Multidimensional path integral calculations with quasiadiabatic propagators: Quantum dynamics of vibrational relaxation in linear hydrocarbon chains

This paper presents the first application of a new method for multidimensional real time quantum dynamics described in a previous Letter [Chem. Phys. Lett. 193, 435 ( 1992)]. The key feature of the method is the use of an improved zeroth order representation in the Feynman propagator, which allows large time steps in the path integral. Use of the adiabatic approximation in the case of a system coupled to a harmonic bath leads to a path integral over the system coordinate with a one-dimensional propagator which is constructed numerically and which corresponds to dynamics along the adiabatic path, and with a nonlocal influence functional that accounts for nonadiabatic effects. We have performed accurate quantum mechanical calculations on the dynamics of CH overtone relaxation in linear hydrocarbon chains by direct numerical evaluation of the path integral in the quasiadiabatic representation. Converged results for the survival probability of the ν=5 and ν= 8 states of HC₆ are reported up to five vibrational periods of the CH stretch and compared to those obtained from standard classical and semiclassical simulations.