Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo

We address the computation of ground-state properties of chemical systems and realistic materials within the auxiliary-field quantum Monte Carlo method. The phase constraint to control the fermion phase problem requires the random walks in Slater determinant space to be open-ended with branching. This in turn makes it necessary to use back-propagation (BP) to compute averages and correlation functions of operators that do not commute with the Hamiltonian. Several BP schemes are investigated and their optimization with respect to the phaseless constraint is considered. We propose a modified BP method for the computation of observables in electronic systems, discuss its numerical stability and computational complexity, and assess its performance by computing ground-state properties for several substances, including constituents of the primordial terrestrial atmosphere and small organic molecules.