Distribution of Reaction Products (Theory) Part 12.-Microscopic Branching in H + XY --+ HX + Y, HY + X (X, Y = Halogens) BY J. C. POLANYI, J. L. SCHREIBER $ AND W. J. SKRLAC t Department of Chemistry, University of Toronto, Toronto M5S 1A1, Canada Received 29th December, 1978 3D trajectory studies are reported for several potential energy surfaces that could serve as models for the reaction H + ICI. This reaction exhibits macroscopic branching to give HCl + I or HI + CI. The surfaces yielded product energy distributions suggestive of significant bimodality in the HCI product, but not the HI; i.e., there was evidence of microscopic branching for the macroscopic branch involving reaction with the more electronegative of the halogen atoms, X. All of the surfaces were characterised by a barrier to approach of H at the C1 end of IC1, but attraction at the I end, in conformity with evidence from molecular beam studies regarding the stability of complexes HYX in contrast to HXY (electronegativity xx > xu).Extensive calculations were performed on one of these surfaces for room temperature (T,",AN, = 300 K) and elevated translational temperature (T,"RANS = 2685 K). The findings were in qualitative accord with the bimodal vibration-rotation distributions of HX observed in infrared chemiluminescence studies of reactions of the type H + X Y . The bimodal distribution could be identified with two dynamically different paths for HCI formation (microscopic branching). The HCI formed with the lower internal energy, Ein,, resulted from reaction of H directly at the C1 end of ICI, whereas the HCI formed with higher Eint was produced by migra- tion of H from the I to the Cl, following a lingering interaction of H with I.Migration occurred late in the encounter, by insertion of H into the extended I-C1 bond. The collision energy dependence of these two microscopic branches (" direct '' and " migratory ") differed notably. The probability of direct reaction, since it involved barrier-crossing (E, = 1.6 kcal mol-'), increased steeply with col- lision energy, whereas the probability of the migratory dynamics fell (E, = 0 kcal mol-' from the I end). As a consequence the HC1 product vibration-rotation distribution altered markedly in going from ETORANS = 300 to 2685 K, in qualitative accord with the findings from an infrared chemilumi- nescence study.By contrast the energy distribution for the other product, HI, showed insignificant bimodality at 300 K, and no dramatic change in product vib-rotational distribution in going to 2685 K; microscopic branching appeared to be negligible for reaction to form HI. This paper presents a model study of the reactions of hydrogen atoms with inter- halogens, XY. The objective was to gain qualitative insight into some of the gross features of these reactions, which have recently become apparent. Two prominent features are the following: (only the first of these features was known when the present calculations were begun). (1) There is a tendency for reaction with one atom of XY (e.g., -+ HX) to yield a bimodal product energy-distribution, and reaction with the other (-+ HY) to yield a " normal " product energy-distribution similar to that observed in reactions H + Y2 --+ HY + Y.The bimodality in the HX product distribution has been termed " microscopic branching ", in order to distinguish it from the " macroscopic branch- ing" to yield the different chemical species, HX and HY. It appears that the $ Present address : Franklin and Marshall College, Lancaster, Pennsylvania 17604, U S A . t Present address: Lumonics Research Ltd, 105 Schneider Rd., Kanata, Ontario K2K lYE, Canada.J . C . POLANYI, J . L . SCHREIBER A N D W . J . SKRLAC 67 halide which gives the anomalous product distribution is the one which contains the more electronegative of the atoms, i.e., the electronegativities are characteristically xx xY.1-3 (2) At moderately enhanced collision energy the anomaly in the HX product ._ energy-distribution, i.e. the microscopic branching, is no longer obser~ed.~ The experiments which have yielded this type of information have been principally infrared chemiluminescence studies. These included studies of the reaction H + ICl + HCl + I, which exhibited marked bimodality in the product energy-distribution for HCl with 300 K reagent~l-~ and no bimodality with the same reagents at 2685 K (mean collision energy % 10 kcal m ~ l - ' . ~ A molecular beam investigation of the closely-related reaction D + ICl--+ DCl + I at a similar enhanced collision energy gave no evidence of bimodality in the product di~tribution.~ The same was true of the product angular and translation energy distribution from a beam study of the alternative macroscopic branch, D + ICl- DI + C1, at the same enhanced collision energy.'j Experimental information for the H + XY reaction H + BrCl with thermal (300 K) reagents is more complete, since both macroscopic branches were amenable to study by infrared chernilumine~cence.~ Reaction with the more electronegative halogen atom (Cl) gave rise to molecular product (HCl) with a bimodal product energy distribution, i.e. this macroscopic branch exhibited microscopic branching.The other macroscopic branch, by contrast, did not; the chemiluminescence from the HBr product was indicative of a singly-peaked product energy-distribution resembling (though not identical to) that for HBr formed in the reaction H + Br,.Experiments on this system at enhanced collision energy have not yet been reported. The reaction is H + CIF -+ HF + C1 or HC1 + F.7 Once again both macroscopic branches were studied in detail. In this case (cf. H + ICl and H + BrCl) the C1 atom was the less electro- negative of the halogen atoms in XY. As had been predicted the HC1 exhibited a unimodal distribution resembling the product of H + C12+ HC1 + C1, whereas the HF product energy distribution had an anomalous form characteristic of micro- scopic branching. Bimodality of product energy-distribution is not unique to the systems H + XY. In earlier experimental work bimodality over product vibrational excitation appeared to be present for H + C12f -+ HCl + C1 (the dagger indicates vibrational excita- tion).' The theoreticaI interpretation, based on 3D cIassicaI trajectory studiess9l0 in- volved a type of branched pathway across the potential-energy hypersurface, i.e., Cl,t in its contracted vibrational phase reacted by way of compressed intermediate configurations, and C12t in its extended phase reacted through stretched intermediate configurations.' This represents a species of microscopic branching.There was also experimental evidence for a bimodal distribution over product rotational energy states. This was observed in the hot-atom reactions C1 + HI --+ HC1 + I ' v l l and H + C12+ HC1 + C1,* as well as in the thermal reaction H + SC1, -+ HC1 + SC1.12 This phenomenon has not yet been the subject of a theoretical study. The model proposed in each cases*1'*12 involved, once again, the existence of two characteristic paths across the potential-energy hypersurface.The paths, in these cases, were conceived of as being a direct path in which the attacking atom A reacted with the end of BC to which it makes its first approach, e.g., A + BC-+ ABC+ AB + C, and an alternative " indirect " path in which A interacted first with (say) C and thereafter migrated to B, i.e., A + CB --+ ACB -% CAB -+ C + AB; i.e. the same chemical products but in different states of excitation (m indicates migration). In the case of the hot-atom reactions the migration stemmed, presumably, from A further reaction H + XY has been studied recently.68 DISTRIBUTION OF REACTION PRODUCTS momentum initially present in the attacking atom A, which caused A to skip (like a stone on water) from one end of CB to the other.The picture outlined in the previous paragraph was speculative. The speculation rested on frequent observation of migratory encounters in early (2D and 3D) trajec- tory studies involving a variety of approximations to the potential-energy hypersurface for reactions of alkali metal atoms with halogens, M + XY.', The system H + XY, which inspired the present study, offered an opportunity for examining the viability of the " direct " versus " migratory " hypothesis in a case where an observed bi- modality of product internal excitation lent particular credence to the microscopic- branching model. A preliminary report on the present 3D trajectory work has already appeared.14 The findings indicated that the direct, as compared with the migratory, hypothesis was indeed a possible one.The trajectory results were in general accord with our earlier c o n J e c t ~ r e ~ * ~ * ~ * ~ ~ * ~ ~ that the part of the product with lower internal excitation involved predominantly direct reaction, with a lower average impact parameter (b), whereas the product exhibiting higher internal excitation derived to a significant extent from migratory encounters characterised by a higher value of (b). The trajectory results indicate that there exists a dynamical link between the macro- scopic and microscopic branching.', The conceptual basis for this link is easily e~ernplified.~ If the approach of A to the B end of BC involves a significantly lower activation barrier than does approach of A to the C end, then (a) AB will be formed by direct reaction and in good yield, whereas (b) AC will be formed by migration plus direct reaction, i.e., AC can exhibit microscopic branching.The total yield of AC will depend on the sum of the probabilities of migration from B plus direct reaction at C. However, until the factors governing the likelihood of migration are made explicit, the interdependence of macroscopic and microscopic branching will involve a weak link. It is interesting, nonetheless, to set this deterministic picture alongside the alterna- tive viewpoint that stems from information theory.15 We have not applied informa- tion theory in the present paper. Ref. (3) shows that the simplest formulation of information theory is insufficient to account for the (macroscopic) branching ratio in H + BrCl. An important contributory cause is likely to be the failure of information theory in its customary formulations to include the effect of differing activation bar- riers for reaction at either end of the molecule under attack.A recent study suggests that this omission can be serious even in the case that the molecule under attack involves chemically similar atoms, the branched reaction being F + HD -+ HF + D or DF + H.16 The conception of alternative direct and migratory reaction dynamics has been employed in a recent beam plus gas study of the system Ba + CF,I -+ BaI + CF3.17 Laser-induced fluorescence indicates a vibrational distribution in BaI that is bimodal. The reaction is postulated to proceed by two mechanisms; direct reaction at the I end of ICF3 with lower (b), and migratory reaction from CF, to I with higher (b).The former process causes BaI to rebound in the backward direction; the latter causes the BaI to be scattered forward with higher vibrational excitation. Similarly it has been proposed l8 that the marked difference in dynamics observed I 9 l t 0 between K + ICH3 -+ KI + CH, and K + CF31 -+ KI + CF, could be due to direct reaction with backward scattering of KI in the former case and migratory reaction with forward scattering of KI, K + CF31 --+ K+CF3-I _", CF3 + K'I-, in the latter case. The most facile migration would be expected to be that of a light atom between slowly-moving heavy atoms.I4 In the reaction H + YX, with which the present paper and its precursors dea1,2v3p14 the light atom is the attacking one, and the inter-J .C . POLANYI, J . L . SCHREIBER AND W. J . SKRLAC 69 mediate HYX (xx > x y ) holds together amply long enough for H to migrate from Y to X. It has recently been pointed out2' that, if X is incident on YH, the same dynamics should apply. Specifically the proposal is that in the reaction Cl + HI -+ HCI + I the atomic motions can be described as C1 + H I 5 ClIH -+ CIHI+ HCl + I, where m indicates, once again, migration of the H. In atomic reactions with polyatomic molecules the attacking atom may react at more than one site to give chemically identical but energetically distinguishable product species. This " alternative site " branching has much in common with macroscopic branching, since it does not involve differing modes of approach to the identical atom, but single modes of approach to differing regions of the molecule under attack.Alternative site branching is exemplified by the case of HF formed in the reaction of F + HCOOH and also F + HCH0.22 One can envisage more complicated situations in which the attack at a given site on the polyatomic can occur by alternate dynamics (e.g., directly or through migration) with the consequence that true microscopic branching is superimposed on alternative site branching. POTENTIAL ENERGY SURFACES AND METHOD OF CALCULATION The dynamics of the model H + XY reaction were assumed to be governed by a single potential energy surface. While energetically allowed, the reaction path H + IC1+ HC1 + I*, producing electronically excited I atoms, is ~nimportant.~ The form of this single potential surface was obtained from the extended London- Eyring-Polanyi-Sat0 (LEPS) equation, used in many previous studies of hydrogen- halogen reactions.23 In this formulation, the interaction potential of the triatomic system is determined by the spectroscopic constants of the diatomic fragment mole- cules, and the " Sat0 parameters ", Si, associated with the three bonds i-HX, HY, XY.Since the HICl system showed the most dramatic bimodality of the systems then studied, the spectroscopic constants of this system were used to specify the potential and the corresponding masses were employed in dynamical calculations. The parameters are listed in table 1 [following the notation of ref. (24), with 3/3 = '/3 in all cases].TABLE 1 .-PARAMETERS EMPLOYED TO GENERATE POTENTIAL ENERGY SURFACES ~~ ~~ parameters common to all surfaces (D, F, G and H) HI IC1 HCI 'Dlkcal mol- 73.78 50.30 106.41 y / A - 1.750 1.847 1.868 re/A 1.604 2.321 1.275 ~~ parameters specific to individual surfaces surface S I C , S"C, E,(H + CII+ HCl t I) E,(H + IC1+ HI + C1) AL(H + CII + HCI + I)/% &(H -t IC1+ HI + Cl)/% S H I A 0.7 0.0 0.2 0.00 0.00 53.6 88.8 B 0.7 0.0 0.0 1.68 0.00 50.0 87.9 C D 0.7 * 0.7 -0.2 -0.1 0.05 0.025 1.52 1.59 0.00 0.00 24.3 37.5 71.6 85.370 DISTRIBUTION OF REACTION PRODUCTS A variety of potential surfaces, differing only in the values of the Si, were con- sidered. Basing our studies on the hypothesis described in the previous section we selected the Si so as to produce surfaces with an attraction between H and the I end of ICl, but a barrier to approach of H toward the C1 end of ICI.Exploratory compu- tations pexformed by C. A. Parr in this laboratory gave evidence of direct and migra- tory trajectories on several surfaces of this type, including surface A of this paper. The work was not, however, pursued to the point where a statistically meaningful product energy distribution was obtained. The classical barriers for the four surfaces on which dynamical calculations were performed are given in table 1, along with a crude measure of product energy release, All% [ref. (24) and references therein]. Typical of the surfaces considered is surface D. Fig. 1 gives the customary collinear cuts through this potential surface.The contours show the barrier to approach of H toward C1 along the ClI axis [fig. l(a)], and the long range attraction of I toward H [fig. l(b)]. For each of the four surfaces considered, classical trajectory calculations were performed to determine the product energy distributions in the two product channels. The initial conditions were selected to simulate a 300 K thermal distribution of re- I I 1 I I 1 1 - 1.0 2.0 3.0 4 .O 5 .O 6 .O [ , / A 20 10 5 2 1 1 2 5 10 20 30J . C . POLANYI, J . L . SCHREIBER AND W. J . SKRLAC 71 FIG. 1.-Collinear potential energy plots of surface D: (a) H i- C11+ HC1 + I, (b) H + IC1+ HI + C1. Note the substantial differ- ence in appearance. For (a), there is a barrier in the entry valley, while in (6) the entry valley is Both plots are presented in skewed and scaled coordinates.characterised by a long-range attraction. agent translational energies and internal states. Trajectories were begun at an initial separation of H from the XY centre of mass of 8 A. The range of impact parameters was subdivided into 0-4 and 4-6 A, and stratified sampling procedures were used to compute all averaged product distribution^.^^ Integrations were performed with a fixed step size fourth-order predictor-corrector numerical integration algorithm of the Adams-Moulton type26 with a step size of 3.0 x The effect of reduced step size on the outcomes of these trajectories is discussed below. A substantial fraction of the trajectories computed in the 300 K batch showed complex behaviour associated with migration of H between I and C1.A detailed s.72 DISTRIBUTION OF REACTION PRODUCTS study of the effect of reduced step-size on the outcome of selected complex trajectories was made. This showed that, while the values of the product energies (V’, R’, T’) for a given product (say HCl) were unaffected by reduction of the step size below 3.0 x s, the nature of the product in some of the trajectories changed as the step size was reduced (ie., HI became the product, for the example cited). A step size of 0.75 x s proved adequate, in the group of 2000 trajectories that were re-run, to give product identity and product attributes invariant with further reduction of step size. s one third of the complex trajectories leading to HC1 switched either to HI or to unreactive outcomes.However, a comparable number of other trajectories, which had given HI or no reaction at the larger step size, gave HCl at the reduced step size. Product distributions for the two groups were compared, and found to be similar. All the conclusions reported here are based on the large step size batch; the calculations using a reduced step size would, we believe, not differ in any significant aspect. Fig. 2 shows the product vibration-rotation distributions obtained for HCl from preliminary studies of surfaces A, B and C, and a more extensive study of surface D which will be described below. While the sample sizes are modest ((100 reactive trajectories for all but surface D), it is clear that all of these surfaces show a more complicated product distribution than has been observed either experimentally or computationally for H + X2 systems.The presence of HC1 in quite high rotational levels is particularly notable. The product distribution of the 300 K H + X2 series is characterised by low product rotational energies (e~perimentally~’?~~ and theoretic- Since the HC1 product distribution from surface D showed the greatest similarity to the experimentally observed distribution from the H + ICl reaction, it was used as the subject of more extensive calculations. In excess of twelve thousand trajectories were run using the initial conditions described above. In addition, three thousand trajectories were run with initial conditions simulating H atoms produced from a 3000 K oven, reacting with IC1 in a 300 K thermal distribution of internal states (effective translational temperature; T&ANs = 2685 K).These latter conditions simulated the reagent energy in experiments of Hudgens and M~Donald.~ At the step size 0.75 x >. ally 8,23,29 - 31 RESULTS ROOM TEMPERATURE The bimodality in product vi bration-rotation energy distribution suggested by preliminary calculations on surface D was confirmed by the more extensive calcula- tions. Fig. 2(D) is the result of the large-scale calculation, done for a 300 K distribu- tion of energies, on surface D. Fig. 3 shows the product translational energy against T’ distribution for both the HC1 and the HI product as given by the 300 K calculation on surface D. The HCl dis- tribution shows a marked peak at low T’ (low product translational energy and conse- quently high internal energy, vibration plus rotation, V’ + R’ = Eint).There is also a broad shoulder on the distribution, extending out to high T’ (low Ef,,). No such bimodal stiucture is apparent in the T‘ distribution for the HI product. We have divided the HC1 products into the two groups suggested by fig. 3(a), for the sake of further discussion. Those with T’ < 15 kcal are termed “ high Eint ”, and those with T’ > 15 kcal, “ low Ef,, ”. These two groups differ notably in other aspects of their product distributions, as summarised in table 2. In fig. 4(a) and 4(6) we show the “ triangle plot ” of fig. 2, surface D, separated into triangle plots for theJ . C . P O L A N Y I , J .L . SCHREIBER A N D W . J . SKRLAC 73 6ot -0 10 20 30 LO 50 60 R'lkcal mot-' 0 10 20 30 LO 50 60 R'l k c a l mol-' - I 0 d E d a u Y ..\ L 0 10 2 0 30 40 50 60 50 LO 30 20 10 ~~~ 0 10 20 30 LO 50 60 R ' / k c a l mol-' R ' l k c a l mol-' FIG. 2.--" Triangle plots " giving product vibration-rotation energy distributions for HCl product of H + ClI, obtained from 3D classical trajectory calculations using potential energy surfaces A, B, C and D (characterised in table 1). In all cases initial conditions were selected to simulate a 300 K thermal distribution of collision energies and reagent CII internal states. Bimodality is apparent to a greater or lesser degree in the results of all four calculations. Variation of the surface parameters had the effect of varying the relative proportions of products from the two microscopic branches, and of altering the product vibrational excitation of the " direct " branch at the left of each triangle. high Ei,, and low Ei,, components of the HCl product.The distribution for the low Ei,, group [fig. 4(b)] is similar to that of HCl produced by H + C12.27 The distribution of the high Elnt group [fig. 4(a)] is markedly different, resembling that for HC1 produced by Cl + H1.25932 Fig. 5 shows the vibration-rotation distribution of the HI product for this same calculation. There is a single " ridge " of high probability extending from Y' = 30, R' = 0 to Y' = 0, R' = 10 kcal mol-'. Our statistics do not permit us to say whether the small double peak along this ridge is real. It is of interest to examine the contributions of the low E;,, and high ,Tint com- ponents to the overall distribution of HCI over product vibration, u ' ; this is shown in fig.6. The vibrational distribution of the high Ei,, group is broader, and is74 DISTRIBUTION OF REACTION PRODUCTS displaced to significantly higher vibrational levels than that of the low Eint group. The two distributions overlap considerably, and the bimodality only evidences itself as a shoulder on the overall HCl distribution. While surface D predicts bimodality of product distribution similar to that of the experimentally observed distribution, it fails to match the experimental di~tribution.~ The ratio between the total amounts in the low Ei,, and high Eint groups is 0.72 for 1 I la 1 - I 0 5 10 15 20 25 30 35 1 FIG.3.-Product translational energy distributions from H + ICI, for a 300 K thermal distribution of initial conditions : (a) relative translational energy distribution of HCl + I, (6) relative translational energy distribution of HI + C1 (the T’ were the exact values computed for each trajectory; cf. fig. 4). In (a) the low T‘component of the HCl + I distribution corresponds to high internal excitation (high ,!?in*), and is associated with large values of V’ and/or R’. The high T’ portion corresponds to low Eint, and hence to lower V’ and R‘. No structure is apparent in the distribution of the HI + CI relative translation in (b). T ’ / kcal mol-’ surface D, while experimentally a similar division of the product HCl into two groups gave a ratio of only 0.25.As noted in the Introduction we regard surface D as no more than a model capable of giving us qualitative insight into some of the gross features of reactions H + XY. For completeness, fig. 6(b) shows the product vibrational distribution of HI. It is essentially flat over the range u’ = 0-2, with no significant indication of bimodal structure along the length of the “ ridge ” mentioned in the discussion of fig. 5. There are no experimental data regarding k(u’) for the HI product of H + ICl. The angular distributions of both HCl and HI are found to be broad and structure- less (fig. 7). While no experimental evidence is available on the angular distributions for this range of collision energies, higher energy data, discussed below, suggest thatJ .C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 75 R’/ kcal rnol -’ 50 LO 30 20 10 0 10 20 30 LO 50 60 R ’ / kcal mol -’ FIG. 4.-Triangle plots of product vibration-rotation energy distributions of the (a) high ,Tint and (6) low Eint components of the HCl + I product of H + CII, with 300 K thermal initial conditions. The T’ values indicated on these two triangle plots, and all other such plots, are approximate values determined on the assumption of a fixed total energy in all products (this assumption is not precisely correct for a thermal distribution of initial conditions).76 DISTRIBUTION OF REACTION PRODUCTS 30c 0 R'kcal mol -' FIG. 5.-Product vibration-rotation energy distribution of the HI + Cl product of H + ICl with 300 K thermal initial conditions.In contrast to the results shown in fig. 1 for surface D, the HI product shows no marked division into low and high EinC fractions. the angular distributions are probably poorly represented by the results of these calcu- lations. As noted below, this should have little effect on the observations regarding the broad features of microscopic branching mechanisms. HIGH TEMPERATURE The results of the 2685 K batch of trajectories, intended to mimic the experimental conditions of Hudgens and M~Donald,~ are shown in figs. 8-1 1. While the HI product translational energy, T', distribution is hardly altered, the HCl distribution has been considerably changed. Only one peak is apparent, with a maximum at x 30 kcal mol-'. The maximum in the large peak (high EinJ of the 300 K HCl T' distribution, shown previously in fig.3, was below 10 kcal mol-', while that of the broad shoulder at 300 K (low Eint) was between 20 and 30 kcal mol-l. As is discussed below, the high Eint group has decreased markedly in importance with increasing translational temperature, so that the T' distribution is dominated by the low Eint group. This observation is supported by the general form of the HC1 vibration-rotation distribution [fig. 9(a)]. The 2685 K triangle plot closely resembles that obtained ex- perimentally at similarly enhanced collision energy for the reaction H + C12+ HCI + C1.* Since it is the low Eint component of the (300 K) HC1 product distribu- tion [fig. (4b)l that resembles H + C12+ HCl + C1, it is reasonable to suppose that it is the " low Eint " mechanism that is the dominant one at 2685 K.The significance of this proposition, as well as further evidence to support it, will emerge from the more detailed analysis to be found in the following section. Once again we find that our model surface (surface D) is only qualitatively in3 . C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 77 o Oi2 0.4 I- T 1.0 x - E -L \ e - 0.5 - - 0 1 2 3 4 V ' FIG. 6.-Relative distribution among vibrational states, of products of H + IC1 with 300 K thermal initial conditions. (a) HCl product (-). The component distributions for low Eint (---) and high Eint (- -) are also shown, normalised so that the sum of the two equals the overall distribution. (Note that f; values indicated on the upper scale are determined in the approximation of a fixed total energy).(b) HI product. To within one standard deviation, the populations of u' = 0, 1 and 2 are all equal for HI.78 DISTRIBUTION OF REACTION PRODUCTS accord with experiment. Hudgens and McDonald4 found that the bimodality shown in fig. 1, surface D, of the present study [and more clearly in fig. 4(a) and (b)] was still discernible in the HCl product of the reaction H + ICI at 2685 K. Our surface D, as noted above, yields an excessive fraction of the low &'nt component at 300 K (roughly 3 times too Much relative to the high Eint, when compared with experiment); consequently at 2685 K the enhanced importance of the low Eint mechanism has the result that this component completely overshadows any contribution from the high 0.4 / a ) 1.c I I I I 0 40 80 120 160 I I I I 8,t,;, I I I 1 160 120 80 LO 0 e f h o l FIG. 7.-Product differential cross-sections for H + ICI with 300 K thermal initial conditions. (a) HCl product: overall (-), low El,,, (- - - -), high Eint (- -). No discernible difference is obtained between the angular distributions of the two fractions. (b) HI product. Eint mechanism that may be hidden in the product energy-distribution recorded in fig. 9(a). The important observation for the present model-study is that the shift toward a greater contribution of the low Eint dynamics at the higher translational temperature is clearly evident in the experimental The product vibration-rotation distribution of HI [fig. 9(b)] shows no such sub- stantial change with increasing translational temperature.The change that does occur is that the mean fraction of the total energy entering product vibration decreases (from 0.34 to 0.22) and the fraction entering rotation and translation increases corre- spondingly (see table 2). This is in accord with the normal pattern of behaviour noted experimentally and theoretically for a number of simple reactions [e.g., ref. (8) and (31)]. The effect of increased TTORaNs on the distribution over u' is shown for the HC1J . C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 79 product in fig. lO(a). Once again the finding is in accord with the notion that the low Eint mechanism for HCI formation dominates at 2685 K on surface D. The maximum of the curve of relative k(u’) lies between u’ = 2-3.This corresponds to a modest downward shift from the low El,, distribution pictured in fig. 6(a), which peaks at u’ = 3-4. It does not resemble the high El,, curve of fig. 6(a), at u‘ = 5-6. I I I , , , I ! I , , , , T y kcal mol -’ 0 10 20 30 4 0 50 60 FIG. 8.-Product relative translational energy distributions for H + ICI with 2685 K thermal initial conditions: (a) HCI product, (6) HI product. The maximum in the HCI distribution has shifted from 10 kcal mol-’ [fig. 3(a)] to 30 kcal mo1-’, while the HI distribution is practically unchanged. The k(u’) for HI [fig. 10(b)] at 2685 K have also shifted to lower levels as compared with k(u’) at 300 K [fig. 6(b)]. Since table 2 shows that the cross-section for reaction has dropped by an order-of-magnitude (Le., the rate constant has dropped to 0.4 times) we conclude that this decrease has mainly affected the levels v’ = 2-3.The angular distributions at the higher translational temperature (fig. 11) are again flat and featureless ; they resemble the lower temperature results. The experi- mental findings for the higher energy range show the HC1 product to be primarily backward ~ c a t t e r e d , ~ ~ much like H + C1, at the same energy, while the HI product (as judged from the DI angular distribution obtained from D + TC1) is sideways peaked. Computational studies by McDonald29 and by Blais and Truhlar3* on the effect of potential anistropy on the angular distribution in systems with a L + HH mass - -80 DISTRIBUTION OF REACTION PRODUCTS R ' / kcal mol -' I bl 30 - 0 10 20 30 R'/ kcal mol -' FIG. 9.-Product vibration-rotation energy distributions for H + 1C1 with 2685 K thermal initial conditions: (a) HCI product, (b) HI product.There may be bimodality in (b). Bimodality is no longer apparent in (a).J. C . POLANYI, J . L . SCHREIBER AND W . J. SKRLAC 81 combination suggest a close connection between these two aspects, but little connec- tion between potential anisotropy and product energy distribution from their surfaces which exhibit repulsive energy release. We expect that the same conclusions would apply to the more complex trajectories we have observed, as the HICl " complexes " do not appear to rotate significantly during the period of close interaction, so that the direction of separation of HC1 and I is still determined in large measure by the angle between the initial ICl bond orientation and the initial direction of approach by the H [see also ref.(34)-(36)]. Appropriate modification of the angular anisotropy of surface D might produce the experimentally observed scattering patterns without significantly altering the prod- uct energy distributions of the two microscopic branches. In fact these latter attri- butes are also in need of alteration if the experimental findings for H + ICl are to be matched quantitatively. DISCUSSION Separation of the HC1 product into a low internal energy (" low Eint ") and a high internal energy (" high Eint ") components, on the basis of fig. 3, permits us to compute cross-section functions, a(T), for the differently excited categories of product molecules.This is made possible by the fact that the k(T') in fig. 3 is the result of a batch of trajectories Monte Carlo selected from a 300 K reagent translational distribu- tion. The individual trajectories can be totalled within successive intervals of reagent translation, T, to yield the cross-section functions recorded in fig. 12. Fig. 12 indicates once again (see the previous section) that the type of dynamics f : I. a Y 0 E 3 0.5 L \ * C 1 I 1 2 3 4 5 6 7 0 9 V'82 DISTRIBUTION OF REACTION PRODUCTS f : V' FIG. 10.-Relative distribution among vibrational states, of products of H + ICl with 2685 K thermal initial conditions: (a) HCI product, (b) HI product. associated with low Eint is becoming more probable as 7' increases, and that the contrary is the case for high Eint dynamics; we surmise from this that the low El,, reaction mode involves the crossing of a potential barrier, whereas the high E;,, does not.Experimental evidence for a declining cross-section in reactions H + X2 pro- ceeding across a negligible barrier has been obtained recently ; 37 theoretical evidence has been available for some time p a ~ t . ~ ~ . ~ ' Table 2 lists activation energies for the low Eint and high Eint components of the HC1 product; they are 1.36 and 0.10 kcal mol-', respectively. Hudgens and Mc- Donald4 compared their experimentally determined yields of low Eint and high Eint HCl for the reaction H + IC1 at high temperature with Polanyi and Skrlac's relative yields at room temperat~re,~ and concluded that the difference in activation energies must be at least 1.1 kcal mol-l, which is in agreement with the results on surface D.The existence of a higher energy barrier for the formation of the low Eint HCl product than the high Elnt component, is in accord with the model proposed in earlier communications from this The model is summarised in the Intro- duction. The low Eint product is formed as the outcome of direct reaction at the C1 end of ClI. Approach from this end of IC1 requires that the system surmount a bar- rier. The high E;,, product is formed by migration from the I end of IC1 to the C1. There is no barrier to approach at the I end, hence there is an energetic advantage to forming HCI by migration from the I end. By contrast it is energetically disadvan-J .C . P O L A N Y I , J . L . SCHREIBER A N D W . J . SKRLAC 1.2 I I I I I 1 I I 4 0 . 4 c IL 4 b 3 ul N \ - u u IN - 1.6 Ol t T 83 FIG. 1 1 .-Product differential cross-sections for products of H + ICI with T;,,, 2685 K therma initial conditions, (a) HCI product, (6) HI product. tageous to form the alternate product, HI, by migration from the C1 end of the molecule, since the C1 end is blocked by an energy barrier. Fig. 13(a) shows equipotential contours for H approaching ICl when the molecule is fixed at its equilibrium bond length, 2.321 A. Approach of H toward C1 requires a minimum of 1.0 kcal mol-l to surmount the barrier. This barrier is only slightly higher for direct collinear approach than for approach from the side; i.e., the cone-of- approach is broad.It is evident that H experiences an attractive force towards the84 DISTRIBUTION OF REACTION PRODUCTS I end of ICI (once again with a wide cone of approach). This is consistent with the proposed model, which describes the second route to HC1 as passing through an inter- mediate in which H is bound to I, but is transferred to Cl before the heavy particles C1 and I separate to such an extent that " migration " is precluded. We have examined bond and force plots of randomly selected trajectories in both groups of HCl products. The following conclusions may be drawn. For the low TABLE 2.-RESULTS OF TRAJECTORY CALCULATIONS ON SURFACE D HI overall <f$> 0.59 <fRI> 0.13 <fi) 0.28 @/A' 3.10 Eac/kcal mol-l 0.63 no. of react. trajectories 356 <e>,,a/o 93 low EI,, 0.48 0.07 0.45 1.30 1.36 87 152 high Eint 0.67 0.34 0.1 8 0.26 0.15 0.40 97 87 1.80 10.36 0.10 0.01 204 1160 <f;> 0.37 < f R > 0.18 <fi> 0.45 <e>,x"l" 93 Bb/& 7.5 Eat/ kcal mol - 1.99 no. of react.trajectories 446 ~ ~~ 0.22 0.32 0.46 1.49 - 1.99 93 89 a Atomic scattering angle, 8 = 0" for backward molecular scattering, 8 = 180" for forward mole- cular scattering, relative to the incoming atomic beam direction. ii is the thermal-average cross- section, which is proportional to the thermal rate constant k; k = (v>3, where ( v > is the average relative velocity, given by (3RT0/2p)''' (To is the translational temperature and p is the reduced mass of the H + ICl system). The translational activation energy is the difference between the mean collision energy for reactive collisions, and the overall mean collision energy; E, = (T')rx - ($)k T L N S .Eint group, the majority of reactions occur by a process in which HCl is formed by direct approach of H toward C1. The newly-formed HC1 leaves with sufficient trans- lational energy to prevent any further interaction of HC1 with I. This kind of dynamics is normal for surfaces with repulsive energy release such as H + Clz. Inspection of trajectories belonging to the high Eint category revealed, as antici- pated, that reaction took place by way of an initial interaction with the I end of the molecule followed by migration to the C1. The migration was observed to occur after the I and the C1 had begun to separate. This is illustrated in the " bond plot " and " force plot " of a typical complex trajec- tory, shown in fig.14. In this encounter migration did not occur until the I-Cl distance had increased from equilibrium (2.321 A) to nearly 4 A. The H atom had undergone several rotations about the I atom, and has oscillated 20 times against the I. The migration of the H atom did not take place until quite late in the encounter. It involved passage through a linear ClHI configuration, since the H passed betweenJ . C . POLANYI, J . L . SCHREIBER AND W . J . SKRLAC 85 the C1 and the I. We refer to this as " insertion " of H into the extended I-Cl bond.14 Insertion was a feature common to almost all of the complex trajectories examined. It is shown clearly, for the sample trajectory on surface D, in fig.15. When the I-C1 distance has increased to 3.75 A, the equipotential contours can be ' \T T / kcal mol -' FIG. 12.-Reactive cross-sections for the low Eint (- - - -) and high EinC (- -) fractions of the HCl product of H + ICl(300 K thermal initial conditions). seen to have altered dramatically [fig. 13(b)] There is no longer a barrier preventing the passage of H through the intermediate configuration IHCl en route to migration; for the configuration with the H between I and C1 there is a marked potential-well. This helps explain the pattern of motion in fig. 15. While Cl and I are still close to one another the motion of H toward C1, as it rotates and vibrates about I (close examination reveals some 5 vibrations) fails to give rise to migration.Instead H rebounds off C1, and the direction of rotation about I reverses (first at position 7, and then once more at position 27). Finally (at position 40) the H is subjected to a strong attraction toward Cl and is drawn into the region between the separating atoms, Cl and I. Insertion has occurred. The acceleration of the H becomes high Eint (vibration and rotation) in an incipient HC1 molecule. The rotation of H around C1 brings the H atom between C1 and I for a second time, at position 57. By this time the I-Cl distance is > 5.5 A, and there is little likelihood of back-migration to the HI. Bond plots computed for trajectories on the other trial surfaces showed similar36 DISTRIBUTION OF REACTION PRODUCTS I CI FIG. 13.-(a) Potential contours for H approaching ICI from arbitrary directions. The molecule is fixed at its equilibrium bond length.The barrier to approach of H toward the C1 end of ICI is seen to decrease as H approaches from more lateral directions. The approach of H toward I is attractive out to large bending angles of the HICl intermediate. (b) Potential contours for H approaching IC 1 from arbitrary directions, when rIC1 = 3.75 A. The zero of energy is the potential of the stretched ICI (zk., the H-ICI interaction potential is plotted, not the full three atom potential). behaviour, namely direct reaction and migratory reaction with insertion, the former leading to low Eint and the latter to high It is evident from an analysis of the dynamics exemplified in fig. 15 that migration, without back-migration, requires a degree of synchronisation between the angular motion of the attacking atom and the linear rate of separation of the particles under attack.The pattern of motion cannot be quite so simply described if the three par- ticles are of more-nearly comparable mass. Nonetheless, the importance of a high degree of rotation of A about B if a " clutching " secondary encounter of A with the departing atom C is to lead to migration + AC, has been noted earlier for reactions of metals with halogen^.'^^^^ This early work showed the importance of attractiveJ. c . POLANYI, J. L . SCHREIBER AND W . J . SKRLAC 87 5 8 I I I I I I I I I I I I I I - - ?.=.a c 0 a J \ U - - 4 - n - I I I I I I I I I I I I I I I I I 1 I - c x . -2001 1 I I I I I I I I I I 0 2 4 6 8 10 12 14 time / 1 0 ~ ~ FIG.14.-Bond and force plot of a reactive H + C11 trajectory showing migration. In the upper panel, r1 = rHI (-), r2 = rlcl (- - - -), r3 = rHCl (- + - a ) and S (. . . . .) = the sum of the shorter two bond lengths. Note that when S is equal to the longest bond length (as occurs at the position marked with *, shortly after t = 12 x In the lower panel, force components along the three bcnds (using the same legend for associating the lines with bonds as in the upper panel) are shown. Initially a highly-vibrating incipient HI molecule is formed while the three atoms are in the HICl arrangement. This complex undergoes several bends, indicated by oscillations of the r3 distance between equality with S (linear), and equality with r2 (bent).Finally, at the asterisk, the ICl distance has increased sufficiently to allow this bend to become an insertion following which an HCl molecule is formed. s), the three-atom system is linear. - 3 .Ol 1 I I I I I J -6.0 -4.5 -3.0 -1. 5 0 1,5 3 .O A FIG. 15.-Atomic coordinates in the x-y plane for an H + ICI trajectory showing insertion. Here the initial conditions were chosen for simplicity to produce a trajectory which remained in a plane. The initial bond formation of H to I and the bending of the HICl complex are clear in steps 1 to 30. At step 30 the ICI relative motion suddenly shows evidence of a mutual repulsion which determines what follows. At step 36, the H, rather than being repelled by lateral approach to the CI, is able to insert between C1 and I.The ClHI complex makes one full asymmetric vibration before falling apart to HCI + I.88 DISTRIBUTION OF REACTION PRODUCTS energy-release at the B end of the molecule permitting reaction out to high impact parameter with consequent angular motion of A about B, and lingering encounters of A with B.13v39 The ranges of reagent parameters that led to migration depended on the potential energy surface and mass combination. A batch of 64 reactive trajectories on surface D using a 300 K reagent energy and equal masses, L + LL, gave z 25 % migration, indicating that on this type of energy surface dualityof reaction path (" microscopic branching ") is not restricted to the extreme L + HH mass combination. Inspection of o v e r 0 0 bond-and-force plots for the 300 K H + ICl reaction on surface D indicated that the alternate product HI was formed exclusively by direct ( i e ., non-migratory) reaction. The attacking H could form HI by approach from the I end of ICl, or as a consequence of a grazing collision from the C1 end. The latter cases did not constitute " migration ", since the atomic separations and forces showed no evidence of incipient formation of an HC1 bond, which would be characterised by an oscillation of the H against the C1. Instead the H passed by C1 at large im- pact parameter b, and subsequently was drawn in to the I. If the line-of-centres momentum between H and C1 was sufficient to carry H over the barrier, so that it became subject to H-Cl attraction, then it remained attached to the C1. Not only is C1 the more electronegative of the two halogen atoms under attack, but it is (for closely related reasons) the atom that binds more strongly to H.In fig. 13(b) it is evident that when the I-C1 bond is stretched (so that I and C1 appear to H akin to isolated atoms) the attraction operating on H, as it inserts, is greater at the C1 end. This is an important additional reason that, at normal collision energies, migration takes place toward the more electronegative atom (+HX) but not away from it (-+HY; in this case HI). A more general statement of the present ob- servations would be that migration is an important route for the formation of the product that bonds more strongly with the attacking atom. Hence microscopic branching occurs in the more exoergic of the macroscopic branches.Microscopic branching would be expected to have the most conspicuous consequences if the alternative dynamics (direct reaction --+HX, and migratory reaction -+HX) occur in different ranges of impact parameter; the presence of a barrier to direct reaction and not to migratory reaction ensures this. The general form of potential-energy surface used in the present work (attracting the attacking atom, A, at the B end of the molecule under attack and repelling it at the C end) is in accord with proposals made by H e r ~ c h b a c h ~ ~ on the basis of simple molecular orbital argument^,^^'^^ and recently documented in the work of Lee and ~ o - w o r k e r s ~ ~ who have been able to observe stable species HYX (xx > xy) in crossed molecular beam studies.For HIF they obtain a figure of 30 kcal mol-' for the stability relative to H + IF.42 The adduct HICl should be stable by a few kcal mol-I, but has not yet been reported. We are indebted to Prof. C. A. Parr for his contribution to the present study at its inception (see section on potential energy surface above). Mr. David Messersmith and the Computer Facility of Armstrong Cork Co., Lancaster, Pa., U.S.A., kindly assisted in the preparation of fig. 13. 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