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 Ŝ2 and Ŝz. 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 Ŝ2 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.