Adaptable Gaussian Bases for Quantum Dynamics of the Nuclei

TLDR: In this article, the authors review several approaches to constructing compact Gaussian bases, scalable to multidimensional systems and yielding exact quantum dynamics: thawed Gaussian wavepacket dynamics, time-independent quasi-random distributed Gaussian base, and time-dependent Gaussian Base guided by quantum trajectories.

Abstract: Compactness of the wavefunction representation is one of the central practical questions in quantum dynamics of high-dimensional molecular systems, because, for general inter-particle interactions, the complexity of a wavefunction grows exponentially with the system size. While expanding the wavefunctions in terms of standard predefined basis sets is well established in the electronic structure theory and computations, it is not so in the quantum dynamics of the nuclei. One ‘family’ of approaches is based on Gaussian functions whose parameters are tailored in some way to the shape of a wavefunction evolving in time, or to the energy and spatial range relevant to the system of interest; the choice of the basis parameters often comes from classical dynamics, semiclassical arguments, or from coupled variational equations, all with their pros and cons. In this chapter, we review in detail several approaches to constructing compact Gaussian bases, scalable to multidimensional systems and, in principle, yielding exact quantum dynamics: thawed Gaussian wavepacket dynamics, time-independent quasi-random distributed Gaussian bases, and time-dependent Gaussian bases guided by quantum trajectories. The non-variational character of these methods and their adaptability to target wavefunctions, combined with recent advances in the on-the-fly electronic structure calculation, make them practical for applications to large molecular systems.