Zen, A; Sorella, S; Gillan, MJ; Michaelides, A; Alfè, D; (2016) Boosting the accuracy and speed of quantum Monte Carlo: Size consistency and time step. Physical Review B - Condensed Matter and Materials Physics , 93 (24) , Article 241118. 10.1103/PhysRevB.93.241118.

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Abstract

Diffusion Monte Carlo (DMC) simulations for fermions are becoming the standard for providing high-quality reference data in systems that are too large to be investigated via quantum chemical approaches. DMC with the fixed-node approximation relies on modifications of the Green's function to avoid singularities near the nodal surface of the trial wave function. Here we show that these modifications affect the DMC energies in a way that is not size consistent, resulting in large time-step errors. Building on the modifications of Umrigar et al. and DePasquale et al. we propose a simple Green's function modification that restores size consistency to large values of the time step, which substantially reduces time-step errors. This algorithm also yields remarkable speedups of up to two orders of magnitude in the calculation of molecule-molecule binding energies and crystal cohesive energies, thus extending the horizons of what is possible with DMC.

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