Vibrational heat-bath configuration interaction with semistochastic perturbation theory using harmonic oscillator or VSCF modals

TL;DR

This paper advances vibrational structure calculations by integrating stochastic perturbation theory with VHCI, enabling larger systems to be treated accurately and efficiently, and introduces a VSCF-based approach with new computational strategies.

Contribution

It introduces a semi-stochastic perturbation correction for VHCI, a new heat-bath criterion for potential energy surfaces, and implements VHCI with a VSCF reference.

Findings

Stochastic PT2 reduces memory bottleneck and allows larger perturbative spaces.

Control of stochastic errors below 1 cm$^{-1}$.

VSCF reference offers marginal accuracy improvements at higher computational cost.

Abstract

Vibrational heat-bath configuration interaction (VHCI) -- a selected configuration interaction technique for vibrational structure theory -- has recently been developed in two independent works [J. Chem. Phys. 154, 074104 (2021); Mol. Phys. 119, e1936250 (2021)], where it was shown to provide accuracy on par with the most accurate vibrational structure methods with a low computational cost. Here, we eliminate the memory bottleneck of the second-order perturbation theory (PT2) correction using the same (semi)stochastic approach developed previously for electronic structure theory. This allows us to treat, in an unbiased manner, much larger perturbative spaces, which are necessary for high accuracy in large systems. Stochastic errors are easily controlled to be less than 1 cm$^{-1}$. We also report two other developments: (i) we propose a new heat-bath criterion and an associated exact implicit sorting algorithm for potential energy surfaces expressible as a sum of products of one-dimensional potentials; (ii) we formulate VHCI to use a vibrational self-consistent field (VSCF) reference, as opposed to the harmonic oscillator reference configuration used in previous reports. Interestingly, we find that with VSCF, the minor improvements to the accuracy are outweighed by the much higher computational cost associated with the loss of sparsity in the Hamiltonian and integrals transformations needed for matrix element evaluation.