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This paper investigates the sensitivity of phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) to the choice of unrestricted Hartree-Fock (UHF) trial wavefunctions in modeling three iron-sulfur clusters. It demonstrates that chemical properties and physical symmetries are better guides than variational energy for selecting mean-field trials. The study reveals that while accurate ground-state energies can be achieved, a rapidly vanishing overlap between the stochastic wavefunction and the UHF trial indicates suboptimal importance functions, potentially leading to sampling bias and artificially negative energies.
Surprisingly accurate ground-state energies for complex iron-sulfur clusters can be obtained with phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) using chemically-motivated mean-field trial wavefunctions, even though the stochastic wavefunction rapidly loses overlap with the trial.
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.
