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

TL;DR

This paper introduces an efficient algorithm for calculating interatomic forces within AFQMC, enabling accurate geometry optimizations and molecular dynamics with minimal additional computational cost.

Contribution

The authors develop a scalable AFQMC-based force calculation method that incorporates Pulay corrections and is suitable for geometry optimization and molecular dynamics.

Findings

Accurate equilibrium geometries consistent with experimental data.

Force calculations add minimal computational overhead.

Method validated on small and larger molecules.

Abstract

We propose an algorithm for accurate, systematic and scalable computation of interatomic forces within the auxiliary-field Quantum Monte Carlo (AFQMC) method. The algorithm relies on the Hellman-Fenyman theorem, and incorporates Pulay corrections in the presence of atomic orbital basis sets. We benchmark the method for small molecules by comparing the computed forces with the derivatives of the AFQMC potential energy surface, and by direct comparison with other quantum chemistry methods. We then perform geometry optimizations using the steepest descent algorithm in larger molecules. With realistic basis sets, we obtain equilibrium geometries in agreement, within statistical error bars, with experimental values. The increase in computational cost for computing forces in this approach is only a small prefactor over that of calculating the total energy. This paves the way for a general and efficient approach for geometry optimization and molecular dynamics within AFQMC.