The Reaction of F + H, +- HF + H A Case Study in Reaction Dynamics B Y JOHN c. POLANYI AND JERRY L. SCHREIBER Department of Chemistry, University of Toronto, Toronto M5S 1 A1 , Canada Received 9th June, 1976 Concepts developed in recent years as a result of experimental and theoretical studies of the dynamics of reactions A + BC 3 AB + C are examined here in trajectory studies of the reaction F + Hz + HF + H-currently the prototype of exothermic reaction. (i) An " early " barrier, characteristic of substantially exothermic reaction, has the consequence that reagent translation is much more efficient than vibration in promoting reaction, even for energies well in excess of the barrier. (ii) High vibrational excitation in the molecular product stems from the release of H-H repulsion while the new bond, F--H, is still extended (termed " mixed energy-release "); the large zero point vibration in Hz introduces variability in the F--H extension and H-H repulsion, and consequently in the breadth of the observed product vibrational distribution.(iii) Since the product vibrational excitation is governed by the attractive plus mixed energy-release, the slope of the outrun of the energy surface is not, per se, a dominant factor governing product vibrational excitation. (iv) Enhanced reagent vibration, ( A V ) , tends to be channelled into enhanced product vibration, {AV'); the efficiency ((AV'> = 0.81 AV) is dependent on the form of energy surface in the region of " corner-cutting ", corresponding to reaction through extended intermediates F--H--H.(v) Enhanced reagent translation is channelled into product translation plus rotation ((AT') + (AR') = 1.12 ( A T ) ) ; the efficiency provides an indication of the energy required to bend and compress the intermediate FH-H. (vi) The rotational dependence of the reactive cross section, a(J), provides a sensitive probe of the region of the potential-energy hyper-surface along the entry valley up to the barrier. (vii) Enhanced reagent rotational excitation at first decreases product vibrational excitation and then increases it according to experiment; this effect has not been reproduced theoretically. (viii) Product rotational excitation derives in large part from the release of repulsion in bent con- figurations : this gives rise predominantly to coplanarity and opposed directions for the product rotational and orbital motions.(ix) Enhanced reagent excitation of all sorts results in significant enhancement in product rotation, due to reaction through more-compressed and bent configurations; the most efficient conversion is from reagent rotation into product rotation ({AR') = 1.2 {AR)). (x) For thermal (300 K) reaction the computed centre-of-mass angular distribution is sharply back- ward-peaked, and similar for all product vibrational levels. (xi) Enhanced reagent vibration or translation shifts the computed mean scattering angle forward, with AT being markedly more effective than A C the " stripping threshold energy " is high, as anticipated for these masses reacting on a strongly repulsive potential-energy surface favouring collinear approach.1. INTRODUCTION The best understood chemical reaction is ortho-para hydrogen conversion, H + H2(0) + H2(p) + H. However, since it neither liberates nor consumes energy, and since it forms a product that is chemically indistinguishable from the reagent, it takes place across a potential-energy surface that is totally symmetric. The vast majority of chemical reactions, by contrast, take place across an asymmetric land- scape. The best understood process of this type at the present time is the exothermic reaction, F + H2 3 HF + H -AH," = 31.9 kcal mol-l. (1)268 THE REACTION OF F+H2+HF+H Product energy and angular distributions have been investigated for this reaction and its isotopic analogues by chemical laser,l infrared chemiluminescence and molecular beam3 techniques.Total rate constants and activation energies have been determined by mass spectrometry4 and by hot-atom experiment^.^ The potential-energy hypersurface of the ground electronic state of FH2 has been the subject of extensive ab initio computations.6 The best ab initio points6b have been fitted to continuous functions, and have served as a basis for both classical8 and quantumg calculations of reaction probability and product energy distribution. A variety of semi-empirical potential functions 798~10-14 h ave been proposed for this reaction, all of them bearing a strong qualitative resemblance to one another and to the ab initio results.s Some of these semi-empirical potential functions have been used for exact collinear quantum calculation^,^^ as well as for comparison of quantum, semi-classical, and classical results, by calculation of collinear reaction probabilities.16 Many of these surfaces have been used for full 3D calculations7*8s11-14 of product distributions by the classical trajectory approach.Recently a preliminary 3D quantum calculation has been rep01-ted.l~ The influence of higher electronic states" is to produce interaction in the region of the barrier and hence, perhaps, a small potential well on the adiabatic surface ahead of the barrier.19 Crossing between nearby FH2 electronic states has been investigated, and found to occur infrequently at thermal collision energies.2o In the present study we attempt to bring together what has been learned to date about the dynamics of F + H2, using the experimental and theoretical studies men- tioned above, as well as computations described in the following sections.Three- dimensional trajectory studies of the F + H2 system began in this laboratory con- temporaneously with the appearance of the first experimental data regarding k( Y', R', T'), the product energy distribution over vibrational, rotational and translational states.2a The computations 7*8s21 have been extended in the present work. We are concerned here with the effect of the various forms of reagent energy on reactivity and on product energy distributions, as well as with the connection between these properties and the form of the potential energy-surface. 2. POTENTIAL-ENERGY SURFACES AND COMPUTATIONAL METHOD A convenient potential form which has been employed for a variety of systems is the extended London-Eyring-Polanyi-Sat0 (LEPS) equation.The information required to specify the full three-atom potential consists of the spectroscopic para- meters of the ground singlet and first excited triplet state of the fragment diatomic molecules. The singlet can be represented by a Morse potential, lE(r) = 'DX(X - 2) X(r) = exp [-l/3(r - re)] and the triplet by an anti-Morse form due to Sato, 3E(r) = 3DX'(X' + 2) X'(r) = exp [-3/3(r - re)] where S is the " Sat0 parameter ". For surface SE1, I/? = "B; for the other surfacesJOHN C. POLANYI AND JERRY L. SCHREIBER 269 '/? # 3j3. The functions Q(r) and J(P) are obtained from the singlet and triplet curves ~ ( r ) = i[w + 3 ~ w i ~ ( r ) = p ~ ( r ) - 3 ~ ( r ) l .The three-body potential function is made up of the Q's and J's associated with each fragment diatomic pair 3 3 ~ ( Y I , r2, rJ = 2 Q i - (f 2 (Ji - J.d2r i = l i > j - 1 where i = 1, 2, 3 corresponds to diatomic pairs AB, BC and AC respectively. A number of surfaces have been used in the present work. The parameters of these surfaces are given in table 1.21 The principal surface, SE1, is shown in fig. 1. TABLE 1 .-POTENTIAL SURFACE PARAMETERS parameters common to all surfaces (SE1-5) : lkcal mol - 140.519 109.483 HF H2 IgjA-1 2.2247 r,lA 0.9171 parameters specific to individual (SE1-5): surface 3BHF 3 h 2 SE1 2.224 7 1.942 SE2 2.224 7 1.6 SE3 2.224 7 2.5 1.942 0.7416 surfaces SHF sH2 0.15 0.08 0.15 0.08 0.15 0.08 SE4 3 .O SE5 2.75 1.875 -0.087 5 0.08 1.675 -0.06 0.17 The potential energy along the minimum-energy path across the collinear cuts through the four hypersurfaces, is recorded in fig.2. Surface SE1 was selected by varying FIG. 1 .-Contours of equal potential energy for surface SE1. The axes rl and r2 correspond to the F-H distance and H-H distance, for the three atoms constrained to lie along a line; reagents are at lower right, products at upper left. The zero of energy corresponds to F + HS. The symbol (x) indicates the positions of the saddlepoint, which has a height E, = 2.16 kcal mol-I. The coordinates have been skewed by an angle of 43.6", and scaled by a factor t~ = 0.7255 (ie., y = ar2, where y is the distance along the ordinate) so that the motion of the representative point across the surface is that of a " sliding mass ".270 THE REACTION OF F+Hz+HF+H SH2 and S,, in preliminary computations until the experimental mean product vibrational excitation and activation energy were obtained in calculations on F + H2 (v = 0, J = 1).This surface is qualitatively similar to the ab initio collinear surface.8 The other surfaces introduce certain systematic variations on SEl , whose effects will be discussed in subsequent sections of this paper. - CI .- - E g 2 0 - L -24 - - 2 8 L -32 - \ \ \ I I I I , u 1.6 1.2 0.8 0.4 u 0.4 0.8 1.2 -Pi- P" P2-P"-+ bond extension / A FIG. 2.-Minimum-energy-path profiles obtained for the collinear arrangement of FHH on surfaces SE1 -, SE2 -----, SE3 - - - - a , SE4 xxxx and SE5 0000. The abscissa is measured in terms of the displacement of the bond from its equilibrium length (pi = Ri - ri') and the mid-line is the point of equal stretching, p* (the point at which p1 = pz = p*).Thus along the left half of the figure, r1 is decreasing to the value vlo + p". At each value of rl, rz is varied in order to obtain the minimum energy. When r1 has decreased to r1 + p* (i.~., p1 -p * has become zero), pz - p* is also equal to zero. Along the right half of the figure rz is increased, and at each value of rz, rl is varied to obtain the minimum energy. Note that along the entrance coordinate at the left SE1, SE2 and SE3 are all coincident, while along the separation coordinate, SEl, SE4 and SE5 are quite similar and overlap over a considerable range. The computational approach used for these calculations was similar to those previously d e s ~ r i b e d .~ ~ . ~ ~ Importance sampling of relative translational energy22 was used to improve the yield of reactive trajectories over the energy range contribut- ing to the room-temperature thermal average cross section 5 (proportional to the rate constant). In the notation of ref. (22), an order n = 4 was employed to fix the shape of the importance sampling function, with the maximum of the sampling function at 2.0 kcal. This gave good agreement between the distribution of sampling points and the reaction function T.a(T) exp (-T/kT"), where T is the reagent translational energy, a is the reactive cross-section, and To is the temperature in kelvin. For the v = 1 batch on surface SE1 and for the batch on SE4, direct sampling from a Boltz- mann flux distribution p(T) cc T exp (-T/kT") proved sufficiently efficient that importance sampling was unnecessary.In all cases, stratified sampling 22 of impact parameter b was employed. This permitted the impact parameter range to beJOHN C. POLANYI AND JERRY L. SCHREIBER 27 1 gradually increased until further contributions to the total cross section (as judged from histograms of b.P(b) against impact parameter) were judged to be negligible. The trajectory computations described in this work comprise over 25 000 trajec- tories computed over a wide variety of initial conditions. Batches for which only reactive cross sections were required were typically 100 to 200 trajectories each. Batches from which product attribute averages or differential cross sections were obtained were generally 1000 to 2000, resulting in a minimum of 27 reactive (for SE1, v = 0, J = 4) to a maximum of 731 reactive (for SE1, v = 0, J = 1, for which over 4500 trajectories were run).3. VIBRATIONAL AND TRANSLATIONAL EXCITATION I N REAGENTS AND PRODUCTS 3.1 REACTIVE CROSS SECTION AS A FUNCTION OF V AND T The reactive cross section a(T) for F + H2 (u = 0, J = 1) is shown in fig. 3(a). The threshold for reaction lies in the range T = 1.0 - 1.5 kcal mol-1 (Tis the relative translational energy). The total energy in the reagents is well above the classical barrier height, E, = 2.16 kcal mol-l, since the H2 molecule in v = 0 has a zero point energy V , = 6.2 kcal mol-l. (We denote vibrational energy relative to the minimum of the potential-well as Ye, and vibrational energy measured relative to 10 2 0 1 l-+o 3.0 0.0 J / kcalmol -' FIG.3(a).-Translational and vibrational energy dependence of the reactive cross section, 0, for F + H2. The solid line shows the histogram obtained by sorting trajectories from the 300 K batch of F + H2 (v = 0, J = 1) according to initial T (translational energy). The abscissa covers the range of T which contributes significantly to reaction at 300 K. The broken line depicts the histogram of u = 0 as V.) This indicates that the zero point energy of vibration is relatively in- effective in carrying the system across the energy barrier. The relative ineffectiveness of zero point vibrational energy, as well as vibrational energy in excess of the zero point, in promoting reaction is illustrated more explicitly in fig.3(b). The effect of increasing Tfrom 0 to 20 kcal mo1-1 (with V, held constant at 1 kcal mol-') is shown in the upper curve of fig. 3(b) and can be contrasted with the effect, shown in the lower curve, of increasing Ye over the same range (while holding T constant at 1 kcal mol-l). It is noteworthy that the contrasting efficiency holds at least up to energies -10 times the energy of the barrier. reactive cross section obtained for u = 1 ( J selected from a 300 K Boltzmann distribution).272 THE REACTION OF F+Hz+HF+H FIG 3(b).-Cross section functions for the reaction F + HI(J = 1). The upper curve shows the cross section cr against T, with the HZ vibrational energy reduced to V, = 1.0 kcal mol-1 (the normal vibration energy of H2(0 = 0) is V.= 6.22 kcal mol-’). The lower curve shows a( Ve), the cross section versus vibrational energy, with Tfixed at 1.0 kcal mo1-’. The positions of the quantum level energies are indicated along the abscissa. If instead of varying the reagent energies independently we keep the total reagent energy constant and alter the apportionment of energy between T and V, we obtain the result shown in fig. 3(c). (The same ‘‘canstant reagent energy ” condition applies to the experimental data recorded in endothermic triangle plots,24 and in certain theoretical studies of other systems made by the trajectory method25 or by the information-theoretic approach.)26 In fig. 3(c) the total reagent energy is held constant at -4 times the barrier energy, while being re-apportioned between T and V,.The preferred degree of freedom is translation, T. I I I I 4.0 5.0 6. .O Ye / t C O l ml -I7 b0 FIG. 3(c).-Cross section for F 4- Hz(J = 1) at a constant total energy T + V= = 9.22 kcal mol-I, iso-energetic with F + H2(u = 0, T = 3.0 kcal mol-I). As T was varied, V, was altered corres- pondingly, to maintain the total energy at a constant value.JOHN C. POLANYI A N D JERRY L. SCHREIBER 273 The strong preference for T over V, should not be construed as meaning that reagent vibration is without effect on the reactive cross section. In fig. 3(a) the cross section function a(T) is given for both v = 0 and v = 1; the v = 1 curve lies well above the v = 0 curve. However, an -12 kcal mol-1 increase in reagent vibra- tion [V(u = 1) - V(u = O)] has given rise to an enhancement of -10 times in the cross section, for T z 2 kcal mol-l; the same enhancement in 0 would result from an approximately 2 kcal mol-1 increase in collision energy.It follows that in this range of energies, reagent translation is roughly 6 times more effective in promoting reaction than is reagent vibration. This specificity of reagent energy was anticipated some years ago on the grounds (i) that substantially exothermic reactions (A + BC -+ AB + C) would tend to have their barrier crests located in the coordinate of approach,27 and (ii) that reagent translation (as evidenced in a model 3D trajectory study) constitutes a more effective source of momentum directed along the coordinate of approach than does reagent vibration.28 The reaction F + H2 + HF + H meets the criterion of being “ substantially exothermic ”.(The designation of a reaction as being substantially exothermic has been interpreted as meaning exothermic by 2 lOkcal m ~ l - ~ . ) ’ ~ This greater effectiveness of T than V in giving rise to exothermic reaction has been demon- strated qualitatively in experiments on two substantially exothermic reactions ; H + Clz -+ HCl + C17 and H + F2 -+ HF + F.29 Surface SE4 was distinguished from the other four energy surfaces in that a(T) showed no discernible threshold even for u = 0; the zero point energy of vibration (which amounts to -3 times the barrier height) is able in this case to give rise to substantial reaction.For surface SE4 the barrier crest-though still situated slightly ahead of the position of equal bond-extension (fig. 2)-is in a region corresponding to significant extension of both the new and the old bonds. As a consequence vibration (which gives rise to stretching of the old bond) is becoming effective in carrying the system across the barrier. The fact that the barrier crest for surface SE4 is located in a region close to the symmetrically-stretched position, i.e., the region where the minimum energy path curves and consequently the potential exhibits curvature which is no longer separable into components along rl and r2, is also evident from the anomalous value for the “ mixed ” force constant at the barrier crest CfiJ in table 2. TABLE 2.-PROPERTIES OF THE POTENTIAL SURFACES SEl SE2 SE3 SE4 SE5 Ec 2.163 2.266 2 .ox 2.249 2.632 r A a 1.434 1.408 1.472 1.275 1.346 r HtH 0.776 6 0.777 0.776 0.842 0.805 f lib -0.120 6 -0.1 18 2 -0.119 1 -0.344 0 - 0.41 6 8 fi’2 0.826 3 0.820 7 0.831 2 2.060 5 1.454 3 $22 4.327 3 4.335 2 4.316 4 2.415 7 3.441 5 % d m 15.6 15.1 26.2 5.3 19.2 %% 56.5 72.0 43.6 61.6 58.6 % d m 27.8 12.9 30.2 33.1 22.1 - - -2.314 -0.959 PC - rHwH a Internuclear separations, at the crest of the energy barrier (A).- - 1 A98 2.153 - - 0.743 0.742 - - Force constants at the crest of The superscript w refers to the potential well in the entry valley (if any). the barrier (mdyn A-1). E is in kcal moP, i’ in A.274 THE REACTION OF F+HZ+HFf-H 3.2 PRODUCTION ENERGY DISTRIBUTION OVER v' AND T' 3.2.1 THERMAL REAGENTS Since the parameters of SEl were adjusted to give agreement in the mean with the product vibrational distribution, the comparison of the product vibrational distribu- tion from the computations with that from experiment is reasonably good (see table 3 and cf.table 4). The " triangle plots " for calculated and experimentally TABLE 3.rOMPARISON BETWEEN COMPUTED RESULTS ON SEl AND EXPERIMENTAL RESULTS computed experimental EJkcaI mol - 1.937 1.6" log A/cm3 s-l mol-l 13.27 <A, 0.665 0.66' <fT) 0.239 0.26 14.2 <fi> 0.095 0.08 k(v?lkmax v ' = 1 0.22 0.31 v' = 2 [ 1 .OO] [ 1.OOJ v'= 3 0.26 0.47 v'= 1 9.98 9.35 v' = 2 6.51 7.06 v'= 3 3.39 2.40 < J'>,* K. H. Homann, W. C. Solomon, J. Warnatz, H. Gg. Wagner and C. Zetzsch, Ber. Bunsenges.Phys. Chem., 1970,74,585; see also R. Foon and M. Kaufman, Prog. React. Kinetics, 1975, 8, 81. * Polanyi and Woodall; ref. 2(c). K. B. Woodall, Ph.D. Thesis (Universityof Toronto, 1970). 7 Neglecting any correction for the spin orbit states of F(2P1,2, 3/2); see ref. (17). TABLE 4.--SUMhURY OF RESULTS FROM MODEL SURFACES (300 K) SE1 SE2 SE3 SE4 SE5(J= 1) o(300 IS)" 0.178 0.126 0.186 1.75 0.237 ETb 2.08 2.18 2.15 0.25 1.78 f2 0.665 0.507 0.859 0.668 0.706 <fR> 0.095 0.135 0.032 0.071 0.094 <emol> 133.3 12.81 109.5 130.0 132.0 computed from is the average T of reactive collisions at 300 K. determined product vibrational and rotational energy distributions are shown in fig. 4(a) and (b). Though the vibrational distributions agree well overall, the calcu- lated distribution is too narrow, in that both k3/k2 and kl/kz are smaller than those determined experimentally.This failing may be associated with the neglect of tunnelling in the classical trajectory calculations. Another defect of the calculated product energy distribution is that the rotational distribution, despite having close to the correct mean value in each vibrational level, appears to be too broad, extending (with relatively low probability) out to too high a rotational energy. This behaviour has been observed on other surfaces.ll (It should be noted that the low probability contours of the calculated distribution are the least certain, since relatively few trajectories fall into this range of vibration plus rotation.) The potential-energy surfaces explored here and elsewhere6-14 for F + H2 are T and J selected from a 300 K Boltzmann distribution. Translational activation energy, EZ = <T>, - 9 kT, where <T>JOHN C .POLANYI A N D JERRY L . SCHREIBER 275 predominantly “ repulsive ”, that is to say the energy-release occurs for the most part as the products separate. The designation of surfaces as “ repulsive ”, in contrast to “ attractive ”, is based on a simple apportionment of the total energy release as between two perpendicular sections of reaction path on the collinear energy s ~ r f a c e . ~ ~ * ~ ~ For SEl this leads to attractive energy release of dL = 1 %, and a repulsive energy- release of 9L = 99%. 30 - I 0 - E - 2 0 0 0 Y \ i 10 F+H*(v=O, I = I )+HF(v’/’)+I exot herrnic I \ \ 0 10 20 30 R ’/ k c a l mol - I FIG.4.-Contours of equal detailed rate constant k( V‘, R’, T’) from theory and experiment. (a) Contours at 0.015, 0.046, 0.077, 0.11 and 0.15 obtained from trajectories calculated on SE1 for F + H2 (u = 0, J = 1). (This J state constitutes -75% of the reactant at 300 K; triangle plots of the distribution from other J states did not differ significantly.) The plot is normalized so that the maximum value is equal to the maximum on the corresponding experimental plot [(b), below]. The relative rates into different v’ levels [normalized to k(v =’ 2) = 1 .OO] are indicated next to the lines which give the positions of the quantum vibrational energies of HF. Note that the zero of vibrational energy is taken to be the energy of HF(u = 0), in accord with the procedure used in constructing such plots from experimental data.The dashed lines indicate approximate values of the translational energy, calculated assuming that the total energy of any trajectory is equal to the average total energy of all reactive trajectories. As the trajectories actually have a distribution of total energies, it is possible for a few trajectories to lie beyond the line nominally indicating T‘ = 0. Since the release of repulsion resembles, superficially, the second half of a strong collision, the question arises as to how this energy comes to be channelled efficiently and preferentially into high states of product vibration. Broadly stated, the explana- tion is that a force applied while a new bond is still under tension gives rise to strong internal e ~ ~ i t a t i o n .~ ~ ~ * ~ ~ ~ ~ ~ ~ ~ ~ ~ A simple collinear model has been used to demonstrate the efficient forcing of oscillation into a tightening oscillator (FOTO).32 On the col- linear potential-energy surface (fig. 1) the release of repulsion while the new bond is still forming corresponds to a trajectory that cuts the corner of the energy surface. Since this is neither solely attractive nor repulsive energy-release, we term it “ mixed ’’ (symbolized do. For a given mass combination the minimum energy path across the collinear surface can be usefully separated into successive sections designated attractive, mixed276 THE REACTION OF F+Hz+HF+H l b ) 40 30 - I - 0 E - 20 Y \ i 10 0 J F+ H2-->H F ( Y j ‘ ) + H exot herrnic 0 10 20 30 1’1 kcal mol -I FIG.4.-(6) Experimental contours of equal detailed rate constant, k( V’, R‘, T’), into product energy levels, adapted from ref. (2c). This plot is normalized so that the sum of values at the (discrete) v‘J’ levels equals unity for 0’ = 2 (the most populous u’ level). Contours are the same as those given in fig. 4(a). The average total energy is estimated from EtOt = -AH: + E, + 3 kTo where -AH: is the enthalpy of the reaction, E, is the experimentally determined activation energy, k is Boltzmann’s constant, and To is 300 K. FIG. 5.-Average fraction of the available energy going into product vibrational excitation, (f:>, from 3D trajectory computations, against % ( d m + A m ) . The values of d m + dm were determined from the collinear minimum-energy paths of surfaces SEl through SE5 by the method of Kuntz er a!.[ref. (30)]. The extreme points at low <f;> and high (f;> are for surfaces SE2 and SE3. The cluster of points at intermediate <A> correspond to surfaces SE4, SE5 and SE1, reading from left to right [i.e., in order of increasing The solid line corresponds to <f;> = %(dm + A,,,) + 26.6. %(&In + Jfm)l.JOHN C . POLANYI AND JERRY L . SCHREIBER 277 and repulsive; d,, A’m and s m - Both the attractive and mixed energy release result in efficient internal excitation. Fig. 5 shows the correlation between %(dm + Am) and the percentage of the total energy that is channelled (on the average) into product vibration, %( V’), for the five energy surfaces used in the present study of the system F + H,.So long as the reactive masses are held invariant, the correlation is This is particularly instructive for the series SE2, SEl, SE3 in which the repulsive shape of the exit valley (i.e., the force along the coordinate of separation) is made progressively greater. On the present evidence this force would appear to be a secondary factor, since the outcome can be understood in terms of the progressive increase in %d, and (particularly) %dm, which characterize the earlier parts of the interaction along the approach coordinate and the curved region of the minimum- energy path. An index of d, 4 and 9 which is of more general applicability is that based on the path of a single collinear trajectory. The trajectory chosen for this purpose corresponds to reaction with a vibrationless molecular reagent, at close to the threshold collision-energy.The course of the trajectory is apportioned in an analogous fashion to that used for characterizing the minimum energy path to yield the corresponding quantities which in this case are designated dT, dT and BT. For F + H2 on SEl, dT = S%,A, = 35% and gT = 57%. As with the minimum path characterization %(dT + JT) underestimates the mean percentage vibrational excitation in the products (( Y’) = 66.5%) despite correlating quite well with the latter quantity from one surface to another, and, in the case of the sum (dT +AT), from one mass- combination to another. In the light of the fact that AT is large for the mass-combination F + H2 on SEl, it becomes interesting to consider whether the variation in magnitude of mixed energy release within a representative batch of trajectories could account for the breadth in the product vibrational distribution.Previous discussion has been con- cerned only with the mean of the product vibrational excitation, and has attempted to relate this to a representative t r a j e ~ t o r y ~ ~ or mean of several trajectories.’lb The wings of the product energy distribution should, on this view, stem from limiting types of trajectory. In general, the route across the collinear surface will depend on the spread of reagent translational energies, vibrational energies and vibrational phases. In the present example inspection of the trajectories shows, as might be expected in view of the large zero point vibrational energy in H,, that the dominant variable is the vibrational phase in H2 at the moment that F approaches closely.The extent of mixed energy release, AT, could be computed for a representative sample of trajectories (rather than for a single trajectory). It is defined by the energy released between the point at which the trajectory deviates from the entry valley by the classical amplitude of vibration, ra, up to the point that the trajectory first reaches the minimum of the exit valley, i.e., rl = r;. The value of r2 at the termination of mixed energy release is designated r . Rather than measure the energy release from r; to r ; we have chosen to ignore the variation in the point of departure from the entry valley, and simply to characterise individual trajectories by their point of arrival in the exit valley, r ; .This is an incomplete measure of the extent of mixed energy release but may be adequate for the present purpose which is to characterize, in a simple fashion, the range of types of trajectories and the consequent breadth in the outcome. Fig. 6 shows nine trajectories at nine equally-probable phase angles, qu.21 (A definition has been used for qv that makes this quantity linear with time for a non- good.llb,14U278 THE REACTION OF F+HpHF+H J' NR ,\ 1.2 1.4 1.6 ' 1- 'I - I / / / / / 12 14 16 1- b, 7 = 1.24 kcol Y =O.OO kcal FIG. 6.-Plots of collinear trajectories for F + HS ( 0 = 0, T = 1.24 kcal mol-') near the threshold for collinear reaction, depicted in the skewed and scaled coordinates described for fig.1. The nine frames represent nine values of the initial vibrational phase angle, qv, which lies in the range [0,360"] ; qv = 0" corresponds to the H2 bond length being completely extended, qv = 180" to H2 completely compressed. Since qv is a uniformly distributed random variable, equally spaced values of qv have equal probability, and the nine values shown span the entire range of possible initial vibrational phase. qv equals (a) 280", (b) 320", (c) 0", ( d ) 40", (e) 80°, (f) 120°, (g) 160", (h) 200", (i) 240". The path of the trajectory is strongly influenced by the vibration phase as the barrier (indicated by the x) is approached. The resulting product vibrational excitations of the reactive trajectories are (a) V' = 21.3,(6) V'= 24.0, (c) V'= 25.8, ( d ) V'= 27.2, (e) V'= 28.3,(h) V'= 26.5, (i) Y'= 17.0.Trajec- tories which were non-reactive are indicated by NR. rotating Morse ~scillator.)~~ The reagent conditions are approximately representa- tive of thermal reaction. Inspection of the figure shows that r ; , and hence (crudely) the extent of " corner-cutting ", increases as the phase angle is increased from ql, = 240" [frame (i)] to qv = 280", 320", O", and 40" [frames (a)-(d)]. The product vibrational excitation, Y', increases continuously along this sequence. This is in accord with the results shown in fig. 7: for most of the trajectories there is a positive correlation between Y' and r . (The points shown in fig. 7 are once again at equal intervals of q0 and, therefore, have equal a priori probability.They include the phase angles used in drawing the previous figure.)279 JOHN C. POLANYI AND JERRY L. SCHREIBER Fig. 7 includes the correlation between V’ and r for a substantially more attractive surface, designated BOPS. This surface was fitted8 to ab initio points computed by Bender et aL6’ Once again the majority of trajectories exhibit increasing V’ with increase in r ; . Due to the substantial contribution to V’ from attractive energy release, the curve of Y’ against r ; is shifted to markedly higher values of V’. For the same reason the correlation between V’ and r ; is no longer as simple as for SEl. (The rise in V’ for the small proportion of trajectories at very low r $ may be due to enhanced attractive energy-release for trajectories that are directed along the entry valley of BOPS.) I I 35k- I 1 -I FIG.7.-Product vibrational excitation V’ from collinear collisions of F + H2 (u = 0) against r 1, the value of r2 when the trajectory first crosses the line rl = r?. The lower curve is the result of trajectories at T = 1.24 kcal mol-’ on SE1; the x’s represent consecutive values of vibrational phase angle (spaced at intervals 20”). The upper curve, BOPS, is the result of collinear trajectories on the surface fitted to ab initio energies [see ref. (S)]. Again, the points (a) represent equally spaced values of the vibrational phase, at intervals of 20”. The mean value of r2” is shown for thermal reaction on SE1 and BOPS, and also for reaction with enhanced reagent vibration and translation on SE1 (downward-pointing arrows).3.2.2. VIBRATIONALLY, TRANSLATIONALLY OR ROTATIONALLY EXCITED The general question of interaction between reagent and product excitation has been discussed in earlier work both from an experimental and a theoretical standpoint (references are given below). The present discussion follows the lines of that given previously’ but provides a somewhat more explicit documentation, for the case of F + HZ, in terms of an illustrative sampling of collinear trajectories of the type introduced in the previous section. The essential points that need to be made in connection with the effect of enhanced reagent energy A V and AT on product V’ and T’ can be anticipated from an inspection of fig. 6. Trajectories that cut the corner of the energy surface and approach the exit valley from the side oscillate across that valley, i.e., they give rise to large V’.By contrast, trajectories that encounter the repulsive wall near the head of the exit valley tend to be accelerated aZong that valley, i.e., they give rise to large T’. The consequences of enhanced reagent energy can be understood if one considers the extent to which the proportions of these characteristic types of behaviour are modified. Fig. 8 shows for SE1 the effect of enhanced reagent vibrational energy (u = 1, REAGENTS, AV, AT OR AR280 THE REACTION OF F+H,-+HF+H T = 1.24 kcal mol-I). The sample given is a small one. It is evident, nonetheless, that there is a shift toward larger r ; than in the previous figure of this type, fig. 6, and a concurrent increase in V'.In one case, frame (b), the values of r ; and V' were so large that the small product translation, T', almost failed to separate the particles before the reagents reformed. In frame (e) T' - 0, and the reagents were reformed. A special set of circumstances is exemplified in frame (d) ; the H2 bond was entering its phase of compression just as the system reached the far side of the energy barrier. /dl FIG. 8.-Plots of selected collinear trajectories for F + H2, u = 1, with the same value of T (= 1.24 kcal mol-') as in fig. 6. Again, the product vibrational energy of the reactive trajectories V' are (a) 40.3, (b) 42.1, ( d ) 25.6, (e) 35.4. A non-reactive trajectory (c) is indicated by NR. qv values are (a) O", (6) 60°, (c) 80", (d) 260", (e) 300".As a consequence the particles were brought to rl = r-10 with r ; N" r20; this is a strongly compressed configuration ABC, located at the head of the exit valley. Acceleration along the length of the exit valley starting from this point gave the products high T', but low V'. (In certain cases these alternative reaction paths, through the extended or compressed intermediate, can give rise to a bimodality in the product-vibrational d i s t r i b ~ t i o n . ) ~ * ~ ~ s ~ ~ The mean value of r z was computed for a larger batch of 1D trajectories having the initial conditions v = 1, T = 1.24 kcal mol-I, and is indicated by an arrow in fig. 7; it exceeds by 4 . 1 A the mean value of rz for the thermal batch of trajectories on the same surface. The value of ( V'>v=l for the full 3D batch exceeded the 3D thermal value of {V') by 9.7 kcal mol-I.It follows that the increase in reagent vibrational excitation, A V, gave rise to an increase in product vibrational excitation (AV') which could be expressed as (AV') = 0.81 AV. (It should be stressed that the symbol A is reserved for an enhancement in reagent energy-in excess of the barrier energy-and the consequent enhancement in product energy ; this conforms to previous pra~tice.)~ Theory has tended to give (AV') z (AV),7 with the exception of H + F2 for which (AV') w 2AV was obtained.23 Experiment in the only well- studied cases gave for F + HCl+ HF + Cl {AV') w AV,7 and for Ba + HF+ BaF + H (AV') N" 0.6 AV.35 It would appear from the behaviour recorded in fig. 8 that the relation between {AV') and A V provides an indication of the geography of the potential surface in the region of corner-cutting, i.e., information concerning the energy required to form a stretched intermediate A - - B - - C.7*23*35*36JOHN C.POLANYI AND JERRY L . SCHREIBER 28 1 Specimen collinear trajectories with enhanced translation in the reagents are recorded in fig. 9 (T = 13.14 kcal mol-l, V = 0.0 kcal mol-'). Once again the large zero point vibrational energy makes possible a variety of trajectories. They are marked by diminished r ; compared with the thermal case (the trajectories of fig. 6). The diminution in ( I - ; ) , taken from a larger collinear batch, is indicated in fig. 7; it amounts to -0.25 A. This is a greater shift than the shift of (Y;) to larger values when a comparable energy was added to the reagent vibration. This is understand- able since there is a barrier to reaction through extended intermediates A - - B - - C , whereas the " sliding mass " can more readily be robbed of its propensity for corner- cutting.There is a corresponding diminution in the fraction of the available energy being channelled into product vibration. A 3D analysis of the effect of enhanced FIG. 9.-Plots of selected collinear trajectories of F + H2, v = 0, with enhanced collision energy T = 13.14 kcal mol-', chosen so that the trajectories are isoenergetic with those in fig. 8. Product vibrational excitation V' are (a) 32.3, (b) 35.5. Non-reactive trajectories are indicated by NR. qv values equal (a) 120", (6) 140", (c) 220", ( d ) 320", (e) 20".collision energy for the mass combination heavy + light-heavy showed the same effect .22 It should be noted, however, that collinear trajectories provide a poor representa- tion of the actual event for the case of enhanced translation. The representative hot- atom reactive encounter is a stripping reaction in which F carries one of the H atoms along in the forward direction, to give more-forward scattered HF.IIC The collinear arrangement precludes this, hence the preponderance of non-reactive events in fig. 9. In 3D, as fig. 3 indicates, the reactive cross-section increases steeply with enhancement in T. A batch of trajectories were performed for F + H2 (u = 0, J = 1) in 3D at an enhanced collision energy T = 13.88 kcal mol-', for comparison with F + H2 (v = 0, J = 1) with T selected from a 300 K distribution.Since this v = 0, 300 K, batch had a mean collision energy { T ) = 2.91 kcal mol-', the enhancement in reagent translation was {AT) = 10.97. The resultant increase in product translational and rotational excitations were (AT') = 5.97 and (AR') = 6.32 kcal mol-l (hence (AV') - - 1.32 kcal mol-'). The efficiency of conversion of enhanced reagent translation into product translation plus rotation was therefore {AT') + <AR') = 1.12 (AT). The large role of (AR') is further evidence of the limited value of the collinear representation. The diminished fractional conversion of the available energy into282 THE REACTION OF F+Hz+HF+H product vibration is, nonetheless, in qualitative accord with the expectation from the collinear trajectories : diminished ( r ;) is indicative of less efficient vibrational excitation.Decreased {f;) with enhanced T has been obtained theoretically and also experi- mentally for F + D2 + DF + D.' Qualitatively similar results regarding the effect of AT have been obtained experimentally for a number of other s y ~ t e m s . ~ , ~ ~ ~ ~ ~ There is experimental and theoretical evidence concerning the effect of modest changes in reagent rotational energy, AR, on the product vibrational excitation in F + H2. Coombe and Pimentellb*c obtained experimental evidence for a decrease in (f'") (the mean fraction of the available energy being channelled into product vibration) when H2(J = 0) was replaced by H,(J = 1).Experimental work in this laboratoryzf confirmed the decrease in (fV) for reagent J = 0 -+ J = 1 and showed that (f'") increased thereafter as J = 1 -+ J = 2. The individual k(u'IJ = 0), k(u'lJ = 1) and k(u'lJ = 2) were also obtained, but in view of the failure of most classical trajectory studies to account properly for the breadth of vibrational distributions, it is advantageous to compare (yV) = fn(J) from theory and experiment. The small (2-3 %) decrease observed experimentally in (yV> for J = 1 as compared with J = 0 and J = 2 is not obtained from the classical trajectory cross sections of Muckerman"" or the detailed rate constants given by Jaffe and Andenonlob or surface SE1;'l all these results are tabulated in ref. (2f). The most striking consequence of enhanced reagent rotation ( J = 0 + 4) on SEl was enhanced product rotational excitation-see section 4.2.2.The increase in reagent rotation for J = 0 -+ 4 was AR = 3.39 kcal mold'; the corresponding enhancement in mean product translational excitation was ( A T ) = 1.82 kcal mol-', and in vibrational excitation (AV') < 0. 4. ROTATIONAL EXCITATION IN REAGENTS AND PRODUCTS 4.1 REACTIVE CROSS SECTION AS A FUNCTION OF REAGENT ROTATIONAL ENERGY The thermal average of the reactive cross section for the reaction F + H,(J), as a function of reagent rotational quantum number J, has been obtained experimentally for J = 0 - 2;39 the function C(J) was found to be approximately invariant with J. The computed ii(J), with a thermal distribution over T(300 K) and with H2 in v = 0, is shown for three potential-energy surfaces in fig.10. Surfaces SEl and SE4 show markedly contrasting 8(J); SE5 is intermediate. None of the surfaces yield B # fn(J). Surface SE5 was selected as an approximation to the observed minimal dependence on J for low J's. Inspection of the energy profiles in fig. 2 shows that surfaces SE1 and SE4 differ in that the former has no well in the entrance channel, whereas the latter has a 2.3 kcal mol-l well, and consequently has its barrier displaced to a somewhat later posi- tion along the entry valley. These alternative surfaces were chosen for examinationz1 since three sets of workers"'-12 using an energy surface without a potential-well in the entry valley computed b(J) with a maximum at J w 1 , whereas Blais and Truhlar,I4 whose surface had a well, obtained an inverted a(J), i.e., one which passed through a minimum at J w 1.Since then Dosser and Sims have obtained an inverted a(J) for F + H2 using a surface with a well in the entry valley, and also one having neither well nor barrier.40 The ab initio results for F + H26 give no evidence of a potential- well. However, Jaffe, Morokuma and GeorgelgC have pointed out that inclusion of the spin-orbit interaction of F gives a lowest electronic state E , for FH2 with a shallowJOHN C . POLANYI AND JERRY L . SCHREIBER 283 well in the entry valley. SE5 of the present study, which gives the smallest dependence of a on J for intermediate J's, is of this general type. Surfaces SEl, SE4 and SE5 are all in satisfactory accord with the experimental product energy distribution.The shift in barrier location is too small to produce a major change in % ( d m +A,,,) (for the extreme cases SEl and SE4 the values of %(dm +Arn) are 43.4 and 38.4 respectively; cf. fig. 5). All three surfaces are, from this standpoint, eligible for consideration. As already remarked, none are fully acceptable on the basis of the present information concerning a(J). It appears that o(J) may provide a valuable probe for a region of the potential-energy hyper- surface to which the product energy-distribution is insensitive, namely the approach to the barrier crest in hyperspace (icy the entry valleys of the energy surfaces with F-H-H collinear-as in fig. 1-and bent). In a previous computation on model surfaces which exhibited a marked variation in the form of a(J), we attributed the observed changes to an alteration in the ratio of the time spent in the approach coordinate to the time required for appreciable rotation of the molecule under attack.41 If this ratio was small then enhanced reagent rotation gave rise to a (modest) increase in reactive cross section.If this ratio was large, enhanced rotation markedly decreased the reactive cross section. The rationale underlying this explanation was that reaction was more probable for collinear A-B-C. For a rapid approach of A to BC the angular momentum of BC could contribute (to a modest extent) to the momentum of approach of A to B, while approximate col- linearity was maintained. For slow approach, the angular momentum of BC would tend to swing A-B-C out of collinearity before B could be transferred to the attacking atom A.This line of reasoning implies that o(J) will invariably decrease in the limit of high J, since the time required for A to approach BC must be finite. FIG. 10.-Thermal average cross section d against reagent rotational quantum number J. The classical angular momentum of the H2 was taken to be 1/J(J + 1)h. SE1-, SE4 ( x 0.1)--, SE5.. .. . . We can apply this type of reasoning to the changes in a(J) recorded in fig. 10. Since SE4 is a more extreme example of the behaviour exempIified by SE5, we contrast SE5 with SEl. The most conspicuous feature of a(J) for SEl is the fall-off in cross section with increasing J. It would appear that with increased J , H, is rotating out of the preferred F-H-H alignment before reaction can occur.In accord with this line of reasoning we found that a modest increase in mean collision energy (obtained by selecting translation from a 500 M distribution instead of 300 K) diminished the284 THE REACTION OF F+H2+HF+H rate of fall-off in a(J) with J. At higher T there is less time for H2 in a given level J to rotate out of alignment. The most striking difference between SEl and SE5 is the earlier fall-off in a(J) with increasing J on SE1, in contrast to the fall-off in a(J) for SE5 which is evident only at the highest J. Inspection of pairs of trajectories having J = 3 on surface SE1 and SE5, with all initial conditions identical but a non-reactive outcome on SE1 and reactive on SE5, showed that on SE5 the long-range attraction associated with the 0.96 kcal mol-l well accelerated F and H2 toward one another, thereby significantly decreasing the time spent in the approach.This more favourable ratio of approach time to rotation time may possibly account for the successful outcome of the collisions on SE5. At sufficiently high J the curve of a(J) diminishes on SE5; the ratio of the time spent in the approach to the rotational time has increased and has become un- favourable to reaction even on SE5. It is anticipated that a(J) will also diminish at high J for surface SE4; however, our computations were not pursued out to suffi- ciently high J for this to be evident. These arguments pre-suppose that there is a preferred direction of approach for reaction.We have referred to the time required for a “ significant ” rotation of the molecule under attack. What is “ significant ” will depend on the sensitivity of the barrier-height to the bending of A-B-C away from the preferred angle. For the surfaces used here and el~ewhere”’~ for FH2 the preferred direction of approach is collinear; the onset of F.H2 repulsion occurs at a smaller F-H separation if F ap- proaches collinearly. Moreover, for this system since the zero point energy exceeds the barrier height it is possible in principle for the F atom to approach while H is greatly extended, and to experience no F*H2 repulsion. (In practice only a very high energy collision would allow F + H2 to approach while H2 remained effectively at full amplitude; this approach would not be along the minimum of the entry valley at r: in fig.1, but along a line parallel to it displaced to ri = r; + 0.14 A.) The potential energy around H2 is shown in fig. 1 1 as a function of rl and of the F-H-H bending angle, for r2 = r: and for r2 = r;. It is evident that a stretch in the H2 bond which occurs while F-H-H is approximately collinear can readily result in close approach along rl, and hence in reaction. Inspection of bond and force plots for 3D trajectories on SE1 suggested a possible explanation for the small enhancement in a from J = 0 to J = 1. For H2(J = 1) there was a greater incidence of trajectories which remained in a close-to-collinear 5 FIG. 11 .-Contours of equal potential energy for F approaching H2 on SE1. The bond length of H2 is fixed, (a) at the equilibrium length rZ0 = 0.75 A, (6) at the vibrational amplitude of H2 (u = 0), r; = 0.88 A.Contour energies are indicated (in kcal mol-I) relative to that of the diatomic with F removed to infinity.JOHN C. POLANYI AND JERRY L . SCHREIBER 285 FIG. 12.-Plots of bondlengths and forces against time for two F + H2 3D trajectories. Bond lengths ri (-), r2 (----), and v3 (. . .. . .. . .) are shown in the top halves of the two figures, as well as the sum of the two shortest bond lengths (-x-x-). Below the bond lengths are shown the components of force along each of the bonds (the force for a given bond has the same line symbol as the bond length). (a) F + H2, J = 0, unreactive. Note the short period during which r3 = rl + r2, indicative of passage through a collinear geometry, during the course of an unconstrained 3D trajectory.FIG. 12.--(b) F + Hz, J = 1, reactive. The collinear arrangement persists for a longer time. configuration over more than one vibrational period. This could be due to the fact that F " follows " the (slowly) rotating H2 for longer than would be the case if F passed by a non-rotating H2. This is illustrated in fig. 12. An analysis of the reactive trajectories for J = 1 on SEl showed a substantial fraction in which the orbital motion of F was approximately co-planar with, and in the same direction as, the rotational motion of H2-in accord with the suggestion made above. Nonetheless this explanation of a(J = 1) > a(J = 0) on SE1 should be regarded as speculative. The initial decrease in a(J) from J = 0 to J = 1 on SE4 and SE5 remains un- explained.* Further studies of the factors governing a(J) are in progress. * The " correspondence principle " used in this work to relate the rotational quantum number, J, to the magnitude of the classical rotational angular momentum, J, is the standard quasi-classical rule J2 = J ( J + 1)P; this is the customary procedure in classical trajectory studies. An alternative correspondence, frequently used in semi-classical studies of rotational energy transfer, is J2 = ( J + :)z tiz. Use of this procedure would increase the angular momentum associated with J = 0 to :h, which would probably cause a(J = 0) and o(J = 1) to be much closer together in value than was found to be the case in our calculation.We are grateful to Prof. Paul Brumer for helpful discussions on this point.286 THE REACTION OF F+H2-,HF+H 4.2 PRODUCTION ROTATIONAL ENERGY AND PLANE OF ROTATION 4.2.1 THERMAL REAGENTS For reactions exhibiting a large repulsive energy release, and having a mass- combination which permits the product repulsion to exert a substantial torque on the newly-formed molecule, there is evidence that the product repulsion is responsible for much of the product rotation.42 It has been proposed that the reaction F + H2 is of this type; 2d the strong repulsion between the products when released in a slightly bent configuration - HL'L - - (H is a heavy atom, and L a light one) is applied at a point well away from the centre-of-mass of HL and therzore exerts a torque on HL.This simple picture provides a ready explanxon of the change in product rotatiozl excita- tion in going from the reaction F + HD -+ HF, to F + H2, to F + D2, to F + HD 3 DF.2d If the supposition that 9 -+ R' (92 is the product repulsion, and R' the product rotational excitation) is correct, then there should be only a minimal dependence of R' on the initial orbital angular momentum, I,'-which in other systms governs R'. That this is so, is shown in fig. 13. Furthermore there should be a tendency for the 14 ' ' ' 1 - 7 j I--- 0' A a 6 b io I;' l ' ~ 1'6 i e ' I L (81 FIG. 13.-Average values of product rotational quantum number J', against reagent orbital angular momentum L, both measured in units of ti, for F + HD, J = 3, T = 3.72 kcal mol-'. The solid line (-) is for the HF product; the broken line (----) for DF product.rotational motion in the HF to be co-planar with the applied repulsive force, and for the H in HF to recoil in the opposite direction to the ejected H. This implies that the angle between the product rotational angular momentum vector, J', and the product orbital angular momentum vector, L', should be OJJLf E 180". An analysis of the product distribution over OJfL/ bears this out, as shown in fig. 14. Correlations between L and R', and distributions over OrL' have been presented previously for other systems,42 but not for F + H2. The plane of product rotation in F + H2 has not been studied experimentally but has become increasingly accessible through new experimental techniques developed by Herschbach and co-wo~kers.~~ 4 .2 . 2 VIBRATIONALLY , TRANSLATIONALLY OR ROTATIONALLY EXCITED REAGENTS; A v , A T OR AR As noted above, product rotation in F + H2 stems in large part from the release Enhanced reagent energy, AV, AT or AR, of repulsion in bent configurations.JOHN C. POLANYI AND JERRY L. SCHREIBER 237 I 1 I I---- appears to contribute to product rotation either by increasing the repulsive energy release, or by increasing the bending in the intermediate, or both. Increase in reagent vibration from v = 0 to u = 1, i.e., by AV x 12 kcal mol-I, increased (R’) on surface SE1 by (AR’) NN 2.4 kcal mol-l. (The major consequence of AV was enhanced (AV’)-see section 3.2.2 above.) By far the greatest part of this enhancement in product rotational excitation occurred in the lower vibrational states of the reaction product.For example, in v’ = 1 (AR’),! = 12.1 kcal mol-I. The tendency for OJtL) = 180” should be especially marked for the low- V‘ product. I I I I 1 I I 40 80 I20 I60 e,,,, / degrees FIG. 14.-Distribution of BJtLt, the angle between the product orbital and rotational angular moment (L’ and J’), for the products of F + HD, J = 3. The translational energy was selected from a 300 K Boltzmann distribution. At the extreme left QJtLP = 0 corresponds to J’ parallel to L’, while at the extreme right O,*,# = 180” corresponds to J’ anti-parallel to L’, as depicted in the insert. HF product -, DF product -----. Since the low v’ product originates from trajectories that pass through a com- pressed configuration (section 3.2.2), we conclude that the substantially enhanced rotation in v’ = 1 is connected with the enhanced repulsive energy release, and/or increased bending, in the FH*H intermediate that leads to low u’.In fact (AR’),. is significant for all 0’; v’ == 1-3. This is indicative of reaction through a more-bent intermediate, since high v’ involves reaction through stretched configurations (with some residual repulsion-the trajectory does not cross the exit valley at r2 = GO). Enhanced reagent translation, AT, markedly increases product rotation on SE1 (3.2.2). The characteristic of trajectories at enhanced translation is that they pass through more-compressed intermediate configurations, and also that they have the requisite energy to cross the higher energy-barriers corresponding to reaction through bent configurations.Both factors will tend to increase R’. An example is given in section 3.2.2. Enhanced reagent rotation AR = 3.39 kcal mol-’, corresponding to J = 0 -+288 THE REACTION OF F+H2+HF+H J = 4, increased the mean product rotational excitation by (AR') = 4.18 kcal mol-1 on SE1. Previous work has shown that there is insignificant correlation between J and J' on a repulsive surface ; the enhanced product rotational excitation cannot there- fore be explained as being an outcome of the conservation of angular When trajectories were separated into those originating from individual J levels 0-4, the following sequence of product rotational excitations were obtained for a reagent translational temperature of 300K: (R'),=, = 1.63 (R'),=, = 2.68, <R')J=2 = 4.44, {R')J=3 = 4.55 (R'),=, = 5.81, all in kcal mol-'.Inspection of the groups of trajectories coming from J = 0, 1, . . ., etc. shows that the mean collision energy for those that react is almost constant for J = 0 -+ 1 and thereafter increases (approximately linearly) by 1.7 kcal mol-' as J = 1 +- 4. This finding can most easily be summarized by saying that in this region of diminishing a(J) (fig. 10) the threshold collision energy for reaction is increasing with J. The 1.7 kcal mo1-' increase in mean collision energy (noted above) must be partially responsible for the increased product rotational excitation due to reaction through more compressed and bent configurations. Increased rotational energy in the reagents could increase the amount of bending in the intermediate, thus further enhancing R'.5. PRODUCT ANGULAR DISTRIBUTION All of the trajectory studies of this system employ repulsive potential energy surfaces that favour collinear approach, and hence all predict predominantly back- ward scattering of the molecular product for the F + H, mass ~ombination.~~ This is in qualitative accord with the DF scattering from F + D2 observed by Lee and co- w o r k e r ~ . ~ ~ However, whereas the molecular beam workers obtained some evidence of changing centre-of-mass angular-distributions for molecular product in the various o' levels, peaking at 180" for all u' but becoming more forward scattered for the higher levels, the trajectory results on SEl failed to give appreciably different angular distri- butions for different 0'.(These are the only computational data.) The results regarding angular distribution of the molecular product on SEl can be summarized as follows. (a) The differential cross section for the molecular product has a mean value (Omol> = 133" for u = 0, J = 1, with T selected from a 300 K distribution. The angular distribution is shown in fig. 15. (6) The mean angle shifts to a slightly more-forward value when the reagent is in o = 1 (T from a 300 K distribution); viz to (Omol) = 120". The breadth of the distribution increases, as shown in fig. 15. (c) We have examined the effect on Omol of repartitioning the reagent energy from vibration into translation. In (b), above, the mean collision energy for reactive en- counters was (T) x 2.0 kcal mol'l; the balance of the energy was in reagent vibration [E(v = 1) - E(u = 0) = 11.89 kcal mol-'1. In (c) we increased T t o 13.88 kcal rnol-' and decreased E(o = 1) to E(v = 0). The differential cross section broadened markedly (fig.15), and the mean became (Omol) = 102". This represents substan- tially more-forward scattering, though the mean angle is still in the backward hemi- sphere. The " stripping threshold energy "36b (the T which gives predominantly forward scattering) is high, as anticipated for this mass-combination reacting across a strongly repulsive potential-energy surface.44 Judging from Muckerman's study1lC of " hot " F + HD, the stripping threshold for F + H2 (ca. 90% of the molecular product scattered into the forward hemisphere) comes at -5 eV.( d ) The value of (Omol) for individual vibrational states Y' of the product is constant within the statistical uncertainty, i.e., to within approximately &5".JOHN - 0.06- JL eJ "2 0.04- N! 0.02- - 3 mm \ - 0 C . POLANYI AND JERRY L . SCHREIBER o.otq,, 1 I , ' I I * I 1 7 --..-- - 7 - - t ......... I - . . . . . . . . . . . . . . . . . . . . . . * . . . - - L----, * : . . ........... .......... i - ......... ---__ S.....".i I I I 1 : .........: 0 , 1 ' 1 ' do 80 I20 do 289 (e) The value of (OmoJ is invariant with reagent rotational excitation in the range J = 0 - 4, to within a similar uncertainty, approximately &6". This work was made possible by a grant from the National Research Council of Canada. J. C. P. thanks the Canada Council for the award of a Killam Memorial Scholarship. J.H. Parker and G. C. Pimentel, J. C/ieru. Phys., 1969, 51, 91 ; ( b ) R. D. Coombe and G. C . Pimentel, J. Cheni. Pliys., 1973, 59, 251 ; (') R. D. Coombe and G. C. Pimentel, J. Chern. Phys., 1973, 59, 1535; (d) M. J. Berry, J. Chen?. Phys., 1973, 59, 6229. '((I) J. C. Polanyi and D. C. Tardy, J. Chem. Phys., 1969,51,5717; ( b ) N. Jonathan, C. M. Melliar- Smith and D. H. Slater, MoZ. Phys., 1971, 20, 93; (') J. C. Polanyi and K. B. Woodall, J. Chem. Phys., 1972, 57, 1574; ( d ) D. S. Perry and J. 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