Green's functions in the theories of radiationless transitions, complex molecular spectra and resonant Raman cross sections: The solution for a generalized model, and its applications to the naphthalene second singlet

Abstract

The Green function method developed for disordered solids is applied here to the theories of radiationless transitions, complex molecular spectra and resonant Raman cross sections. A generalized model in which all the molecular states of interest are embedded in both a radiative and a non-radiative continuum is used. A recipe is provided for the evaluation of Green's functions for such a generalized model. It is shown that, in general, for n discrete states ( n-impurity problem), the present formulation calls for the inversion of 2 n × 2 n matrix. This is to be compared with the simple molecular problem (no radiative and non-radiative damping) where n interacting states would require the diagonalization of an n × n matrix. The green functions so evaluated can, then, be used to describe such diverse properties and phenomena as the radiationless transitions, resonant Raman cross sections, line shapes, lifetimes, quantum yields, etc. Specifically, the complex spectrum of the second singlet state of naphthalene is discussed within such a model as an example. A brief discussion on the inadequacies of traditional Raman intensity theories is also included.