Nonadiabatic Translations in Polyatomic Molecules

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Abstract
It is assumed that electronic relaxation is due to the nonadiabatic interactions omitted from the Born–Oppenheimer adiabatic approximation. The first step in the present development is to transform the expression for the rate constant as given by Fermi's golden rule so as to simultaneously evaluate the product of the density of states and the square of the absolute value of the interaction matrix element. By then introducing an approximation based on the physical meaning of nonadiabatic interactions, it is shown that the radiationless rate constant can be expressed in terms of known electronic and vibrational molecular parameters thereby providing a basis for calculating radiationless rate constants. The present theory is distinguished from previous theories of electronic relaxation by its emphasis upon the interaction matrix elements as opposed to the Franck–Condon factors. The present theory also predicts a position dependence for the effect of deuterium substitution on the radiationless rate constant in aromatic hydrocarbons and is in qualitative agreement with the recent results of Watts and Strickler [J. Chem. Phys. 49, 3867 (1968)] on partially deuterated napthalenes.

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