Time averaging the semiclassical initial value representation for the calculation of vibrational energy levels. II. Application to H2CO, NH3, CH4, CH2D2

Abstract

A method recently developed for calculating vibrational spectral densities of molecules, previously tested successfully on ${\mathrm{H}}_2\mathrm{O},$ is applied here to several larger molecules. The method relies on use of a time averaging procedure in the conventional semiclassical (SC) initial value representation (IVR) expression for the spectral density. The convergence of the SC-IVR average over the phase space of initial conditions (of classical trajectories) is greatly enhanced by time averaging and is generally achieved with as few as 1000 trajectories per degree of freedom. Furthermore, meaningful results can be obtained with only a single trajectory propagated for a long time. (For systems with chaotic dynamics, however, the phase space average converges more slowly.) Results for vibrational energy levels of ${\mathrm{H}}_2\mathrm{CO},$ ${\mathrm{NH}}_3,$ ${\mathrm{CH}}_4,$ and ${\mathrm{CH}}_2{\mathrm{D}}_2$ are reported and compared with quantum mechanical calculations available in the literature. The accuracy of the time-averaged SC-IVR is very encouraging, with the vibrational energy levels consistently in agreement with the quantum results to a few parts in a thousand.