Accurate Hellmann-Feynman forces from density functional calculations with augmented Gaussian basis sets

TL;DR

This paper shows that using augmented Gaussian basis sets in density functional calculations significantly reduces Pulay forces, enabling accurate Hellmann-Feynman force computations for large systems and improving molecular simulations.

Contribution

The study demonstrates that augmented Gaussian basis sets suppress Pulay forces, allowing Hellmann-Feynman forces to match analytical accuracy for geometry optimization and molecular dynamics.

Findings

Pulay force can be minimized with augmented basis sets

HF forces achieve accuracy comparable to analytical forces

Enables reliable large-scale molecular simulations

Abstract

The Hellmann-Feynman (HF) theorem provides a way to compute forces directly from the electron density, enabling efficient force calculations for large systems through machine learning (ML) models for the electron density. The main issue holding back the general acceptance of the HF approach for atom-centered basis sets is the well-known Pulay force which, if naively discarded, typically constitutes an error upwards of 10 eV/Ang in forces. In this work, we demonstrate that if a suitably augmented Gaussian basis set is used for density functional calculations, the Pulay force can be suppressed and HF forces can be computed as accurately as analytical forces with state-of-the-art basis sets, allowing geometry optimization and molecular dynamics to be reliably performed with HF forces. Our results pave a clear path forwards for the accurate and efficient simulation of large systems using ML densities and the HF theorem.