Efficient molecular quantum dynamics in coordinate and phase space using pruned bases

TL;DR

This paper introduces a new basis combining PvB and Weylets for efficient quantum dynamics simulations in coordinate and phase space, demonstrating significant speed-ups and compactness in high-dimensional systems.

Contribution

The authors develop projected Weylets, a novel basis that merges PvB and Weylets, enabling more efficient and compact quantum dynamics calculations in multiple dimensions.

Findings

Coordinate-space localization enhances pruning efficiency.

Pruned dynamics significantly faster than unpruned methods.

Projected Weylets outperform pruned DVR in high-dimensional cases.

Abstract

We present an efficient implementation of dynamically pruned quantum dynamics, both in coordinate space and in phase space. We combine the ideas behind the biorthogonal von Neumann basis (PvB) with the orthogonalized momentum-symmetrized Gaussians (Weylets) to create a new basis, projected Weylets, that takes the best from both methods. We benchmark pruned dynamics using phase-space-localized PvB, projected Weylets, and coordinate-space-localized DVR bases, with real-world examples in up to six dimensions. We show that coordinate-space localization is most important for efficient pruning and that pruned dynamics is much faster compared to unpruned, exact dynamics. Phase-space localization is useful for more demanding dynamics where many basis functions are required. There, projected Weylets offer a more compact representation than pruned DVR bases.