Energy Distribution Among Products of Exothermic Reactions. II. Repulsive, Mixed, and Attractive Energy Release

Abstract

A series of two-dimensional classical kinematic computer calculations have been made on the hypothetical exothermic exchange reaction A+BC→AB+C, −ΔH=48.5 kcal mole−1. Product energy distribution (vibration, rotation, and translation; Evib, Erot, Etrans) was obtained as a function of initial position, impact parameter, and kinetic energy (αi, b, and Ekini). All eight different combinations of light (L=1 amu) and heavy (H=80 amu) masses were examined. Eight different potential-energy hypersurfaces were explored. All were obtained from an empirical extension of the London—Eyring—Polanyi—Sato (L.E.P.S.) method. The hypersurfaces were categorized in terms of the percentage attraction, A⊥, and percentage repulsion R⊥, read off the collinear three-dimensional surface. This categorization was shown to be helpful in arriving at a qualitative understanding of the product energy distribution to be expected from all the mass combinations reacting on these extended L.E.P.S. hypersurfaces. However, it was also shown that the A⊥, R⊥ categorization could only be of (approximate) quantitative value in predicting product energy distribution for the case that the atomic masses satisfy the inequality mA≪mB, mC. For all other mass combinations three types of energy release must be distinguished; attractive energy release (A approaching BC, at normal BC separation), mixed energy release (A still approaching BC, while BC extends), and repulsive energy release (AB at normal separation retreating from C). These three types of energy release, symbolized A, M, and R were defined. The value of the concept was tested by obtaining % A, M, and R for each mass combination on several energy surfaces of markedly different characteristics, from part of a single collinear trajectory, and then plotting A+M against the mean vibrational excitation, % 〈Evib〉, obtained from a representative group of trajectories on the full hypersurface. For all mass combinations on all the surfaces examined it was found that % (A+M)∼% 〈Evib〉. There was a tendency on surfaces with appreciable repulsive character (significant % A⊥ for the reaction A+BC to give less vibration if A=L than if A=K. This light-atom anomaly became very marked as A⊥ became large. These phenomena could be understood if it was recognized that the mixed energy release had two components; late attractive MA and early repulsive MR, whose proportions on a particular energy surface were characteristic of that surface and were linked to the proportions of A⊥ and R⊥ for the surface. The greatest variation in 〈Evib〉 with the nature of the hypersurface occurred for the mass combination L+KK, owing to the low % M that characterized this mass combination on all surfaces. It was again found that a potential-energy hypersurface with a large proportion of repulsive character (R⊥>A⊥) provided the most likely qualitative explanation for the relatively low percentage vibrational excitation found experimentally in the atomic hydrogen+halogen reactions. Of all the energy surfaces the most repulsive (large R⊥) gave product energy distributions which were most sensitive to changes in the masses of the reagents, owing to the fact that M was largely MR. Trajectories became more complex, and Evib more sensitive to b, the more attractive and less directional the surface. The range of b's, | bmin | to | bmax |, leading to reaction increased (for all mass combinations) on the more attractive surfaces; at the same time reaction became restricted to small intervals of b instead of occurring at every b within the range | bmin | to | bmax |. On a highly attractive (A⊥=87%) and nondirectional surface, complex trajectories, corresponding to multiple encounters of the three atoms, became important. This was accompanied by a diminution in 〈Evib〉 and an increase in 〈Erot〉 and 〈Etrans〉, which was interpreted as a transition toward a statistical distribution of energy among the products. It was pointed out that it is a general law of motion that for any given interaction potential in any number of dimensions the dynamics of a reaction involving masses mA, mB, mC, shall be identical to that for any other masses mA*, mB*, mC*, provided mA*/mA=mB*/mB=mC*/mC.