Energy and capacity time correlation functions for investigation of vibrational energy relaxation

Vibrational energy relaxation of a diatomic solute in a liquid solvent is investigated by means of the generalized Langevin equation. The vibrational energy, velocity and capacity time correlation functions (TCFs) are considered. It is shown that the detailed structure of the energy TCF contains an initial fast (subpicosecond) decay segment that is followed by weak oscillations on the background of an exponential relaxation curve. The direct method for evaluating the relaxation rate constant from equilibrium molecular dynamics simulations of a flexible solute is proposed and implemented. The closed form expressions for the memory function and for the relaxation rate constant in terms of quantities accessible from the simulations are derived. The simulation results for rigid and flexible solutes are compared and analyzed.