A Scalable Route to First-Order Response Properties with Correlated Sampling Phaseless Auxiliary-Field Quantum Monte Carlo

To make useful connections with experimental measurements,
correlated
electronic structure theories must accurately predict chemical properties
in addition to energies. We present a finite-difference based algorithm
to compute first-order response properties with phaseless auxiliary-field
quantum Monte Carlo (ph-AFQMC) that relies on a branching correlated
sampling approach. Focusing on electric dipole moments, we show that
mean-field trial wave functions are sufficient to obtain high accuracy
relative to CCSD(T) and experimental measurements for a set of 21
molecules, ranging in size from 2 to 18 atoms in their equilibrium
geometries. As with energies, the quality of predicted dipole moments
can be systematically improved with the use of correlated trial wave
functions, even (or especially) in strongly correlated regimes. We
show that the challenges faced by low-order perturbation theories
in predicting the dipole moment of hydrogen fluoride across its dissociation
coordinate are overcome with ph-AFQMC when using relatively simple
trials. The key advantage of our approach over those previously reported
for ph-AFQMC is its scalability to large system sizes with a phaseless
bias no worse than that of a typical ground-state energy calculation;
we routinely converge dipole moments for systems with more than 1000
basis functions.