Theory of vibrational energy transfer among diatomic molecules in inert matrices

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Abstract
The purpose of the present paper is to develop a theory for the transfer of vibrational energy from a vibrationally excited diatomic molecule (donor) to another diatomic molecule (acceptor) in an inert matrix. The vibrational–vibrational (V–V) energy transfer is observable when the concentrations of the donors and acceptors are high enough so that the time for direct relaxation to the phonon bath and the radiative lifetime of the excited donor are comparable to or longer than the V–V transfer time. We calculate the microscopic, i.e., site-dependent, V–V transfer rate constant through the long range phonon-modulated interaction between the donor and the acceptor using a canonical transformation. Förster’s spectral overlap relation between the emission spectrum of the donor and the absorption spectrum of the acceptor is derived as an approximation to the present theory. Some numerical results demonstrating strong dependence of the V–V transfer rate constant on the corresponding vibrational energy mismatch are presented. It is shown that the resonant (zero-phonon) and exothermic (phonon-assisted) V–V transfer rate constants depend only weakly on the temperature of the matrix. The microscopic, i.e., site-dependent, master equation associated with the present model, which is important in describing the time-dependent vibrational populations of the molecules involved in the V–V transfer, is also obtained.