High-order geometric integrators for the local cubic variational Gaussian wavepacket dynamics

TL;DR

This paper introduces high-order geometric integrators for local cubic variational Gaussian wavepacket dynamics, improving efficiency and preserving geometric properties in quantum simulations of complex systems.

Contribution

The authors develop symplectic, time-reversible, and norm-conserving integrators specifically for local cubic variational Gaussian wavepacket dynamics, reducing computational costs.

Findings

Integrators are efficient and preserve geometric properties.

Numerical tests on a multi-dimensional Morse potential show effectiveness.

Conserves effective energy at small time steps.

Abstract

Gaussian wavepacket dynamics has proven to be a useful semiclassical approximation for quantum simulations of high-dimensional systems with low anharmonicity. Compared to Heller's original local harmonic method, the variational Gaussian wavepacket dynamics is more accurate, but much more difficult to apply in practice because it requires evaluating the expectation values of the potential energy, gradient, and Hessian. If the variational approach is applied to the local cubic approximation of the potential, these expectation values can be evaluated analytically, but still require the costly third derivative of the potential. To reduce the cost of the resulting local cubic variational Gaussian wavepacket dynamics, we describe efficient high-order geometric integrators, which are symplectic, time-reversible, and norm-conserving. For small time steps, they also conserve the effective energy. We demonstrate the efficiency and geometric properties of these integrators numerically on a multi-dimensional, nonseparable coupled Morse potential.