Multidimensional quantum dynamics with explicitly correlated Gaussian wave packets using Rothe's method

TL;DR

This paper extends Rothe's method to efficiently propagate multidimensional explicitly correlated Gaussian wave packets, enabling accurate quantum dynamics simulations in complex systems with fewer basis functions.

Contribution

It generalizes Rothe's method for arbitrary multidimensional ECGs, demonstrating high-accuracy dynamics with a small number of basis functions in complex potentials.

Findings

Quantitative reproduction of multidimensional dynamics with 20-40 Gaussians.

Accurate spectra obtained with minimal basis functions.

Method applicable to strong-field molecular dynamics beyond Born-Oppenheimer.

Abstract

In a previous publication [J. Chem. Phys., 161, 044105 (2024)], it has been shown that Rothe's method can be used to solve the time-dependent Schr\"odinger equation (TDSE) for the hydrogen atom in a strong laser field using time-dependent Gaussian wave packets. Here, we generalize these results, showing that Rothe's method can propagate arbitrary numbers of thawed, complex-valued, explicitly correlated Gaussian functions (ECGs) with dense correlation matrices for systems with varying dimensionality. We consider the multidimensional Henon-Heiles potential, and show that the dynamics can be quantitatively reproduced using only 30 Gaussians in 2D, and that accurate spectra can be obtained using 20 Gaussians in 2D and 30 to 40 Gaussians in 3D and 4D. Thus, the relevant multidimensional dynamics can be described at high quality using only a small number of ECGs that give a very compact representation of the wave function. This efficient representation, along with the demonstrated ability of Rothe's method to propagate Gaussian wave packets in strong fields and ECGs in complex potentials, paves the way for accurate molecular dynamics calculations beyond the Born-Oppenheimer approximation in strong fields.