Multiple potential energy surfaces in a semiclassical study of molecular collisions

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Abstract
A semiclassical treatment of multiple (electronic) potential energy surfaces in molecular collisions is presented. Focusing on three surfaces, this treatment can be regarded as a generalization of a previous semiclassical treatment restricted to two surfaces [J. Chem. Phys. 56, 5637 (1972); 60, 2340 (1974)]. Suitable approximations lead to the formal simplicity of the elimination of nonadiabatic coupling terms by the analytic continuation of potential surfaces to their complex intersection points. The analysis first considers the semiclassical evaluation of the electronic propagator, which is a function of the nuclear path and appears inside a nuclear path integral. Then the nuclear path integral is evaluated by the method of steepest descent to yield S‐matrix elements connecting initial and final states of a collision. The nuclear normalization for the S matrix is presented in its usual form, and possible corrections to this form are discussed. Finally, certain modifications of the treatment that might be necessary when dealing with different collision systems are mentioned.