Benchmark Phaseless Auxiliary-Field Quantum Monte Carlo Method for Small Molecules

TL;DR

This paper presents a scalable implementation of the phaseless auxiliary-field quantum Monte Carlo method, demonstrating its accuracy and efficiency for small molecules, and explores modifications to reduce overcorrelation issues.

Contribution

The paper introduces a scalable Fortran implementation of ph-AFQMC and investigates modifications to improve accuracy and reduce overcorrelation problems in molecular calculations.

Findings

Achieves a mean absolute deviation of 1.15 kcal/mol for the HEAT set.

Modified algorithm matches original accuracy with fewer determinants.

Yields accurate binding energies for water clusters, within 0.5 kcal/mol of CCSD(T).

Abstract

We report a scalable Fortran implementation of the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) and demonstrate its excellent performance and beneficial scaling with respect to system size. Furthermore, we investigate modifications of the phaseless approximation that can help to reduce the overcorrelation problems common to the ph-AFQMC. We apply the method to the 26 molecules in the HEAT set, the benzene molecule, and water clusters. We observe a mean absolute deviation of the total energy of 1.15 kcal/mol for the molecules in the HEAT set; close to chemical accuracy. For the benzene molecule, the modified algorithm despite using a single-Slater-determinant trial wavefunction yields the same accuracy as the original phaseless scheme with 400 Slater determinants. Despite these improvements, we find systematic errors for the CN, CO$_2$, and O$_2$ molecules that need to be addressed with more accurate trial wavefunctions. For water clusters, we find that the ph-AFQMC yields excellent binding energies that differ from CCSD(T) by typically less than 0.5 kcal/mol.