Calculating Vibrational Energy Relaxation Rates from Classical Molecular Dynamics Simulations:  Quantum Correction Factors for Processes Involving Vibration−Vibration Energy Transfer

A convenient starting point for calculating vibrational energy relaxation rate constants is Fermi's golden rule, which relates the rate constant to the Fourier transform of a certain quantum-mechanical force−force time-correlation function. Often, researchers replace this Fourier transform by the Fourier transform of the analogous classical time-correlation function multiplied by a quantum correction factor. This approach has the great advantage that the classical time-correlation function and its Fourier transform can be calculated easily from a classical molecular dynamics simulation. The disadvantage is that it is often unclear what form one should take for the quantum correction factor. In this paper we suggest several possible forms for this factor for vibrational energy relaxation processes involving intermolecular vibration−vibration energy transfer. We apply our results to vibrational energy relaxation in the B state of carbonmonoxy-myoglobin.