Quantum Monte Carlo facing the Hartree-Fock symmetry dilemma: The case of hydrogen rings

TL;DR

This paper investigates the Hartree-Fock symmetry dilemma in quantum Monte Carlo calculations for hydrogen rings, showing that symmetry-adapted wave functions yield lower energies and more accurate nodes than symmetry-broken solutions.

Contribution

It demonstrates that symmetry-adapted Hartree-Fock wave functions are preferable for hydrogen rings in quantum Monte Carlo, highlighting the importance of spatial symmetry in trial wave function selection.

Findings

Symmetry-adapted HF wave functions produce lower energies.

Symmetry-adapted wave functions have more accurate nodes.

Spatial symmetry is crucial for good trial wave functions.

Abstract

When using Hartree-Fock (HF) trial wave functions in quantum Monte Carlo calculations, one faces, in case of HF instabilities, the HF symmetry dilemma in choosing between the symmetry-adapted solution of higher HF energy and symmetry-broken solutions of lower HF energies. In this work, we have examined the HF symmetry dilemma in hydrogen rings which present singlet instabilities for sufficiently large rings. We have found that the symmetry-adapted HF wave function gives a lower energy both in variational Monte Carlo and in fixed-node diffusion Monte Carlo. This indicates that the symmetry-adapted wave function has more accurate nodes than the symmetry-broken wave functions, and thus suggests that spatial symmetry is an important criterion for selecting good trial wave functions.