Theory of radiationless transitions in polyatomic molecules. The intermediate case

A theory of radiationless transitions that spans the intermediate case between the small “molecule” and “big molecule” limits is presented. The theory is applicable to spectra and picosecond time evolution experiments concerning states such as the vibronically perturbed second excited single state of naphtalene studied by Wessel. An important philosophy used in the paper is the “unbunding” of the time-dependent and stationary state aspects of this problem. This view has been strongly emphasized by Rhodes and allows each part of the problem to be handled separately without being limited by the approximations of the other. The single-sharp-level-embedded-in-a-continuum model is used, and the stipulation that the sharp level carries all the oscillator strength is retained. However no limiting restrictions are placed on the nature of the continuum nor the interaction matrix elements. Thus the theory encompasses both the statistical limit and the small molecule limit as well as all cases intermediate between these and should therefore be of more interest to the experimentalist. The exact Green function for this problem is obtained, allowing the observed absorption spectrum and time evolution experiments under various excitation conditions to be exactly related in a practical way. Transformation between an observed spectrum and unperturbed zero-order states is possible and should be of use to the spectroscopist when trying to analyze spectra in regions of massive perturbative mixing.