Semiclassical Approaches to Complex Chemical Simulation in Real Time

Abstract

Semiclassical (SC) theory offers a pedagogically rich connection between quantum and classical perspectives of nature, and, furthermore, is a promising approach to incorporating quantum effects into molecular dynamics simulations. However, a variety of numerical challenges associated with SC methods, such as the cumbersome search for special trajectories, or the integration of highly oscillatory functions (i.e. the SC ``sign problem"), generally renders SC theory impractical for all but very simple, low-dimensional systems. In this dissertation we derive a variety of mixed quantum-classical (MQC) representations of the real-time correlation function within the SC initial value representation (SC-IVR) using the modified Filinov filtration (MFF) technique. The most promising of these methods are subsequently tested on a number of low- and high-dimensional systems. Each of these methods have three significant advantages. (1) They offer a significant improvement upon the SC-IVR ``sign problem." (2) They offer mode-specific quantization in a dynamically consistent framework. And (3) they are significantly easier to implement than other leading SC-IVR methodologies. The extension of these methods to nonadiabatic systems is made as well. We conclude that, in future studies of a variety of non-equilibrium molecular systems, particularly those that exhibit strong nuclear quantum effects such as interference, the novel SC-IVR methods presented here should prove to be very powerful.