TRANSLATIONAL EXCITATION Effect of Translational Energy on Reaction Dynamics BY ROGER GRICE Chemistry Department, University of Manchester, Manchester M13 9PL Received 14th February, 1979 1. INTRODUCTION Some of the first molecular beam studies on the effect of initial translational energy on reactive scattering were concerned with the reactions of alkali metal atoms. The use of effusive beam sources severely limited the range of translational energy which could be explored by velocity selection of the alkali metal beam with a slotted disc velocity selector. However, the low intensity of the alkali metal atom beam resulting from such an arrangement is compensated by the high efficiency of surface ionisation detection which can be used with alkali metal species. An earlier Faraday Discussion included a summary' of reactive scattering data on the K + CHJ reaction which exemplifies the range of information which may be obtained by these techniques.Similar results have been obtained2 for the K + Iz, RbF, CsF, HCl reactions. The relatively simple electronic structure of the potential energy surface imposed by the prevalence of ionic interactions in alkali metal atom reactions often permits inter- pretation3 of the reactive scattering data in terms of simple but effective models of the reaction dynamics. A particularly compelling example of the power of such models is illustrated by the lucid interpretation4 of the reactive scattering of alkali metal atoms by carbon tetrachloride molecules presented at this Discussion. The effect of initial translational energy on the dynamics of some non-alkali-metal reactions has been studied using effusive beam sources.The reactions of hydrogen atom^^*^ with halogen molecules, of fluorine atoms6 with hydrogen chloride and oxy- gen atoms' with iodine molecules have been studied using low pressure microwave discharge sources to produce low energy beams and thermal dissociation sources to produce higher energy beams. The reaction of fluorine atoms with deuterium mole- cules has been studied' as a function of initial translational energy by varying the temperature of the nozzle source of the deuterium beam. This technique is possible in this case only because the deuterium molecules are much lighter than the fluorine atoms, which are produced by effusion from a nickel oven and velocity selected by a slotted disc velocity selector.These early studies represent a pioneering stage which is now being transformed by the development of supersonic nozzle beams of atoms and free radicals seeded in inert buffer gases. These sources provide intense beams with narrow velocity distri- butions which can be readily varied by changing the molecular weight of the buffer gas. The measurement of angular and velocity distributions of reactive scattering from these beams is greatly assisted by the use of cross-correlation time-of-flightR . GRICE 17 analysis in place of the much less efficient conventional time-of-flight m e t h ~ d . ~ ' ~ Full contour maps of the differential reaction cross-section can now be measured as a function of initial translational energy for an increasing range of reactions.Particu- larly when these differential reaction cross-sections are augmented by measurements of product internal state distributions, they should provide a basis for the develop- ment of models for non-alkali-metal reaction dynamics. Since the electronic struc- ture of the reaction potential energy surface for non-alkali-metal species is often more complicated than that of alkali-metal species, we may expect that such comprehensive experimental information will be necessary for substantial theoretical progress to be made. 2. ADVANCES IN EXPERIMENTAL TECHNIQUE The production of supersonic alkali-metal atom beams seeded in inert buffer gas may be achieved9*'' in a manner analogous to the production of seeded beams of stable molecules," by the admission of buffer gas to a heated oven which maintains an appropriate alkali-metal vapour pressure.Supersonic beams of unstable atoms seeded in inert gases may be generated by thermal dissociation of diatomic molecules diluted by a high pressure of buffer gas in a high temperature oven constructed of inert materials. In this way, supersonic beams of hydrogen,12 fluorine13 and other halogen l4 atoms have been produced respectively from tungsten, nickel and graphite ovens. An alternative method of generating supersonic atom beams involves the use of a high pressure discharge through a dilute mixture of a diatomic precursor in excess inert buffer gas. A supersonic oxygen atom beam was first produced in this manner from a radio-frequency discharge by Miller and Patch." A microwave discharge source16 has been used in our laboratory to produce supersonic oxygen and chlorine atom beams.Oxygen atom beams seeded in He and Ne cover the energy range E = 13-35 kJ mol-' with Mach numbers M = 5-7 and intensities of (1-5) x lo1' atom sr-' s-l. A radio frequency oxygen atom discharge source has recently been developed at Berkeley17 which gives a higher degree of dissociation but is much more elaborate and more susceptible to discharge through the source chamber residual gas and hence requires higher pumping speed. Direct current discharge sources have been used to produce supersonic beams of hydrogenI8 and nitrogen l9 atoms. Thus an extensive range of supersonic atom beam sources suitable for studying the transla- tional energy dependence of reactive scattering is now available and we may expect supersonic free radical sources to be available in the near future.Depending upon the masses of the accelerated species and the buffer gas and also the temperature of the source, seeded nozzle beams will generally be the method of choice for producing molecular beams in the energy range 5-200 kJ mol-'. However, the use of rotor accelerated beams is enjoying a revivalZo after prolonged neglect following the pioneering work of Bull and Moon.21 The absence of buffer gas in rotor accelerated beams may offer advantages in some experiments, though the intensity is generally much lower than seeded nozzle beams. At energies above those which can be achieved by seeded nozzle beam sources > 400 kJ mol-', the charge exchange source becomes the method of choice.The velocity compression technique outlined at this DiscussionZ2 offers a method of maximising the rather low intensities available from this type of source in time-of-flight experiments. The single pulsing method of time-of-flight analysis used with a mechanical chop- per d i s ~ ~ , ~ in reactive scattering measurements or with voltage modulation of a charge exchange source," suffers from a very low duty factor, typically < 5%. This may be improved substantially by use of the pseudo-random cross-correlation time-of-flight18 TRANSLATIONAL EXCITATION method which enjoys a duty factor ~ 5 0 % . The cross-correlation method was first used by Hirschy and Aldridge23 to measure the velocity distribution of an Ar beam but its application to the measurement of velocity distributions of reactive scattering has followed 24-26 only recently.The implementation of the cross-correlation method in our laboratory 27 involves a mini-computer interface which drives a pseudo random chopper disc in synchronism with the advance of the channel address register. Time- of-flight data are stored in a random access memory which permits narrow channel widths 2 300 ns with negligible dead time Z S ns between channels. Data are transferred periodically to the minicomputer which performs the deconvolution and analysis of the accumulated data. The improved efficiency of data retrieval together with the higher intensity of reactive scattering and well defined kinematics provided by supersonic nozzle beams permits direct inversion28 of laboratory data to obtain a full contour map of the differential reaction cross-section.3. RECENT STUDIES OF REACTION DYNAMICS The systems so far studied with supersonic seeded beams and cross-correlation time-of-flight analysis show a wide range of reaction dynamics with differing depend- ence on initial translational energy. The improved resolution of the differential reaction cross-section and its dependence on initial translational energy is now providing much more detailed information and models of reaction dynamics which have been used to explain more limited data are becoming inadequate. The com- pleteness which is now attainable may be judged from the contour map of the differen- tial reaction cross-~ection,~~ shown in fig.1, for the 0 + CS, reaction with 0 atoms 0 cs2-02 *cs FIG. 1.-Polar contour map of 0s flux from 0 + CS2 with 0 atoms seeded in He as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translational energy E = 38 kJ mol-'. Incident 0 atom direction is denoted by 0 = O", incident CS2 direction 0 = 180".R . GRICE 19 seeded in He buffer gas giving an initial translational energy E = 38 kJ mol-'. In this case, velocity distributions measured at 27 laboratory scattering angles have been inverted directly to obtain a contour map of the differential reaction cross-section covering the full range of centre-of-mass scattering angle 8 = 0 - 180". The re- action follows a stripping mechanism whereby 0s product scattering peaks in the forward direction 8 = 0" with respect to the incident 0 atom beam.There is a constant intensity in the backward hemisphere which is lower than that of the forward peak by a factor x3.5. This reaction has also been s t ~ d i e d ~ ~ , ~ ' at lower initial translational energy E = 13 kJ mol-' using an 0 atom beam seeded in Ne. The differential reaction cross-section was found to be ~ n a l t e r e d ~ ~ . ~ ' over this range of initial translational energy when proper account of the variation in total energy avail- able to reaction products Etot is taken into account by calculating the fraction of this energy disposed into product translation. The reaction of C1 atoms with Br, mole- cules has been studied3' using C1 atoms seeded in He and Ar to cover the translational energy range E = 28-74 kJ mol-'.This reaction also exhibits a stripping mechan- ism with BrCl product scattered very sharply into the forward direction 8 < 40" and very little product scattered at wider angles. Hence these stripping reactions are each governed by an attractive potential energy surface with exoergicity released in the entrance valley. The sharpness of forward peaking for the C1 + Br2 reaction reflects its low exoergicity ADo = 25 kJ mol-' compared with the initial translational energy. In contrast the 0 + CS, reaction has a higher exoergicity ADo = 87 kJ mol-.l which exerts a greater influence on the reaction dynamics and maintains the intensity of wide angle scattering. In both cases the reaction dynamics indicate that reaction occurs in collisions with impact parameters at least comparable to the hard sphere collision diameters b 3 A. However, the small values of the total reaction cross- sections Q = 3-14 A2 indicate the presence of a significant orientation require- ment32*33 for each of these reactions.at an initial translational energy E = 31 kJ mol-', also gives OCl product scattering in the forward direction, The reaction of 0 atoms seeded in He with C1, 0 C l 2 ' 0 ~ * C I - -200 100 m s-1 FIG. 2.-Polar contour map of OC1 flux from 0 + C12 with 0 atoms seeded in He as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translational energy E = 31 kJ mol-I.20 TRANSLATIONAL EXCITATION as indicated by the contour map of the differential reaction cross-section shown in fig.2. However, the lower intensity data at wide angles 8 2 50" have a product trans- lational energy lower than that in the forward direction by a factor x 3 . Analysis of additional laboratory angular distribution data which were not included in deter- mination of the contour map of fig. 2, indicates the presence of a minor peak in the backward direction (8 = 180") with a relative height 0.3 j-- 0.1. More limited meas~rements~~ with 0 atoms seeded in Ne at an initial translational energy E = 13 kJ mol-1 indicate that the height of the backward peak increases to 0.55 & 0.15. Thus the reaction appears to proceed via a short-lived collision complex35 whose life- time increases with decreasing initial translational energy.However, the osculating complex assumes that all collision complexes are bound by a hollow on the potential energy surface and that the product translational energy distribution is independent of scattering angle. Clearly this is inappropriate to the 0 + Clz reaction which might more properly be regarded as consisting of a stripping com- ponent arising from collisions at large impact parameters and wide angle scattering arising from collisions at smaller impact parameters. The displacement reactions 0 + CF,I -&I+ CF, 7 100 m s-1 FIG. 3.-Polar contour map of 0 1 flux from 0 + CFJ with 0 atoms seeded in He as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translation energy E = 32 kJ mol-'. of F and C1 atoms with vinyl bromide molecules36 also appear to proceed via a short- lived complex and do show a modest variation in product translational energy with scattering angle, with higher energies in the forward and backward directions.As shown in this Di~cussion,~~ such a modest variation in product translational energy can be explained in the context of the osculating complex model by considering the coupling of product angular and translational energy distributions which is enforced by conservation of the total angular momentum of the complex. The iodihe atom abstraction reactions of F atoms seeded in Ar and He with CHJ molecules13 also proceed via a short-lived collision complex whose life-time depends on initial trans- lational energy. In this case, the product translational energy distribution is found to be independent of scattering angle to within the accuracy of the experimental data, in accord with the simplest version35 of the osculating complex model.The iodine atom abstraction reaction of 0 atoms with CFJ has been studied3'p3* using 0 atoms seeded in He and Ne to cover the range of initial translational energyR. GRICE 21 E = 14-32 kJ mol-'. The contour map of fig. 3 shows that the differential reac- tion cross section for 0 atoms seeded in He is essentially isotropic. However, the contour map of fig. 4, showing the differential reaction cross-section for 0 atoms seeded in Ne, indicates that 01 reactive scattering favours the backward hemisphere with respect to the incident 0 atom direction, at lower initial translational energy.This rebound mechanism suggests that reaction occurs only at small impact parameters in lower energy collisions but that the maximum impact parameter for reaction increases slightly with initial translational energy. The angular distributions of re- active scattering are in accord with a hard sphere scattering whereby product repulsion arises from induced repulsive energy release4' at small inter-nuclear distances. This model predicfs4O the conversion of initial translational energy into product trans- lational energy for the thermoneutral 0 + CF31 reaction, as is found to be roughly the 1100 1000 4 900 t 80° 4 70° 0 + CF,I -QI + CF, 100 m 5-1 FIG. 4.-Polar contour map of 0 1 flux from 0 + CFJ with 0 atoms seeded in Ne as a function of centre-of-mass scattering angle 8 and velocity u, at an initial translational energy E = 13 kJ mol-'.case for the average values of these energies. However, the product translational energy distributions for 0 + CF31 are strongly skewed with respect to the initial translational energy distribution as illustrated in fig. 5 for 0 atoms seeded in He. This suggests that there is also substantial energy exchange with internal modes of the CF3 radical and this is confirmed by the product translational energy distributions also shown in fig. 5 for the reactions41 of 0 atoms seeded in He with C2F51 and C3F71 molecules. The energy disposed into product translation decreases as the complexity of the departing radical increases along the series CF3, C2F5, C3F7 despite the increasing reaction exoergicity 42 along this series. Clearly transfer of energy to internal modes of the departing radical is becoming more effective as the complexity of the radical increases; an effect which has also been observed39 in the reactions of alkali metal atoms with alkyl iodides.The angular distributions shown in fig. 5 are nominally isotropic for all these I atom abstraction reactions with 0 atoms seeded in He, though with some indication of sideways peaking particularly for C2F51. The reaction of 0 atoms with tetrafluoroethylene molecules22 TRANSLATIONAL EXCITATION 1 .o X 3 d c 0.0 t c 0.5 t I 0 .o !# 0 30 60 90 120 150 180 c.m. angle, 8 / O I - 0 30 60 90 120 translational energy, ['/ kJ rnol-' FIG. 5.-Product angular and translational energy distributions for the reaction of 0 atoms seeded in He with perfluoroalkyl iodide molecules.The arrow indicates the initial translational energy E = 32 kJ mot-'. (-) CF31, (- - -) c3&I and ( 0 *) C2FSI. is presently being using 0 atoms seeded in He to give an initial translational energy E = 31 kJ mol-l. This reaction is of particular interest since it involves the cleavage of a carbon-carbon double bond rather than the exchange of single bonds in the metathetical reactions which have so far been studied in molecular beam experi- ments. Preliminary results shown in fig. 6 indicate that the angular distribution favours the forward hemisphere and the product translational energy distribution accounts for only a small fraction of the very large total energy available to reaction products E,,, = 430 kJ mol-'.Thus it is possible that the reaction produces an electronically excited triplet CF2(3BI) rather than the ground singlet CF2(lA1), as suggested by recent discharge flow and flash photolysis experiment~.~~ The transla- tional energy dependence of the total cross-section for the H, D + Br, reactions has been measured l2 using a supersonic H or D atom beam and laser induced fluorescenceR . GRICE 23 0 20 40 60 80 100 120 140 160 180 c.m. angle, 8 / O 0 50 100 150 200 250 translational energy, U kJ mol-' FIG. 6.-Product angular and translational energy distribution for the reaction of 0 atoms seeded in He with tetrafluoroethylene molecules at an initial translational energy E = 31 kJ mol-'. detection of the Br atom products.The cross-section depends on initial relative velocity rather than translational energy. In addition to the use of seeded beams of reactive atoms and free radicals, beams of stable molecules seeded in inert gasesz5 continue to be used to explore the trans- lational energy dependence of chemical reactions. This is well exemplified by the study of the Ba + N,O reaction reported4s at this Discussion, where electronically excited BaO* is detected by chemiluminescence measurements. The reactions of B and Ho atoms with N,O molecules, which also yield chemiluminescent products BO* and HoO*, have been studied46 as a function of translational energy using evaporation of a thin B or Ho film by an intense pulsed laser to produce an energetic atom beam.The endoergic reaction of Hg atoms with I, molecules has been studied4'24 TRANSLATIONAL EXCITATION using Hg atoms seeded in H2 driver gas to cover the energy range E = 87-250 kJ mol” and is found to proceed via a long-lived collision complex. Similarly, the reaction of SbFS seeded in H, and He driver gases with a range of organic halide molecules has been to yield ionic products due to abstraction of a halide anion by the SbFS molecule. Collisions at very high energies are usually dominated by inelastic collisions to the exclusion of reaction as illustratedz2 in this Discussion. However, the collisional dissociation 49 of CsCl molecules by energetic inert gas atoms (A = Ar, Kr, Xe) seeded in Hz exhibits an associative dissociation channel in the threshold region A + CsCl -+ ACs+ + C1-.(2) Associative and reactive ionisation has been observeds0 for the reactions of a large range of metal atoms M with Oz molecules, where the metal beam is produced by sputtering and velocity selected by a slotted disc velocity selector M + O2 -+ MOz+ + e- --f MO+ + 0 + e-. Carbon atoms also shows0 reactive ionisation with 0, molecules. (3) 4. THEORETICAL INTERPRETATION The increasing scope and accuracy of experimental measurements of the depend- ence of reactive scattering on initial translational energy offers both a challenge and an opportunity to further theoretical investigations. The theoretical problem divides into two parts; first the determination of the potential energy surface for the reaction and secondly the description of scattering in terms of nuclear motion over the surface.Progress in the determination of potential energy surfaces was reviewed at a recent Faraday Discussion (62) and requires little further comment here, other than to note the construction of an empirical potential energy surfaces1 for the Hg + I2 reaction which has been adjusted to agree with the main features observed in reactive scattering experiments 47 on this system. The diatomics-in-molecules method has been useds2 to calculate a potential energy surface for the Ff + H2 reaction and the valence bond methods3 for the H + Br, reaction. While the quantitative accuracy of such calcula- tions may be uncertain, they have the important property of correctly including the topology32 of the potential energy surface.Paradoxically, the empirical s1 and semi-empiricals2 methods have the advantage over ab initio methodss3 that the surfaces may be adjusted to fit experimental observations. The correlation of ex- perimental data and the reaction potential energy surface has traditionally relied on Monte Carlo calculations of classical trajectories for the nuclear motion. This method continues to be refineds4 and is exemplified in this Discussions5 by a detailed study of H atom migration in the dynamics of the H + ICl reaction and its dependence on reactant translational energy. In contrast, quantum mechanical calculations of the nuclear motion have often inspired more awe than physical insight. Thus it is particularly reassuring to see semi-classical methods of quantum mechanics being applied further to classical trajectory calculations in this Di~cussion.~~ This approach identifies quantum phenomena in a physically appealing manner which is more apt for the interpretation of experimental results.It is also stimulating to see calcu- lations presented at this Discussions7 of the effect of intense non-resonant laser irradia- tion on the dynamics of the F + H2 reaction; perhaps this is a case where theory will provoke experimental measurements. New problems of theoretical interest are being posed by the increase in experi-R . GRICE 25 mental measurements on the reaction dynamics of polyatomic systems. In the reactions of atoms with triatomic molecules, the disposal of energy into product rotation is not restricted by the conservation of total angular momentum as in the reactions of atoms with diatomic molecules.Models based on Walsh molecular orbital theory have been proposed 2938 to rationalise product rotational excitation, as arising from excitation of bending modes of the transition state followed closely by scission of the bond about which bending occurs. In reactions with more than three atoms in the transition state, many internal modes of vibration and internal rotation influence the reaction dynamics. When the collision complex lives for many rota- tional periods, energy is equilibrated equally over all accessible modes subject to conservation of angular momentum and the theory of unimolecular reactions may be applied59 with some success. However, collision complexes which persist for only a fraction of the rotational period do not achieve complete energy equilibra- tion and differing internal modes may be expected to have differing effects on the reaction dynamics.As the number of modes involved increases, the reaction dy- namics differ increasingly from the simple models appropriate to the reactions of atoms with diatomic molecules since the dynamics must be averaged over the phases of many modes. At present there is little theoretical work to provide guidance in the analysis of polyatomic reaction dynamics proceeding via a short-lived transition state. However, the increasing scope and detail of experimental measurements may now provide adequate information for the interpretation of these more complicated and chemically more representative systems, R.B. Bernstein and A. M. Rulis, Faraday Discussion Chem Soc., 1973, 55, 293. ' K. T. Gillen, A. M. Rulis and R. B. Bernstein, J. Chem. Phys., 1971,54,2851; S . Stolte, A. 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