High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions: Further Details and Comparisons

TL;DR

This paper introduces an advanced Monte Carlo sampling method combined with coupled-cluster theory to accurately compute electronic energies, extending previous work to include higher excitations and demonstrating its effectiveness on challenging molecular systems.

Contribution

It extends the coupled-cluster Monte Carlo approach to include triples and quadruples, enabling more accurate energy calculations for complex electronic structures.

Findings

Successfully recovers CCSDT and CCSDTQ energies in challenging cases

Demonstrates robustness in systems with electronic quasi-degeneracies

Provides a semi-stochastic approach for high-level coupled-cluster calculations

Abstract

We recently proposed a novel approach to converging electronic energies equivalent to high-level coupled-cluster (CC) computations by combining the deterministic CC($P$;$Q$) formalism with the stochastic configuration interaction (CI) and CC Quantum Monte Carlo (QMC) propagations. This article extends our initial study [J. E. Deustua, J. Shen, and P. Piecuch, Phys. Rev. Lett. 119, 223003 (2017)], which focused on recovering the energies obtained with the CC method with singles, doubles, and triples (CCSDT) using the information extracted from full CI QMC and CCSDT-MC, to the CIQMC approaches truncated at triples and quadruples. It also reports our first semi-stochastic CC($P$;$Q$) calculations aimed at converging the energies that correspond to the CC method with singles, doubles, triples, and quadruples (CCSDTQ). The ability of the semi-stochastic CC($P$;$Q$) formalism to recover the CCSDT and CCSDTQ energies, even when electronic quasi-degeneracies and triply and quadruply excited clusters become substantial, is illustrated by a few numerical examples, including the F-F bond breaking in ${\rm F}_{2}$, the automerization of cyclobutadiene, and the double dissociation of the water molecule.