Thawed Gaussian wave packet dynamics: a critical assessment of three propagation schemes

TL;DR

This paper critically evaluates three Gaussian wave packet propagation schemes, finding that only the time-dependent variational principle (TDVP) provides physically accurate results across various regimes, unlike the approximate methods.

Contribution

The study provides a comprehensive assessment of three propagation schemes, highlighting the superiority of the TDVP-based method for reliable wave packet dynamics simulations.

Findings

TDVP scheme accurately models wave packet behavior

Heller's scheme fails to predict tunneling and shows unphysical oscillations

Extended semiclassical scheme exhibits unphysical self-trapping

Abstract

We assessed three schemes for propagating a variable-width (thawed) Gaussian wave packet moving under the influence of Morse or double-well potentials with parameters that are chemically representative. The most rigorous scheme is based on the time-dependent variational principle (TDVP); it leads to realistic behaviour of the center and width of a wave packet in all investigated regimes. Two other approximate schemes, Heller's and the extended semiclassical ones, demonstrate various aberrations. Heller's scheme does not properly account for various zero-point energy-related effects, is unable to predict tunneling, and more importantly, exhibits completely nonphysical unbound width oscillations. The extended semiclassical scheme, which was developed to address some of the shortcomings of the Heller counterpart, demonstrates another unphysical behaviour: self-trapping of a trajectory in both Morse and double-well potentials. We conclude that only the TDVP-based scheme is suitable for problem-free dynamical simulations. This, however, raises the question of how to utilize it efficiently in high-dimensional systems.