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.