Nonadiabatic interactions in unimolecular decay. II. Simplified formalism

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Abstract
Simplified semiclassical formulas are derived for the study of the nonadiabatic transition probability between two electronic states. They are expressed in terms of the coupling function g (R) equal to the matrix element of the d/dR operator between adiabatic states. It is shown that if g (R) keeps the same sign for all values of R, the integration of the classical‐trajectory equations in the adiabatic basis depends on a particular function T (S) only, which is the well‐known Massey parameter. This function plays a role similar to the t (s) function introduced by Delos and Thorson in their ’’close coupling model.’’ The present method is an extension of the treatment suggested by Rosen and Zener and assumes that ΔE, the energy difference between adiabatic energies, can be considered as constant. The significance of this is investigated. In simple cases, the transition probability can be expressed in terms of an adiabatic parameter χ only, defined by Eq. (32). Formulas are given for the isotopic effect, and for the influence of the excitation energy on the transition probability. In a polyatomic molecule, different kinds of couplings must be distinguished, depending on the nature of the internal coordinates which vary along the nuclear trajectory.