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