Semiclassical mean-trajectory approximation for nonlinear spectroscopic response functions

Abstract

Observables in nonlinear and multidimensional infrared spectroscopy may be calculated from nonlinear response functions. Numerical challenges associated with the fully quantum-mechanical calculation of these dynamical response functions motivate the development of semiclassical methods based on the numerical propagation of classical trajectories. The Herman-Kluk frozen Gaussian approximation to the quantum propagator has been demonstrated to produce accurate linear and third-order spectroscopic response functions for thermal ensembles of anharmonic oscillators. However, the direct application of this propagator to spectroscopic response functions is numerically impractical. We analyze here the third-order response function with Herman-Kluk dynamics with the two related goals of understanding the origins of the success of the approximation and developing a simplified representation that is more readily implemented numerically. The result is a semiclassical approximation to the nth-order spectroscopic response function in which an integration over n pairs of classical trajectories connected by distributions of discontinuous transitions is collapsed to a single phase-space integration, in which n continuous trajectories are linked by deterministic transitions. This significant simplification is shown to retain a full description of quantum effects.