Quantum Dynamics and Vibrational Relaxation

The accurate numerical calculation of general quantum time correlation functions for many-body systems is not possible at present. We discuss several schemes for obtaining approximate quantum time correlation functions using as input only the corresponding classical results, and assess the merits of each scheme by considering three exactly solvable model problems. We then turn to the problem of the vibrational energy relaxation of a high-frequency oscillator in a liquid, where the relaxation rate constant can be related to a certain quantum force−force time correlation function. Focusing specifically on the case of liquid oxygen, we calculate the classical force−force time correlation function using a molecular dynamics simulation and then determine various approximations to the relaxation rate constant by applying the schemes considered earlier. The Egelstaff scheme is found to lead to reasonable agreement with experiment.