Nonresonant energy transfer interactions between randomly distributed guest molecules in host lattices

Abstract

In this paper, we derive an expression for the rate constant of energy transfer processes in which the energy mismatch between the donor and acceptor excited states are dissipated through the phonon modes of the host lattice. The adiabatic states are written as products of the donor and acceptor molecular wavefunctions, and nonadiabatic couplings between the stationary states result from Coulomb interactions between the valence electrons of the donor and acceptor molecules. The Boltzmann‐averaged rate constant is calculated in first‐order perturbation theory using the linear‐response time‐correlation function. The resulting expression, given in the weak‐coupling limit, relates the rate constants to the off‐resonance energy gap, the frequencies of the accepting modes, and the potential surface displacement parameters. The theoretical results are applied to a numerical analysis of available experimental data on nonresonant interactions between rare earth ions in crystalline hosts. The present formulation is compared with related theories of multiphonon electronic relaxation and of vibrational relaxation of molecules in host lattices.