QUANTUM AND CLASSICAL RELAXATION RATES FROM CLASSICAL SIMULATIONS

The time correlation function for a harmonic quantum mechanical system can be related to the time correlation function for a corresponding c lassical system. Although straightforward to derive and well known in other contexts, this relationship has been unappreciated in the contex t of vibrational relaxation, where time correlation functions obtained from classical molecular dynamics have been used to predict relaxatio n rates for a quantum solute in a classical solvent.: This inconsisten t treatment-quantum solute, classical solvent-predicts a relaxation ra te which is slower than if the entire system, both solute and solvent, were treated classically. We demonstrate that if the classical time c orrelation functions are rescaled to account for the ratio of quantum to classical fluctuations, providing a quantum mechanical treatment fo r the solute and the solvent, the relaxation rates and the entire abso rption spectrum are the same as for a purely classical treatment. Our conclusions are valid when the solute and solvent dan be described by a set of effective harmonic normal modes, and can also be valid when;a nharmonicities are present.