Nonradiative vibrational relaxation of diatomic molecules isolated in solid rare-gas matrices

Abstract

An approximate quantum-theoretical expression for the rate of nonradiative vibrational relaxation of a diatomic molecule embedded in a rare-gas matrix is derived. The rare-gas matrix is assumed to have the normal structure of the crystalline rare gas, the diatomic being a substitutional impurity. Since the forces acting between the atoms of the crystal are much weaker than the force binding the atoms of the diatomic, the vibrational modes of the crystal lattice are assumed not to interact with the internal diatomic vibrational mode in zero order. The rotation of the diatomic is neglected. The lattice modes corresponding to each diatomic state, which are determined in the harmonic approximation, are assumed parallel (i.e., harmonic potentials for each mode are simply displaced with different force constants). The rate of nonradiative transition of the diatomic impurity between vibrational levels α and β, Wα→β, is calculated from the Fermi ``golden rule'' expression thermally averaged over the initial states of the lattice. By approximating the perturbative coupling matrix element responsible for the relaxation process by its value at the initial equilibrium configuration of the lattice, the rate expression is effectively simplified to a vibrational overlap integral, which is reduced to an exponential time integral and then evaluated by the saddle-point method. The explicit dependence of Wα→β upon the temperature and upon various microscopic parameters characterizing the system is demonstrated. Experimental data for the relaxation of CO in an Ar matrix in the temperature range 6–18 K are fitted quite well by the theoretical expression.