 23, only for channel 2. Note that there is no overlap between the windows in fig. 23 and fig.24, but there are time intervals that correspond to bound trajectories on the ground-state potential-energy surface that appear as zero amplitude in both plots. The results of quantum-mechanical calculations of wavepacket propagation on the excited-state and ground-state potential-energy surfaces, for a variety of diff erent excited- state potential-energy surfaces and a range of pulse delays, show that this expectation is fulfilled. I will give only one illustration of the results of the quantum-mechanical calculations of Tannor, Kosloff and Rice; details can be found in ref. (2) Suppose that the ground-state potential-energy surface is as shown in fig. 20 and the excited state minimum is displaced to larger distance relative to the ground-state minimum, the frequencies in the symmetric and asymmetric stretch coordinates are roughly equal, and the force constants are in the same range as their ground-state values.Equipotential contours for the excited-state surface are shown in fig. 25(a). Fig. 26(a)- (c).show the excited-state wavefunction at t = 200,400 and 600 a.u., respectively, before the second pulse. Clearly, the quantum-mechanical amplitude is spreading severely, as the wavepacket migrates toward the soft part of the Morse potential. Fig. 26(d) shows the amplitude on the ground state surface at t = 1000 a.u., after the second pulse. The selectivity out channel 2 is virtually complete (no amplitude exists from channel 1). Thus far the examples studied show a variety of behaviour ranging from virtually 100% selectivity to poor selectivity.An excited-state potential-energy surface with shorter equilibrium bond lengths, deeper wells and/or higher barriers than those the ground-state potential-energy surface proves to be the most useful intermediary for this selectivity of reactivity scheme. Although these changes in molecular parameters on excitation are not common, there are cases for which they occur. Alternatively, one may use the Tannor-Rice scheme with the roles of excited state and ground state reversed. Consider starting out in the ground vibrational state of the excited electronic state. This is the initial condition for ordinary emission spectroscopy. Then one may use a two-pulse sequence to stimulate amplitude down to the ground electronic state224 .F General Discussion r 1000 2000 t (a.u.) 3000 1000 2000 3000 t (a.u.) Fig.25. (a) Anharmonic excited-state potential-energy surface. The classical trajectory that originates from rest from the ground-state equilibrium geometry is shown superposed. (b) Probability (0 or 1) of exit from channel 1 as a function of excited-state propagation time. (c) Same as ( b ) only for exit from channel 2. and back up to the original electronic state. Now the steepness of the ground-state surface barriers accelerate the nuclear motion so that enough kinetic energy is acquired for dissociation on the excited-state surface; also the tighter bonds on the ground state serve to focus the wavepacket. In short, vibrational energy acquired on the steeper of the two potential-energy surfaces may be used to break a bond on the flatter of the two potential-energy surfaces.The two choices of initial and final surface mentioned can be thought of as examples from a spectrum of possibilities inherent in a more general scheme for achieving selectivity of reactivity. That more general scheme involves use of some electronic state to assist selectvity of product formation, but allows the initial and final states to be different. Imagine a Franck-Condon transition from some initial state to an intermediate electronic state followed, after a controlled delay, by a transition to a third electronic state (which could be the initial state). If the final-state potential-energy surface and the intermediate-state potential-energy surface have the right properties, use of shaped pulses and control of pulse separation will permit selectivity of reactivity of the final-state potential-energy surface. It is also possible to imagine the use of detuning from resonance with the intermediate electronic state as a tool to augment control of the timescale for evolution in that state.Clearly, there are many ways in which the Tannor-Rice ideas must be extended. Amongst the more important extensions needed are variational optimization of the shape, duration and separation of the pulses used to generate the selectivity of reactivity and analysis of the changes induced by inclusion of all degrees of freedom of the molecule (say in the sense of a reaction path Hamiltonian, or a dynamical path Hamiltonian).General Discussion 225 Fig.26. Magnitude of the excited-state wavefunction before the second pulse. ( a ) t = 200 am, (b) t = 400 a.u., ( c ) t = 600 a.u. Note the wavepacket spreading is still significant, as the wavepacket approaches the soft part of the Morse potential. ( d ) Ground-state wavefunction at t = 1000 a.u., after the second pulse. There is complete selectivity out of channel 2, while the classical mechanics predict selectivity for exit out of channel 1. The shortest pulses available at the present time are of the order of 10-3Ofs. The classical windows found in the examples studied by Tannor, Kosloff and Rice (which refer to model systems with hydrogen masses) are of the order of a few fs. The overall timescales should become longer by about a factor of five for somewhat larger masses than assumed in the model systems studied to date.Thus the experimental testing of the Tannor-Rice scheme is at the very edge of the existing technology. 1 D. J. Tannor and S. A. Rice, J. Chem. Phys., 1985,83, 5013. 2 D. J. Tannor, R. Kosloff and S. A. Rice, J. Chem. Phys., in press. 3 A. Messiah, Quantum Mechanics (Wiley, New York, 1958), vol I. 4 All the anharmonic potential-energy surfaces have a functional form as described in F. T. Wall and R. N. Porter, J. Chem Phys., 1962,36, 3256. 5 E. J. Heller, J. Chem. Phys., 1977, 65, 1289. 6 P. Brumer and M. Shapiro, J. Chem. Phys., submitted. 7 T. A. Holme and J. S. Hutchinson, Chem. Phys. Lett., 1986, 124, 181.226 General Discussion Prof. M. Quack and Dr H. J. Thone (ETH Ziirich) said: Brumer and Shapiro have proposed an interesting new method of coherent radiative control of unimolecular reactions.' Although their new proposal is highly stimulating and imaginative, one should not forget that some of the older proposals for mode-selective reaction control by i.r.-laser chemistry with intense, coherent, monochromatic light sources in the i.r.have not been adequately addressed by experiments, so We wish to report in this context some results on the i.r.-laser-induced photofragmentation of mono- and di-chromophoric, isotopically labelled fluor~butanes.~ The basic system is shown in the following scheme: H H H H I I I I F-C-C-C-C-F I I I I D H H H J -HF \ H H H H H H H \ I l l I l l / I l l I I \\ I H C=C-C-C-F+ F-C-C-C D H H D H H C-H. Previous studies on the spectroscopic properties of the -CH,F chromophore and the CHDF chromophore6 indicate that they both absorb near 1040 cm-', whereas only the CHDF chromophore is also preferentially excited near 930 cm-', thus giving possibly localized excitation in the parent compound on very short timescales.Our experiment, which uses on purpose collisions at high buffer gas pressures as a clock, can be represented by the following, highly simplified kinetic scheme (with obvious notation). When one makes the quasi-steady-state assumption in this scheme, one finds for the product ratio, which is a measure for the mode or site selectivity in the parent compound Here, cA stands for the product [2H,]-4-fluorobut-l-ene and cB stands for [4-*H1]-4- fluorobut-1-ene. Because the two reaction channels differ only by a small secondary isotope effect, one has (ka/kb) = 1. Thus the selectivity can be promoted in either of two ways: (i) exciting the reactant with ultrashort laser pulses to very high excitation with very fast reaction and thus large kb/ kintra (the qualitative discussion remains valid although the quasi-steady-state assumption does not); (ii) increasing kdes by increasing the buffer gas pressure. In our experiments, we have used partly self-mode-locked multi-mode pulses (single transverse mode with unstable resonator optics) from a Lumonics TEA 103-2 CO, laserGeneral Discussion 227 with parallel irradiation up to 20 J cm-2 and also focussed irradiation from a high- repetition-rate TEA 821 HP C02 laser. No significant intramolecular (“mode”) selec- tivity was found with buffer gas pressures of He, N2 and C02 up to 1 atm.’ This indicates that kintra is larger than ca. 10” s-’. High isotope separation factors ( i e . intermolecular selectivity) in mixtures of 1,4-difluorobutane with the monodeutero compound demon- strate that the -CHDF chromophore in difluorobutanes can indeed be selected at t d 935 cm-’. To our knowledge this experiment in i.r.-laser chemistry is the first adaption of the idea of isotope labelling of symmetrically equivalent reaction centres, which has been used in chemical activation systems by Doering’ and Rabinovitch and coworkers,* and which is ideally suited to eliminate fallacious conclusions from secondary effects. In i.r.-multiphoton excitation we have to combine this with the idea of the localized i.r.-chromoph~re.~?~ Although our experiment has provided evidence against mode selectivity on times- cales > lO-”s in the reaction system considered, the prospects will be more favourable under either of the following conditions: (i) shortening the timescales of reaction for very highly excited molecules to the picosecond and subpicosecond range by using very intense excitation pulses; (ii) using specifically designed molecules, in which kintra is reduced. Work in both directions should be pursued and is being planned in our laboratory. In both cases use is made of the rates of certain competing intramolecular processes and of intramolecular coherence in contrast to making use of coherence properties of the light as proposed by Brumer and Shapiro. We may mention that a generalized rate equation scheme for optical pumping and intramolecular redistribution, although more complex than the oversimplified scheme discussed above, is not in contradiction to the coherent, monochromatic excitation with i.r.-laser source^.^ Whether for a given molecule the rate-equation treatment is valid depends upon the laser properties and detailed spectroscopic properties of the molecule, which are not generally available. However, the rate-equation treatment will often be a good working hypothesis for tests of site or mode selectivity by rate control. 1 P. Brumer and M. Shapiro, Faraday Discuss. Chem. SOC., 1986, 82, 177. 2 M. N. R. Ashfold and G. Hancock, in Gus Kinetics and Energy Transfer (The Chemical Society, London, 3 M. Quack, Adv. Chem. Phys., 1982, 50, 395. 4 D. W. Lupo and M. Quack, Chem. Rev., in press. 5 M. Quack and H. J. Thone, Chem. Phys. Lett., to be published. 6 M. Quack and H. J. Thone, Ber. Bunsenges. Phys. Chem., 1983,87, 582. 7 W. von E. Doering, J. C. Gilbert and P. A. Leermaker, Tetrahedron, 1968,24,6863; W. von E. Doering, ETH Kolloquium, 1983; W. von E. Doering and W. H. Ehlhardt, J. Am. Chem. SOC., 1987, in press. 8 J. D. Rynbrandt and B. S. Rabinovitch, J. Phys. Chem., 1971, 75, 2164. 1981), vol. 4 p. 73

ISSN:0301-7249    

DOI:10.1039/DC9868200187

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986, 82, 229-240 Molecular Photofragmentation with Many Infrared Photons Absolute Rate Parameters from Quantum Dynamics, Statistical Mechanics, and Direct Measurement Martin Quack* and Emile Sutcliffe Laboratorium fur Physikalische Chemie der ETH Zurich (Zentrum), CH-8092 Zurich, Switzerland Peter A. Hackett and David M. Rayner Laser Chemistry Group, Division of Chemistry, National Research Council of Canada, Ottawa K1A OR6, Canada The quantum-dynamical and statistical mechanical foundations of the definition and determination of absolute rate parameters for molecular photofragmentation with infrared lasers are discussed briefly and are illus- trated with model calculations. A new experiment is reported, which allows the measurement of iodine atom yield in real time as a function of fluence during the laser pulse for the fragmentation of perfluoroalkyl iodides C,F2,+11 (n = 1-10).The data are evaluated quantitatively in terms of the absolute rate coefficients. The results are compared to results from indirect measurements and to theoretical calculations. The importance of the transi- tion from non-linear case C behaviour to linear case B behaviour is demon- strated for CF31 in the experimentally accessible intensity range. The transi- tion falls in the intensity range predicted quantitatively from a simple theoretical model. Infrared-multiphoton excitation and photofragmentation of polyatomic molecules is becoming a mature branch of chemical reaction dynamics.'-4 Potential applications range from the production of free radicals for use in spectroscopy and kinetics' to laser isotope separation with a potential for large-scale technology.6 The two central questions leading to an understanding of the dynamics of the infrared laser-induced photofrag- mentation are these.(i) What is the distribution of product states (chemical and physical channels)? (ii) What is the absolute rate of photofragmentation as a function of radiation parameters and initial states of the reactant molecules? Whereas there are numerous studies available on product state d i s t r i b ~ t i o n s , ~ ~ ~ ~ ~ - * there exist relatively few investigations of absolute rates. Previous determinations of absolute rate parameters have been based mostly upon an indirect technique first proposed in 1978."-15 Although this technique should be able to provide reliable values in many cases, an important drawback has been the absence so far of any direct check of the method by comparison with quantitative real time measurements.Recently a new technique for the time-resolved measurement of iodine atom concentrations via visible laser-induced multiphoton ionization has been developed. We shall report here new results for quantitative rate determinations for the series of perfluoroalkyl iodides. The outline of the paper is briefly as follows. We first discuss the definition and determination of absolute rate coefficients on the basis of quantum-mechanical calcula- tions for a realistic triatomic model system. These results are of use in identifying certain phenomena in the experiments. We then outline the foundations of the steady-state rate coefficient and the incubation time and fluence on the basis of the statistical mechanical master equation.We then give a brief survey of the experimental technique. The last section summarizes the main experimental results and their interpretation on the basis of the theoretical concepts. 229230 Photofragmentation with Many Infrared Photons Theoretical Background for the Determination of Rate Coefficients for Infrared Laser Photofragmentation A straightforward starting point for the theoretical description of infrared laser photo- fragmentation is pTovided by the differential equation for the matrix representation U of the time evolution operator in the basis of spectroscopic molecular states:19 h dU 2.n d t i--=H(t)U.The time-dependent hamiltonian may be assumed to be periodic in time in the ideal limiting case of a strictly monochromatic, classical wave: (+t) = w+v COS (wt + 7). W is the diagonal matrix of molecular eigenfrequencies, which may include imaginary contributions for molecular resonances decaying into continua. w is the laser frequency (phase shift r ] ) and V the coupling matrix; for instance, in the dipole approximation (spectroscopic states & and + j ) Eo is the electric field amplitude of the classical, z-polarized wave (unit vector ez) of constant intensity and p the dipole-moment operator. In practice one solves for U in order to obtain the time-dependent molecular amplitude vector 6 and the density matrix P 6( t) = U( t)b(O) P( t) = U( t)P(O)U+( t).Because of the imaginary part of the hamiltonian, the trace of P is not constant, as it is taken over the states of the undissociated molecule only. On this basis one may define a rate coefficient by means of the time-dependent fraction F R of remaining reactant: F,=C pj i d l n FR k(t) = - - d t a (7) This definition is quite general and results directly from quantum-mechanical first principles. However, it does not guarantee that k(t) is in some way a simple or even constant quantity. The second route to the definition of the rate coefficient passes via the derivation of a statistical-mechanical master equation for coarse-grained level populations: l9M. Quack, E. Sutclife, P. A. Hackett and D. M. Rayner 23 1 3 2 c e I - 1 0 0 10 F / J cm-* 5 Fig. 1.Logarithmic reactant fluence plot for loss from the lowest three levels of ozone, including rotational vibrational structure in the stretching region. I. == 40 GW cm-2. For details of the model see ref. (21) and (22). The calculations represent essentially converged quantum results under the conditions mentioned. C = 1045 cm-', To = 0.5 cm-', T = 0 K. Values of I l l o marked on the curves. We note that the nature of the approximate master equation (9) and its derivation from first principles is not trivial in general and that, in particular, the rate coefficient matrix K cannot be taken to be always proportional to intensity, as is sometimes implied in the phenomenological rate equation treatments. The definitions of the rate coefficient through eqn.(7) and (10) are, of course, identical, but the level of approximation at which they are computed is different, because eqn (9) is of less general validity than eqn ( 1 ) . However, for eqn (9) with an irreducible K one has a rigorous time limit: lim k( t) = k(st) = - A l . t+m k(st) is the constant steady-state rate coefficient, which is equal to - A l , the largest eigenvalue of K. If K is reducible one has several independent problems with one k(st) for each block." This is just one example of the general emergence of a 'rate constant' which may be used as a unique parameter to characterize the rate of reaction both theoretically and experimentally, where we use the measurement of reactant or product concentration F R = 1 - F p = cR( t)/CR(O).(12) The above theoretical summary should provide the necessary background for under- standing the origin of the rate coefficient. We shall now present two examples from quantum model calculations for a very small molecule, ozone, and statistical-mechanical calculations for the smallest molecule investigated experimentally below, CFJ For more details on the general theory and the models we refer to ref. (5) and (19)-(21). Fig. 1 shows -In FR for the decay from the lowest three levels in the multiphoton excitation of ground-state ozone, basically converged including the rovibrational struc- ture for both stretching vibrations. The intensity is variable in the GW cm-2 range, but constant for the individual functions, hence F = It. The lines are reasonably straight over large ranges of F and t, thus allowing the definition of k(st) even for such a highly232 Photofragmentation with Many Infrared Photons 11 10 n - ' r n r: Y v U 2d d 9 9 8 0 O1 0 -1 0 1 1% ( I / 10) Fig.2. Approximate rate constants evaluated from results presented in fig. 1 as a function of intensity (- - -). The 300 K results (-) are for a separable slice of the thermal 300 K population covering ca. 10% of the rovibrational partition function non-statistical situation, and furthermore the yield is dependent on intensity, and not just fluence. The intensity dependence decreases with increasing intensity. This second point is illustrated further in fig. 2 The intensity dependence of k(st) changes from ca. I* to I' at the highest intensities.Whereas in this example only the loss from the lowest levels is considered, similar results are also obtained for models with excitation to threshold and reaction,22 although no fully converged quantum calculations are then possible. Fig. 2 illustrates further the effect of initial temperature. If instead of a pure state initially one has a 300 K ensemble, one obtains a rate coefficient which is about a factor of two lower on average. Of course, strictly speaking one might now reduce the problem, defining several rate coefficients. However, (i) the problem is not fully reducible and (ii) the average behaviour is so smooth that a definition of an average k(st) presents no problems. Let us now consider the result of a statistical-mechanical model calculation using the unified case B-case C master equation for the infrared photofragmentation of CFJ.The fundamental model has been presented before.20 It includes a non-linear intensity dependence, and we make use of the empirical bandwidth factor ;/A; = 4 suggested in ref. (13) in order to place the calculations on an absolute scale in the intensity range covered by the experiments. In this sense our calculation is a prediction of the experi- mental result presented below. The result is shown in fig. 3 for intensities between 2 and 200 MW cm-2. It is seen that after a pronounced delay phenomenon, which arises from the pre-steady-state multistep excitation, linear steady-state behaviour is approached. The yields and slopes depend upon intensity: This implies a non-linear intensity dependence of k(st) k(st) = ~ 1 " ~ ' .M.Quack, E. Sutcliffe, P. A. Hackett and D. M. Rayner 233 3 0 0 1 2 3 FIJ cm-* Fig. 3. Theoretical model calculation for infrared photofragmentation of CF,I using the unified statistical-mechanical model for cases B and C of ref. (2) and the empirical adjustments of ref. (13). The numbers for the various functions indicate the time-independent intensity in MW cm-2. Case B is the high-intensity limit (weakly intensity dependent). The dashed line includes the dissociation after the pulse for 200 MW cm-2 (i.e. -In Fg). However, at the highest intensities above 200 MW cmP2 according to this model calcula- tion case B is approached, where the yields become essentially fluence-dependent, namely for case B" [ K1 Z f( I)] *= K I I ( t)p dt Even in case B eqn (15) and (16) are only approximations, but then the constant parts in K can be treated as small perturbations.Hence one has also k( st) = XI = kI( st) I (17) with an intensity independent kI( st) [strictly a weakly intensity-dependent kI( st)]. We stress that the model at the basis is highly oversimplified, because spectroscopic para- meters are still incomplete23 for, say, a generalized case C cal~ulation.~~ However, it will be of interest to see to what extent the effects in fig. 3 are born out by experiment, qualitatively and quantitatively. Experimental In essence the experiment consists of defining first the time dependence of the infrared laser fluence during single-mode pulses derived from a TEA COz laser: F( t ) = I( t') dt'.I: This is necessary to provide the independent variable in eqn (16), i.e. fluence. Secondly, we measure the time-dependent iodine-atom yield Fp( t), which is directly related to FR = 1 - Fp. In practice we assume that iodine atoms are produced in the ground state, P3,2, which is monitored by visible-laser five-photon ionization, using 474.3 nm radi- ation, which allows a near-resonant three-photon transition followed by a two-photon234 Photofragmentation with Many Infrared Photons 1 I Fig. 4. Block diagram of the experimental apparatus (see the detailed description in the text). transition to the ionization continuum. Exited iodine atoms ('PI,:) were also probed at 477.7 nm. The ions were detected in the interaction cell, which is a diode-type ionization detector. Fig.4 provides a survey of the experimental arrangement. An 820 Lumonics C02 laser operates on a single line, single transverse mode, TEMoo, and single longitudinal mode by means of a grating, IRIS 1, and a low-pressure intracavity C02 discharge cell as shown. The radiation propagates through an attenuation cell with C4F1,, and is focussed by a 50 cm Ge lens into the interaction cell. The energy of the C02 laser pulses is measured by various pyroelectric detectors. The beam fluence profile is measured with a 25 nm pinhole by PYRO3, when the interaction cell is removed. The time- dependent C02 laser intensity is measured by photon drag detectors (PD), which are also used for triggering. Briefly, this allows one to define the total pulse energy, the total pulse fluence in the small interaction region (uia the beam profile) and the time-dependent fluence (via the time-dependent intensity).The COz laser light is stopped by the 1 cm CaF2 window of the interaction cell, which serves as a volume absorber. Tunable visible radiation is derived from a Molectron model DL16P, Coumarine 480, dye laser pumped by a Lumonics 860-1 excimer laser operating at 308 nm. It is probed by two Hamamatsu phototubes (PT1 and PT2) and propagates collinearly, but in opposite direction to the C02 laser radiation into the interaction cell. It is focussed into the cell by a 10 cm focal length suprasil lens. Typical pulse energies are 2 mJ, pulse widths 0.01 nm and pulse duration ca. 10ns. The spot size of the visible laser is much smaller than the spot size of the C02 laser, and great care was taken to ensure that only a region of constant C 0 2 laser fluence (ca.3 cm long) was probed by the multiphoton ionization detection (initially this was a problem, for reasons to be discussed in detail elsewhere2'). The time between the infrared laser and visible laser was measured via PD1 and PT2. The temporal pulse shapes for a given C02 laser wavelength are accurately reproducible. Absolute iodine atom yields were obtained by assuming a saturation value of one, an assumption which was checked in several ways.25 A Tektronix 4052 microcom- puter was used to acquire, display, store and process all data. More experimental details will be reported elsewhere25 [see also ref. (16)-(18)]. Problems that arose and were controlled include geometrical effects from the overlap of the two lasers, infraredM.Quack, E. Sutclifle, P. A. Hackett and D. M. Rayner 23 5 Fig. 5. ( a ) Time-dependent intensity for a typical single-mode laser pulse and its time-integrated normalized fluence (right-hand side). ( 6 ) Time-dependent I-atom yields for several typical sets of experiments. focal-spot variations due to the C4FI0 attenuator cell, impurity generation, optimum choice of the dye laser wavelengths and the generation of iodine atoms via visible-laser photolysis. Fig. 5 shows some typical data. In the upper part the time-dependent intensity is shown together with the corresponding normalized time integral. A substantial fraction of the total pulse energy is contained in the low-intensity part of the pulse.The lower part of the figure shows the corresponding iodine-atom yields for various conditions. C4F91 was obtained from Columbia, all other compounds from PCR. All compounds were checked by gas chromatography and mass spectrometry. There were no gross impurities from other, interfering substances (in particular other iodides), and I2 was removed by passage over alumina. The substances were vacuum-distilled and degassed. They were allowed to flow through the interaction cell at pressures of ca. 10 Pa, i.e. the experiments are collisionless in the relevant timescales. The flow of fresh gas proved to be necessary in order to avoid interference from the products accumulated during photolysis. Results and Discussion The time-dependent fluence and time-dependent iodine atom yields from data sets as shown in fig.5 were combined to provide the fraction of remaining reactant FR as a function of fluence. These are displayed in fig. 6,7 and 8 in the form of the logarithmic reactant fluence plots of -In FR as a function of F for the three examples CFJ, C4F91 and C7FI5I, respectively. It is immediately clear that they show the characteristic theoretical shape with a pronounced delay phenomenon and a constant limiting slope. The limiting slope provides the rate coefficient k,(st) in eqn (17) if the yield function is independent of laser intensity. This was checked by varying the total pulse fluences236 Photo fragmen ta tion with Many Infrared Photons 3 0 0 1 2 3 FIJ cmp2 Fig. 6. Logarithmic reactant fluence plots showing the experimental results for CF,I photofrag- mentation with two different peak intensities of 288 MW cm-2 (0) and 66 MW cm-2 (dashed line).The two functions coincide below 1.5 J cm-2. For the 66 MW cm-2 pulse the numbers 66, 30 and 6 indicate the local intensity during the course of the pulse. The open circles are from the indirect experimental result in ref. ( 14) (including after-pulse dissociation). Further measure- ments show the absence of an intrinsic intensity dependence at high intensities and strong intensity dependence at I < 60 MW cm-2. fluence/ J cm-’ Fig. 7. Logarithmic reactant fluence plot for C4F91 photofragmentation at various peak intensities (0, 174 MW cmP2; ., 90 MW cm-’; 0, 36 MW cm-’). There is no intensity dependence of the yields.M.Quack, E. Sutclife, P. A. Hackett and D. M. Rayner 237 fluence/ J cm-2 Fig. 8. Logarithmic reactant fluence plots for C,F,,I photofragmentation at various peak intensities (0, 150 MW cm-2; B, 89 MW cm-2; 0, 51 MW cm-2; 0, 26 MW cm-2). There is no intensity dependence of the yields. at constant shape, and therefore the peak intensity of the pulses over a range of about a factor of 20. As shown in the figures, for C4F91 and C7FJ no intensity dependence of the yield was observed, whereas for CF31 the yield at high fluence but low intensity dropped below the high-intensity limiting value assumed to be approached with a peak intensity of 288 MW cm-2. An example for the intensity dependence is shown in fig. 6 for the case of a peak intensity 66 MWcm-2.It shows the drop of yield at high fluences in the form of a 'turnover' already discussed previously.26 The most natural interpretation of this turnover would be in terms of a reducible rate matrix, with some molecules being easily dissociated, without any intensity dependence, and others less easily and highly intensity dependent. Although a reducible rate coefficient matrix is to be expected because of the initial thermal distribution," this effect having been postulated for CF31 before in the oversim- plified two-ensemble and although we have been able to evaluate the data on this basis in a seemingly consistent fashion, a closer look at the data together with the theoretical calculation presented in fig. 3 indicates anther effect to be dominant. We have indicated in fig.6 the intensity for three points during the pulse with a peak intensity of 66 MW cmP2. From these points it is seen that the yield starts to turn over from the high-intensity limit only at the point where the intensity drops below 30 MW cm-2. Most of the remaining fluence is then delivered at intensitites decreasing to 6 MW cm-2 and below. An examination of fig. 3 shows that, indeed, it is not expected that for CF31 these intensities are sufficient to provide intensity-independent dissociation. Rather, the photofragmentation yield drops dramatically in this intensity range both experimentally and theoretically. Physically this arises from the low-energy steps (up to 5 or 10 photons, depending upon intensity) being dominated by case C at the lower intensities, where the population distribution has its sharp maximum at low energies.We conclude that23 8 Photofragmentation with Many Infrared Photons Table 1. Rate coefficients for CF31 + nhv --* CF3 + I k(st)/s-' I/MW cm-* line ref. 1.1 x 105 2 . 0 ~ lo5 4.0 x 105 6.5 x lo5 3.3 x lo5 7.8 x lo5 1.6 x lo6 1.25 x lo6 1075 cm-' 1075 cm-' 1076 cm-' 1075 cm-' 1078 cm-' 1075 cm-' 1075 cm-' 1075 cm-' 28 29 30 31 31 27 14 this work this is the dominant effect contributing to the turnover at low peak intensities observed for CFJ. However, a comparison of experiment and theory also provides some indication for a reducible rate coefficient matrix. The incubation fluence Fl , i.e. the intercept of the straight limiting line is ca. 0.7 J cm-2 experimentally, whereas it is ca.0.9 J cm-2 in the model. Although the interpretation is not unambiguous, the simplest explanation of this effect is that a part of the molecular ensemble reacts at a higher rate, contributing to the early rise of the experimental yield function. This is not unexpected. However, we wish to point out the quantitatively good agreement between experiment and theory for the high-intensity yield and the intensity ranges at which a drop in yield is observed. This absolute agreement is particularly notable because the theoretical model was formulated long before the present direct measurements became available, even if the model did include previous empirical knowledge (the 'rule of thumb' for an effective ;/At = 4). The rate coefficient for CF31 photofragmentation on the R(14) line of the C02 laser is, from the present experiment, ca.1.25 x lo6 (I/MW cm-2) s-' in the intensity-propor- tional range. This can be compared to the theoretical case B limiting values of ca. 1.6 x lo6 and including weak case C effects near 200 MW cmP2 of 1.45 x lo6. The present results can also be compared to previous indirect yield and rate-constant measurements with deconvolution over the beam pr0fi1e.l~ The earlier data are given by the open circles in fig. 6 , providing a rate coefficient of 1.6 x lo6 (IIMW cm-2)s-1, in excellent agreement with the present, much more accurate and directly obtained results. A major error in the present data stems from the absolute fluence determination (ca. 20% error), and the total error of the rate coefficient may be ca.30-40%, whereas the results of ref. (14) were claimed to be accurate to about a factor of 2 only. The agreement between the two sets of data is even better if one notes that the data in ref. (14) include the dissociation after the pulse, i.e. -In F g , which is above -In&. A theoretical estimate for the difference is shown in fig. 3; however, this is intensity-dependent and does not provide a different slope, in theory." Table 1 also summarizes some rate coefficients evaluated from other indirect measurements in the literature. The agreement is not generally very good, but the discrepancies probably have trivial experimental explanations in many of the earlier (and also in some of the more recent) experiments. Of course, low intensities and different pumping frequencies may also account for some of the differences.Table 2 summarizes the rate data for all the alkyl iodides measured in the present investigation. Because the final evaluation of these data is still in progress, we present this table and the resulting discussion as a preliminary report. Nevertheless, a number of general trends are clearly visible. These are not going to change in any important fashion with a more detailed evaluation. First, CFJ and QFsI are to be separated from the other molecules because they show a very strong frequency dependence and some intensity dependence (the full frequency dependence has been measured for C2F51,M. Quack, E. Sutclifle, P. A. Hackett and D. M. Rayner Table 2. Summary of rate data for the alkyl iodide reactions C,F2,+II --* CnF2,+' + I with nhv of 9R(14) (1074 cm-') compound k,/cm2 J-' F,/J cmP2 CF31 C2F51 (925 cm-') n-C3F71 i-C3F71 C4FJ C6F13I C2FJ 1.25 0.06 0.62 0.60 0.64 0.55 0.75 0.77 0.95 0.85 0.7 2.0 2.4 3.5 4.6 2.0 2.8 3.9 2.5 4.0 239 although only two values are given in the table).All of the other compounds are pumped with a frequency far to the red of the main, very strong and broad C-FF, stretching absorption band systems. The pumping is thus dominated by the wings of the absorption, which is expected to move into closer resonance for the highly excited molecules. If this is true, the reaction-threshold bottleneck assumption, together with group additiv- it^,^* would predict a slight increase in the rate coefficient with increasing chain length, as observed.Secondly, the effect on the incubation fluence is predicted both as an effect from the number of oscillator^^^ and as an effect from the off-resonant pumping, which slows down the initial excitation steps. The observed trends are not too systematic but they are, at least, not inconsistent with these ideas. Evaluations, which include more spectroscopic information are needed in order to obtain more definite statements. Conclusions Absolute rate coefficients for photofragmentation after infrared multiphoton absorption arise as approximate theoretical concepts from quantum dynamics and statistical mechanics. They allow us to quantify the rates of infrared photochemical reactions with a single parameter at steady state, which can be complemented by the incubation or activation fluence. Such parameters should be comparable and transferable between different laboratories, if measured accurately.We have demonstrated here that the real-time measurement of both fluence and reaction yield during the irradiation pulse allows us to measure accurately these rate parameters. Our results for the collision-free, primary dissociation yield of the perfluoroalkyl iodides show clearly the theoretically expected shape for plots of -In FR us. F, with a pronounced incubation phenomenon arising from the stepwise nature of infrared multiphoton excitation and with the straight- line steady-state limit. For CF31 and C2F51 some non-linear intensity dependence could be demonstrated by the variation of the peak intensities of the pulses.It is concluded, by comparison with a simple theoretical model based on the unified case B-case C master equation, that the transition from non-linear behaviour to intensity-proportional rate coefficients occurs in the expected intensity ranges. The intensity-proportional rate coefficients could be determined and they agree well with a previous indirect deterrnina- tion and with a theoretical estimate. The quantification of the non-linearity at low intensities would require real-time measurements with shaped No non- linearities were found for the higher members (C, to C,,) of the perfluoroalkyl iodides, for which we could determine the intensity-proportional rate coefficients and the incuba- tion fluence. This is consistent with the validity of a case B master equation for these molecules.240 Photofragmentation with Many Infrared Photons Assistance with the early experiments from M.Humphries is gratefully acknowledged, as well as discussions with D. Lupo and G. Seyfang. This work was in part supported by the Schweizerischer Nationalfonds and the Schweizerischer Schulrat. References 1 V. S. Letokhov and B. S. Moore, Sou. J. Quantum Electron., 1977, 66, 4317. 2 P. A. Schulz, Aa. S. Sudbo, D. J. Krajnovitch, H. S. Kwok, Y. R. Shen and Y. T. Lee, Annu. Rev. Phys. 3 M. N. R Ashfold and G. Hancock, in Gas Kinetics and Energy Transfer (The Chemical Society, 4 M. Quack, Adv. Chem. Phys., 1982, 50, 395. 5 M. J. Rossi, J. R. Barker and D. M. Golden, J. Chem. Phys., 1979, 71, 3722. 6 A. Outhouse, P.Lawrence, M. Gauthier and P. A. Hackett, Appl. Phys. B, 1985, 36, 63. 7 J. S. McKillop, R. J. Gordon and R. N. Zare, J. Chem. Phys., 1982, 77, 2895. 8 D. Feldman, H. Zacharias and K. H. Welge, Chem. Phys. Lett., 1980,69,466. 9 J. R. Beresford, G. Hancock, A. J. MacRobert, J. Catanzarite, G. Radhakrishnan, H. Reisler and C. Chem., 1979,30, 379. London, 1981), vol. 4, p. 73. Wittig, Faraday Discuss. Chem. SOC., 1983, 75, 21 1. 10 J. C. Stephenson and D. S. King, J. Chem. Phys., 1983, 78, 1867. 11 M. Quack, Ber. Bunsenges. Phys. Chem., 1978,82, 1252; Ber. Bunsenges. Phys. Chem., 1979,83, 757. 12 M. Quack, J. Chem. Phys., 1979, 70, 1069. 13 M. Quack, Chimia, 1981,35, 463. 14 M. Quack and G. Seyfang, J. Chem. Phys., 1982, 76,955. 15 D. Lupo and M. Quack, Chem.Phys. Lett., 1986, 130, 371; Chem. Rev., in press. 16 D. Rayner and P. A. Hackett, Chem. Phys. Lett., 1984, 110,482. 17 P. A. Hackett, P. John, M. Mayhew and D. M. Rayner, Chem. Phys. Lett., 1983,96,139; D. M. Rayner, C. Willis and P. A. Hackett, Rev. Sci. Instr., 1982, 53, 298; D. M. Rayner and P. A. Hackett, J. Chem. Phys., 1983, 79, 5414. 18 D. M. Rayner and P. A. Hackett, Isr. J. Chem., 1984, 24, 232. 19 M. Quack, J. Chem. Phys., 1978,69, 1282. 20 M. Quack, Ber. Bunsenges. Phys. Chem., 1981, 85, 318. 21 M. Quack and E. Sutcliffe, J. Chem. Phys., 1985,83, 3805. 22 M. Quack and E. Sutcliffe, Chem. Phys. Lett., 1984, 105, 147. 23 H. Burger, K. Burczyk, H. Hollenstein and M. Quack, Mol. Phys-, 1985, 55, 255. 24 M. Quack and E. Sutcliffe, Chem. Phys. Lett., 1985, 121, 315. 25 P. A. Hackett, D. M. Rayner, M. Quack and E. Sutcliffe, work in progress. 26 M. Quack, P. Humbert and H. van den Bergh, J. Chem. Phys., 1980,73, 247. 27 V. N. Bagratashvili, V. S. Dolzhikov, V. S. Letokhov, A. A. Makarov, E. A. Ryabov and V. V. Tykht, Sou. Phys. JETP, 1979,50, 1975; V. N. Bagratashvili, V. S. Doljikov, V. S. Letokhov and E. A. Ryabov, in Laser Induced Processes in Molecules, ed. K. L. Kompa and S. D. Smith (Springer Verlag, Barlin, 1979), p. 179. 28 S. Bittenson and P. L. Houston, J. Chem. Phys., 1977, 67, 4819. 29 T. B. Simpson, J. G. Black, I. Burak, E. Yablonovitch and N. Bloembergen, J. Chem. Phys., 1985,83, 30 D. M. Golden, M. J. Rossi, A. C. Baldwin and J. R. Barker, Acc. Chem. Res., 1981, 14, 56. 31 V. N. Bagratashvili, S. I. Ionov, M. V. Kuzmin and G. V. Mishakov, Chem. Phys. Lett., 1985, 115, 149. 32 M. Quack and H . J. Thone, Ber. Bunsenges. Phys. Chem., 1983,87, 582. 33 M. Quack, Ber. Bunsenges. Phys. Chem, 1979,83, 1287. 34 R. D. McAlpine and D. K. Evans, Faraday Discuss. Chem. SOC., 1983, 75, 261. 35 M. N. R. Ashfold, C. G. Arkins and G. Hancock, Chem. Phys. Lett., 1981, 80, 1. 628. Received 12th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200229

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986,82, 241-250 Infrared Predissociation of the Ar-HD van der Waals Molecule Ian F. Kidd and Gabriel G. Balint-Kurti" School of Chemistry, Bristol University, Bristol BS8 1 TS The theory of photodissociation and predissociation processes is briefly discussed and the results of accurate quantum calculations for the infrared predissociation of the Ar-HD van der Waals molecule are presented. The absorption lineshapes for infrared radiation in the range 3866-3906 cm-' have been computed for transitions originating in all 11 bound states of the van der Waals complex. A selected few of these lineshapes are presented and discussed in detail. Every one of the 29 absorption processes in the frequency range studied leads to the eventual dissociation of the complex.The final quantum state distribution of the HD products has been computed for all the transitions. Comparisons are made between observed and com- puted linewidths for those cases where the former are available. Comparison is also made of the present theoretical results with those of other theories. The system provides an excellent testing ground for theories of photodissoci- ation processes. An increasing awareness of the important role played by van der Waals molecules in atmospheric and interstellar processes has led to their investigation in many recent e~perimental'-~ and theoretical5-' ' studies. In this paper the details of the photodissoci- ation of the Ar-HD van der Waals complex by infrared radiation are discussed. The complex is only bound by 25.5952 cm-' in its lowest state.Consequently the absorption of an infrared photon in the energy range 3866-3906 cm-' always leads to its photodis- sociation. The direct photodissociation process has a very small cross-section except for energy regions just above the threshold for the production of a new quantum level of the Ar+ HD photofragments. This fact is easily rationalised in terms of the poor overlap between the bound-state and continuum-state wavefunctions in the Ar- HD stretching coordinate. The poor overlap results from the relatively large amounts of energy which must be converted into relative translational motion of the photofragments. '*,13 The major contributions to the photon absorption probabilities therefore occur in the vicinity of resonances or quasibound states.In scattering-theory language these resonances in the final-state continuum wavefunction are referred to as Feschbach resonance^'^*'^ and arise from the trapping of energy in the HD internal motion, thus making it unavailable to the Ar-HD relative translational motion. In the language of spectroscopy the reson- ances are characteristic of predissociation processes. Some of the observed peaks in the photodissociation cross-sections are, in the present case, due to shape resonances in the upper dissociative state. These are caused by the temporary trapping of the Ar-HD system inside a centrifugal barrier. who reported the S , ( O ) absorption spectrum of Ar-HD taken at a temperature of 77 K. This absorption spectrum corresponds to the transition The experimental study which has motivated our calculations was that of McKellar, hu Ar-HD(v"=O,j"=O) - [Ar-HD(v'= 1, j ' = 2 ) ] * + Ar+HD(v,j).( 1 ) The ( v , j ) quantum numbers refer to the vibration and rotation of the HD fragment, which is only loosely bound to the Ar. There are two bound states in the Ar-HD well 24 1242 Predissociation of the Ar-HD van der Waals Molecule for zero total angular momentum, J=O. The lowest state, with Ar-HD vibrational quantum number n = 0, is bound by 25.5952 cm-', while the n = 1 state is bound by only 2.3552 cm-'. As the total angular momentum J is increased the n = 1 vibrational level is pushed up into the continuum, above the dissociation threshold, by the centrifugal force. These previously bound states become shape resonances just above the dissoci- ation limit.Similar quasibound states are present in the Ar-HD( v = 1, j = 2) manifold of states, and they become apparent through the shape of some of the absorption cross-sections to be discussed below. A preliminary report on some of the present work has previously been p~blished.~ In that paper the energy levels of all 11 bound states of the system were given, and the overall theoretically computed S, (0) absorption spectrum was compared with the experi- mental one. In the present paper a more detailed analysis of individual photodissociation cross-sections is presented. A full calculation of the photodissociation cross-section requires the calculation of an integral of the dipole moment function of the system multiplied by both the initial bound-state and the final continuum or scattering-state wavefunctions.This calculation is here performed exactly, within certain numerical limits. Several other investigations of this and similar processes have relied on the analysis of the final-state scattering wavefunction only. Comparison is made between our present predictions and those of such calculations.'7~'s Theory The cross-section for absorption of photons by a van der Waals complex in an initial quantum state with total angular momentum Ji may be written in the form" where !P(EiJiMiPi) is the initial bound-state wavefunction, 6 -p is the component of the dipole moment in the direction of the polarisation of the light and +-(a; Efvjmj) is a scattering wavefunction which asymptotically has a plane-wave component travelling outwards into the direction with solid angle a, and with fragments in states with quantum numbers vjmj.Both the ground-state and the continuum-state wavefunctions are solutions to sets of coupled differential equations. The difficult bound continuum integral appearing in eqn ( 1 ) is evaluated using the artificial channel method of Shapiro." In this method the integral is obtained indirectly as an S matrix element between the artificial channel and the channels of the photodissociative continuum manifold of states. The details of the underlying theory of the artificial-channels method2' have been presented else- where6,*' and are not discussed here. The method is exceptionally well suited to the calculation of bound states and photodissociation probabilities involving loosely bound systems such as van der Waals m01ecules,~-~*~~ although many successful applications to more strongly bound systems have been made.23-26 The potential-energy surface used to generate the bound-state and continuum-state wavefunctions was the BC3(6,8) potential of LeRoy and C a r l e ~ ? ~ while the dipole- moment function was based on that of Dunker and Gordon28 and was identical to the one used in our study of Ar-H2.6 The potential-energy curve used to compute the vibrational-rotational wavefunctions of the HD diatomic was that of Kolos and Wolniewic~,~~ to which their adiabatic and relativistic corrections had been added.The calculated energy levels of the HD molecule differed by only 0.004-0.8 cm-' from experiment3' for the quantum levels which play an important role in the photodissoci- ation process under discussion. In order to correct for this small error, the computed HD vibrational-rotational wavefunctions were used only to calculate the matrix elementsI.F. Kidd and G. G. Balint-Kurti 243 of the interaction potential needed in setting up the coupled differential equations for the bound and continuum wavefunctions, while the experimentally determined31 energy levels were used to calculate the asymptotic channel wavevectors. The fact that the centre of mass of HD is displaced from the centre of the HD bond causes some problems in the calculation of the matrix elements of the potential and of the dipole moment function. These problems were overcome by replacing many of the analytic integrations used in the analogous Ar-H, problem6 by numerical Gauss-Hermite and Gauss-Legendre quadratures.A more detailed discussion of such technical details will be given in a future p~blication.~, Tests were carried out to ensure the convergence of the calculations with respect to all numerical aspects.6 Details of these tests will also be reported elsewhere.32 As a consequence of the tests the numerical accuracy of the present calculations is estimated to be as follows. The energies of the absorption resonances could be computed correct to f0.03 cm-’ (errors are expected to place the lines at too high an energy), the linewidths could be estimated to within 1 ‘/o and the photodissociation cross-sections to three significant figures.For most of the graphs and calculations reported, a regular energy grid with a spacing of 0.1 cm-’ was used, and this grid size is the limiting factor in the accuracy to which many of the numbers are reported. For the bound-state manifold a basis of HD vibrational-rotational wavefunctions with quantum numbers u = 0, j = 0, 1 and 2 was used, while for the upper dissociative manifold HD functions corresponding to v = 1, j = 0, 1, 2 and 3 were included. This led to sets of coupled differential equations with up to 16 coupled channels. By including only HD( ZI = 1 ) states in the description of the dissociative continuum wavefunction, vibrational predissociation processes have been neglected. These processes were found to have cross-sections which were lop6- times smaller than rotational predissociation processes when both were possible for the Ar-H, system.6 For an initial bound state with total angular momentum quantum number Ji, three separate photodissociation calculations corresponding to Ji -+ Jf = Ji and to Ji --+ Jf = Jik 1 must, in general, be carried out.In total 29 such photodissociations calculations were performed. Each calculation yielded from two to six resonance peaks in the photodissociation cross-section. At every photon energy both partial [ eqn( l ) ] and total photodissociation cross-sections were computed. The total integral photodissociation cross-section, which is essentially the absorption lineshape for the transition, is obtained by summing the partial cross-sections of eqn (2) over all product fragment quantum states: do‘( Ef I EiJiPi) = 1 a( Efvj I EiJiPi). uj (3) Results and Discussion There are far too many cross-sections to report all of them indiscriminately.The three basic cross-sections out of the J” = 6, n” = 0 bound state ( n ” is the Ar-HD vibrational quantum number) are therefore selected as illustrative of some general features. Fig. 1 shows the total photodissociation cross-section for the J’ = 5 +- J” = 6, n” = 0 transition. The peaks in the photodissociation cross-section marked N, P and R correspond to AZ = -3, -1 and +1 transitions, respectively. Ar-HD orbital angular momentum quantum numbers, Z, were assigned to each of the bound and quasi-bound levels of the system in line with past ~ o r k . ’ ~ , ~ ~ The peak at 3896.8 cm-’ is due to a metastable upper state with Ar-HD vibrational quantum number n’= 1.True bound states of Ar-HD with n”= 1 only exist for J ” = 0, 1 and 2 (and v ” = 0, j ” = 0). In the upper v ’ = 1, j ’ = 2 manifold, when the lower lower-lying states of the HD molecule are purposely omitted from the calculations, bound states with n’= 1 are found up to J ’ = 3. We may therefore conclude that the244 Predissociation of the Ar- HD van der Waals Molecule 20 I I I I I I I I I 0 3865 3875 3885 3895 3905 photon energy/cm-’ Fig. 1. Total Ar-HD photodissociation cross-section for the transition J“ = 6, n”= 0, u” = 0, j”= O+ J ‘ = 5. Calculations were performed on a regular energy grid with a spacing of 0.1 cm-’. ( a ) N(n’=O), (6) P(n’=O), (c) R(n‘=O) and ( d ) N(n’= 1). peak at 3896.8 cm-’, which has been assigned an 1‘ quantum number of 4, corresponds to an excitation to a shape resonance in the Ar-HD vibrational motion of the upper state.This is confirmed by plotting out the partial cross-section for the production of Ar + HD( v‘ = 1, j ’ = 2). This partial cross-section accounts for 96% of the intensity of this absorption line, and makes no contribution at all to the other three peaks as they lie at too low an energy. Fig. 2 shows the total photodissociation cross-section for the J’ = 6 + J” = 6, n” = 0 transition. This transition has only two peaks corresponding to P and R branches. In this case an N branch would have 1’ = 3. As j’ = 2 for the upper state coupling j ‘ and 1’ to give J’ could not give a J’ of 6.The N branch is therefore absent. There is an extremely weak transition to the n‘ = 1 upper state. This transition is 2.5 x lop3 weaker than the main R-branch transition. Fig. 3 displays the J’ = 7 +- J” = 6, n” = 0 transitions. The figure shows a small, barely visible peak at 3899.4 cm-’. This peak is due to a P branch transition to an upper state with n’ = 1. It shows up much more clearly on the plot of the j’ = 2 partial cross-section than in that of the total photodissociation cross-section. Corresponding peaks, for lower initial J” quantum numbers, lie at energies higher than the T branch transition. As the J” quantum number increases these P and T branch peaks first approach each otherI. F. Kidd and G. G. Balint-Kurti “ I 0 35 - 30 - 2 v, ‘ 25- 2 1 e .- c, s 20- v) d (d + 15- 10 - 5 - a ) 3865 3875 3885 245 photon energy/cm-’ Fig.2. Total Ar-HD photodissociation cross-section for the transition J” = 6, n” = 0, D” = 0, j ” = O + J ’ = 6 . ( a ) P(n’=O) and ( b ) R(n’=O). and then swap positions. Table 1 gives the resonance positions, linewidths and partial cross-sections for all the transitions shown in the figures. Fig. 4 shows a typical total photodissociation cross-section originating in a state with Ar-HD vibrational quantum number n”= 1. The interesting feature to be seen in this transition is the strong T-branch peak at 3890.7 cm-’. The peak lies at an energy above the threshold for the production of Ar+HD(u’= 1, j’= 2) and arises from a shape resonance in the Ar-HD scattering wavefunction. This fact is most clearly seen from the partial cross-section for the production of the HD(v’= 1, j’= 2) fragment.The cross-section for this process accounts for 78% of the amplitude in the peak at 3890.7 cm-’ in the total cross-section. The N and T branches of the spectrum display well separated peaks due to individual transition^.^"^ McKellar16 has extracted linewidths from the observed spectra for these lines. The experimental and calculated linewidths are compared in fig. 5. The comparison is seen to be generally satisfactory. These and all other calculated linewidths and resonance energies compare well with those of other calculation^.'^^'^ Significant dis- crepancies with the calculations of Hutson and LeRoy17 show up only in the magnitudes of the partial cross-sections or product quantum-state distributions. Very roughly speak- ing the present full photodissociation calculations predict ca.10% more product in the final HD( v’ = 1 , j ’ = 1) product states than do the close-coupling scattering calculation^.^^246 Predissociation of the Ar- HD van der Waals Molecule 3! 3c 2t 2 ‘0 ? 2c 0 .- 4- s v) v) $ l ! - cd 0 * Y 1 c 5 ( b ) . photon energy/ cm- ’ Fig. 3. Total Ar-HD photodissociation cross-section for the transition I” = 6, n” = 0, v’’ = 0, j”=O_* J’=7. ( a ) P(n’=O), ( b ) R(n’=O), (c) T(n‘=O) and ( d ) P(n’= 1). The above conclusions are illustrated by the numbers presented in table 2. The table compares our calculated predissociation resonance energies, linewidths and final frag- ment quantum-state distributions for some transitions proceeding through intermediate resonance states with total angular momentum J’ = 5, with those predicted by Hutson and LeRoy.17 In the present calculations an intermediate resonance state may participate in more than one absorption line.This is the case for the three resonance states studied in the table, and the lineshapes for both transitions involving the same intermediate state are independently analysed. The resonance energies, linewidths and final-state distributions involving a given intermediate level are almost identical, thus confirming the view that the intermediate state is the important entity and not, in this instance, the pathway leading to it. The discrepancies between the presently computed final quantum- state distributions and those of Hutson and LeRoyI7 are illustrated by the figures given in the last two columns of the table.Conclusions Full photodissociation calculations have been carried out for the Ar-HD van der Waals molecule in the photon energy region around the HD( v” = 0, j ” = 0) - HD( v’ = 1, j ’ = 2)Table 1. Photodissociation cross-sections for transitions out of the J” = 6, n” = 0, d’ = 0, jr‘ = 0 bound state of Ar-HD” quantum number of metastable states photon energy line- partial cross-sections/A2 total cross-section branch of at resonance width J’ n’ v’ j ’ spectrum /cm-’ /cm-’ a(j’=O) a(j’= 1) c.(j’=2) /A2 5 5 5 5 6 6 7 7 7 7 0 0 0 1 0 0 0 0 1 0 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 N P R N P R P R P T 3875.281 3882.73 1 3891.642 3896.8 3882.623 3 892.1 44 3882.123 3892.493 3899.4 3903.530 0.78 0.30 0.54 0.2 0.22 0.17 0.72 0.23 0.4 0.33 6.95( -7) 1.03( -6) 1.62( -7) 9.5(-8) 0.00 0.00 7.65( -8) 1.1 1 (-6) 4.2( -9) 1.58( -6) 1.89( -5) 5.96( -6) 2.95( -6) 2.3(-6) 3.13( -5) 4.80( -5) 2.52( -6) 7.96( -6) 1.3( -7) 3.02( -5) 0.00 0.00 0.00 0.0 0.00 0.00 0.00 0.00 1.1 (-7) 3.33( -6) 1.96( -5) 6.99( -6) 3.11( -6) 2.4( -6) 3.13( -5) 4.80( -5) 2.59( -6) 9.07( -6) 2.4( -7) 3.52( -5) a Resonance energies which are quoted to an accuracy of >0.1 cm-’ are obtained by fitting the calculated points to a Fano lineshape [see ref.(6)]. In the cases where this was not possible the resonance energies and cross-sections are quoted to only one decimal place. The notation 6.95( -7) signifies 6.95 x lo-’. P P248 Predissociation of the Ar- HD van der Waals Molecule 501------ 3875 3885 3895 3905 0 3865 photon energy/cm-’ Fig.4. Total Ar-HD photodissociation cross-section for the transition J” = 1, n”= 1, u” = 0, j ” = O + J ’ = 2 . ( a ) T(n’=O), ( b ) P(n’= l ) , ( c ) R(n‘= 1) and ( d ) T(n’= 1). transition energy. The effects of all three essential ingredients of a photodissociation process, i.e. ( 1) the ground-state wavefunction, (2) the dipole-momentum function and (3) the upper-state dissociative continuum wavefunction, have been fully included in the calculations. As a result quantitative photodissociation cross-sections and lineshapes have been calculated. Previous calculations on this system have only treated the scatter- ing in the upper state manif~ld.’~*’~ Our calculations show that for rotational predissoci- ation processes in the Ar-HD system these scattering calculations give reliable estimates of the line positions and widths.For a quantitative prediction of the photodissociation cross-sections, and for the modelling of the spectrum, the effects of the dipole-momentum function and of the ground-state wavefunction must be included, as has been done here. The present paper considers some of the individual photodissociation cross-sections which contribute to the overall infrared S,(O) absorption spectrum of Ar-HD. The overall spectrum has been discussed in a previous brief p~blication,~ where a comparison of computed and experimental spectra was presented. Computation of this spectrum involved taking the average of many different cross-sections, of the type presented here, over the thermal distribution of initial Ar-HD quantum states.The good agreement achieved in the predicted line positions7 and line width^'^"^ (see fig. 5 ) confirms that the potential of LeRoy and CarleyZ7 provides a good descriptionI. F. Kidd and G. G. Balint-Kurti 249 0 1 2 3 4 5 6 7 8 9 10 I‘ Fig. 5. Comparison of calculated (open symbols) and experimental (closed symbols) linewidths for the N (squares) and T (circles) branches of the S , ( O ) infrared absorption spectrum of Ar-HD. Table 2. Comparison of resonance energies, linewidths and photofragment quantum-state distribu- tions for selected resonance lines having final-state total angular momentum J’ = 5“ fraction of fraction of products in products in E/cm-’ r/cm-’ j ’ = O j ’ = 1 transitions proceeding through resonance state with quantum numbers J’ = 5, n‘ = 0, I’ = 3 N-branch transition (present work) -21 .650b 0.78 0.036 0.964 P-branch transition (present work) -21.651 0.78 0.030 0.970 Hutson and LeRoy17 -21.645 0.795 0.157 0.843 transitions proceeding through resonance state with quantum numbers J’ = 5, j ’ = 0, I‘ = 5 P-branch transition (present work) -14.200 0.30 0.147 0.853 R-branch transition (present work) -14.201 0.30 0.142 0.858 Hutson and LeRoy17 - 14.198 0.297 0.229 0.774 transitions proceeding through resonance state with quantum numbers J’ = 5, n’ = 0, I’ = 7 R-branch transition (present work) -5.289 0.54 0.052 0.948 T-branch transition (present work) -5.289 0.54 0.054 0.946 Hutson and LeRoy17 -5.287 0.536 0.157 0.843 All the intermediate resonance states have quantum numbers u’ = 1, j ’ = 2.The resonance energies are measured relative to the Ar+ HD( u = 1, j = 2) dissociation threshold.250 Predissociation of the Ar- HD van der Waals Molecule of the potential surface in the well region. The disagreement between theory and experiment' in the relative intensities of the lines indicates shortcomings in the dipole- moment function of Dunker and Gordon.** Qualitatively it seems that the range parameter pI2 in the dipole moment function should be increased. We thank M. Shapiro for valuable comments and collaboration in related research which has greatly contributed to the present work. We also thank the S.E.R.C. for the provision of computational facilities and I.F.K.thanks the S.E.R.C. for a studentship. References 1 A. S. Pines, and B. J. Howard, J. Chem. Phys., 1986, 84, 590. 2 J. M. Hutson and B. J. Howard, Mol. Phys., 1982, 45, 769. 3 K. C. Janda, Adv. Chem. Phys., 1985,60, 201. 4 D. D. Evard, F. Thommen and K. C. Janda, J. Chem. Phys., 1986, 84, 3630. 5 I. F. Kidd, G. G. Balint-Kurti and M. Shapiro, Faraday Discuss. Chem. SOC., 1981, 71, 287. 6 I. F. Kidd and G. G. Balint-Kurti, J. Chem. Phys., 1985, 82, 93. 7 I. F. Kidd and G. G. Balint-Kurti, Chem. Phys. Lett., 1984, 105, 91. 8 J. A. Beswick and M. Shapiro, Chem. Phys., 1982, 64, 333. 9 N. Halberstadt, Ph. BrCchignac, J. A. Beswick and M. Shapiro, J. Chem. Phys., 1986, 84, 170. 10 C. J. Ashton, M. S. Child and J. M. Hutson, J. Chem. Phys., 1983, 78, 4025. 11 J. M. Hutson, D. C. Clary and J. A. Beswick, J. Chem. Phys., 1984, 81, 4474. 12 M. S. Child and C. J. Ashton, Faraday Discuss. Chem. SOC., 1977, 62, 307. 13 G. E. Ewing, Faraday Discuss. Chem. SOC., 1982, 73, 325. 14 R. D. Levine, Quantum Mechanics of Molecular Rate Processes (Clarendon Press, Oxford, 1969). 15 R. G. Newton, Scattering Theory of Waves and Particles (McGraw-Hill, New York, 1966). 16 A. R. W. McKellar, Faraday Discuss. Chem. SOC., 1982, 73, 89. 17 J. M. Hutson and R. J. LeRoy, J. Chem. Phys., 1983, 78, 4040. 18 K. K. Data and S-I. Chu, Chem. Phys. Lett., 1983, 95, 38. 19 G. G. Balint-Kurti and M. Shapiro, Chem. Phys., 1981, 61, 137. 20 M. Shapiro, J. Chem. Phys., 1972, 56, 2582. 21 G. G. Baht-Kurti and M. Shapiro, Adv. Chem. Phys., 1985, 60, 403. 22 E. Segev and M. Shapiro, J. Chem. Phys., 1983, 78, 4969. 23 E. Segev and M. Shapiro, J. Chem. Phys., 1982, 77, 5604. 24 M. Shapiro and R. Bersohn, J. Chem. Phys., 1980, 73, 3810. 25 G. N. A. van Veen, T. Baller, A. E. de Vries and M. Shapiro, Chem. Phys., 1985, 93, 277. 26 M. Shapiro and H. Bony, J. Chem. Phys., 1985, 83, 1588. 27 R. J. LeRoy and J. S. Carley, Adv. Chem. Phys., 1980,42, 353. See also U. Buck, H. Meyer and R. J. 28 A. M. Dunker and R. G. Gordon, J. Chem. Phys., 1978, 68, 700. 29 W. Kolos and L. Wolniewicz, J. Chem. Phys., 1965, 43, 2429; 1968,49, 404; 1964, 41, 3663. 30 I. F. Kidd, Ph.D. Thesis (Bristol University, 1984). 31 A. R. W. McKellar, W. Goetz and D. A. Ramsay, Astrophys. J., 1976, 207, 663. 32 I. F. Kidd and G. G. Baht-Kurti, to be published. LeRoy, J. Chem. Phys., 1984, 80, 5589 for an improved potential surface. Received 9th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200241

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. Soc., 1986,82, 251-260 Vibrational Predissociation of the Nitric Oxide Dimer Michael P. Casassa, John C. Stephenson and David S. King* Molecular Spectroscopy Division, National Bureau of Standards, Gaithersburg, Maryland 20899, U.S.A. Details of experimental measurements of the total energy distribution and time dependence of the vibrational predissociation of the nitric oxide dimer excited to v1 are presented. Energy-disposal measurements indicated the fragments are described by an average rotational energy (ER) = 75 cm-', full equilibration of the lambda doublet species, approximately equal popula- tions in both spin-orbit states, no significant degree of alignment, an isotropic flux distribution and an average kinetic energy of (EK) = 400 cm-' per frag- ment.Although ca. 75% of the available energy went into the fragment translation, the predissociation proceeded at a rate > lo8 s-'. Vibrational predissociation is observable for van der Waals (vdW) molecules since a single quantum of vibrational excitation in a constituent of such a cluster generally exceeds the vdW binding energy of the complex. Thus, vibrational excitation leads to the rupture of the weak vdW bond. Herein lies the appeal of these systems as models for vibrational dynamics: rich and dramatic photochemistry is turned on by excitation to low-lying vibrational levels. The resulting vibrational energy flow and dissociation, proceeding from a well defined state along a single potential-energy surface, can be compared to theoretical predictions. A combination of time-resolved and final-state-resolved measurements are needed to thoroughly characterize the predissociation dynamics of these clusters. Experimental observables include product kinetic, rotational and vibrational energy distributions, vector velocity and angular momentum distributions and dissociation lifetimes.There have been many studies of vibrational energy flow within electronically excited states of vdW molecules. Owing to experimental difficulties, however, most studies involving ground electronic states of vibrationally energized clusters have been limited to the measurement of infrared absorption and photodissociation spectra.' In this paper, experiments are discussed which utilize molecular beams and pulsed- laser techniques to characterize the rates and mechanisms important in the predissoci- ation of the nitric oxide dimer excited to the ( u1 = 1 ) lever of the electronic ground state.NO Dimer The structure of the ground state of the nitric oxide dimer has been determined by microwave spectroscopy2 to have C,, symmetry with a 2.24 A N..-N separation and a 99.6" ONN angle. The two NO stretching fundamentals of this structure have been observed at 1870 and 1789 ~ m - ' . ~ ' ~ These are characterized as the u1 symmetric stretch and the u4 antisymmetric NO stretch, respectively. The high-resolution spectrum of the u4 band has recently been p~blished.~ That of ul has not yet been reported since it lies near the NO fundamental at 1876 cm-'; however, the u,+ u4 combination band at 3630 cm-' has been ~haracterized.~ Brechignac et aL5 reported photodissociation of nitric oxide clusters following excitation in the u4 band region.In our laboratory, photodissociation of the dimer and 25 1252 Vibrational Predissociation of (NO), larger clusters has been observed following excitation of the vl band at 1869.79 cm-'.6 The photochemistry which is observed is: hv 7 (NO), - (NO);(v,) - 2NO(J,R,A)+EK where final states are designated by their total angular momentum J, the electronic angular momentum 0, and the lambda doublet component A. EK is the relative kinetic energy of the fragments and r = kili is the lifetime of the energized complex. The (NO), vdW bond energy Do is ca. 700 ~ m - ' , ~ , ~ so that photodissociation produces ca. 1000 cm-' of excess energy to be absorbed by product degrees of freedom and relative kinetic energy.Owing to the small NO rotational constant ( B = 1.7 cm-'), energy-gap argu- ments' would lead to the expectation of a long-lived vibrationally excited dimer. Experimental Van der Waals complexes were formed by expansions of gas mixtures through the 0.75 mm diameter nozzle of a pulsed free jet. The valve was of the Gentry-Giese design and produced molecular pulses of 70 ps full-width at half-maximum (f.w.h.m.) duration. The complexes were excited by the pulsed output of a hybrid, line-tunable CO, laser.7 The infrared pump pulses were of TEMoo single longitudinal-mode character. The pulse length was controlled electro-optically to be a temporal square wave of either 50 or 2 ns duration.Since for the nitric oxide dimer excitation wavelengths in the 5 +m spectral region are required, the temporally modified i.r. output was frequency-doubled in AgGaS,. Conversion efficiencies of ca. 1% were obtained. The pump laser traversed the molecular beam at a distance of 15 nozzle diameters downstream. At a backing pressure of 65 PSIA,? the on-axis molecular beam density in this region was ca. 10'' ~ m - ~ . At some short time after the excitation pulse (ie. 40* 10 ns), the nitric oxide fragments formed from the vibrationally excited vdW complexes were probed by laser-excited fluorescence techniques (LEF).' The probe laser was a frequency-doubled Nd3+:YAG pumped dye laser with a 9 ns f.w.h.m. duration and either a 0.3 or 0.017 cmi' f.w.h.m. bandwidth at 44200cm-'.When tuned to resonance with an A NO(V'= 0; J ' ) + X NO( V = 0; J, R, A) transition, the resulting LEF intensity is proportional to the density of NO fragments in the level (J, R, A) at the time td during which the probe laser passed through the beam chamber. The fluorescence was collected byf/0.8 optics, passed through spectral filters to discriminate against laser scatter and a spatial filter to define the viewing region and detected by a solar blind (CsTe) photomultiplier tube. The LEF signals were recorded using a gated integrator and were normalized shot-by-shot to probe laser energy. The state distributions of the fragments were determined by scanning the wavelength of the probe laser. By sufficient narrowing of the bandwidth of the excitation laser (ie.to 0.017 cm-') the kinetic energy of the fragments was determined by Doppler profile measurements. The i.r. pump and U.V. probe lasers were aligned to be either collinear or at right angles. The Gaussian i.r. beam radius was Ri.,. = lo-* cm. In the colinear experiments, the radius of the probe laser was smaller than that of the i.r. beam, RU,". = 5 x cm, such that the results obtained in this configuration correspond to photolysis products formed by pulses of uniform known intensity. In the perpendicular configuration, independent control over both the orientation of laser electric vectors and propagation directions allows for the assessment of fragment flux distributions and possible alignment. Unless stated otherwise, the results reported herein were obtained with a delay fd = 40 ns between the leading edges of the pump and probe laser pulses.t 1 PSiA = 6940 Pa.M. P. Casassa, J. C. Stephenson and D. S. King 253 Results Chemistry A recurring question in the study of vdW complexes is the identity of the carrier of the bands. A quadrupole mass spectrometer (QMS) was used in a differentially pumped molecular beam chamber to characterize the monomer/ dimer/polymer contributions for mixtures of NO in He and HZ. During the 2 Hz valve operation the steady-state background ressure in the source chamber was < Torr;? inside the detector chamber it was < 10- Torr. Expansion gas mixtures were adjusted to obtain compositions which maximized the dimer : monomer and dimer : polymer ratios. The QMS utilized an electron impact ionizer and was operated with electron energies of 100 eV for the He expansions and 62 eV for H,.The output of the QMS was amplified and accumulated in a signal averager at 5 ps per channel resolution. The areas under the peaks were digitally integrated for analysis. The pressure dependence of the m/ e = 30 monomer signal was linear with backing pressure for Po < 65 PSIA, becoming sub-linear above this pressure. In addition, the m/ e = 30 signal exhibited a linear dependence on the NO mole fraction for a variety of mixtures within the range < XNO < 3 x lo-*. For He expansions with backing pressures of 27 < Po (PSIA) < 125 the m/ e = 60 feature demonstrated a quadratic depen- dence on XNO, as required from a kinetic standpoint for the mole-fraction scaling of the dimer.This quadratic dependence on XNO was also observed in the LEF photolysis- yield measurements. Pressure-dependence data for the m / e = 60 signal in expansions of 0.34% and 1 YO NO/He and 1 YO NO/ H2 showed Pi.7*.3 scaling. This further confirms that the m/ e = 60 peak represents the dimer species (to the extent that dimer formation is controlled by three-body collisional events, the formation of dimeric species should ideally show PA behaviour). The observed pressure dependence of the m/ e = 90 'polymer' feature was ca. PA.". We also measured the pressure dependence of the LEF-detected photodissoci- ation-yield experiments, hoping to confirm that dimer photolysis was the predominant source of NO product. Results of such LEF yield us.Po experiments (for the He expansion) also gave ~i.~*.~ scaling. P Spectroscopy Although high-resolution spectroscopy is the best means to identify vdW complexes and to illuminate their structures, this is not the primary aim of these experiments. Indeed, the line-tunable laser source used in these experiments does not lend itself to undertaking spectroscopic studies. Survey photodissociation spectra are, however, required to locate the appropriate vdW absorptions. Photodissociation spectra of the (NO), v 1 transition are presented in fig. 1. The 5 p m i.r. pump was of 50 ns duration, with a constant pulse energy of 55 pJ, corresponding to a uniform intensity of 3 x lo6 W cm-2 in the region probed by the U.V. laser. This figure includes results for two different expansions: a 1% NO-He mixture used at a backing pressure of 85 PSIA (circles) and a 0.67% NO-H2 mixture at 125 PSIA (crosses).These expansion conditions were chosen because they exhibited little-to-negligible polymer photodissociation at 1870 cm-' (see below). The two spectra were normalized to each other at 1869.79 cm-' [the excitation frequency of the frequency-doubled P(30) transition of the C02 laser]. Only at 1865.9 cm-' [frequency-doubled P(32)] is there any significant difference in the respective photodissociation spectra. The H2 expansion is 'warmer' than that with He, the uncomplexed NO being described by rotational temperatures of 5 K and < 1 K, respectively. The apparent difference in the photodissociation spectra may represent t 1 Tom= 101 325/760 Pa.254 Vibrational Predissociation of (NO), - + ;f o o p $ 0 I I I t + , P Q 01 0 , + 1870 1890 excitation frequencylcm-' Fig.1. Photofragmentation spectra of the nitric oxide dimer. Results are shown for two different expansions, with relative fragmentation yields normalized at 1869.79 cm-' [frequency-doubled P(30)]. E,,, = 55 pJ. 0, 1% NO-He, 85 PSIA; +, 0.67% NO-H,, 125 PSIA. contributions to the spectra by warmer dimers, or it may arise from nitric oxide complexes with H,; this point has not yet been fully explored. The intensity dependence of the photolysis yield was measured with the probe laser tuned to probe fragments in the J = 1.5-4.5 levels of the F2 spin-orbit state, and aligned colinear with the 1870 cm-' pump source. Results obtained using an expansion of 1% NO in He at Po = 85 PSIA was fitted, using a linear least-squares procedure, to an 1°.67 power dependence for 2 x lo4 < I/ W cm-, < 10'. Final-state Distributions Final-state distributions will be presented for two different expansions excited by the frequency-doubled output of the CO, laser at 1870 cm-': 1% NO in He at a backing pressure of 85 PSIA and 0.67% NO in H2 at 125 PSIA.These conditions give rise to photolysis fragments that can be attributed to the fragmentation of the dimer, with <5% contribution from polymer or complexes with carrier gas (see below). Rotational excitation spectra such as shown, in part, in fig. 2 were recorded with counter-propagating lasers to assure probing photolysis events occurring in regions of constant uniform intensity.The electric vector of the probe laser was set, using a half-wave retardation plate, to the magic angle to remove any polarization effects from these measurements. The observed linewidths in these excitation spectra represent the U.V. laser bandwidth. The spectra were recorded at a probe-wavelength scan rate corresponding to 8 channel- steps across a laser resolution element (f.w.h.m.). The area under each well resolved rovibronic transition was numerically integrated and divided by the appropriate spectro- scopic linestrength to obtain populations in each (J, a) level. Spectroscopically, P and R branch transitions ( A J = f 1, triangles) probe the A+ lambda-doublet species, whileM. P. Casassa, J. C. Stephenson and D. S.King 255 excitation laser frequency 100 200 300 400 rotational + spin-orbital energy/cm-' Fig.2. Portion of a photofragment excitation spectrum, probing fragments formed in the F2 spin-orbit state, and the resulting fragment-state distributions. An expansion of 1% NO in He at 85 PSIA was used. The filled symbols represent populations in levels in the higher-lying F2 spin-orbit state; the open ones, the Fl state. 0, 0, Populations in the A- lambda-doublet species; A, A, the A+ species. Q branch transitions (AJ = 0, circles) probe the A- species. (The lambda-doublet designations distinguish relative orientations of nuclear and electronic angular momentum.) The data for states of energy <450 cm-' (>97% of all population lies in these levels) are well fitted by the rotational temperatures Tr( Fl) = 101 * 11 K and Tr( F2) = 112 f 12 K; where the lower ( Fl) and higher ( F2) energy spin-orbit states were considered as separate ensembles.The ratio of total population in the two spin-orbit states is F2/Fl = 0.9 f 0.2. Fitted curves for these population distributions are drawn through the data. The population distributions for the two aforementioned expansions were essentially indistin- guishable. Although the effects of state-changing collisions became apparent at long time delays, the reported results were invariant for the shorter time delays (using the 2 ns pump-laser pulse) of 10- 150 ns. In fig. 2 the lambda-doublet and spin-orbit components are distinguished through the use of circles/triangles and filled/open symbols.It is apparent from this figure that there is no significant difference in lambda-doublet populations; they are populated statistically (these species are essentially isoenergetic). The two spin-orbit states differ in energy for a given value of J by an amount ca. equal to the spin-orbit separation, 121 cm-'. The relative total populations in these two spin-orbit states are substantially different from the value expected if the spin-orbit and nuclear rotational degrees of freedom were equilibrated, as observed for NO fragments formed from a number of thermal processes. If this condition were achieved, the populations in the F2 state (solid symbols) would have been a factor of five lower than observed. That the ratio of spin-orbit populations is near unity implies a strong256 Vibrational Predissociation of (NO), Fig.3. Doppler profile of NO ( J = 3.5, F2) fragments formed from the v l vibrational predissoci- ation of the nitric oxide dimer. The rest frequency vo = 44 093.39 cm-'. spin correlation in the dissociation mechanism. It is consistent with reaction proceeding Many direct electronic ph_otodissociation reactions result in an alignment of the For the NO A-X band system, high-J Q-branch transitions are polarized parallel to the axis of nuclear rotation. Thus a measure of the polarization dependence of the LEF signal can in principle map out the alignment of the rotating fragments, i.e. their rn, distribution. Using counter-propagating lasers and monitoring LEF signal intensities from fragments in levels J<9.5 the electric vector of the probe laser was rotated, with respect to the electric vector of the pump laser, through 180" using a half-wave retardation plate.Slight corrections to the observed behaviour were required owing to a small polarization dependence of the apparatus response. These were made immediately after the alignment measurements by flowing NO through the chamber and repeating the polarization measurements on this isotropic sample. The final results indicated a polarization anisotropy" IRI < 0.1; i.e. no significant alignment of the fragments. Kinetic-energy distributions and fragment flux distributions were measured with the lasers aligned perpendicular to each other and to the molecular-beam flow axis. Doppler profiles were measured with a U.V.probe-laser bandwidth of 0.017 cm-'. Fig. 3 presents a typical Doppler profile obtained for an expansion of 0.67% NO in H2 at a backing pressure of 125 PSIA. The probe laser was tuned to the Q2,(3.5) transition (Eint = 145 cm-'), and aligned with its direction of propagation perpendicular to the electric vector of the pump laser. This Doppler profile is nearly rectangular in shape with an f.w.h.m. of 0.165 cm-'. Essentially identical Doppler profiles were recorded for an expansion of 1% NO in He at 85 PSIA in this geometry and for both expansions in a geometry where the probe laser propagated in a direction parallel to the electric vector of the pump laser. Anisotropy in the fragment flux (as might be expected if the vibrational predissoci- ation process were prompt) should appear as a pump-probe geometry dependence in the observed Doppler profiles.The similarity of Doppler profiles obtained with the probe laser propagating both parallel and perpendicular to the electric vector of the pump laser indicated that the fragment flux was isotropic in space. This is consistent with the predissociation occurring on a timescale longer than the ca. 35 ps rotational (NO),(%)+ NO(F*)+NO(F,).M. P. Casassa, J. C. Stephenson and D. S. King 257 0: 2 1'0 laser frequency/cm-' -0.2 Fig. 4. Doppler profile of NO ( J = 8.5, F , ) fragments formed from the vibrational predissociation of (NO),, for x 2 3. The rest frequency uo = 44 208.38 cm-'. period of the dimer. More importantly, this spherical symmetry in the flux allows for the derivation of a fragment velocity distribution from these two sets of Doppler profiles.Computer simulations of Doppler profiles taking into account the actual laser resolution, pump-laser photon energy, and final-state distributions, assuming the dimers in the expansion to be essentially equilibrated with the beam temperature ( T = 1-5 K), and allowing the internal energy of the cofragment to be randomly chosen from the values available gave good fits to the observed f.w.h.m. = 0.165 f O . l cm-' top-hat Doppler profiles. This gives an average per-fragment kinetic energy of 400 * 50 cm-', correspond- ing to a vdW bond energy of 800* 150 cm-'. Although the observed dependences of NO-fragment LEF and m / e = 60 signals on NO mole fraction and backing pressure suggest these results are due to the vibrational predissociation of the nitric oxide dimer, it is the observed Doppler profiles that make the strongest argument for this.Photodissociation of either NO-He or NO-H2 species can be excluded based on conservation of energy and momentum. The resulting Doppler profiles from these species would be top-hat in character with f.w.h.m. of 0.13 and 0.095 cm-', respectively. Upon increasing the backing pressure with the 1% NO in He expansion above 85 PSIA, the observed Doppler profiles began to show evidence for the presence of fragments formed from the vibrational predissociation of polymer species. Fig. 4 shows a Doppler profile for an expansion with 3% NO in He at 135 PSIA. This profile was Gaussian in shape with a f.w.h.m.of 0.090cm-', was independent of pump-probe geometry and corresponded to an average per fragment kinetic energy of 250* 50 cm-'. Under these expansion conditions the NO fragments were characterized by a rotational temperature of T, = 85 * 20 K. In contrast to the dimer results, the spin-orbit and nuclear rotational degrees of freedom appeared to be equilibrated, with only 15% of the total population being in F2 states. The average per fragment internal energy was therefore 75 f 20 cm-' for an average per fragment energy release of 325 cm-'. If the dissociation258 0 z 0 Vibrational Predissociation of (NO), 0 20 time delay/ns Fig.5. Time dependence of the NO ( J = 3 . 5 , F2) fragments formed from the v1 vibrational predissociation of the nitric oxide dimer.The photolysis pulse duration was 2ns. (-) The instrumental response function, (- - -) the anticipated fragment appearance behaviour if the dimer were to dissociate with a 20 ns lifetime. reaction we monitor under these conditions were (NO), ---* 3 NO, conservation of energy would imply the trimer bond energy to be 900 cm-'. There is, however, no conclusive evidence that we are monitoring either fragmentation of the trimer, nor that this is the preferred fragmentation channel. The above fragmenta- tion mechanism, (NO), -+ NO + (NO):, and fragmentation of larger polymers would all allow the measured NO fragments to have a wide range of kinetic energies and therefore exhibit Gaussian-like Doppler profiles (unlike the results from the more- restricted dimer dissociation, which gave a narrow kinetic energy distribution).Although most dimer has been converted to trimer/polymer in the 3% NO in He expansion at 135 PSIA (as evidenced by the complete transformation of Doppler profiles), the mass spectrometer m / e = 60 feature and NO fragment LEF signals continue to show Pt7 and quadratic mole-fraction scaling. Rates The nanosecond laser measurements have shown the (NO), vl dissociation to be prompt, occurring with a lifetime <lo-* s. Fig. 5 shows results obtained with counter-propagating 2ns i.r. dissociation pulses and 9 n s 'Gaussian' U.V. probe pulses. Both lasers were detected with the same fast LN,-cooled Au/Ge detector, therefore the absolute timing of the two pulses was accurately known. The data points in the figure are the average of many shots at each time delay.The time delay between arrival of pump and probe pulses was varied electronically in 1 ns increments. The timing jitter during data acquisition was typically *2ns. The solid curve drawn through the data in this figure corresponds to the system response obtained by integrating the known laser pulse profiles and assuming instantaneous dissociation. The dashed curve is drawn for the expected time-dependent behaviour of the fragment LEF( t ) signal if the vibrationally excited dimer dissociated with a 20ns time constant. The observed signal rises much faster than this expectation and very closely follows the system response function, indicating a dissociation lifetime <lo-* s. Discussion Our LEF-based energy-partitioning measurements are most readily explained as arising from the photolysis of the NO dimer.Contributions to the fragment LEF signal dueM. P. Casassa, J. C. Stephenson and D. S. King 259 to the dissociation of species such as NO-He or NO-H2 can be excluded by conservation of energy and momentum. Under conditions where there is substantial polymer in the expansion, i.e. as indicated by the m/ e = 90 intensity, the photodissociation spectrum changes due to contribution from the dissociation of these (NO), species. Specifically, the product Doppler profiles become narrow and 'Gaussian' in character and the spin-orbit ratio F2/F1 drops from a value near unity to a value of 0.15 to 0.2. This leads us to assign the observed Doppler top-hat profiles and equilibration of spin-orbit states to characterize dimer-only photolysis.Comparison of the NO-fragment yield results to the LEF intensities of the uncomplexed NO monomer implies that ca. 5% of the monomer can be complexed prior to substantial formation of polymers. There is no evidence in the MS results for the presence of either (NO),-He or (N0),-H2. However, the photolysis of these species could be consistent with our energy partitioning results ( i. e. conserving energy and momentum), requiring the dissociation mechanism (NO),( u,)-He + NO( J, R, A) + NO-He, for example. The results clearly indicate that the vibrationally excited dimers dissociate at a rate > lo8 s-' to produce fragments wherein ca. 75% of the available energy goes into translational energy. Although the isotropic flux distribution of the fragments suggests that the vibrationally excited dimer survives for at least one rotational period (e.g.> 35 ps at these beam temperatures), this indirect, lower-limit determination depends on the assumption that non-rotating dimers would give rise to an anisotropic distribution. By analogy to direct electronic photodissociation results, wherein fragment alignment and non-statistical distributions of lambda doublets were observed (reflecting electronic symmetry constraints on the dissociation pathways)," the absence of fragment alignment and the statistical distribution of lambda doublets support the notion that the vibra- tionally excited complex survives several vibrational periods. The measured ratio of fragments formed in the two spin-orbit states was 0.9k0.2.There are two ways to evaluate this number. The first is to consider there to be no correlation between spin-orbit states of the two separating fragments. The ratio of populations in the spin-orbit states could then be described in terms of a 'spin-orbit temperature' T,, = 1650 K. Alternatively, a strong spin-orbit correlation constraining the separation of the two fragments along a potential-energy surface asymptotically going to NO(F,)+ NO(F,) would give a value of 1.0 for this ratio, consistent with the observed ratio. This mechanism would imply that there is at least a 121 cm-' barrier for dimer formation. Menoux et aL4 have reported the results of i.r. intensity measurements of the dimer u4 fundamental and ( ul + u,) combination band in a static cell at temperatures of 118 to 138 K.From Van't Hoff plots a value of the dimer heat of formation of -2.25f 0.25 kcal mol-' (at 128 K) was derived. This corresponds to a vdW bond energy Do = 590 f 90 cm-'. From the results of our energy-distribution measurements, conservation of energy directly gives a value of Do = 800* 150 cm-', in fair agreement with the i.r. intensity measurements. Dissociation rates and energy partitioning following u4 excitation at 1789 cm-' and excitation of the ul + u4 combination band3.4 at 3630 cm-' are currently being explored. Especially interesting will be the comparison of results obtained following excitations of the nearly isoenergetic u4 band, with its i.r. transition moment parallel to the vdW bond, and the perpendicular-polarized u1 band.The two vdW vibrational modes of (NO),, which correspond to nuclear displacements which break the vdW bond, are u2 (263 cm-') and v3 (170 cm-'). Both have the same CZv point group Al symmetry as does u l ; u4 has B2 ~ymmetry.~ The lowest-energy vdW mode, the u6 torsion (88 cm-'), has A, symmetry. Conservation of symmetry upon dissociation would demand that dimers excited to either v1 or u4 relax through channels of different total symmetry. If IVR does not give a statistical (i.e. random) distribution of energy on the timescale of dissociation, then this might give rise to different fragment rotational and spin-orbit260 Vibrational Predissociation of (NO), state distributions and different product appearance rates for v1 us. v4 excitation. Excitation of the vl + v4 combination band at 3630 cm-' will provide the complex with sufficient excess energy to produce vibrationally excited fragments. Such excitation is readily determined by our LEF measurements and is suggested by theory to be the preferred dissociation channel. References 1 For a review see K. C. Janda, Adv. Chem. Phys., 1985, 60, 201. 2 C. M. Western, P. R. R. Langridge-Smith, B. J. Howard and S. E. Novick, Mol. Phys., 1985, 44, 145; 3 C. E. Dinerman and G. E. Ewing, J. Chem. Phys., 1970,53, 626. 4 V. Menoux, R. LeDoucen, C. Haeusler and J. C. Deroche, Can. J. Phys., 1984,62, 322. 5 Ph. Brechignac, S. DeBenedictis, N. Halberstadt, B. J. Whitaker and S. Avrillier, .I Chem. Phys., 1985, 6 M. P. Casassa, J. C. Stephenson and D. S. King, J. Chem. Phys., 1986,85, 2233. 7 J. C. Stephenson and D. S. King, J. Chem. Phys., 1983, 78, 1867. 8 D. S. King and J. C. Stephenson, J. Chem. Phys., 1985, 82, 2236; Chem. Phys. Lett., 1985, 114, 461. 9 R. Vasudev, R. N. Zare and R. N. Dixon, J. Chem. Phys., 1984,80, 4863. S. G. Kukolich, J. Mol. Spectrosc., 1981, 98, 80. 83, 2064. 10 P. Andresen, G. S. Ondrey, B. Titze and E. W. Rothe, J. Chem. Phys., 1984, 80, 2548. Received 19th May, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200251

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

Faraday Discuss. Chem. SOC., 1986, 82, 261-273 Photodissociation of Negative Ions and their Clusters A. W. Castleman Jr," C. R. Albertoni, Kurt Marti,t D. E. HuntonS and R. G. Keesee Chemistry Department, 152 Davey Laboratory, The Pennsylvania State University, University Park, 16802 Pennsyluania, U.S.A. Studies of the dissociation dynamics of cluster ions provide insight into the process of energy disposal for mass-selected species. Detailed investigations are reported for two systems; one, CO,(H,O), (O< n <3), comprising a heteromolecular system and the other, (SO2);, a homomolecular anion. In the case of COT, the unhydrated parent ion is observed to have a bound electronic excited state, through which absorption of a second photon proceeds to a repulsive state, leading to the ejection of 0-.Cluster dissoci- ation is initiated by the ,A, + ' B , transition from the ground to a weakly bound excited state of the core ion, leading to the loss of all water molecules within the time of observation. This is in direct contrast to collisional dissociation processes, which lead largely to the loss of a single water molecule per collision. In the photodissociation of COY, COi(H20) 1,2,3, and ( SOz) r, considerable excess energy is partitioned into relative translation of the photoproducts. Through studies of energy release in (SO,), with photons of parallel and perpendicular polarization, evidence has been obtained that the lifetime of the complex preceding photodissociation is less than a rotational period. The implications of the findings are discussed in terms of phase-space theory.Photodissociation spectroscopy is a valuable technique for probing the spectroscopic and dynamic structure of reactive or weakly bound species such as negative ions and ion clusters."* Study of these weakly bound systems offers an opportunity to observe solvation effects, compare the behaviour of members of homologous series and investi- gate intramolecular energy transfer. A great variety of new questions dealing with the dynamics and the mechanisms of the photodissociation process itself are raised by such studies. The identity of the fragments into which the cluster dissociates following laser excitation and the ways in which initial energy is partitioned among the various degrees of freedom of the fragments are of particular interest.An advantage of studying ion clusters is the relative ease of incorporating methods to determine the energy release upon dissociation. This greatly enhances the power of the technique, since analysis of the kinetic energy distributions of the fragment ions indicates where the excess energy of the photons is channelled by the dissociation process and, hence, helps identify the specific steps in the dissociation mechanism. Vibrational predissociation can occur when one of the molecular subunits absorbs an amount of energy larger than the bond dissociation energy of the cluster. Coupling between the core vibrational modes and the cluster vibrations allows energy to move from one mode to the other throughout the cluster. Most cluster photodissociation experiments have involved neutral van der Waals (vdW) molecules in which the individual moieties are bound together by very weak dipole-dipole, dipole-induced- dipole or dispersion forces.Generally, vibrational predissociation, in which a small t Ciba-Geigy, Bern, Switzerland. $ Permanent address: Air Force Geophysical Laboratory, Hanscom Air Force Base, Massachusetts, U.S.A. 26 1262 Photodissociation of Negative Ions and their Clusters amount of energy is transferred from the initially excited mode of the cluster to the cluster bonds, is the observed dissociation mechanism. In most such cases, the energy associated with one vibrational quantum in a molecular entity of the cluster exceeds the dissociation energy of the cluster. Though vibrational predissociation of vdW molecules is commonly observed, energy- release measurements in these systems are rare.However, energy-resolved detection of the photofragments in infrared, single-photon dissociation of benzene5 and water clusters6 has been accomplished. The most probable dissociation channel deposits all excess energy into vibration and rotation of the fragments rather than into translation. The probability of observing a dissociation channel with energy Et in translational motion of the fragments is found to decrease exponentially as exp ( - E,/E,); Eo is generally less than 0.01 eV. Two independent theoretical treatments of the vibrational predissociation process in vdW dimers also predict that the dissociation channel of highest probability is the one that deposits the least energy into relative translation.Jortner and Beswick7 describe a distorted-wave or energy-gap model in which the coupling between the initial and final states is strongest when the energy difference between the states is small. Ewing,* who has given particular consideration to hydrogen-bonded dimers, has employed a momentum-gap model. The overlap between the initial bound state of the dimer and the plane-wave representation of the final state of the dissociated fragments is greatest when the relative translational energy of the photofragments is zero. This paper presents results of studies of the dissociation dynamics of mass-selected cluster ions using an intracavity dye laser pumped with an argon-ion laser. Detailed investigations are reported for two systems, one composed of COY and its hydrates and a second involving (SO2);.The bonding of all of these cluster anions exceeds the energy associated with one quantum of vibration in the core ion representing the chromophore. In each case, photodissociation leads to considerably more energy being partitioned into translation than expected based on statistical considerations of phase-space theory. Experimental The apparatus used for energy-resolved photodissociation spectroscopy of mass-selected cluster ions has been described in detail elsewhere.’ It consists of an ion source, a system of electrostatic ion optics to control the position and energy of the ion beam, a Wien velocity filter to mass-select a particular species for investigation, an argon-ion laser pumped tunable dye laser crossing the ion beam perpendicularly, a triple screen retarding field energy analyser, a quadrupole mass spectrometer and associated signal acquisition and control electronics.A gas mixture chosen to give the ions of interest is introduced into the source, which is held at a fixed pressure. The filament temperature is increased to initiate electron emission and concomitant ion production. The ions effusing from the source are accelerated, collimated, mass-selected and focused into the intracavity region of the dye laser. Photodissociation occurs in the interaction region, which is surrounded by a cylindrical screen held at a well defined electrical potential. The dye laser cavity has been extended to a length of 1 m to include the ion-beam apparatus.In the SO2 (SO,) experiments a model 310A Spectra Physics polarization rotator was also added to the dye cavity. Rhodamine 6G in the dye laser provides light between 565 and 640 nm when pumped with the 514.5 nm line of the argon-ion laser; the intracavity power is typically 20-25 W. The laser wavelength and intensity are monitored with the small amount of light that leaks through the high-reflectivity mirror. The bulk of this light is directed into a Spectra Physics model 404 power meter and a fraction is directed into a MacPherson model 255 monochromator. The monochromator is calibrated with the 632.8 nm line of an HeNe laser and is accurate to 0.2 nm. A Cary 219 spectrometer isA. W. Castleman et al. 263 used to measure the absorbance spectrum of the high-reflectivity mirror.This absorbance is used to convert the measured leakage power at each wavelength into intracavity power. At the interaction region, the dye laser beam is 1.3 mm in diameter, so the laser flux is slightly less than 2 x lo3 W cm-2. A standard Coherent three-element birefringent filter with a specified bandwidth of 50 GHz is used to control the laser wavelength. A computer-controlled stepping motor is directly coupled to the micrometer driven birefrin- gent filter, allowing automatic control of the laser frequency. A chopper positioned between the argon and dye lasers is synchronized with the data-collection electronics and permits continuous collection of a signal and background channel. The intensities of parent ions and all photofragment ions are monitored by the quadrupole mass spectrometer as a function both of laser frequency and ion kinetic energy in order to determine the spectroscopic structure of the parent ions and the dynamics of the dissociation process.In order to perform an energy analysis, the two outer screens of the energy analyser are held at the same potential as the surrounding ion optical elements, while the centre screen is scanned over the range of repulsive potentials. Only ions whose energies are equal to or greater than the centre potential are able to pass through the analyser and be detected; all other ions are repelled. This experiment yields the integral of the laboratory frame energy distribution. The actual energy distribution is generated by numerically differentiating the raw data using least-squares polynomial smoothing.'OJ Collision-induced dissociation (CID) of the parent ions is the major source of background 'noise' in the photodissociation experiments. The CID mechanism is confirmed by observing the increase of the laser-off channel intensity with increasing pressure in the vacuum chamber. It is important to note that a clear distinction is made between processes that do and do not involve laser excitation of the ions by the continuous monitoring of laser-on and laser-off channels. Results and Discussion co, In the photon energy range 1.95-2.2 eV, photodissociation of COT leads to 0- and C02 fragments. The photodissociation spectrum obtained with our instrument shows a well defined sharp structure, which reproduces the spectra obtained in earlier The spectral structure is taken as evidence for excitation to a bound intermediate state.An important finding of the present study comes from analysis of the photodissoci- ation dynamics of Cog, which proves that there are two distinct dissociation mechanisms (see fig. 1). The two mechanisms are distinguished more by the time required for dissociation following excitation. In the first, rapid dissociation of the parent ions occurs within the field-free interaction region after laser excitation. In the second mechanism, laser excitation leads to an excited state of Cog that has a sufficiently long lifetime to survive the beam transit time from the laser interaction region to the energy analyser, a time on the order of 10 ps.Dissociation of this long-lived excited state occurs upon collision, after passage of the parent ions through the energy analyser. The nature of the laser excitation step in both mechanisms was investigated by measuring the dependence of the intensity of each mechanism on the laser wavelength. The spectra for the mechanisms are nearly identical, indicating that they share a common photon excitation step (see inset fig. 1). Hiller and Vestal14 have observed a two-photon power dependence for photodissociation of COT at a number of wavelengths. In order to confirm that our unimolecular fast dissociation is the same process observed by Hiller and Vestal14 and Moseley et a1.,l5 we have conducted several power studies and found identical results.264 Photodissociation of Negative Ions and their Clusters 1 I I I I 1 1 4 1 5 4 3 2 1 0 -1 -2 -3 retarding potential/V Fig.1. Energy analysis of 0- photofragments form COY. Step A: 0- photofragment produced by CAPD (discussed in text). These 0- ions have wavelength dependence shown in the inset A. Step B: 0- photofragments produced by TPDD (discussed in text). Wavelength dependence shown in inset B. Analysis of the kinetic-energy release distribution of the fast mechanism shows that the relative intensity of photofragments is peaked at zero total centre of mass fragment kinetic energy and drops off approximately exponentially to zero intensity at a kinetic energy release of ca. 0.5 eV. In addition to this main part of the distribution, there is a small increase in intensity in the forward scattered direction at higher kinetic-energy values.This is a real effect arising from the small step in the integral of the distribution due to collection of a small number of collision-assisted 0- fragments that dissociate before passage through the energy analyser. The fact that the distribution is peaked at a kinetic-energy release of zero indicates either that the angular distribution of photofragments is spatially isotropic or that the anisotropy favours scattering perpendicular to the beam axis. In view of the fact that an anisotropic distribution of photofragments has been observed,12 the projection of energy along the beam axis could be substantially smaller than the total energy released. Our data are consistent with a mechanism that deposits a relatively large amount of energy into relative translation of the photofragments. The total amount of energy available for partitioning into relative translation is the energy of the two 599 nm photons, 4.17 eV, minus the bond dissociation energy, 2.27 eV, leaving an excess energy of 1.87 eV.We observe that at least 0.4 eV is partitioned into relative translation, corresponding to at least 20% of the total available energy. The Wigner- Witmer rulesI6 indicate the number of COY electronic states that corre- late with each set of dissociation products and also the symmetry of each such state. The calculation shows that there are three electronic states of COT that correlate with 0-+CO,. These are the ,B1 ground state and two additional states of symmetries ,Al and 2B2. The Wigner-Witmer rules do not enable these states to be ordered energetically, nor do they allow a determination of whether they are bound or repulsive. The model of the electronic structure of COT that best explains the photodissociation data is shown in fig.2. For reasons to be discussed below, the three states correlating with 0- + C02 are thought to be the ground state, a ,A, intermediate weakly bound state [as identified by Moseley et aL12] and finally a 2B2 repulsive state. Our results support the existence of an intermediate state and so our model of the photodissociationA. W. Castleman et al. 265 \ c@- + c 4 3 >, 1 x 2 P E: 1 0 dissociation coordinate Fig. 2. Model of COT electronic surfaces. The two-photon direct dissociation (TPDD) mechanism involves steps ( l ) , (2) and (3).The collision-assisted photodissociation (CAPD) mechanism involves steps ( l ) , (4), (5) and a collision. See text for further details. mechanisms must include these features. In diagrams of these states, the horizontal dissociation coordinate axis is schematic, but the vertical energy axis is drawn to scale. The two-photon direct dissociation (TPDD) process observed in the present experi- ments is the same process seen in the low-background-pressure beam experiments conducted by Hiller and Ve~ta1.l~ Fig. 2 delineates the three steps that, in our view, offer the most reasonable account of this photodissociation mechanism. Photodissoci- ation is initiated by a 2A, t 2 B 1 bound-bound transition that carries the ion from the ground state to the intermediate weakly bound excited state.The sharp features observed in the photodissociation spectrum arise from the vibrational structure of the intermediate 2Al state. A fraction of the ions excited to the 2A1 state absorb a second photon through a 2B2 +- 2Al transition. Following this excitation to the repulsive surface, dissociation to the observed photofragments occurs within one vibrational period. The assignments of the symmetries of the two excited states involved in TPDD come from the necessity of dipole-allowed transitions between the states. In CZU symmetry, the selection rules are: 2A1 +- 2B1 x-polarized 2B2 +- 2A, y-polarized 2B2 +- 2Bl forbidden. The assignments given in fig. 2 represent the only combination of the three symmetries that alloys low-energy transitions between the states to occur.The A 'B2 state of C02 lies 5.7 eV above the ground state,16 clearly beyond the range of photon energies used in this experiment. 0- does not have a bound electronically excited state.17 The energies of excited metastable states of 0- are not known, but can be estimated from the fact that 0- is isoelectronic with F. The lowest-energy electronic excitation of F is 3s + 2 p at an energy of 12.7 eV.'* The analogous transition in 0- is266 Photodissociation of Negative Ions and their Clusters expected to be equally energetic. We conclude that neither the first excited state of CO, nor that of 0- is accessible within the range of photon energies employed. The C02 and 0- photofragments must both be in the electronic ground state, and so one of the three electronic surfaces correlating with C02 + 0- must be a repulsive surface.Neither Moseley and coworkers 1 2 , 1 3 nor Hiller and Vestal14 observed any photodis- sociation at photon energies below ca. 1.8 eV, suggesting that the intermediate state does not extend substantially lower in energy than 1.8 eV above the ground state of COY, though loss of overlap between the two states could also contribute to the lack of photon absorption at low energy. Along the dissociation coordinate, the intermediate state cannot extend higher in energy than its dissociation limit. The minimum depth of the intermediate well, therefore, is the difference between the energy of the dissociation limit and the energy at the bottom of the well, 1.8 eV.For asymptotic correlation with ground state 0- + C02, the well depth is no less than 0.47 eV, whereas correlation with the next-higher-lying CO,+O gives a minimum binding energy of the state of 2.3 eV. The extremely large binding energy predicted by the second possibility leads us to favour correlation with 0- + C02. We therefore make the assignment that the intermediate bound state involved in the TPDD mechanism is the third state that correlates with CO2+O- and has a well depth of ca. 0.5 eV. The assignment of 2A, symmetry to this state again arises from the necessity of dipole-allowed transitions from the ground state. It is important to note that the dominant cause of negative-ion excited-state instability, autodetachment to the neutral, is inoperative in the case of this ,Al state of COT owing to the very high electron affinity of 2.7 eV.19 Finally, we consider the identity of the final state of the second transition.Because we have assumed that direct excitation to the dissociation continuum is unlikely, the second photon transition must either lead directly to the repulsive state that correlates with 0- + C 0 2 or to a second bound excited state that is predissociated with respect to that repulsive state. Having assigned two of the three states that correlate with C02 + 0- to the 2B, ground and 2A1 first excited bound states, the third must be the requisite repulsive state with 2B2 symmetry. If a predissociative model is correct, the second, high-lying bound state must be accessible from the ground state with two photons in the range 1.8 to 2.4eV.The vibrational levels of the state must therefore span the entire range from 3.6 to 4.8 eV. This requirement makes it difficult to choose a reasonable asymptotic limit for the correlation of this state to fragments. Correlation with CO,+O, is the most likely possibility. This fragment ensemble, however, probably lies below the necessary 4.8 eV, and would not allow vibrational levels associated with the dissociation coordinate to exist at high enough energy. Correlation with a higher lying fragment ensemble such as CO,*+O leads to an excessively large minimum well depth. The only consistent possibility is a predissociating state that correlates with CO, + 0 along the dissociation coordinate, but with a higher dissociation limit in another dimension of the six-dimensional vibrational hypersurface.The final states of the second transition could then be bound vibrational levels of the other dimension. Such levels could extend to energies as high as 4.8 eV above the ground state of the ion and in particular could lie above the asymptotic energy of the CO,+O fragments. This hypothetical high-lying bound state would suffer from instability toward both electronic predissociation to O-+CO, and autodetachment to C03 neutral. In addition, above a total energy of 4.1 eV, the asymptotic energy of CO,+O, an additional vibrational predissociation channel to COY + 0 would be available. Only one of these three is the necessary channel leading to the observed photofragments. Though competition from the other two does not preclude the observed channel, the effects of the additional channels should appear in the photodissociation spectrum.In particular, competition from the vibrational predissociation channel is expected to decrease the intensity of the photodissociation spectral features. Total excitation to an energy of 4.1 eV corresponds267 A. W. Castleman et al. Table 1. Summary of photodissociation observations for C03(H20)o,,,2,3 relative species dissociation channel branching ratio cross-section ~ co, 0- + c02 looo/o 1 C03H20 COT + H20 0- + C02 + H20 CO,(H20)2 COT + 2H20 C0,(H20) + H20 > 99.9% < 0.1 O/O > 92% < 8% 56*4 62* 15 COT( H20)3 COT + 3H20 > 84% 70 f 25 C03H20 + 2H2O < 5% COT( H20)2 + H20 < 1 1 O/O to two-photon excitation at 2.05 eV or ca.600 nm. Fig. 2 shows that 2.05 eV lies in the middle of a relatively uniform band of features, in contradiction with the high-level predissociation model. In addition, the COY photofragments which would be the product of vibrational predissociation to Cog + 0 are not observed. We conclude that the second transition in TPDD is 2B2 + 2A1, directly to the repulsive 2B2 state. The collision-assisted photodissociation (CAPD) mechanism is consistent with the same framework of electronic surfaces. CAPD is initiated by the same 'A, t 2 B , single-photon transition that occurs in the two-photon mechanism. Rather than second- photon absorption, however, this mechanism continues with internal conversion, a step which returns the ion to the ground potential surface.Redistribution of the resulting vibrational energy leaves the ground state vibrationally hot and leads to an enhanced CID cross-section. Collision with a background molecule dissociates the ion. The dissociation channels that are energetically accessible to any species are determined by the photon energy and the energies of the bonds to be broken in the dissociation process. The bond-dissociation energies of the COT hydrates have been measured previously in this laboratory.20 Each water molecule is bound to the core ion by CQ. 0.6 eV, though water molecules are attached to larger clusters somewhat less strongly than to smaller clusters. As discussed earlier, the least energetic dissociation channel of the core COY ion is production of 0- and C02 fragments at an energy of 2.27 eV.Similarly, dissociation of water molecules into 0 and OH requires 5.11 eV. Single-photon excitation in the range of wavelengths used for this experiment is able to provide 1.95-2.20 eV to the clusters. This is insufficient energy to open the molecular dissociation channels involving breakup of the core CO, or the water molecules.'6 The only available channels are those that we will term the cluster bond dissociation channels, in which the molecular constituents remain intact and only the cluster bonds themselves are broken. The results of the present experiments on photodissociation of COT water clusters are summarized in table 1. For each of the four C03(H20)0,1,2,3 species, the table lists branching ratios into each observed dissociation channel as well as the total photodissoci- ation cross-section relative to the unclustered COT ion.The only photodissociation channel observed for the COT hydrates is loss of all attached water molecules in the reaction268 Photodissociation of Negative Ions and their Clusters Reaction (1) is the most energetic of the cluster bond-dissociation channels, requiring cleavage of all core ion-water bonds. The minimum energy required by reaction (1) is obtained by summing the bond energies for each COT-water bond. It is an important observation that, in the larger clusters where multiple dissociation channels are open energetically, loss of all ligands is the only observed channel. Photodissociation spectra of the first two hydrates were obtained over the range of photon wavelengths studied for the bare ion.Under the cold ion-source conditions, which gave well resolved sharp structure in the spectrum of the unclustered ion, there was little remnant structure in the spectra of either cluster [see ref. (21)J If no energy is released upon dissociation and the parent ion beam is monoenergetic, the parent and fragment ions would appear as single peaks. Because the fragment has a lower mass than the parent, the fragment peak is expected to appear at a less-repulsive value of the retarding field. The location and the width of both parent and fragment peaks are used with the aid of the equations detailed in ref. (9) to calculate the amount of energy released by the fragmentation process into relative translation.Briefly, an analysis is made as follows: the raw data are first smoothed and differenti- ated and the zero point of the energy scale is shifted to the interaction region potential. This procedure gives values for the parent beam energy, Eb, and the projection of fragment energies along the beam axis, El,. The energy released into relative translational energy of the fragments is then obtained from where Of is the angle that the fragment ion makes with the beam axis, M the parent mass, m, the fragment ion mass and m2 the neutral fragment mass. In carrying out calculations, we have combined all electrostatic-potential calibration factors into a single correction factor which we attribute largely to contact potential effects.This correction factor is treated as an adjustable parameter and is assigned the value that satisfies the equality EIX = ml/MEb at E, = 0. This value of El, corresponds to the centre of the measured fragment energy distribution. Energy analysis experiments on the three COY hydrates are qualitatively the same. The parent kinetic-energy peaks all appear at approximately the same retarding voltage. The kinetic-energy distributions of the photofragment COY ions all have single peaks well separated from the parent peaks. Additional experiments show that the positions of the photofragment peaks move in response to changes in the interaction region potential, whereas the positions of the parent peaks do not. The integrated probability of a given kinetic-energy release was calculated for each of the COY hydrates and is shown in fig. 3.The integrated probability is the probability of having a kinetic-energy release greater than or equal to a given value. For comparison, the dotted curve in each is the result of a statistical phase-space calculation based on the method of Chesnavich and Bowers.22 The results for all three COT hydrates indicate that more energy is partitioned into translation than is predicted by phase space. The average percentage of available energy that is channelled into relative translation is 27'/0, 18% and 27% for the first, second and third hydrates, respectively. In all of the photodissociation experiments conducted on the COT hydrates, including the observation of dissociation channels, overall cross-sections, spectra, energy-release distributions and pressure dependences, all of the cluster species behave essentially in the same fashion.This leads us to conclude that all of the clusters undergo photodissoci- ation by the same mechanism. The spectroscopic evidence in the case of the CO, hydrates is consistent with the overall envelope of the cluster-photodissociation spectrum reported by Smith et aZ.,*' being essentially identical to the band of the features of the unclustered ion that lies between 1.8 and 2.4 eV. The interpretation of this observation was that the core COTkinetic energy/eV I I I I I I 1 1 1 1 1 ( b ) * " . " 1 1 1 1 1 1 1 1 ' I ( c ) - kinetic energy/eV Fig. 3. Integrated probability distributions for kinetic-energy release in the photodissociation of the COY hydrates.( a ) CO;(H,O), ( b ) C03(H20)2, ( c ) C03(H20)+270 Photodissociation of Negative Ions and their Clusters ion absorbs photons in the cluster the same way that it does as an unclustered ion. The water molecules were thought to be only a small perturbation to the electronic structure of the core ion, and the cluster electronic states were taken to be very similar to the ion states. Our present results are in agreement with this previous study, and we conclude that the model of the unclustered COT electronic structure can be used as a basis for the analysis of the cluster-photodissociation mechanism. There are two possible mechanisms for the photodissociation of the COT hydrates that are consistent with the observed results.These mechanisms are discussed using the same electronic surfaces that are responsible for bare ion dissociation. No attempt has been made to model the slight effect of the water molecules on the positions of these three electronic states. Our observation of no pressure dependence of photofragment intensity indicates that the cluster-dissociation mechanism begins with the photon excitation process. In the first mechanism, the initial transition within the clusters is the same bound-bound 2A1 e 2 B 1 transition that initiates the two unclustered ion photodissociation mechanisms. There are no other electronic transitions of the core ion that are accessible in this energy range, nor are there ligand or cluster transitions that can account for the absorption of the light.The excited 2A, state is repulsive along the coordinate that leads to dissociation of the water. The second mechanism also begins with the 2Al + 2B, transition. Following initial excitation to the 2Al bound state, internal conversion returns the core ion to the ground electronic surface. As in CAPD, rearrangement of the resultant vibrational energy among all the vibrational modes of the cluster occurs very quickly. Whereas in the case of the bare ion there was insufficient energy supplied to the ion by the photon to cause dissociation, in the clusters the initial excitation energy is substantially greater than the bond dissociation energies of the cluster bonds. Complete cluster bond dissociation requires 0.61 eV for the first cluster, 1.20 eV for the second and 1.77 eV for removing all water from the trihydrate.The initial photon energy in all the experiments is larger than any of these dissociation requirements. Internal conversion in the core ion leaves the cluster vibrationally predissociated and dissociation of the cluster bonds happens as soon as sufficient vibrational energy has been deposited in the cluster vibrations. Previous r e s ~ l t s ~ - ~ for the vibrational predissociation of van der Waals molecules have shown that the most probable dissociation channel deposits all excess energy into vibration and rotation rather than into translation. The bond energies of van der Waals molecules are typically so weak that a Av= -1 transition is of sufficient energy to dissociate the bond. In the case of the COY hydrates neither a Av = - 1 nor - 2 transition would result in bond dissociation.The current experiments are unable to distinguish between the repulsive and predis- sociative mechanisms. The difference between the two mechanisms is the lifetime of the excited state and would be reflected in the anisotropy of the dissociation process. The repulsive mechanism would be highly anisotropic; the predissociative mechanism would be isotropic as the excited molecule will rotate before dissociation. Experiments are underway to determine the anisotropy of the dissociation process for the COY hydrates. The photodestruction of SO,(SO,) has been reported to be a broad, smooth peak with a maximum near 2.1 eV, having a total cross-section of 1.9 x Product iden- tification was not made in the earlier experiments, but our results show that SO, is, indeed, the sole photofragment ion, as speculated by the previous authors.Power studies at 600 nm (2.07 eV) indicate that the dissociation is a one-photon process. Energy analysis experiments, which we performed at different laser polarizations, show that the measured laboratory frame energy distribution of the fragment ions isA. W. Castleman et al. 27 1 kinetic energy/eV Fig. 4. Integrated probability distribution for kinetic-energy release in the photodissociation of SO,( SO*). widest when the laser polarization is along the ion-beam axis. The integrated probability of a given kinetic-energy release us. kinetic energy was calculated (fig. 4). The experi- mental results (solid curve in fig.4) indicate that 50% of the fragments have a kinetic- energy release of 0.2 eV or greater. For comparison, the result of a statistical phase-space calculation for the photodissociation of SO,( SO2) is also shown (dotted curve).22924 Phase space predicts that much less energy is released into relative translation of the products. The angular distribution of the photofragments from a dissociation event yields information on the nature of the transition and the lifetime of the excited state. The probability of product recoil per solid unit angle is2' where q5 is the recoil angle with respect to laser polarization, P2(c0s 4 ) is the second Legendre polynomial and p is the anisotropy parameter. The value of p ranges between 2 for a pure parallel transition, 0 for an isotropic transition and - 1 for a pure perpendicular transition.Physically, the anisotropy parameter can be thought of as the product of two angle dependences; one relating the angle between the internuclear axis and transition dipole moment and the second between the internuclear and dissociation axis.26 The second arises as a result of molecular rotation, which occurs after photon absorption and before dissociation. Further confirmation that the dissociation process is non-statistical comes from analysis of the angular distribution of the SO, photofragments. Bowers and coworkers2' have published a trial-and-error method for fitting the value of the anisotropy parameter to experimental energy distributions. Our experimental laboratory energy distributions of the SO, photofragment are best fit by an anisotropy parameter of 1.2, indicating the dissociation is rapid with respect to rotation.*' The relatively large amount of energy that is released into relative translation and the value of the anisotropy parameter both suggest that the photodissociation of272 Photodissociation of Negative Ions and their Clusters 3 2 >, --.x aD 0 0 1 dissociation coordinate Fig. 5. Model of SO,(SO,) electronic surfaces. SO,(SO,) occurs by direct dissociation to a repulsive state. In order to determine the relative positions of the pertinent electronic surfaces it is necessary to look at the energetics of the various molecules. The dissociation energy of SO,( SO,) is 1.04 eV.28 The electron affinity of SO, is 1.1 eV.29 The heat of dimerization of neutral SO2 is 0.19 eV.30 By using these values in a thermodynamic cycle, a value of 1.95 eV for the electron affinity of (SO,), is found.This value is in agreement with the results obtained from charge-transfer experiments3' and recent photoelectron experiment^.^, The model of the electronic surfaces that is consistent with these data is shown in fig. 5 and agrees with the recent results of Bowers and which we received in preprint form after the present work was completed. The authors thank Prof. M. T. Bowers for providing us with a copy of his phase-space computer progam. Support by the National Science Foundation (grant no. ATM-82- 04010) and the Department of the Army (grant no. DAAG29-85-K-0215) is gratefully acknowledged. References 1 T.D. Mark and A. W. Castleman Jr, Adv. At. Mol. Phys., 1985, 20, 65. 2 S. R. Leone, Adu. Chem. Phys., 1982,50, 225. 3 M. A. Hoffbauer, K. Liu, C. F. Geise and W. R. Gentry, J. Chem. Phys., 1983, 78, 5567. 4 D. S. Bomse, J. B. Cross and .I. J. Valentini, J. Chem. Phys., 1983, 78, 7175. 5 M. F. Vernon, J. M. Lisy, H. S. Kwok, D. J. Krajnovich, A. Tramer, Y. R. Shen and Y. T. Lee, J. Phys. 6 M. F. Vernon, D. J. Krajnevich, H. S. Kwok, J. M. Lisy, Y. R. Shen and Y. T. Lee, J. Chem. Phys., 7 J. A. Beswick and J. Jortner, Adu. Chem. Phys., 1981, 47, 3634, and references therein. 8 G. E. Ewing, J. Chem. Phys., 1979, 71, 3143. Chem., 1981, 85, 3327. 1982, 77, 47.A. W. Castleman et al. 273 9 D. E. Hunton, M. Hofmann, T. G. Lindeman and A. W. Castleman Jr, J.Chem. Phys., 1985,82, 134; D. E. Hunton, M. Hofmann, T. G. Lindeman, C. R. Albertoni and A. W. Castleman Jr, J. Chem. Phys., 1985,82, 2884. 10 A. Savitzky and M. J. E. Golay, Anal. Chem., 1964, 36, 1627. 11 P. D. Willson and S. R. Polo, J. Opt. Soc. Am., 1981, 71, 599. 12 J. T. Moseley, P. C. Cosby and J. R. Peterson, J. Chem. Phys., 1976, 65, 2512. 13 G. P. Smith, L. C. Lee and J. T. Moseley, J. Chern. Phys., 1979, 71, 4034. 14 J. F. Hiller and M. L. Vestal, J. Chem. Phys., 1980, 72, 4713. 15 J. T. Moseley, J. C. Hansen, M. M. Graff and F. G. Grieman, Bull. Am. Phys. Soc., 1980, 25, 1139. 16 G. H. Herzberg, Electronic Spectra (Van Nostrand Reinhold, New York, 1966). 17 H. S. W. Massey, Negative Ions (Cambridge University Press, Cambridge, 3rd edn, 1976), chap. 4; H. Hotop and W. C. Lineberger, J. Phys. Chem. Ref: Data, 1975,4, 539. 18 C. E. Moore, Atomic Energy Levels, Natl Bur. Stand. Bull., 1971, 34. 19 S. P. Hong, S. B. Woo and E. M. Helmy, Phys. Rev. A, 1977, 15, 1563. 20 R. G. Keesee, N. Lee and A. W. Castleman Jr, J. Am. Chem. SOC., 1979, 101, 2599. 21 G. P. Smith, L. C. Lee, P. C. Cosby, J. R. Peterson and J. T. Moseley, J. Chem. Phys., 1976, 68, 3818. 22 W. J. Chesnavich and M. T. Bowers, Prog. React. Kinet., 1982, 11, 137; W. J. Chesnavich and M. T. Bowers, in Gas Phase ion Chemistry, ed. M. T. Bowers (Academic Press, New York, 1979), p. 119; computational program supplied by M. T. Bowers. 23 R. V. Hodges and J. A. Vanderhoff, J. Chem. Phys., 1980, 72, 3517. 24 H-S. Kim and M. T. Bowers, J. Chem. Phys., 1986, 85, 2718. 25 R. N. Zare, Mol. Photochem., 1972,4, 1 ; G. E. Busch and K. R. Wilson, J. Chem. Phys., 1972,56,3638. 26 Sze-cheng Yang and R. Bersohn, J. Chem. Phys., 1974, 61, 4400. 27 M. F. Jarrold, A. J. Illies and M. T. Bowers, J. Chem. Phys., 1983, 79, 6086. 28 R. G. Keesee, N. Lee and A. W. Castleman Jr, J. Chem. Phys., 1983,73, 2195. 29 R. J. Celotta, R. A. Bennett and J. L. Hall, J. Chem. Phys., 1974, 60, 1740. 30 J. J. Breen, K. Kilgore, K. Stephan, R. Sievert, B. D. Kay, R. G. Keesee, T. D. Mark, J. van Doren 31 K. H. Bowen, G. W. Liesegang, R. A. Sanders and D. R. Herschbach, J. Phys. Chem., 1983, 87, 557. 32 J. T. Snodgrass, J. V. Coe, C. B. Freidhoff, K. M. McHugh and K. H. Bowen, unpublished results. and A. W. Castleman Jr, Chem. Phys., 1984, 91, 305. Received 9th June, 1986

ISSN:0301-7249    

DOI:10.1039/DC9868200261

出版商:RSC    

年代:1986

数据来源: RSC

摘要:

GENERAL DISCUSSION Dr G. Hancock ( Oxford University) said: In infrared multiple-photon excitation experiments, when the different effects of laser fluence and intensity are to be measured quantitatively, then the laser pulses need to have well defined temporal and spatial profiles. Infrared pulse shaping using an i.r. Pockels cell can achieve this, but one of the problems which occurs with such a method is that the effects of low-intensity background radiation leaking through the switching crystal can be quite marked. Such radiation can be of appreciable fluence as it persists for a timescale considerably longer than that of the shaped i.r. pulse. Saturable absorbers can help to remove this: we have found for instance that intensity dependences of the i.r. absorption cross-sections in SF6 can almost disappear if the long-time low-intensity radiation is present, and this is probably due to very efficient (greater than gas kinetic) collisional enhancement effects, for example by rotational hole-filling. Do any such effects appear in the results presented by Prof.Quack's group? Dr P. A. Hackett, Dr D. M. Rayner and Dr M. Humphries (NRC Ottawa) said: In their paper read at this Discussion Quack et al. presented quantitative data on the infrared multi-photon dissociation (i.r. MPD) of perfluoroalkyl iodides.' They followed the time-development of the iodine atom concentration (2P3/2, hereafter I), monitored quantitatively via 3-photon resonant ionization, throughout an i.r. laser pulse of extremely well defined intensity profile.This time-dependent information was then transformed via the measured i.r. pulse intensity profile to give the fluence dependence of the product yield in an absolute and quantitative fashion. These results demonstrated, for the first time and in a direct way, the generality and applicability of the theoretically predicted, sometimes intensity-proportional rate constants in i.r. MPD. Rate constants were reported for the i.r. MPD of 9 different perfluoroalkyl iodides. For C4F91 the rate constant was proportional to intensity over the full range of the experiments with a value of kI = 0.55 cm2 J-' and an incubation fluence (Fl) of 2.0 J cm-2. For CF31, the rate was intensity-dependent, reaching an intensity-independent value of 1.25 cm2 J-' at intensities > 200 MW cm-2 with an incubation fluence of 0.7 J cme2.This result was shown to be in good agreement with previous indirect determinations.2b Below 60 MW cm-2 the rate for CF31 i.r. MPD was strongly intensity-dependent. The form of the observed intensity dependence and the value of the intensity-independent rate parameters ( kI, Fl) were in good agreement with theoretical predictions and model calculations.' In the midst of this happy agreement between theory, model, and indirect and direct measurement a new observation has been reported. Dietrich, Quack and Seyfang have studied the i.r. MPD of both CFJ and C4F91 by monitoring the time-dependent i.r. absorption of reactant and 'product' molecule^.^ Their experiment is at somewhat lower intensities than ours. They report that neither of these molecules dissociates during the i.r.laser pulse, the timescale of our experiments, rather that they dissociate after the i.r. pulse with exponential first-order rates in the regime of 2 x lo6 s-'. One suggestion put forward by Dietrich et al. for the discrepancy of the dissociation times recorded by the two experiments was that the multiphoton ionization signal arises predominantly from the photolysis, by the dye laser, of vibrationally excited iodide molecule^.^ This sugges- tion cannot be rejected out of hand as we ourselves have reported that multiphoton ionization signals due to spin-orbit excited iodine atoms hereafter I*) arise solely by this mechani~m.~ In the analysis of the data presented in Prof. Quack's paper at this 275276 Genera I Discussion Discussion it was assumed that no I atoms are produced by this i.r.-visible double- resonance dissociation (DRD), i.e.the I*/(I + I*) branching ratio in the photolysis of vibrationally excited perfluoroalkyl iodides was ca. 1. In this comment we draw upon published work related to this problem and present several new pieces of data. The data are relevant to: ( a ) the time-dependence of the I and I* signals at times longer than those reported in the paper under Discussion; (6) the timescale for the after-pulse dissociation; and ( c ) the I*/I branching ratio for DRD. All data support the interpretation of the i.r. MPD of perfluoroalkyl iodides presented in the paper. The experimental arrangement was as in the paper with two important exceptions.In some experiments a plasma shutter was used to terminate the i.r. pulse. Secondly, some experiments reported here used lenses to focus the i.r. radiation into the interaction region with shorter focal length than the 50cm focal-length lens used by Quack and co-workers. This has the important consequence that not all the data presented here are derived from regions of precisely uniform fluence/flux as the data of their paper. This is not a consequence of the smaller radii of the i.r. focus but of their smaller Rayleigh range and is due to the finite length of the volume probed by the MPI effect. Thus, although the peak i.r. fluence is well defined the data presented here do not quantitatively refer to only that fluence. However, the spirit of this contribution is to investigate qualitatively the source of the discrepancy with the observations of Dietrich et al., for which the data are adequate.The results presented in the paper characterise the i.r. MPD reaction for 400 ns after the beginning of the i.r.-laser pulse. This timescale was chosen for three reasons, the most important being that the reaction was over on this timescale. The secondary motivators were that the collisional time constant, assuming a gas-kinetic bimolecular rate constant of 2 x lo-'' cm3 molecule-' s-', at the pressure (10 Pa) of our experiments was 2 ps and that migration from our finite-diameter i.r. beam occurred on a similar time-scale. Thus our experiments were clearly free from collisional and/ or diffusion effects. In order to investigate the i.r.MPD process on a longer timescale we report results in which both collisions and diffusion play a role. In the upper panel of fig. 1 we present data on the i.r. MPD of CFJ at 560 mTorrt over the range 0-10 ps. There is no evidence for slow dissociation. Rather we see the rather normal I and I* signals modified at long times by collisional and diffusion effects. Thus, the I signal rapidly reaches a plateau value which decays due to diffusion of iodine atoms from the irradiated volume, whereas the I* signal rapidly rises and falls as vibrationally excited molecules are first created and then destroyed (dissociation) by the i.r.-laser pulse. The small secondary maximum in the I* signal is most reasonably attributed to the creation of vibrationally excited molecules, as cold molecules diffuse into the interaction region and undergo collisions with vibrationally excited fragments. This secondary peak occurs after some 20 collisional time constants.Fig. 1( b ) shows the long-time behaviour for CFJ in the absence of collisions in the range 0-1 ps. The pressure for this experiment was 10 Pa. Migration from the probe regions is now collision-free and reflects the nascent velocity of 1 fragments. Note from this panel that there is no slow production of I atoms, that the I atoms decay at an appreciable rate; and, that all I atoms decay in < 1 ps. These observations are explained by assuming that all the iodine-atom signal arises from iodine atoms which have acquired excess translational energy via the unimolecular cleavage of the C-I bond.5 The amount of energy acquired is fully consistent with RRKM modelling and molecular-beam mass-spectrometry measure- ments.6 71 Tom= 101 325/760 Pa.Genera 1 Discussion 1 - 0 ' 277 ( b ) I 1 I 1 I \ \ 0.4 0.8 1.2 1.6 interpulse time/ps Fig.1. i.r. MPD of CF31 on the microsecond timescale. ( a ) The time evolution of I (- - -) and I* signals (-) through the full SLM pulse of ref. ( 1 ) focussed by a 10 cm focal length lens to give a peak intensity of CQ. 400 MW cmP2. The CFJ pressure was 75 Pa. ( b ) The time evolution of the I signal (0) using the clipped pulse of ref. (5) focussed by a 25 cm focal-length lens to give a peak intensity of ca 300 MW cm-*. The CF31 pressure was 1.3 Pa. The curve through the data points models the concentration decay assuming that C-I bond cleavage releases 1.1 kcal mol-' to product translation, whereas the slower decay is that expected for vibrationally excited molecules with a solely thermal (293 K) velocity distribution. The experiments reported in fig.1 used considerably higher intensities than did Dietrich et aL3 However, results obtained at lower intensities are also consistent with our explanation. The most striking of these results were obtained using the clipped C02 laser pulse. These results probe the timescale of the unimolecular dissociation and have already been p~blished.~ The timescale of the observations was 0-250ns; both CF31 and C6F131 were examined. The conclusion of the study was that the unimolecular dissociation was fully consistent with RRKM theory.For CF31 the dissociation (after pulse) was prompt. No time-evolution of the I yield was observed in the 150ns after C02 pulse ter~ninated.~ For C6FI3I there was a slow time-evolution, whose rate depended on the pulse en erg^.^ In fig. 2 we present additional data for this system (C6F131). Again, slow time-evolution is seen. Interestingly, both the I and I* signal show similar, if reversed, behaviour. The I signal slowly grows, whilst the I* signal slowly decays with similar time constant. This observation shows that, for C6F131 at least, the molecules which undergo DRD may be considerably above the ground-state dissociation limit and that the timescale for dissociation (production of products) is closely linked to the timescale for I* signal loss (loss of reactants).This correlation is further explored in fig. 3 which details the time-dependence of the I and I* signals in i.r. MPD of CF31 under conditions entirely analogous to those278 General Discussion I I I I I ( b ) 50 100 150 200 250 interpulse time/ns Fig. 2. After pulse reactions for i.r.-excited C6FI3 I: ( a ) I, (b) I*. These data were obtained for 6.6 Pa C6FI3I, excited by the clipped i. r. pulse of ref. (7) focussed to a peak intensity of 90 MW cm-* by a 25 cm focal-length lens. The i.r. pulse intensity profile is shown as the shaded area. The I data were obtained using MPI at 485.5 nm. This transition is strongly Stark-shifted by the i.r. laser and no signal is observed during the i.r. pulse? After the pulse turns off, the I data rise with a unimolecular rate of 2.8 x lo7 s-', solid curve.The I* signal monitored at 477.7 nm shows no Stark-shifting and decays with a similar time constant. used in Prof. Quack's paper. Note the similarity in the rate of loss of the I* signal and the rate of increase of the I signals at long times. This observation, coupled with an independent measurement of the relative detectivity for I* and I implies that ( a ) the DRD is saturated and that ( 6 ) the i.r. MPD is reaching a steady state.' Note that at low fluence the ratio of I/I* tends to zero. This implies that the branching ratio for the DRD is unity. Furthermore, note that the minimum value of the branching ratio is determined by the condition that the contribution to the I signal due to the i.r. MPD cannot be less than zero. This condition limits the branching ratio to values>0.8.Corrections to the observed I signal using this limiting branching ratio do not appreciably alter our conclusions regarding the intensity dependent rate parameters for CF31. The effect would be to slightly increase F,, leaving kI unaffected. Finally, note that at high intensities both the I and I* signals reach limiting values, 1.0 and 0, respectively, on the timescale of 20 ns. This observation implies that there is no delay in the i.r. MPD of this molecule, at least at high intensities. Similar behaviour was observed for all 9 molecules studied. We have examined all our published and unpublished data for i.r. MPD of per- fluoroalkyl iodides and have found no evidence to support Dietrich's observation of slow unimolecular dissociation of CFJ and C,F& All available evidence supports the proposals presented in the paper under discussion.Admittedly, we have not reproduced the conditions used by Dietrich, equally well he has been unable to reproduce the conditions used by US.^ The two observations could be reconciled if the branching ratioGeneral Discussion c----------- 1.0 (a) f 279 I I I 0.5 I I 0 1 1.0 t /--------- // / / 0.04 1 interpulse time/ns Fig. 3. Quantum yields of I and I* in i.r. MPD/DRD MPI of CF31. These data were obtained using 10 Pa of CF,I excited using the full SLM pulse focussed by a 50 cm focal-length lens.' The I [474.3 nm (- - -)] and I* [477.7 nm (-)I signal heights have been quantified.* The peak i.r. intensities (MW cm-2) were: ( a ) 280, ( b ) 55, ( c ) 3.for DRD were found to be dependent on the vibrational energy content of the molecule. We cannot reject this possibility, indeed it has been predicted theoretically and it is a point worthy of further Thus we cannot completely rule out the interpretation offered by Dietrich et al. at this time.3 We note that the i.r. MPD of CFJ is intensity-dependent.' At low intensities not all molecules are dissociated. Thus, considerable vibrational energy may remain to be relaxed after the i.r. pulse. There are two mechanisms for this relaxation, the first is diffusion of excited molecules out of the irradiated region. The second is collisional- induced dissociation. Energy transfer (V to V) occurring within the irradiated region does not remove the excitation.Thus collision-induced dissociation occurs in competi- tion with diffusion. Measures taken to prevent diffusional loss (increased beam size, increased pressure) increase the inevitable probability that collision-induced dissociation will be observed. At 10 Pa the collisional time constant is 2.0 ps; at 100 Pa it is 200 ns. Our measurements relate to collisionless i.r. MPD of perfluoroalkyl iodides. 1 M. Quack, E. Sutcliffe, P. A. Hackett and D. M. Rayner, Faraday Discuss. Chem. SOC., 1986,82, 229. 2 (a) S. Bittenson and P. Houston, J. Chem. Phys., 1977, 67, 4819; ( b ) M. Quack and G. Seyfang, J. 3 P. Dietrich, M. Quack and G. Seyfang, Faraduy Discuss. Chem. SOC., 1986, 82, 280. 4 D. M. Rayner and P. A. Hackett, Isr. J. Chem., 1984, 24, 232.5 D. M. Rayner and P. A. Hackett, J. Chem. Phys., 1983, 79, 5414. 6 Aa. A. Sudbo, P. A. Schultz, E. R. Grant, Y. R. Shen and Y. T. Lee, J. Chem. Phys., 1979, 70,912. Chem. Phys., 1982, 76,955.280 General Discussion 7 D. M. Rayner and P. A. Hackett, Chem. Phys. Lett., 1984, 110,482. 8 P. A. Hackett, D. M. Rayner, M. Humphries, M. Quack and E. Sutcliffe, to be published. 9 M. Shapiro, J. Phys. Chem., 1986, 90, 3644. 10 S. C. Givertz and G . G. Baht-Kurti, J. Chem. SOC., Faruday Trans. 2, 1986, 82, 1231. Mr P. Dietrich, Prof. M. Quack and Dr G. Seyfang (ETH Ziirich) said: The laser chemistry group at NRC has developed over the last years an extremely elegant and highly sensitive technique for studying the time evolution of iodine atom concentration in the i.r.-photochemistry of perfluoroalkyliodides. ’,, In the paper at this meeting3 it was shown that quantitative evaluation and theoretical analysis of the time-dependent iodine-atom signal leads to incubation and rate coefficient data [k(st)], which are quantitatively consistent with indirect results for CF31 i.r.-photolysis4 and semiquantita- tively, at least, with theoretical predictions concerning k( st) and the non-linear intensity dependence in the transition range between case B and case C.’ Although the technique of time-resolved iodine-atom observation li2 seems to be ideally suited to investigate the type of system considered in ref.(3), it would be of interest to develop techniques which have a wider applicability. We have, over the last few years, built up a facility to measure the transient i.r.-absorption during and after pulsed-laser excitation using C.W.CO, lasers and diode lasers as probe sources. This facility allows us to investigate the relaxation kinetics in unimolecular systems in the gas p h a ~ e , ~ . ~ to study the i.r. spectra of ‘hot’ molecules (under collisional, thermal and collision-free, non-thermal conditions) and to measure the kinetics of reactant decay and product formation in i.r.-photochemistry. We have used the technique to obtain data relating to CF31 and C4F91, investigated also in ref. (3) and in addition C2F4S2 and c-C,F,, which had previously been studied in our laboratory by the indirect, static photolysis technique.”1° Although our experiments and their analysis have not yet been completed, we report here some preliminary results in relation to ref.(3). This seems to be adequate also because in the course of our work some very preliminary data have appeared on CF31, using time-resolved U.V. probing, which may require reinterpretation.8 The experimental set up is shown in fig. 4. The far-field output of a Lumonics 103-2TEA COz laser with unstable resonator optics passes the reaction cell nearly antiparallel to the probe beam of a tunable diode laser. The angle between the probe and the excitation beam is < 1”. The central part of the probe beam is selected by a small hole of 1.5 mm diameter in the mirror behind the reaction cell. With geometrical optics this would ensure that the effective probe-beam diameter is smaller, by at least a factor of two-three, than the diameter of the excitation beam. The signal from an HgCdTe detector with a rise-time of 10 ns is digitized by a Tektronix transient digitizer, which is triggered by the signal from a photon-drag detector arising from the laser pulse.Two filter cells are used to suppress scattered light and to avoid interference of the excitation laser pulse with the probe laser. In some experiments we used a line-tunable C.W. C02 laser as probe laser. With this set-up it is possible to measure i.r. spectra of highly excited molecules. In the example shown in fig. 5 CF31 was heated by collisional energy transfer from laser-excited SF, to a temperature of ca.950 K. The crosses indicate the absorption cross-sections of hot CF31 at the probe CO, laser wavenumbers.The temperature is calculated from the absorbed energy and the heat capacity of the sample. It is reached, typically, after a relaxation period of 20-30 ps. The densely structured spectrum is a high-resolution spectrum of CF21 at room temperature, taken on our BOMEM DA002 interferometric spectrometer system [see also ref. ( 1 l)]. One notes the relatively large absorption cross-section of hot CF31 in the low- wavenumber range, 1040- 1060 cm-’. The time-evolution of absorption after i.r. multi- phonon excitation was followed as well at many of the wavenumbers shown in fig. 5 and, in addition, outside this range, probing presumably the formation of the product CF3 from CF31 around 1110 cm-’ with a diode laser (see below).General Discussion 28 1 F- I trigger photon pyroelectric detector Fig.4. Experimental set-up. The excitation laser generates the beam marked by A. A portion of the beam is directed onto a photon-drag detector by a beam splitter (BS) to trigger the transient recorder (TEK 7912 AD). Most of the beam passes through the reaction cell; the energy is measured by a pyroelectric detector. The output of a tunable diode laser (TDL) is made parallel by three off-axis parabolic reflectors (OAP) and passes through the reaction cell with an angle < 1" to the excitation beam. A monochromator (MC) is used for mode-selection, a HgCdTe detector (MCT) detects the time-dependent probe intensity. L1 and L2 are lenses. In the i.r.-photolysis experiments samples of 2 to 50Pa were irradiated with laser pulses of 1 to 5 J cmU2 and average intensities of 10 to 50 MW cm-2 in the maximum of the pulse.Because of mode-beating the actual peak intensities are higher. Fig. 6 shows a typical result for the first part of the time-evolution of the absorption of CFJ after laser excitation together with the laser pulse and the time-dependent fluence [ F( t -+ 00) = 3.65 J cm-*]. There seems to be little change of absorption during the laser pulse. Similar results are obtained at other frequencies around 1070 cm-' also with a diode laser. The result does not depend strongly upon fluence nor upon pressure. At much higher buffer gas pressures between 100 and lo4 Pa a marked pressure dependence was found and investigated. At the low pressures < 50 Pa the collision time is ca.500 ns (depending upon the assumed cross-section). When probing at t > 1100 cm-' one finds an increase of absorption, which matches the kinetics of CF31 decay and can be attributed to CF3 formation. When observing at very low wavenumbers around 1040 cm-' one finds first a fast increase of absorption during the laser pulse. This can be attributed to the excitation of CF31. Subsequently, one finds decay with the same time constants as at other probe wavenumbers. Qualitatively similar observations are made for other molecules. The results are summarized in table 1. The k(st) values from the indirect evaluation of bulk measure- ments are in good agreement with those from the direct time-resolved measurement of I-atom yields, when available. However, it is not entirely clear why in the present experiments such a large component is found for molecules decaying slowly only after the pulse.The following possible explanations can be discussed. (i) The i.r.-absorption technique may not be sensitive during the laser pulse. It may be noted, however, that qualitatively similar (quantitatively somewhat different) results are obtained with u.v.-laser probing.8282 General Discussion 1.4 1.1 0.8 0.5 0.2 1040 1050 1060 1070 1080 1090 C/ cm-' Fig. 5. 1.r. spectrum of CF31 after laser heating. X, Absorbance of the probe after laser heating at different C02-laser lines, the structured spectrum is a high-resolution f.t.i.r spectrum at room temperature. p(CF,I) = 50 Pa, L = 8 cm, Ta' - 950 K. (ii) RRKM theory may be inadequate to describe the unimolecular decay. Indeed, it is known from detailed adiabatic channel calculations with angular momentum conservation that RRKM theory is inadequate to properly describe product translational energy distributions in the decay of perfuoroalkyliodides.'2 However, rather drastic assumptions would have to be made to find a large, slow component after the pulse, independent of Auence.(iii) The time-resolved measurements of iodine atoms are perhaps really probing the excitation above threshold and not the dissociation rate directly, if superexcited molecules dissociate into ground-state iodine atoms only with visible laser photolysis. (iv) Unusual intensity and fluence effects may render the direct comparison of our results with the iodine absorption measurements at high intensity with an SLM laser impossible.Our intensities are lower than most of the intensities used in ref. (3), but there is overlap for C4F91 in a range where no intensity effect was found in ref. (3). Fluence may be more of a problem because of diffraction effects. However, increasing the excitation-beam surface by a factor of four using a powerful TEA600 laser at high fluence did not alter the results, and diffraction experiments with various apertures indicated the possible effects to be borderline, although they cannot be fully excluded. In the most extreme case, one would probe molecules at intermediate fluence just above threshold for dissociation which are, therefore, long-lived. (v) Unusual collisional effects may still occur with large cross-sections and some compensation from diffusion and energy transfer.Work is in progress to elaborate the proper analysis of the results along these and other possible lines of thought.General Discussion 283 160 120 0 40 80 120 160 200 t/ns Fig. 6. Time-evolution of the i.r. absorption of CF31 after laser excitation. CEx(R16) = 1076.0 cm-', cpp,(R14) = 1074.6 cm-', p(CF31) = 50 Pa. ( a ) Transmitted probe intensity [c(CF,I)( t ) ] ; (b) time- dependent fluence, F( t ) = I( t')dt'; (c) temporal pulse profile (intensity), I( t ) . The results for (a) and (b) are very similar if one uses a smooth SLM laser pulse. Table 1. Summary of results k(st)/ lo6 s-l I/MW cm-2 time-resolved kIR/ lo6 s-' reaction bulk ratea iodine abs. (after pulse)b CF,I-, CF3+I 1.6 1.25 2.7 f 0.7 C4F91 + C4F, + I 0.6 0.55 4.2 f 0.5 c-C4F8 --* 2C2F4 1.6 2.6 f 1 .O C2F4S2 + 2CF2S 3.2 2.0* 1.0 a The general uncertainty in the indirect bulk rates is a factor of ca.2. The ranges of rate constants under a variety of conditions (fluence, frequency etc.) are indicated. 1 D. M. Rayner and P. A. Hackett, J. Chem. Phys., 1983, 79, 5414. 2 D. M. Rayner and P. A. Hackett, Chem. Phys. Lett., 1984, 110, 482; Isr. J. Chem., 1984, 24, 232. 3 M. Quack, E. Sutcliffe, P. A. Hackett and D. M. Rayner, Faraday Discuss. Chem. SOC., 1986,82, 229. 4 M. Quack and G. Seyfang, J. Chem. Phys., 1982, 76, 955. 5 M. Quack, Chimia, 1981, 35, 463. 6 M. Quack, Ber. Bunsenges. Phys: Chem., 1984, 88, 94. 7 P. Gozel, B. Calpini and H. van den Bergh, Isr. J. Chem., 1984, 24, 210.8 B. Abel, L. Brouwer, B. Herzog, H. Hippler and J. Troe, Chem. Phys. Lett., 1986, 127, 541. 9 M. Quack and G. Seyfang, Chem. Phys. Lett., 1981, 84, 541. 10 M. Quack and G. Seyfang, Ber. Bunsenges. Phys. Chem., 1982,86, 504. 11 H. Burger, K. Burczyk, H. Hollenstein and M. Quack, Mol. Phys., 1985, 55, 255. 12 M. Quack, in Intramolecular Dynamics, ed. J. Jortner and B. Pullmann (D. Reidel, Dordrecht, 1982), p. 371.284 General Discussion Dr D. W. Lupo and Prof. M. Quack (ETH Ziirich) said: Although full master equation calculations are important for a complete study of the time-evolution of multiphoton i.r. photofragmentation, including non-linear intensity effects, it is also desirable to find a simple analytical expression for k(st). Such an expression should yield reliable estimates for k(st) in the case B limit 1-3 from molecular parameters, and be calculable in a matter of a few minutes on a pocket calculator.The experimentalist could use such an expression to make a first comparison between experiment and theory. We have obtained, by generalization of the expression for the reaction threshold bottleneck limit of k( st) with a semiclassical density of state^,^ the following expression for k ( ~ t ) : ~ - ~ k( st) / s- ’ a‘sQ;, b with s being the number of molecular vibrational degrees of freedom, the resonant absorption frequency, ET the reaction threshold energy, Ez the zero-point molecular vibrational energy, G the integrated absorption strength of the resonant band and I the radiation intensity. The primes indicate the reduced units I’ = I/MW crnp2, G’ = G/pm2 (.”: , A;’, Ek, E k ) = ( 6, , A;, ET, Ez)/ 1000 cm-’.A value for the effective coupling width A.V” of Av” = 6,/4 has been suggested on the basis of empirical evidence.6 The coefficients A and A, are corrections to the semiclassical expression for the density of states, modelled after the forms of Whitten and Rabinovitch7 and Haarhoff ,* respectively, but in practice set equal to 0 or 1 or treated as parameters. Eqn (1) was optimised by least-squares fitting of the parameters a’, a, b and c (when applicable also A or A,) to a data set of 37 exact values of k(st) obtained from case B master equation results for model systems to yield a universal set of parameters for a given form of eqn ( 1 ) . The data set included loose and tight transition states, 5 to 17 atomic molecules, threshold energies from 7400 to 41 000 cm-’, zero-point energies from 3000-26 000 cm-’, and excitation quanta (C,) from 930 to 4280 ~ m - ’ .~ The fits which include either A or A, as parameters agree with the exact k(st) values in the worst case within a factor of two. For most cases one has much better agreement. More restrictive fits, including for example only loose or tight transition states, agreed even better with exact results for the corresponding systems and will be discussed el~ewhere.~ Table 2 shows a summary of experimental values of k(st) obtained from bulk photolysis, exact values of k(st) from a case B master equation, where they have been calculated, and analytical estimates from eqn ( 1).We see excellent agreement between the values of k(st) from the master equation and the values from eqn (1). Thus this simple analytical expression is sufficient for a first comparison of the statistical theory of i.r.-laser photochemistry with experiment in the limit of linear intensity dependence, although full master equation calculations are still important for a detailed analysis. When comparing experiment and theory, one must note sometimes the ambiguities in the choice of G in the case of overlapping bands and quite generally in the empirical coupling bandwidth A 6. 1 M. Quack, J. Chem. Phys., 1978, 69, 1282. 2 M. Quack, Ber. Bunsenges. Phys. Chem., 1979,83, 757. 3 M. Quack, Ber. Bunsenges. Phys. Chem., 1979, 83, 1287. 4 D. Lupo and M.Quack, Chem. Rev., 1987, in press. 5 D. Lupo and M. Quack, Ber. Bunsenges. Phys. Chem., to be published. 6 M. Quack, Chimia, 1981, 35, 463. 7 E. Z. Whitten and B. S. Rabinovitch, J. Chem. Phys., 1963, 38, 2466. 8 P. C. Haarhoff, Mol. Phys., 1963,6, 337; 1963, 7, 101.General Discussion 285 Table 2. Comparison of experimentally determined absolute rate coefficients for multiphoton i.r.-laser photofragmentation from bulk photolysis with exact master equation predictions (theory, exact) and with simple analytical estimates from eqn (1) reactant k(st)/s-' I / M W cmd2 theory, exact simple estimate CF31a C2F4S2b c-C~F, CC13Fd C2HC12F3 CHC12Ff CDC12Ff C4H,Fg C4HsDFg C4H,DF2 CF3Brh C4HsF2 1.6 x lo6 3.2 x lo6 (1076 cm-') 7.9 x lo5 (955 cm-') 2.0 x lo6 5.1 x lo5 1.4 x lo6 2.5 x lo5 2.3 x lo5 (1075 cm-') 2.1 x lo5 (944 cm-') 1.0 x lo5 1.4 x lo5 2.3 x lo5 1.7 x lo5 9.0 x 105 1.6 X lo6 1.3 x lo6 5.4x lo6 5.3 x lo6 7.3 x lo5 6.0 x lo5 1.8 x lo5 1.4 x lo5 1.5 x lo5 1.1 x lo5 4.3 x lo5 4.3 x lo5 8.7 x lo5 8.7 x lo5 5.0 x lo5 2.5 x lo6 1.7 x lo6 1.3 x lo6 4.4 x lo5 The simple estimates are the averages of values for two options of eqn (1).Option 1 is with a = 3.48 x lo6, a = 1.27, b = 2.07, c = 2.49, A = 0.37, and Al = 0. Option 2 is with a = 4.95 x lo6, a = 1.46, b = 2.14, c = 2.69, A = 1, and A , = 0.73. a M. Quack and G. Seyfang, J. Chem. Phys., 1982,76,955. M. Quack and G. Seyfang, Chem. Phys. Lett., 1981,84, 541. M. Quack and G. Seyfang, Ber. Bunsenges. Phys. Chew., 1982, 86, 504. D. Lupo, M. Quack and B. Vogelsanger, Helv. Chim.Acta, 1987, 70, 129. P. Gozel, H. van den Bergh, D. Lupo, M. Quack and G. Seyfang, to be published. M. Quack and H. J. Thone, Chem. Phys. Lett., to be published. R. 0. Kiihne and M. Quack, to be published. D. Lupo and M. Quack, Chem. Phys. Lett., 1986, 130,371. Dr M. R. Levy (Newcastle-upon-Tyne Polytechnic) and Mr R. 0. Brickman, Dr D. M. Cox and Dr A. Kaldor (Exxon) said: The paper of Quack, Sutcliffe, Hackett and Rayner' has dealt with the i.r. multiphoton decomposition of small to medium-sized organic molecules (4-32 atoms). Their observation of a transition from strong to weak intensity dependence (case C + case B ) nicely fits in with the expectations from increas- ing molecular complexity. We have been inve~tigating,~~~ by double-resonance and molecular-beam techniques, the i.r.dissociation of a series of somewhat larger molecules, with 44-61 atoms: U02L2B, where L = (CF3C0)2CH and B = (CH30)3P0, (C2H50)3P0, (C4H90)3P0 (TMP, TEP, TBP, respectively). The absorption s p e ~ t r a ~ ' ~ (fig. 7) have a near-Lorentzian band at ca. 954 cm-', assigned to the UO, asymmetric stretch and regarded until now as completely homogeneously broadened;6 and a phosphate C-0 stretch at ca. 1068 cm-'. Dissociation of U02L2B to UO,L,+ B is ca. 150 kJ mol-' endothermic and is complicated by an initial isomerisation to a species with a slightly bathochromically shifted absorption profile; but near 100% yields at low fluence have been claimed for both isomerisation and di~sociation.~ Our double-resonance measurements, on U02L2TMP excited at 10P8, used a very similar arrangement to that of Dietrich et aL,' reported in this Discussion.However, we probed at many CO, laser frequencies. The magnitudes of the induced transients at delay times of 200 ns (laser pulse just over) and 5 p s are shown in fig. 8. A 'red feature' (the isomer) is formed initially, then decays more slowly to form a 'blue feature',286 General Discussion 0 .o 900 950 1000 1050 1000 wavenumber/ cm- ' Fig. 7. F.t.i.r. absorption spectra4*' of U02L2TMP (-), U02L2TEP (- - -) and U02L2TBP ( - - * ). The latter two were normalised to the first by the assumption that the uranyl oscillator strength at 10.6 pm remains constant. free U02L2. This result clearly demonstrates the importance of probing at a range of frequencies in i.r.-i.r.double-resonance experiments. The magnitude of the isomer red shift is only ca 2.3 ~ m - l , ~ so the isomerisation enthalpy change is expected to be quite small. Initially, isomerisation increases rapidly with fluence. However, in contrast with the earlier measurements: both our molecular beam2 and double resonance3 results find that, above ca. 0.5-0.65, isomer yield becomes much less efficient (fig. 9). A similar situation holds for the overall dissociation yield. Our molecular beam experiments involved monitoring the depletion of various ions in a quadrupole mass spectrometer, following intersection of the beam with a pulsed Gaussian laser profile at 90". The measured depletion DM at a peak (axial) fluence Fo is proportional to D(Fo, x) dx, where x is the distance along the molecular beam axis from the laser axis; and extraction of the true axial depletion is not trivial.2 The isomerisation data were fitted very satisfactorily with a simple functional form like that shown in fig.9 (although a small degree of curvature is possible); but the overall dissociation yields cannot be extracted so easily. Fig. 10 therefore shows dissociation yields integrated across the laser profile for U02L2TMP, U02L2TEP and U02L2TBP, excited at both 10.6 and 9.4 pm. The curves underestimate the true yield D(Fo) at low depletion and overestimate it close to saturation, since DM continues to rise, owing to 'filling-in' across the Gaussian laser profile. The apparent saturation level reached turns out to be ca. twice the true saturation level.The levelling out starts earlier at 10.6 p m owing to loss of interaction with isomerised molecules (at 9.4 p m there is no change in the absorption profile). Because of the uncertainty in overall dissociation yield, it was not possible to plot our results in the same format as Quack et aL,' i.e. -In [ 1 - D( FO)] against Fo. However, a linear dependence of the form shown in that paper would not fit our data whenGeneral Discussion 287 970 960 940 950 P20 P16 P12 P8 P4 R4 R6 R12 R16 P22 P18 P14 PlO P6 R6 R10 R14 RIB Fig. 8. Line-to-line frequency dependence of induced signals at t = 200 ns (0) and t = 5 ps (0) for irradiation of U02L2TMP at 10P8 with TEA laser axial fluences (in mJ cm-') as shown. For each set of data, points above the baseline correspond to induced transparency.The data are normalised to unity induced transparency at P6, t = 5 ps, fluence = 175 mJ cm-'; and the separation between successive baselines is 2.0 units. For fluences Q 175 mJ cm-2, the TEA laser pulse length was truncated at 130 ns (65 ns f.w.h.m.); at higher fluences, a slightly longer pulse was employed.288 General Discussion 1 I I I 1 .o fluence/mJ cmp2 Fig. 9. Isomerisation yields for U02L2TMP irradiated at 10P8: 0, yields at 200 ns after start of laser pulse, from double-resonance measurements; (-), (- - - ), functional forms used to fit molecular-beam data at 1 ms after laser pulse (a small degree of curvature is possible before the initial saturation, and the onset of the secondary rise is not known precisely, hence dashed lines).At the lowest fluences, isomerisation appears to be incomplete at 200 ns. 1.0 1 t t 0.5 0.0 c 4 peak fluence/mJ Fig. 10. Approximate fluence dependence of integral dissociation yields 1 ms after the laser pulse, from molecular beam experiments on U02L2TMP (-), U02L2TEP (- - -) and U02L2TBP ( - - * ), at (a) 1OP8, 10PlO and 10P10, respectively, and (b) 9P8, 9P18 and 9P18, respectively.General Discussion 289 integrated across the laser profile. Our results imply a turnover analogous to that of CFJ [fig. 6 of ref. (l)] at -In FR=0.7-1.0, but atfluences well below 100 mJ ern-,. At fluences S438 mJ cm-, (intensity d 6 MW ern-,), the overall dissociation yield at 10P8 showed no significantly intensity dependence. Homogeneous broadening in these molecules has been considered to arise from resonant interaction of the pumped mode with close-lying 'bath' states ( CJ the contribu- tion by Quack's group8 to a recent Discussion).Vibrational inhomogeneous structure was believed to be absent as there is no shift in the band centre with temperat~re.~ It was thus anticipated that molecules would continue to absorb C 0 2 laser photons at the same frequency until dissociation occurred. The observation of a saturation in isomerisa- tion and dissociation indicates that not all molecules absorb equally efficiently, i.e. the absorption band is not completely homogeneously broadened. In view of the size of the molecules, and the high internal energy content and density of states, this is a surprising result. Clearly, structure remains in the absorption profiles even though it appears, at low resolution, to be absent.Like the ethylene dimer considered by Peet et aL9 later in this Discussion, it may be necessary to tune across the 75 MHz bandwith of a CO, laser to resolve such structure." However, although some U02L2B molecules require only a single photon for isomerisation, the mechanism of homogeneous broadening is unlikely to be the same as for the van der Waals molecules; in the ethylene dimer, predissociation was responsible: but in the U02L2B molecules the main cause is likely to be interaction with the quasicontinuum of vibrational modes, as already indicated. Quack and Thone" have found a distinct lack of mode selectivity in pumping 1,4-difluoro-l-deuterobutane in the CHDF and CH2F bands at 930 and 1040cm-', respectively.In our case, exciting U02L2B molecules at 10.6 and 9.4 pm, the only 'mode selectivity' was due to loss of interaction with isomerised molecules at 10.6 pm (see comments above on fig. 10). Below the onset of saturation, dissociation yields for the same molecule appear to depend only on the number of photons absorbed, i.e. the product of fluence and absorption cross-section; and, in line with general RRK expecta- tions, dissociation at lod3 s becomes less efficient as the total number of oscillators increases. 1 M. Quack, E. Sutcliffe, P. A. Hackett and D. M. Rayner, Furaday Discuss. Chem. SOC., 1986, 82, 229. 2 M. R. Levy, D. M. Cox and A. Kaldor, Chem Phys., in press. 3 M. R. Levy, R. 0. Brickman and A. Kaldor, Chem Phys., in press.4 R. G. Bray, D. M. Cox, R. B. Hall, J. A. Horsley, A. Kaldor, G. M. Kramer, M. R. Levy and E. B. 5 R. G. Bray, personal communication. 6 R. B. Hall, A. Kaldor, D. M. Cox, J. A. Horsley, P. Rabinowitz, G. M. Kramer, R. G. Bray and E. T. 7 P. Dietrich, M. Quack and G. Seyfang, Furaday Discuss. Chem. SOC., 1986, 82, 280. 8 K. von Puttkamer, H-R. Dubal and M. Quack, Faruduy Discuss. Chem. SOC. 1983, 75, 197. 9 A. C. Peet, D. C. Clary and J. M. Hutson, Furuduy Discuss. Chem. SOC., 1986,82, 327. 10. M. Snels, R. Fantoni, M. Zen, S. Stolte and J. Reuss, Chem. Phys. Lett., 1986, 124, 1 . 1 1 M. Quack and H. Thone, Furuduy Discuss. Chem. SOC., 1986, 82, 226. Priestley, J. Phys. Chem., 1983, 87, 429. Maas Jr, Adv. Chem. Phys., 1981,47, 639. Prof. M.Quack, Dr E. Sutcliffe (ETH Ziirich), Dr P. A. Hackett and Dr D. M. Rayner (NRC, Ottawa) replied: In the discussion of our paper a number of pertinent questions were raised, which show that many of the fundamental problems in photofrag- mentation after i.r.-multiphoton excitation still need detailed investigation, even exclud- ing the interesting question as to the potential for large-scale technology.'*2 We shall reply to these questions following a logical order. Dr Hancock mentioned the importance of controlling intensity and fluence quantita- tively. In the iodine atom detection experiments intensity and fluence are very well controlled, although intensity is not constant throughout the pulse. This allowed us to290 General Discussion give quantitative results on the real-time fluence dependence in case B, but only qualitative results concerning the non-linear intensity dependence in case C.The non-linear intensity dependence of rate coefficients could be quantified somewhat better using the technique of rectangular pulse shaping pioneered by Hancock and coworkers, and Although this has been known for some time and has been suggested repeatedly, to our knowledge no such data are available until now [see ref. (2)]. Because of the problems of leaking radiation after the rectangular pulse mentioned by Dr Hancock, we would suggest that such measurements be made using time-resolved detection, as in our work, and final evaluation as a function of fluence and intensity instead of time and intensity for obvious reasons.Dr Hancock has also mentioned the possibility of whether leaking tail radiation might be responsible for the long-time dissociation observed in the infrared probing experiments. This point has been investi- gated experimentally in some detail by changing on purpose the tail contribution to fluence and we believe that we can exclude any important effect from this. In the iodine atom probing experiments the effects related to this are fully contained in the evaluation. For the short-time observation phase in both the Ottawa and Zurich experiments dominant collisional effects seem to be extremely unlikely and no pressure dependence was found with fairly large pressure variations (see also the respective comments from the two groups536). We think that the pressure and time conditions in Dr Hancock’s experiments are not comparable to the initial time period of our experiments.We would strongly recommend that Dr Hancock uses his rectangular pulse shaping technique to investigate CFJ. One must note in this context certain problems with the monochroma- ticity of such pulses, which will affect the interpretation of non-linear intensity effects. However, these problems could be accounted for, theoretically. Dr Levy and coworkers have presented data on most interesting reaction systems. It would be worthwhile to continue such experiments, following the real-time course of reactant and product concentrations at well defined fluences. Dr Levy has himself already addressed the problems arising when fluence is not fully controlled over the region of observation.He might wish to consider also evaluation using least-squares fitting and convolution techniques as discussed in ref. (7). Dr Levy has also pointed out the finding of turnovers in the logarithmic reactant fluence plots of their data. In order to prevent a misunderstanding which has occurred repeatedly in the literature, we should point out that a turnover can arise because of a combination of non-linear intensity effects combined with a time-dependent decrease of intensity, as discussed in our paper. A turnover can also arise in case B with completely linear intensity dependence [for theoretical model calculations see ref. (8), fig. 181. If the combination of linear intensity dependence with a turnover in Dr Levy’s report is real, this second case, which arises from the reducibility of the case B rate coefficient matrix, would be applicable.Loosely speaking, the bandwidth contains then inhomogeneous contributions, which may occur even with a temperature-independent position of the band maximum, although at least the width of the band should be temperature dependent in this case [see ref. (9)]. This does not imply that structure would be easily observable at room temperature in the spectrum of such a large molecule. As both these comments have addressed the role of non-linear intensity dependence in i.r.-multiphoton excitation, possibly in relation to inhomogeneity, we would like to summarize some current aspects of the origin of the non-linear intensity dependence. Several common proposals are given as to the origin of the non-linear intensity depen- dence.(i) The contribution from the direct or Goeppert-Mayer multiphoton processes in the first few steps induces the non-linearity. Although in principle possible, this would imply that the first steps are not following a quasi-resonant stepwise mechanism. Theoretical calculations indicate this to be unlikely under typical conditions. lo Almost no direct experimental checks are available, but one experiment on Fe(CO), i.r.-General Discussion 29 1 photofragmentation exists, where strong pumping at the C0,-laser frequency just half of a strong absorption band, gives no detectable reaction, whereas weak pumping of a fundamental near 2000 cm-' gives appreciable reaction." We think that the direct and Goeppert-Mayer mechanisms are generally too inefficient in the i.r.-multiphoton excita- tion of polyatomic molecules to be important (they are important with electronic excitation in the visible).(ii) The second qualitative suggestion proposes to separate the molecular ensemble in two parts, one linearly reactive, one non-reactive. The non-reactive molecules are then believed to be made reactive by non-linear 'power-broadening effects'. There are several problems with this explanation, as it cannot account for the non-linear intensity dependence if all molecules are in the same ground state initially. Also it gives no quantitative recipe to calculate the non-linear intensity dependence. (iii) A very simple quantitative treatment of non-linearity arises from the statistical case c master equation.12 (iv) When statistical approximations are not valid and quantum interference between individual quantum states are important one may have other unusual effects, such as a decrease of rates with an increase of inten~ity.'~ Finally, we wish to reply to the comments raised by Dietrich et al.and by Hackett et al. Much of the relevant information is already contained in these comments. It may be appropriate, however, to provide some summarizing statements concerning the current status of our understanding. ( a ) Even if the iodine atom probing experiment were measuring the excitation rate above threshold and not the dissociation rate directly, the result for k(st) could still be compared to theory and to the indirect measurement, because the specific rate constants above threshold hardly affect k(st).We have made model calculations changing k(E, J ) from statistical theory to lower values (by factors of 10, lo2, lo3), which leads only to small changes in k(st).14 This implies inversely that consistency of the indirect results for k( st) with the iodine atom probing results does not imply that the latter are measuring dissociation rates directly. ( b ) Theoretically, the production of only ground-state iodine atoms from superex- cited iodides by visible photolysis seems unlikely, as the relevant average excitation in the CI bond is low for the large molecules, even above threshold. If this argument is accepted, the interpretation of the iodine atom yield measurements as detecting dissoci- ation directly seems to be unavoidable in agreement with the statements of Hackett et aL,' although direct experimental proof is unavailable.(c) Very drastic assumptions beyond the failure of RRKM theory are necessary to explain a slow dissociation component at high fluences, for instance that CFJ has k ( E , J ) of ca. 3 x lo6 s-' up to twice its dissociation energy.14 Adiabatic channel model calculations including angular momentum effects, which have been obtained a long time ago" and have been repeated recently16 using a simplified model definitely cannot explain a large slow component in the dissociation of CF31 at high fluence, in contrast to the proposal of ref. (16). ( d ) The infrared probing experiments would be best explained by assuming that a relatively large volume is viewed because of diffraction effects, which is dominated by regions of low fluence, just sufficient to excite molecules above threshold where they slowly decompose. Also collisional effects with huge cross-sections might play a role on the longer timescales relevant for the low effective fluence.The difficulty with this explanation is the lack of experimental evidence in favour of effects that are large enough, quantitatively. We thus conclude that, although there remain still open and exciting questions with regard to all of these experiments, the good comparison of direct and indirect experi- ments with each other and with theory in our paper would remain unaffected. The question of slow after-pulse dissociation (presumably at low effective fluence) remains292 General Discussion an interesting topic to be investigated in more detail in order to answer the remaining unresolved questions.More direct experiments measuring the iodine atom concentra- tion, for instance by near-infrared absorption or single-photon excited fluorescence in the v.u.v., would be helpful and are planned. 1 A. Outhouse, P. Lawrence, M. Gauthier and P. A. Hackett, Appl. Phys., 1985, B36, 63. 2 D. W. Lupo and M. Quack, Chem. Rev., 1987, in press. 3 M. N. R. Ashfold, C. G. Atkins and G. Hancock, Chem. Phys. Lett., 1981, 80, 1. 4 R. D. McAlpine and D. K. Evans, Furaday Discuss. Chem. SOC., 1983, 75, 261. 5 P. A. Hackett, D. M. Rayner and M. Humphries, Furuday'Discuss. Chem. SOC., 1986,82, 275. 6 P. Dietrich, M. Quack and G.Seyiang, Faraduy Discuss. Chem. SOC., 1986, 82, 280. 7 M. Quack and G. Seyfang, J. Chem. Phys., 1982, 76, 955. 8 M. Quack, Ber. Bunsenges. Phys. Chem. 1979, 83, 757. 9 K. von Puttkamer, H. R. Dubal and M. Quack, Furaduy Discuss. Chem. SOC., 1983,75, 197. 10 M. Quack and E. Sutcliffe, J. Chem. Phys., 1985, 83, 3805. 1 1 Mei-Kuen Au, P. A. Hackett, M. Humphries and P. John, Appl. Phys., 1984, B33, 43. 12 M. Quack, J. Chem. Phys. 1978, 69, 1282; Ber. Bunsenges. Phys. Chem., 1981, 85, 318. 13 M. Quack and E. Sutcliffe, Chem. Phys. Lett., 1983, 99, 167. 14 D. W. Lupo and M. Quack, Ber. Bunsenges. Phys. Chem., to be published. 15 M. Quack, Ber. Bunsenges, Phys. Chem., 1979,83, 1287; M. Quack, in Intramolecular Dynamics, ed. J. 16 B. Abel, L. Brouwer, B. Herzog, H.Hippler and J. Troe, Chem. Phys. Lett., 1986, 127, 541. Jortner and B. Pullman (D. Reidel, Dordrecht, 1982), p. 371. Dr J. M. Hutson (Cambridge University) said: Drs Kidd and Balint-Kurti have presented beautiful calculations of photodissociation spectra for Ar- HD. They obtain good agreement with the positions and widths of the experimental lines, but there are some remaining discrepancies in line intensities, which they attribute to deficiencies in the induced dipole moment function of Dunker and Gordon.' This was determined by manual fitting to McKellar and Welsh's 1971 spectra of Ar-H,, which were not fully resolved;2 in particular, the P and R branches of the S , ( O ) band were strongly overlapped, and this severely restricted the precision with which Dunker and Gordon could disen- tangle the different angular coefficients in the dipole moment function.However, McKellar has since remeasured the spectra at much higher res~lution,~ and Prof. R. J. Le Roy and I have used these spectra to determine both improved potential-energy surfaces4 and improved dipole moment functions5 for the rare gas-H, systems. Following Dunker and Gordon, the transition dipole for the v = 1 + 0 transition is written in terms of radial functions go,( R ) , 9,,( R ) and 9623( R ) , which are the coefficients of different angular components. These are parametrized as functions of the inter- molecular distance R Boi(R)=Doi ~ ~ P [ P ( R ? - R ) I + D ~ ( R ? / R ) ~ B , ~ ( R ) = D , ~ ~ ~ ~ [ P ( R ~ ' - R ) ] + J S Q ~ R - ~ where R?= 3.581 71 8, is the equilibrium distance for H2-Ar? a = 11.096 a: is the polarizability of the Ar atom, and Q is the matrix element of the H2 quadrupole moment between the states concerned, Q = 0.0784,0.0880 and 0.0721 eai for the S , ( O ) , Q1( 1 ) and S,(1) bands, respectively.6 The exponent parameter P was fixed at 2.80 8,-' for all three angular terms, and the remaining four parameters were determined by direct least-squares fitting to the peak intensities of 150 lines from McKellar's 1982 spectra.Preliminary values of the fitted parameters are Dol = 1.52 f 0.37 mD, D7 = -0.47 f 0.33 mD, D2, = -0.42 f 0.03 mD and D23 = 0.004 f 0.017 mD. The dispersion term D7(R00/R)7 does appear to be necessary to reproduce the intensity profile of the Ql(0) band accurately, but D7 was very highly correlated with Do, in the fits.It may be noted that the uncertainty in DZ3 is greater than its value, indicating that 9623(R) is very strongly dominated by the quadrupole-induced dipole term.General Discussion 293 Since this work was done, McKellar has measured infrared spectra of Ar-H, under even higher resolution, so that the results given here should be regarded as preliminary. Nevertheless, it would be very interesting to see whether these improved dipole moment functions result in improved agreement with the experimental intensities for Ar- HD. 1 A. M. Dunker and R. G. Gordon, J. Chem. Phys., 1978, 68, 700. 2 A. R. W. McKellar and H. L. Welsh, J. Chem. Phys., 1971, 55, 595. 3 A. R. W. McKellar, Faraday Discuss. Chem. SOC., 1982, 73, 89. 4 R.J. Le Roy and J. M. Hutson, J. Chem. Phys., 1987, 86, 837. 5 J. M. Hutson and R. J. Le Roy, to be published. 6 G. Karl and J. D. Poll, J. Chem. Phys., 1967,46, 2944. Dr D. S . King (N.B.S., Gaithersburg, USA) said: Nitric oxide dimers, when excited to the v = 1 level of vl (the symmetric N-0 stretch), dissociate to produce equal populations in the Fl and F2 fine-structure states. Both fragments have very little rotational excitation, in fact ca. 75% of the available energy goes into the kinetic energy of the separating fragments. To understand fully the molecular dynamics of such a process, it is important to know both the fragment energy distributions and the timescale of the predissociation process. We have measured the predissociation rates for the nitric oxide dimer in the v = 1 levels of both the v,-symmetric and v4-antisymmetric stretches using a picosecond (ps) infrared (i.r.) laser pump-ps ultraviolet ( u.v.) laser probe technique.' Both pump and probe laser pulses were derived from the same mode-locked C.W.YAG laser. This master source was frequency-doubled and used synchronously to pump two tunable visible dye lasers. The outputs of these dye lasers were amplified in pulsed dye amplifiers pumped by 2 ns pulses from a frequency-doubled Q-switched YAG laser operating at 20pulse s-'. Visible pulses of ca. 0.5 mJ energy were obtained. The bandwidths of these dye lasers were 3 cm-' f.w.h.m. The pulses gave 7.5 ps f.w.h.m. autocorrelations and a 10 ps f.w.h.m. cross-correlation. The yellow dye laser was tuned to w1 = 17 341 cm-'.Its amplified output was frequency-doubled and the second har- monic subsequently mixed with a portion of the 1064nm output from the Q-switched YAG. The resulting 5 pJ of U.V. radiation served as the probe, exciting the NO ( F , , J = 1.5-7.5) fragments on the P,, bandhead of the A-X band system. The second, red dye laser was tuned to a fequency 0, = 15 552 or 15 471 cm-' such that difference frequency mixing, w1 - o,, generated 5 p J i.r. pump pulses at either 1789 or 1870 cm-' for exciting the beam-cooled nitric oxide dimer v4 or v1 modes, respectively. Nitric oxide dimers were formed in the beam apparatus described above using expansion conditions demonstrated through fragment energy distribution measurements to be dominated by the (NO), species.The ps i.r. and U.V. pulses traversed the beam chamber colinearly, the passage of the i.r. pulse defining t = 0. The U.V. probe pulses traversed a variable optical delay before passing through the beam chamber. The resulting laser-excited fluorescence was detected as described above. The temporal appearance of the NO fragments followed the behaviour where the signal at delay t increased at a rate determined by the predissociation lifetime of the vibrationally excited dimer. Excitations of v1 and v4 resulted in observed signals S ( t ) well fitted by single exponential decays. The lifetime obtained for excitation of vl at 1870 cm-' was Tvp = 880* 260 ps. Excitation of v4 at 1789 cm-' gave a value Tvp = 39* 8 ps, a factor of 22 shorter. These results are inconsistent with standard theories of statistical unimolecular dissociation.Although momentum gap arguments predict a value for Tvp(v4) < Tvp(vl), the predicted difference would be less than a factor of 2. The origin of this strong, mode-specific behaviour might result from non-adiabatic effects294 General Discussion since the 211 states of the separated NO monomers will combine to create many low-lying electronic states. 1 M. P. Casassa, A. M. Woodward, J. C. Stephenson and D. S. King, J. Chem. Phys., 1986, 85, 6235. Prof. P. L. Houston (Cornell University, USA) said to Dr King: You showed in fig. 3 the Doppler profile of the Q2,(3.5) transition. Did you also look at P- or R-branch transitions? Differences in the Doppler profiles would indicate that there is an angular correlation between the recoil velocity vector and the angular momentum vector.Dr D. S . King (NBS, Gaithersburg, USA) said: We have only measured fragment Doppler profiles for Q-branch transitions. Measurements of such profiles for Q us. P, R transitions might, in principle, disclose correlation between fragment velocity and angular momentum (cJ the papers by Houston et al. and Docker et ul. and related discussion). However, in the present (NO), dissociation experiments, the NO fragments are formed predominantly in low-1 states. For low-J NO molecules, represented by Hund's angular momentum coupling case A, Q and P, R branch transitions are not cleanly polarized parallel with and perpendicular to the axis of rotation as they are, for example, for the high-1 CO fragments you described in your paper.Therefore, within the accuracy of our Doppler width measurements (cJ fig. 3 of our paper at this Discussion), we would not expect to resolve differences in Doppler profiles characteristic of such correlations. Prof. K. F. Freed (University of Chicago, USA) said: Dr King showed striking data on the NO van der Waals dimer in which the v4 antisymmetric vibration has significantly faster predissociation rate than the v1 symmetric stretch. There are precedents in having predissociation rates that strongly depend on the vibration excited in the van der Waals molecule. One example is the (HF), van der Waals dimer.' However, the two HF molecules in this dimer are inequivalent, and this accounts for the expectation of a significantly different vibrational predissociation rate with excitation of the two different HF stretches.' The NO van der Waals dimer, however, is symmetric so the vl and v4 vibrations are truly the symmetric and antisymmetric NO stretches and it is, therefore, more difficult to perceive the origins of a significantly different vibrational predissociation rate for the two.I would like to suggest that perhaps the symmetry of the molecule2 plays a strong role in this vibrational predissociation. If V is the total potential energy of interaction of the two NO molecules, then the predissociation is driven by the coupling (6' V/C~Q*)~Q* where Q+ is the vl vibrational coordinate and Q- is the v4 vibrational coordinate. A simplistic coplanar pairwise additive interaction model would indicate that the v4 vibration couples more strongly to counter-rotations of the two NO molecules, while the vl vibration Q' couples more to the relative translational motion of the NO molecules. Thus, it would be expected that rotation participates more significantly in the v4 decay than in the vl decay, thereby producing the more rapid decay of v4.It will be interesting to study predissociation in other symmetric van der Waals dimers to see if similar symmetry-induced behaviour is observed. 1 N. Halberstadt and Ph. Brhchignac, J. A. Beswick and M. Shapiro, J. Chem. Phys., 1986,84, 170 2 K. F. Freed, J. Am. Chem. SOC., 1980, 102, 3130. Mr M. R. S. McCoustra and Dr J. Pfab (Heriot-Watt University) said: Dr King reported full equilibration of the lambda doublet populations in NO from the photodis- sociation of its dimer.In contrast to slow dissociation, rapid predissociation or dissoci- ation processes from a repulsive surface led to non-equilibrium lambda doublet popula- tions. Unequal lambda doublet populations in NO have been observed recently in theGeneral Discussion 295 1.00 0.80 c, z .a r i J 7 0.60 e E -. k 9) 0.40 e 2 13 0.20 0.00 0 0 0 0 0 o o 0 Q 0 0 5 29 33 37 41 J” 5 Fig. 11. The degree of electron alignment6 as a function of J for NO (d’= 1) from the 355 nm photodissociation of jet-cooled methyl nitrite (El) compared to the predictions of the model6 (-). photodissociation of N02,1 dimethylnitrosamine? methyl nitrite3 and t-butyl nitrite.4 We have recently investigated the 355 nm photodissociation of both jet-cooled methyl and t-butyl nitrite, which had previously only been studied at room temperat~re.~’~ In both cases, we find that jet-cooling of the precursor enhances significantly the lambda doublet specificity as observed by Andresen et al.for OH from H20.’ Fig. 11 presents our results for methyl nitrite and fig. 12 those for t-butyl nitrite. In each case the squares represent the experimental values for NO (v”= 1 ) and the full lines represent the calculated degree of electron alignment using the predictions of the one-electron overlap model of Andresen.6 Clearly, the lambda doublet selectivity is higher in the photodissoci- ation of t-butyl nitrite than for the methyl derivative for reasons that are not yet clear, and the agreement with the model is excellent for high J of NO from the dissociation of the former. 1 L.Bigio and E. R. Grant, J. Phys. Chem., 1985, 89, 5855. 2 M. Dubs, U. Briihlmann and J. R. Huber, J. Chem. Phys., 1986, 84, 3106. 3 F. Lahmani, C. Lardeux and D. Solgadi, Chem. Phys. Lett., 1986, 129, 24. 4 D. Schwartz-Lavi, I. Bar and S. Rosenwaks, Chem. Phys. Lett., 1986, 128, 123. 5 P. Andresen, G. S. Ondrey, B. Titze and E. W. Rothe, J. Chem. Phys., 1984, 80, 2548. 6 P. Andresen and E. W. Rothe, J. Chem. Phys., 1985, 82, 3634. Prof. M. Quack (ETH, Ziirich) said: In the work of Sarre and coworkers and Castleman and coworkers we have seen beautiful examples of the observation of positive molecular ions and negative cluster ions in the gas phase, respectively. In this context I have two questions.296 General Discussion J” Fig.12. The degree of electron alignment6 as a function of J for NO (u”= 1) from the 355 nm photodissociation of jet-cooled t-butyl nitrite (0) compared to the predictions of the model6 (-). (i) Has Prof. Castleman seen any evidence for the solvated doubly charged ion CO;-( H20) ? Although the long-range repulsion of two negative charges would seem to be unfavourable, chemical intuition suggests that short-range chemical forces (solva- tion) should overcome the repulsion. (ii) Would not the doubly charged cation 3He4He2t be an interesting candidate for high-resolution photofragment spectroscopy by vibrational excitation? The He;+ ion has been observed by mass spectrometry’ and has been calculated2 to have a metastable potential minimum in the electronic ground state at 70 pm separated by a barrier of ca.12 000 cm-’ from the stable dissociation channel 2 He+. The 3He4He2+ ion should have a substantial transition moment for rovibrational transitions. The higher-lying rovibra- tional states should be increasingly predissociated and would thus be observable by photofragment spectro~copy.~ A major difficulty would be the preparation of the doubly charged ion, but this may be overcome.’ Photofragment spectra might provide informa- tion about this particularly interesting potential of an unusual chemical bond. 1 M. Guilhans, A. Gareth Brenton, J. H. Beynon, M. Rabrenovic and P. von Ragui Schleyer, J. Chem. 2 H. Yagisawa, H. Sat0 and T. Watanabe, Phys. Reu. A, 1977, 16, 1352.3 P. J. Sarre, J. M. Walmsley and C. J. Whitham, Faraday Discuss. Chem. Soc., 1986, 82, 67. SOC., Chem. Commun., 1985, 210. Prof. A. W. Castleman Jr (Penn. State University, USA) said: That is a very interesting and pertinent question. As you well know, there are many examples of multiply charged anions and cations in the condensed phase. However, in the gas phase the situation is quite different. Consider for instance cations. In order to cluster some atoms or molecules about a doubly charged cation, as a first step a collision is required betweenGeneral Discussion 297 the doubly charged ion and the ligand. This almost invariably would lead to a charge transfer with the separating collision partners each retaining a single charge. Despite the fact that the solvation energies should enable the eventual formation of doubly charged stable cations at large sizes, methods for producing these in the gas phase have so far not been successful except for one or two exceptions.In the case of cations, ones which are stable against Coulomb explosion have been produced by electron impact ionization of very large neutral clusters. The smaller sizes rapidly dissociate, undoubtedly owing to the separation of two charges where the Coulomb forces of the two charged particles exceed the cohesive energy of the cluster. In the case of anions, the literature is replete with reported observations of small inorganic doubly charged ones, but subsequent studies have invariably shown the earlier reportings to be suspect. As far as clusters go, there is currently only one system for which a doubly charged ion has been reported, namely for ( O J - (work of Mark and collaborators).This work has not been verified. We, and I suppose others, are currently searching for new methods of producing these studies which will have direct solvation analogies. Prospects for their study represent a potentially exciting new area of research. Dr P. J. Sarre (University of Nottingham) said: I agree that a study of 3He4He2+ would be fascinating, and in principle a spectrum of this ion could be recorded by infrared laser photofragment spectroscopy. As Prof. Quack pointed out, the main problem is to generate a sufficiently strong ion beam. The charge-stripping technique' yielded a beam of only 6 x In connection with this interesting suggestion, it is worth noting that a related laser photofragment spectrum of Ni+ in the visible region has been recorded by Cosby et aL2 A.1 M. Guilhaus, A. G. Brenton, J. H. Beynon, M. RabrenoviC and P. von Raguk Schleyer, J. Chem. SOC., 2 P. C. Cosby, R. Moller, and H. Helm, Phys. Rev. A, 1983, 28, 766. Chem. Commun., 1985, 210. Prof. R. N. Zare (Stanford University, U.S.A.) said: Assume that you have a hydrated negative ion of the general form X-(H20),. Let us also suppose that it is irradiated by a beam of photons with sufficient energy to photodetach the electron or to cause loss of water molecules. How do these two processes compete as a function of n, the number of water molecules bound to X-? Prof. A. W. Castleman Jr (Penn. State University, USA) said: As you recognize, the electron affinity of a cluster should vary in a more-or-less continuous fashion from the value for the isolated particle toward the electron affinity/work function of the bulk media.Of course, each small cluster system will obviously display its own individual trends from size to size and a perfectly smooth curve should not be expected until rather large values of n are attained. Currently, only limited information is available on this highly interesting problem. From our bond-energy measurements of ligands to various anions, we can directly calculate through thermodynamic cycles the change in the electron affinity as a function of cluster size. We have done this for a number of anionic ligand systems for degrees of aggregation up to ca.five or six. Direct observations of varying electron affinities as a function of cluster size are very sparse. Bowen (John Hopkins) and Lineberger (Colorado) have both reported a few measurements of the electron affinity of small cluster systems, and their techniques appear to be very promising ones to answer the intriguing questions raised by this line of research. In our work, we have studied the bonding of SO2 to SO, and have deduced the electron affinity of the species (SO,), to be 1.95 eV compared to 1.1 eV for SO,. In the case of our photo- dissociation studies we see competitive channels involving both the ejection of SO2 from the (SO,); as well as photodetachment from the dimer anion. Our measurements, as well as those of the other investigators, are currently in progress.298 General Discussion Prof.J. P. Simons (Nottingham University) said: In much of the work employing C.W. or pulsed supersonic nozzle beam sources, the possibility of cluster formation is countenanced, but assumed to be unimportant. This may not always be true. Recent experiments conducted with a pulsed jet expansion source of H202 in Ar or He,’ were intended to explore the influence (if any) of parent molecular rotation on the dynamics of its photodissociation at 248 nm. In the event, the rotational energy disposal in the OH( X ) fragments remained unaffected until the stagnation pressure rose above ca. 90 Torr, when there was a progressive change in the rotational population distribution. It became bimodal, with an increasing non-inverted component in the lowest levels, and a decreasing contribution from the ‘excited’ distribution peaking at N = 7 .The rotational cooling of the fragment was not a consequence of rotational cooling of the parent molecule however, since the Doppler profiles of the rotational features also revealed a bimodal translational distribution. For example, profiles which previously displayed a central dip, now showed a very narrow central feature, superimposed on the vestiges of the original, Doppler-broadened profile. The overall photofragment population included a major fraction which was rotationally and translationally cold. The only means of translational cooling would have to be ‘collisional’ in nature, not with surrounding molecules since these were too few in number, but through internal ‘collisions’ within a cluster.It is suggested that the very cold component of the photofrag- ment population distribution is associated with fragments which just manage to escape the ‘cluster-cage’. (Similar results were obtained in Frankfurt with 193 nm radiation by A. U. Grunewald, K-H. Gericke and F. J. Comes.) Now the question to Prof. Castleman is ‘how can we ascertain the cluster distribution when the molecules involved are (i) neutral and (ii) non-fluorescent’? 1 M. P. Docker, A. Hodgson and J. P. Simons, unpublished work. Dr P. A. Gorry (University of Manchester) said: Prof. Simons has highlighted a significant problem in cooling molecules by supersonic expansion, that of cluster forma- tion. It is essential that clusters be avoided if comparison with bulb experiments is to be meaningful, but it is often very difficult to determine the extent of any clustering.In recent experiments with our variable-geometry translational photofragment spec- trometer’ we developed a procedure for ensuring the absence of any cluster contribution to the photofragmentation. Taking the simplest case of a dimer, the photofragmentation is a three-body process in which one of the photodissociation products is an undissociated monomer. Since the translational energy is disposed into three fragments the monomer scatters at angles close to the molecular beam (although light fragments may still reach significant laboratory angles). By monitoring the photofragment mass spectrum at 10” from the beam we were able to observe large photofragment monomer peaks from several of the alkyl iodides under study.These persisted even at nozzle temperatures of 140 “C and dilution ratios of 5 : 1. We found, however, that the cluster content could be removed entirely by driving the pulse beam2 at lower voltages. At a low enough voltage the ribbon covering the nozzle orifice does not lift sufficiently to give unrestricted flow through the nozzle and the resultant expansion occurs from a lower ‘local’ stagnation pressure. The mach number is lowered by this process but we still estimate final rotational temperatures in the 35-50 K range. By this procedure we are quickly able to ascertain the conditions under which clustering occurs, although the size distribution of the clusters is not determined. 1 N.P. Johnson, M. D. Barry and P. A. Gorry, J. Phys. E, 1986, 19, 808. 2 M. D. Barry, N. P. Johnson and P. A. Gorry, J. Phys. E, 1986, 19, 815. Prof. A. W. Castleman Jr (Penn. State University, USA) said: Studies of the dynamics of formation and dissociation, and the changing properties of neutral clusters at success-General Discussion L - - parent ion dauqhter ion L 299 ’UK -u, channel tron ground r cf lcct ron 1 . : ! parent ions - - - - - - - - :* i ; neutral beam - . . : -L - - : : . . . . . . . laser daughter ions !f . . grounb u; I I : I ’ I -I- ($ ground UU Fig. 13. ( a ) Schematic diagram of time-of-flight mass spectrometer with reflection where daughter ions are reflected before parent ions. ( b ) The electrostatic potentials.ively higher degrees of aggregation, enable basic investigations that serve to connect the gas and condensed phase. The progressive clustering of a molecule involves energy transfer and redistribution within the molecular system, with attendant processes of unimolecular dissociation taking place between growth steps. Related processes of energy transfer and dissociation are operative during the reorientation of molecules about ions following the primary ionization event employed in detecting clusters via mass spectrometry. Dissociation has been a plaguing problem in making definitive one-to-one correlations between detected ion clusters and those neutral ones responsible for the primary process under investigation. Recent advances in the field of molecular-beam research, coupled with lasers and time-of-flight mass spectrometry, enable the details of these various processes to be investigated.A major advance in the study of these processes has become available through the use of a reflection technique introduced into the drift region of a time-of-flight mass spectrometer. Using single and two-colour tunable pulsed lasers, the excess energy introduced into a cluster can be well controlled within the limitations of that dictated by the difference in potential energy between the neutral and ionized state of the cluster. The power of these techniques has been demonstrated in our laboratory through a variety of studies including investigations of hydrogen-bonded clusters ( NH3) and Clusters of the desired molecules are formed via adiabatic cooling from a pulsed nozzle system, with detection of the products following MPI being made in a time-of- flight mass spectrometer located beyond the ionization region (see fig. 13).The combina- tion of ionization and mass selection has the advantage of direct mass determination of the probed clustered molecules. Because of the weak bonding in complexes, dissocia- tive ionization may possibly complicate the spectroscopic assignments. In our work multiphoton ionization is accomplished using a Q-switched Nd : YAG laser to pump simultaneously two tunable dye lasers whose output is frequency-doubled in KDP crystals. The arrangement allows continuous tunability from the visible down to 216.5 nm, with a maximum output of 1 to 29 MJ per pulse (6 ns duration) in the U.V.The results show that fragmentation can be greatly suppressed through the use of two-colour resonance-enhanced photoionization, whereby the ionization process is accomplished with the use of little excess energy in contrast to one-colour experiments. (CH3OH)n.300 General Discussion Fragmentation can be investigated directly using a reflectron, where the ions are directed into a reflecting electric field which is positioned off -axis at the end of the drift tube. This reflecting electric field decelerates and reflects the ions in a homogeneous electric field to the entrance of the second particle detector that is positioned above the TOF lens (see fig. 13). In this case, ions which do not dissociate between the ion lens and the reflectron give rise to a normal TOF mass spectrum [see fig. 14(a)].However, product ions which arise due to dissociation processes occurring between the ion lens and the reflectron, form an additional spectrum that becomes superimposed on the spectrum of the original parent ions with a time difference between corresponding mass peaks [see fig. 14(b)]. These product ions arise due to the fact that following ionization of an ammonia moiety within a neutral cluster, protonated cluster ions of the form (NH,), - H+ are formed rapidly ( < l o ns) via an internal ion-molecule reaction. NH, monomer units are lost on a longer timescale owing to the excess energy created as the ammonia molecules in the cluster reorient from their original configuration to incorporate the structure of the newly formed NH: entity.The dissociation process occurring via loss of one NH, unit (NH,); H' + (NH3),-1- H++NH, was investigated' for various ion cluster sizes from n = 4 to 20. Fig. 14(c) shows a spectrum obtained with the reflectron where only the daughter ions (from the loss of one ammonia molecule during the flight in the field-free region prior to the reflectron) are reflected. This is accomplished by reducing the applied potential at the end of the reflectron (i-e., UK< U,, see fig. 13), whereupon only the lower kinetic energy products are reflected. Further reduction of the reflecting potential UT (with UK< UT) improves the ability to discern small contributions from more extensive dissociation. Through studies of collision-induced dissociation as a function of pressure, both collision-induced cross-sections and unimolecular dissociation rates can be derived.Another example of the prospects provided by an investigation of clusters using pulsed lasers comes from recent work on progressive shifts in the electronic state of a probe molecule due to clustering with a solvent.* We have used both one- and two-colour resonance-enhanced multiphoton ionization to investigate the S, +- So .rr-electron transition shifts in phenylacetylene and p-xylene due to the effects of solvent particle shifts. Two-colour techniques suppress effects due to fragmentation. For example, in the case of one-colour MPI experiments where the excess energy is 0.66 eV, substantial satellite peaks to the red of the main resonance of p-xylene are evident in the MPI spectrum of p-xylene as a result of fragmentation of the argon complexes of p-xylene.The satellite peaks correspond to bathochromically shifted S, +- So resonances of the argon complexes that have fragmented to p- xylene+ upon ionization. Little evidence of fragmentation is seen where the use of a two-colour technique enables near-threshold ionization from the shifted S, resonances of the clusters. 1 0. Echt, P. D. Dao, S. Morgan and A. W. Castleman Jr, J. Chem. Phys., 1985, 82,4076. 2 P. D. Dao, S. Morgan and A. W. Castleman Jr, Chem. Phys. Lett., 1984, 111, 38; P. D. Dao, S. Morgan and A. W. Castleman Jr, Chem. Phys. Lett., 1985, 113, 219. Mr M. R. S. McCoustra and Dr J. Pfab (Heriot-Watt University) said: We have discovered recently that the rotational distribution of NO from the 355 nm photolysis of jet-cooled dimethylnitrosamine is much colder than that reported for the room- temperature parent.' Without knowledge of the electronic spectrum of the jet-cooledGeneral Discussion 301 T r I I I I I I I I I I 1 time of flight/ps ;I I ia 1 1 ' 1 5 i I 1 1 I I time of flight/ps time of flight/ps Fig.14. (a) A conventional TOF mass spectrum of H+(NH3), clusters from the multiphoton ionization of ammonia clusters at 266 nm. (b) Time-of-flight mass spectrum taken using the reflectron. The potentials U, (0.996 U,) and U, (2.0 U,) are chosen such that all ions are reflected but with the daughter ions arriving at the particle detector earlier than their corresponding parent ions. (c) Time-of-flight mass spectrum taken using the reflectron.U, (0.0 V) is lowered to eliminate the parent ions. Both spectra ( b ) and ( c ) are accumulated ion signals over 2460 laser shots.302 General Discussion parent under the same conditions, it is difficult to exclude photolysis of a dimer or complex of the parent with the rare gas used for expansion as the source of the apparent cooling of the fragment in this particular predissociation process. If the parent fluoresces in competition with dissociation, its excitation spectrum in the jet will reveal such complications. Where the fluorescence yield is too low to obtain excitation spectra it is necessary to scan the dissociation laser and to record photofragment yield spectra at a fixed probe laser wavelength.The latter technique may also permit one to exclude experimental complications from complexation and dimerisation in direct dissociation processes. Finally, we wish to point out in this context, that jet-cooling can have a marked effect on the lambda doublet selectivity of a 211i photofragment formed in a direct dissociation or rapid predissociation. The example of the 355 nm photodissoci- ation of jet-cooled methyl nitrite and t-butyl nitrite is particularly pertinent as discussed in our comment following the paper by M. P. Casassa et al. 1 M. Dubs, U. Bruhlmann and J. R. Huber, J. Chem. Phys., 1986, 84, 3106. Dr P. Rosmus, Dr H-J. Werner and U. Manz (University of Frankfurt) said: It is perhaps interesting to note that the H20- ion itself is a cluster. According to our MC-CI calculations,' there are several local minima on the bound parts of the H,O- potential- energy surfaces, namely for the linear 0- - - .H2 cluster in the 21: and 211 states, which are separated by barriers from other linear structures OH - - H-(211) and OH- - H(,Z) and from the neutral H20+e. 1 H-J. Werner, U. Manz and P. Rosmus, J. Chem. Phys., submitted. Mr J. M. Philippoz, Dr H. van den Bergh and Dr R. Monot (EPFL, Lausanne, Switzerland) said: The experiments of Castleman and coworkers on the photodissoci- ation of COT hydrates show that in these systems a large fraction of the available energy goes into relative translational motion of the products. These authors suggest two mechanisms to explain this observation. (1) The photoexcited ,A1 state of C0,(H20), is repulsive along the coordinate that leads to removal of a water molecule.(2) The 2A1 state is internally converted into the ground 2B1 state, after which vibrational predissociation of this highly vibrationally excited ground-state level causes loss of a water molecule. We wish to report a similar observation to Castleman's here, in which also a high fraction of the available energy in the photodissociation of a cluster appears as fragment recoil energy. Our measurements are on the neutral 12Xe system, which, in contrast to the experiments of Levy and coworkers on similar 1,-rare gas complexes,' is excited above its B-state dissociation limit ( i e . not to bound levels of the B state). We discuss a model which tentatively explains our results.The mechanism we suggest is a non- adiabatic electronic transition which is accompanied by a large amount of energy released into the relative motion of the photofragments. Such a model might be a third, and alternative, explanation of the observation by Castleman et al. in the CO,(H,O), photodissociation. The relevant 1,Xe potential-energy curves are shown in fig. 15. These are in fact the I2 potential curves, but the energy changes induced by the van der Waals bond with xenon are not too different in the ground and electronically excited states in the range which concerns US.^ Levy et al. have measured that excitation to a bound level in the B state leads to predissociation with little energy going into recoil of the products, i.e. more or less following an energy-gap law.For excitation above the B-state dissociation limit, completely different behaviour is ~bserved.~ In this energy region, essentially twoGeneral Discussion 303 21 20 19 18 I I I t I I I + 2.6 G*' 2.7 2.8 Fig. 15. The relevant I2 potential-energy curves. The horizontal line near 20 045 cm-' indicates the B-state dissociation limit. The upper wavefunction corresponds to 488 nm excitation. The lower wavefunction (solid line) is such that its derivative (dashed line) gives the maximum overlap with xp = 20 490 cm-'. Thus, the non-adiabatic transition with d/dr coupling (see text) predicts u'= 30 to be the most populated I2 B level in the dissociation of 1,Xe at 488 nm. c 500 510 520 530 540 550 560 570 h/nm Fig. 16. Fluorescence from I2 (B 3110+u) produced by excitation of 12Xe above its B-state dissoci- ation limit, at 496.5 nm.One observes transitions from u'= 18-40 to u"= 0-3.304 General Discussion xenon 0.15 L: -3 0.10 CI s a a 0) .I U 4 0.05 & 0.00 18000 19000 20000 energy/ cm-' Fig. 17. Relative vibrational populations of the B state of free I2 after photodissociating 1,Xe at 496.5 nm (O), 488 nm (0) and 476.5 nm (A). The energy is relative to X, d'= 0. different pathways are possible: (a) The 1-1 bond breaks and (b) the I,-Xe bond breaks. In our experiments we observe only the latter case, in which an electronically excited I2 is formed and fluoresces to the ground state. Analysis of this resolved fluorescence yields the vibrational level populations in the I, B state. As we know the initial total energy content of the cluster after photoexcitation as well as the internal energy of the I2 product and the approximate dissociation energy of the van der Waals bond: the amount of energy going into translational energy of the fragments is obtained directly from these quantities. This indirect measurement of recoil energy contrasts with Castleman's elegant direct observation of translational energy with a retarding field anal yser. Fig. 16 shows a fluorescence spectrum measured with A = 496.5 nm photodissociating 12Xe in a free jet. The relative vibrational populations in the I2 B state extracted from three such measurements obtained at three excitation wavelengths are shown in fig. 17. Broad distributions of vibrational states are observed (f.w.h.m. ca. 10 vibrational levels). Furthermore, one sees that the distributions shift to higher vibrational levels when higher energy photons are used to photodissociate the 12Xe complexes. In fig. 18, the measured mean fragment recoil energies (open circles) are shown together with: ( a ) a result from quasi-classical trajectory calculations carried out on the B-state potential by Noorbatcha et al.' and ( 6 ) results from an impulsive energy transfer model in which the 12Xe is linear and the maximum possible energy goes into relative translational motion of the products. There is clearly a large discrepancy between these model calculations and the measured values. Together with Beswick we have recently proposed another model in which a non- adiabatic transition occurs between the initially excited I l l l u state and the B state.6 The coupling operator between these two states can either be of the Franck-Condon type (fig. 18, squares) or of d/dr type (non Born-Oppenheimer coupling) (crosses). The latter apparently gives the best agreement with the experimental results. This agreement is not as good for 12Ar and 12Kr. Finally, it should be mentioned that we have alsoGeneral Discussion 305 1500 - I E h F 8 1000 - ._ 8 2 U 1 W li 500 available energylcm-' 4 000 4500 5000 I I I + + 0 0 0 0 A 0 0 I 20 000 21 000 E,,,/cm-' Fig. 18. Most probable product recoil energy in the photodissociation of 1,Xe in function of the excitation energy: 0, experimental results extracted from fig. 17; 0, impulsive model calculations, A, the quasi-classical trajectory calc~lation;~ 0, calculations with a non-adiabatic transition using Franck-Condon-type coupling; + , calculations with a non-adiabatic transition using d/dr coup- ling. The available energy is E,, - EvdW bond - EB,ot=O. obtained preliminary rotationally resolved distributions of the I2 product in the photodis- sociation of I ~ M . ~ 1 W. Sharfin, K. E. Johnson, L. Wharton and D. H. Levy, J. Chem. Phys., 1979, 71, 1292. 2 N. Goldstein, T. L. Brack and G. H. Atkinson, J. Chem. Phys., 1986, 85, 2684. 3 J. M. Philippoz, H. van den Bergh and R. Monot, J. Phys. Chem., in press. 4 W. A. Wensink and J. D. W. Van Woorst, Chem. Phys., 1985, 99, 155. 5 I. Noorbatcha, L. M. Raff and D. L. Thompson, J. Chem. Phys., 1984, 81, 5658. 6 J. A. Beswick, R. Monot, J. M. Philippoz and H. van den Bergh, J. Chem. Phys., in press. 7 J. M. Philippoz, R. Monot and H. van den Bergh, Helv. Phys. Acta, 1986, 59, 1089.

ISSN:0301-7249    

DOI:10.1039/DC9868200275

出版商:RSC    

年代:1986

数据来源: RSC