Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking

TL;DR

This paper reviews the phaseless auxiliary-field quantum Monte Carlo method in quantum chemistry, assesses its performance on main group chemistry and bond-breaking, and provides recommendations for its application based on system complexity.

Contribution

It offers a comprehensive overview and performance assessment of ph-AFQMC, including practical guidelines for its use in main group and multi-reference systems.

Findings

ph-AFQMC achieves accuracy between CCSD and CCSD(T) for single-reference systems

It outperforms multi-reference perturbation methods in multi-reference cases

ph-AFQMC is computationally more efficient than MRCI for dynamic correlation

Abstract

In this work, we present an overview of the phaseless auxiliary-field quantum Monte Carlo (ph- AFQMC) approach from a computational quantum chemistry perspective, and present a numerical assessment of its performance on main group chemistry and bond-breaking problems with a total of 1004 relative energies. While our benchmark study is somewhat limited, we make recommendations for the use of ph-AFQMC for general main-group chemistry applications. For systems where single determinant wave functions are qualitatively accurate, we expect the accuracy of ph-AFQMC in conjunction with a single determinant trial wave function to be between that of coupled-cluster with singles and doubles (CCSD) and CCSD with perturbative triples (CCSD(T)). For these applications, ph-AFQMC should be a method of choice when canonical CCSD(T) is too expensive to run. For systems where multi-reference (MR) wave functions are needed for qualitative accuracy, ph-AFQMC is far more accurate than MR perturbation theory methods and competitive with MR configuration interaction (MRCI) methods. Due to the computational efficiency of ph-AFQMC compared to MRCI, we recommended ph-AFQMC as a method of choice for handling dynamic correlation in MR problems. We conclude with a discussion of important directions for future development of the ph-AFQMC approach.