On the calculation of vibrational energy relaxation rate constants from centroid molecular dynamics simulations

Abstract

We explore the use of centroid molecular dynamics (CMD) for calculating vibrational energy relaxation (VER) rate constants of high-frequency molecular vibrations in the condensed phase. We employ our recently proposed linear-response-theory-based approach to VER [Q. Shi and E. Geva, J. Chem. Phys. 118, 7562 (2003)], to obtain a new expression for the VER rate constant in terms of a correlation function that can be directly obtained from CMD simulations. We show that the new expression reduces to a centroid Landau-Teller-type formula in the golden-rule regime. Unlike previously proposed CMD-based approaches to VER, the new formula does not involve additional assumptions beyond the inherent CMD approximation. The new formula has the same form as the classical Landau–Teller formula, and quantum effects enter it in two ways: (1) The initial sampling and subsequent dynamics are governed by the centroid potential, rather than the classical potential; (2) The classical force is replaced by the corresponding centroid symbol. The application of the new 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 molecule coupled to a short linear chain of Helium atoms; (3) A “breathing sphere” diatomic molecule in a two-dimensional monoatomic Lennard-Jones liquid. It is confirmed that CMD is able to capture the main features of the force–force correlation function rather well, in both time and frequency domains. However, we also find that CMD is unable to accurately predict the high-frequency tail of the quantum-mechanical power spectrum of this correlation function, which limits its usefulness for calculating VER rate constants of high-frequency molecular vibrations. The predictions of CMD are compared with those obtained via the linearized-semiclassical initial-value-representation (LSC-IVR) method, which does yield accurate predictions of high-frequency VER rate constants. The reasons underlying these observations are discussed in terms of the similarities and differences between these two approaches. © 2003 American Institute of Physics.