The energy gap law for non-radiative decay in large molecules

Abstract

A general theory of non-radiative intramolecular decay in large molecules is formulated using the methods of solid state physics and the harmonic approximation. The predicted dependence of the decay rate on the energy gap ΔE between electronic origins gets characteristic forms in two limiting cases: the string electronic-vibrational coupling case (gaussian in ΔE, Arrhenius-type barrier climbing between electronic states, small isotope effect) and the weak coupling case (nearly exponential variation with ΔE, domination by the highest frequency modes and marked deuterium isotope effect). Using some semi-empirical estimates, but without unduly simplifying the physical situation, we can explain semi-quantitatively the data on electronic relaxation in large organic molecules.