Capturing Strong Correlation in Molecules with Phaseless Auxiliary-Field Quantum Monte Carlo Using Generalized Hartree–Fock Trial Wave Functions

Generalized Hartree-Fock (GHF) is a long-established electronic structure method that can lower the energy (compared to spin-restricted variants) by breaking physical wave function symmetries, namely <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>S</mml:mi><mml:mo>^</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mover><mml:mi>S</mml:mi><mml:mo>^</mml:mo></mml:mover><mml:mi>z</mml:mi></mml:msub></mml:math>. After an exposition of GHF theory, we assess the use of GHF trial wave functions in phaseless auxiliary field quantum Monte Carlo (ph-AFQMC-G) calculations of strongly correlated molecular systems including symmetrically stretched hydrogen rings, carbon dioxide, and dioxygen. Imaginary time propagation is able to restore <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mover><mml:mi>S</mml:mi><mml:mo>^</mml:mo></mml:mover><mml:mn>2</mml:mn></mml:msup></mml:math> symmetry and yields energies of comparable or better accuracy than CCSD(T) with unrestricted HF and GHF references, and consistently smooth dissociation curves─a remarkable result given the relative scalability of ph-AFQMC-G to larger system sizes. The present exploration of model strongly correlated systems marks a promising starting point for future studies of more chemically relevant molecules, and demonstrates that ph-AFQMC-G provides a highly accurate (and, in contrast to active-space-based trials, relatively black box and always size-consistent) description of challenging systems exhibiting, e.g., antiferromagnetic coupling and/or geometric spin frustration.