Intramolecular Radiationless Transitions

TLDR

Born–Oppenheimer zero‑order excited states are mixed by configuration interaction, broadening the state into a Lorentzian line shape, and molecular structure influences the relevant parameters. The paper develops a theory of intramolecular radiationless transitions in isolated molecules. The theory models the optically excited state as a superposition of eigenstates, yielding an exponential nonradiative decay whose linewidth and lifetime depend on the square of the interaction energy between the zero‑order state and nearby vibronic states, and it derives criteria for unimolecular radiationless transitions. When the vibrational state density exceeds the reciprocal of the interaction matrix element, radiationless transitions are predicted to occur.

Abstract

In this paper we consider a theory for intramolecular radiationless transitions in an isolated molecule. The Born–Oppenheimer zero-order excited states are not pure in view of configuration interaction between nearly degenerate zero-order states, leading to the broadening of the excited state, the line shape being Lorentzian. The optically excited state can be described in terms of a superposition of molecular eigenstates, and the resulting wavefunction exhibits an exponential nonradiative decay. The linewidth and the radiationless lifetime are expressed in terms of a single molecular parameter, that is the square of the interaction energy between the zero-order state and the manifold of all vibronic states located within one energy unit around that state. The validity criteria for the occurrence of an unimolecular radiationless transition and for exponential decay in an isolated molecule are derived. Provided that the density of vibrational states is large enough (i.e., exceeds the reciprocal of the interaction matrix element) radiationless transitions are expected to take place. The gross effects of molecular structure on the relevant molecular parameters are discussed.