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We propose an algorithm for accurate, systematic and scalable computation ofinteratomic forces within the auxiliary-field Quantum Monte Carlo (AFQMC)method. The algorithm relies on the Hellman-Fenyman theorem, and incorporatesPulay corrections in the presence of atomic orbital basis sets. We benchmarkthe method for small molecules by comparing the computed forces with thederivatives of the AFQMC potential energy surface, and by direct comparisonwith other quantum chemistry methods. We then perform geometry optimizationsusing the steepest descent algorithm in larger molecules. With realistic basissets, we obtain equilibrium geometries in agreement, within statistical errorbars, with experimental values. The increase in computational cost forcomputing forces in this approach is only a small prefactor over that ofcalculating the total energy. This paves the way for a general and efficientapproach for geometry optimization and molecular dynamics within AFQMC.

Calculation of interatomic forces and optimization of molecular geometry with auxiliary-field quantum Monte Carlo