Semiclassical Theory of Vibrational Energy Relaxation in the Condensed Phase

Abstract

This paper presents the first application of semiclassical methodology to the calculation of vibrational energy relaxation (VER) rate constants in condensed phase systems. The VER rate constant is treated within the framework of the Landau-Teller formula and is given in terms of the Fourier transform, at the vibrational frequency, of the force-force correlation function (FFCF). Due to the high frequency of most molecular vibrations, predictions based on the classical FFCF are often found to deviate by orders of magnitude from the experimentally observed values. In this paper, we employ a semiclassical approximation for the quantum-mechanical FFCF, that puts it in terms of a classical-like expression, where Wigner transforms replace the corresponding classical quantities. The multidimensional Wigner transform is performed via a novel implementation of the local harmonic approximation (LHA). The resulting expression for the FFCF is exact at t = 0, and converges to the correct classical limit when h → 0. Quantum effects are introduced via a nonclassical initial sampling of both positions and momenta, as well as by accounting for delocalization in the calculation of the force at t = 0. The application of the semiclassical method is reported for three model systems: (1) a vibrational mode coupled to a harmonic bath, with the coupling exponential in the bath coordinates; (2) a diatomic coupled to a short linear chain of helium atoms; (3) a breathing sphere diatomic in a two-dimensional monatomic Lennard-Jones liquid. Good agreement is found in all cases between the semiclassical predictions and the exact results, or their estimates. It is also found that the VER of highfrequency molecular vibrations is dominated by a purely quantum-mechanical term, which vanishes in the classical limit.