Computing vibrational energy relaxation for high-frequency modes in condensed environments

Abstract

In this paper we consider vibrational relaxation of high-frequency impurity modes in condensed environments as a computational problem. Linear response theory provides convenient routes for this computation: The vibrational relaxation rate is obtained as a Fourier transform of a force–force time correlation function. However, numerical difficulties arise for processes characterized by a direct relaxation of high-frequency modes into an environment characterized by a relatively low cutoff frequency. It is shown that modern signal processing procedures can significantly enhance the efficiency and accuracy of the needed computation. Since the relevant “signal” can be very small, the computation can be very sensitive to boundary conditions, and care must be taken to avoid artifacts. The computation may be facilitated by using the expected functional form, exponential dependence on the impurity frequency for high frequency, and fitting the parameters of this form from the simulation. It is emphasized that this exponential dependence seems to be the correct functional form, in spite of theoretical arguments in favor of a Gaussian dependence. The main difficulty in the numerical evaluation of the relaxation rate of high-frequency modes results from the fact that at low temperature the dynamical behavior of such modes is essentially quantum mechanical. We demonstrate this issue by considering vibrational relaxation of an impurity CO molecule in a low-temperature Ar matrix. The results obtained for this system by estimating the quantum correction to the classical force–force correlation function are consistent with experimental results, which indicate that under these conditions the relaxation of the vibrationally excited CO is dominated by radiative decay.