Dynamical pruning of the multiconfiguration time-dependent Hartree method (DP-MCTDH): An efficient approach for multidimensional quantum dynamics

TL;DR

This paper introduces two dynamical pruning strategies for the multiconfiguration time-dependent Hartree method, significantly improving computational efficiency for multidimensional quantum dynamics simulations.

Contribution

It develops and demonstrates two novel dynamical pruning strategies for MCTDH, enhancing efficiency and applicability to larger, more complex quantum systems.

Findings

Pruning primitive basis functions reduces computational cost for small systems.

Pruning SPF configurations yields speed-ups of 5 to 50 times.

Strategies enable handling higher-dimensional systems more efficiently.

Abstract

We present two strategies for combining dynamical pruning with the multiconfiguration time-dependent Hartree method (DP-MCTDH), where dynamical pruning means on-the-fly selection of relevant basis functions. The first strategy prunes the primitive basis that represents the single-particle functions (SPFs). This is useful for smaller systems that require many primitive basis functions per degree of freedom, as we will illustrate for NO$_2$. Furthermore, this allows for higher-dimensional mode combination and partially lifts the sum-of-product-form requirement onto the structure of the Hamiltonian, as we illustrate for nonadiabatic 24-dimensional pyrazine. The second strategy prunes the set of configurations of SPF at each time step. We show that this strategy yields significant speed-ups with factors between 5 and 50 in computing time, making it competitive with the multilayer MCTDH method.