Vibrational adiabaticity and reaction coordinate

The term vibrational adiabaticity was introduced [87] to describe some results of the computer experiments of Wall et al. [88]. They were pioneers in the use of classical mechanical trajectories of the atoms to study chemical reactions theoretically, using electronic computers. Using classical trajectories for the collinear transfer of an H atom, H + H2 — H2 + H, they found that when the vibrational energy of H2 was equal to (u + l/2)h v, and the energy barrier to reaction decreased by an amount (u + 2) hv- hv+), where v is 0 or unity v is the H2 vibration frequency and v+ is the symmetric stretch H—H—H frequency in the TS. The question was how to explain this quantum-like result in a purely classical trajectory calculation. 

Had the calculations been quantum mechanical rather than classical, the above result would have implied that somehow a vibrational quantum number v remained constant during the motion along the reaction coordinate, even though the nature of that vibrational motion changed drastically, from an H2 vibration to a symmetric stretch in the H3 TS and then to an H2 vibration in the product H2. 

The classical counterpart of v is the action variable /, which equals fpdq, where the integral is over one vibrational cycle of the vibration. In old quantum theory (or, later, the WKB theory), / is related to v by / = (u + l 2)h. Thus, it occurred to me that the above lowering of the energy barrier for the motion along the reaction coordinates could be rewritten as l(v— v ) and so the results of Wall imply that the classical vibrational action I was constant along the reaction coordinate in this system. 

It seemed appropriate to term this behavior vibrational adiabaticity . Indeed there were also earlier quantum mechanical results for this reaction [89], for which I found a similar behavior [87]. Furthermore, many years before, Hirschfelder and Wigner [90] suggested the equivalent of a vibrational adiabaticity for reactions. The main question, however, was how to treat this approximate dynamical behavior in a physical way. For this purpose, I introduced a coordinate system which passed smoothly from 

These coordinates in Fig. 1.10, or their extension [53] to three dimensions, are appropriate when the curvature of C is small. Non-adiabatic vibrational transitions then arise from both the curvature and from any rapid change of vibrational frequency as the system moves along the reaction coordinate s [91, 92]. However, in reactions such as the H transfer in AH + B — A + HB in Fig. 1.5, the curvature is so large that there is a tendency for the H to cross from one valley (reactants) to the other (products) at a constant AB distance (the Franck-Condon principle) and 

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