Mixed Semiclassical Initial Value Representation Time-Averaging Propagator for Spectroscopic Calculations

TL;DR

This paper introduces a mixed semiclassical initial value representation method for spectroscopic calculations that reduces computational cost significantly while maintaining accuracy in peak positions compared to full quantum results.

Contribution

A novel mixed semiclassical approach utilizing time-averaging and hierarchical propagation methods, with a separable approximation that enhances computational efficiency.

Findings

Peak positions match quantum calculations closely

Overtone intensities are somewhat lower than exact results

Computational cost is reduced by about an order of magnitude

Abstract

A mixed semiclassical initial value representation expression for spectroscopic calculations is derived. The formulation takes advantage of the time-averaging filtering and the hierarchical properties of different trajectory based propagation methods. A separable approximation is then introduced that greatly reduces (about an order of magnitude) the computational cost compared with a full Herman-Kluk time-averaging semiclassical calculation for the same systems. The expression is exact for the harmonic case and it is tested numerically for a Morse potential coupled to one or two additional harmonic degrees of freedom. Results are compared to full Herman-Kluk time-averaging calculations and exact quantum wavepacket propagations. We found the peak positions of the mixed semiclassical approximations to be always in very good agreement with full quantum calculations, while overtone peak intensities are lower with respect to the exact ones. Given the reduced computational effort required by this new mixed semiclassical approximation, we believe the present method to make spectroscopic calculations available for higher dimensional systems than accessible before.