Selecting optimal unrestricted Hartree-Fock trial wavefunctions for phaseless auxiliary-field quantum Monte Carlo: Accuracy and limitations in modeling three iron-sulfur clusters

TL;DR

This study evaluates how the choice of unrestricted Hartree-Fock trial wavefunctions affects the accuracy of phaseless auxiliary-field quantum Monte Carlo in modeling complex iron-sulfur clusters, highlighting the importance of chemical and symmetry considerations.

Contribution

It demonstrates that chemical properties and symmetries should guide trial wavefunction selection in ph-AFQMC, and reveals the limitations of UHF trials in strongly correlated systems.

Findings

Accurate ground-state energies can be obtained despite suboptimal overlaps.

Sampling bias can lead to artificially negative energies in ph-AFQMC.

Symmetry and chemical property considerations are crucial for trial wavefunction choice.

Abstract

Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has emerged as a promising electronic structure method for correlated electronic systems. However, the quality of its predictions depends critically on the choice of trial wavefunction, and it is not obvious how to make an optimal choice especially for strongly correlated states of large systems. Mean-field wavefunctions are compelling trial wavefunction candidates as they map directly to chemical concepts and can be obtained with $O(N^4)$ cost. Yet in the strongly correlated regime one faces a symmetry dilemma and the existence of multiple nearly-degenerate solutions. In this work we investigate active space models of [2Fe-2S]$^{2+}$, mixed-valent [4Fe-4S]$^{2+}$, and [4Fe-4S]$^{4+}$ and explore the sensitivity of ph-AFQMC to the choice of unrestricted Hartree-Fock trial wavefunction. We find that chemical properties and physical symmetries, rather than the variational energy, ought to guide the choice of mean-field trial for ph-AFQMC (or reference state for coupled cluster models), and show that surprisingly accurate ground-state energies for these systems can be obtained. However, in all cases we find a rapidly vanishing overlap between the stochastic wavefunction and the UHF trial, indicating that the trials are suboptimal importance functions. By analogy to a similar situation in the stretched helium dimer cation, we show how this sampling bias pushes ph-AFQMC towards artificially negative energies, which evidently can be compensated for by the phaseless bias in certain cases.