Non-orthogonal determinants in multi-Slater-Jastrow trial wave functions for fixed-node diffusion Monte Carlo

TL;DR

This paper explores the use of non-orthogonal determinants in multi-Slater-Jastrow trial wave functions to improve the accuracy of quantum Monte Carlo calculations, demonstrated on the C2 molecule.

Contribution

It introduces a method for optimizing non-orthogonal determinants in trial wave functions, showing improved energies in QMC calculations over traditional orthogonal approaches.

Findings

Non-orthogonal determinants improve variational energies.

Non-orthogonal determinants enhance fixed-node DMC energies.

Energy improvements are on the order of a few tenths of an eV.

Abstract

The accuracy and efficiency of ab-initio quantum Monte Carlo (QMC) algorithms benefits greatly from compact variational trial wave functions that accurately reproduce ground state properties of a system. We investigate the possibility of using multi-Slater-Jastrow trial wave functions with non-orthogonal determinants by optimizing identical single particle orbitals independently in separate determinants. As a test case, we compute variational and fixed-node diffusion Monte Carlo (FN-DMC) energies of a C$_2$ molecule. For a given multi-determinant expansion, we find that this non-orthogonal orbital optimization results in a consistent improvement in the variational energy and the FN-DMC energy on the order of a few tenths of an eV. Our calculations indicate that trial wave functions with non-orthogonal determinants can improve computed energies in a QMC calculation when compared to their orthogonal counterparts.