Response properties in phaseless auxiliary field quantum Monte Carlo

We present a method for calculating first-order response properties in phaseless auxiliary field quantum Monte Carlo by applying automatic differentiation (AD). Biases and statistical efficiency of the resulting estimators are discussed. Our approach demonstrates that AD enables the calculation of reduced density matrices with the same computational cost scaling per sample as energy calculations, accompanied by a cost prefactor of less than four in our numerical calculations. We investigate the role of self-consistency and trial orbital choice in property calculations. We find that orbitals obtained using density functional theory perform well for the dipole moments of selected molecules compared to those optimized self-consistently.