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We address the computation of ground-state properties of chemical systems andrealistic materials within the auxiliary-field quantum Monte Carlo method. Thephase constraint to control the fermion phase problem requires the random walksin Slater determinant space to be open-ended with branching. This in turn makesit necessary to use back-propagation (BP) to compute averages and correlationfunctions of operators that do not commute with the Hamiltonian. Several BPschemes are investigated and their optimization with respect to the phaselessconstraint is considered. We propose a modified BP method for the computationof observables in electronic systems, discuss its numerical stability andcomputational complexity, and assess its performance by computing ground-stateproperties for several substances, including constituents of the primordialterrestrial atmosphere and small organic molecules.

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