Computation of forces and stresses in solids: Towards accurate structural optimization with auxiliary-field quantum Monte Carlo

TL;DR

This paper presents a method using auxiliary-field quantum Monte Carlo (AFQMC) to accurately compute forces and stresses in solids, enabling precise structural optimization and phonon spectrum calculations in bulk materials.

Contribution

The paper introduces a novel AFQMC-based approach for calculating energy derivatives in solids, overcoming previous technical challenges and enabling full geometry optimizations.

Findings

Accurate force and stress calculations in solids using AFQMC.

Implementation of back-propagation for energy gradients.

Feasibility of geometry optimization and phonon spectrum computation.

Abstract

The accurate computation of forces and other energy derivatives has been a long-standing challenge for quantum Monte Carlo methods. A number of technical obstacles contribute to this challenge. We discuss how these obstacles can be removed with the auxiliary-field quantum Monte Carlo (AFQMC) approach. AFQMC is a general, high-accuracy, many-body total-energy method for molecules and solids. The implementation of back-propagation for pure estimators allows direct calculation of gradients of the energy via the Hellmann-Feynman theorem. A planewave basis with norm-conserving pseudopotentials is used for the study of periodic bulk materials. Completeness of the planewave basis minimizes the effect of so-called Pulay terms. The ionic pseudopotentials, which can be incorporated in AFQMC in exactly the same manner as in standard independent-electron methods, regulate the force and stress estimators and eliminate any potential divergence of the Monte Carlo variances. The resulting approach allows applications of full geometry optimizations in bulk materials. It also paves the way for many-body computations of the phonon spectrum in solids.