Bond breaking with auxiliary-field quantum Monte Carlo

TL;DR

This paper applies the phaseless auxiliary-field quantum Monte Carlo method to study bond stretching in molecules, demonstrating improved accuracy over traditional methods and exploring the impact of different trial wave functions.

Contribution

It introduces the use of phaseless AF QMC with various trial wave functions to accurately model bond dissociation, outperforming coupled cluster methods.

Findings

Phaseless AF QMC yields better accuracy than CCSD(T) in potential-energy curves.

Using multi-determinant trial wave functions improves results across bond dissociation.

The method's computational cost is justified by increased accuracy.

Abstract

Bond stretching mimics different levels of electron correlation and provides a challenging testbed for approximate many-body computational methods. Using the recently developed phaseless auxiliary-field quantum Monte Carlo (AF QMC) method, we examine bond stretching in the well-studied molecules BH and N$_2$, and in the H$_{50}$ chain. To control the sign/phase problem, the phaseless AF QMC method constrains the paths in the auxiliary-field path integrals with an approximate phase condition that depends on a trial wave function. With single Slater determinants from unrestricted Hartree-Fock (UHF) as trial wave function, the phaseless AF QMC method generally gives better overall accuracy and a more uniform behavior than the coupled cluster CCSD(T) method in mapping the potential-energy curve. In both BH and N$_2$, we also study the use of multiple-determinant trial wave functions from multi-configuration self-consistent-field (MCSCF) calculations. The increase in computational cost versus the gain in statistical and systematic accuracy are examined. With such trial wave functions, excellent results are obtained across the entire region between equilibrium and the dissociation limit.