Solvent induced vibrational relaxation in diatomics. I. Derivation of a local relaxation rate

A local rate is derived for the vibrational population relaxation of a diatomic in a simple liquid or dense gas. The total relaxation rate of the system is obtained as the canonical ensemble average of the local rate. The rate expression is amenable to computer simulations in which the canonical average is performed by a Monte Carlo procedure. The vibrational motion is separated from the other degrees of freedom by an adiabatic approximation which treats the vibration as fast compared with the other motions. The adiabatic vibrational energies and the nonadiabatic couplings between vibrational states depend on the solvent configuration. These vibrational energies and couplings are obtained from quantum perturbation theory. The transitions between vibrational states are described semiclassically and the canonical averaging uses the classical canonical density for solvent configurations. The resulting procedure is a mixed quantum–semiclassical–classical simulation technique.