Effects of vibrational relaxation on molecular electronic transitions

Abstract

In this paper we explore the implications of the coupling between nonradiative electronic relaxation and vibrational relaxation in excited electronic states of large molecules. The physical model involved a two electronic level molecular system interacting with a harmonic medium via linear coupling terms in the molecular nuclear coordinates. Two models were advanced for the molecule-medium coupling which involve single phonon decay and alternatively double phonon (or rather phonon-vibron) decay. The functional form of our final results is independent of the specific model adopted for the vibrational relaxation. The molecular Hamiltonian and the intramolecular coupling were recast in terms of second quantization formalism where the nonadiabatic coupling operator was modified by a Franck Condon shift operator. The coupling between electronic and vibrational relaxation processes was formulated in terms of a generalized interaction picture, where the intramolecular coupling was treated to second order while the vibrational relaxation was handled to ``infinite order'' by the Wigner Weisskopf approximation as applied to the equations of motion for the nuclear operators for the normal molecular modes. The nonradiative decay rate of an excited electronic state was expressed in terms of a generalized time correlation function. We were able to demonstrate that our general expressions reduce to the (time independent) decay rate of a single vibronic level in the limit of slow vibrational relaxation and to a modified expression for the (time independent) decay rate of the thermally averaged electronic manifold in the limit of fast vibrational relaxation. In the general case of coupled electronic-vibrational relaxation the decay probability is time dependent. In the low temperature limit the nonradiative decay rate can be expressed in terms of a superposition of exponential functions.