Noise Tolerant Force Calculations in Density Functional Theory: A Surface Integral Approach for Wavelet-Based Methods

TL;DR

This paper presents a surface integral method for calculating quantum forces in density functional theory that improves accuracy over traditional approaches, especially for wavelet-based orbitals, and supports machine learning applications.

Contribution

The authors introduce a surface integral approach for force calculations in DFT that enhances accuracy and robustness for wavelet-based methods, surpassing the Hellmann-Feynman theorem.

Findings

Surface integrals provide more accurate forces than Hellmann-Feynman in wavelet-based DFT.

The method yields forces consistent with potential energy surfaces.

Forces are suitable for training machine learning potentials.

Abstract

We introduce a method for computing quantum mechanical forces through surface integrals over the stress tensor within the framework of density functional theory. This approach avoids the inaccuracies of traditional force calculations using the Hellmann-Feynman theorem when applied to multiresolution wavelet representations of orbitals. By integrating the quantum mechanical stress tensor over surfaces that enclose individual nuclei, we achieve highly accurate forces that exhibit superior consistency with the potential energy surface. Extensive benchmarks show that surface integrals over the stress tensor offer a robust and reliable alternative to the direct use of the Hellmann-Feynman theorem for force computations in DFT with discontinuous basis sets, particularly in cases where wavelet-based methods are employed. In addition, we integrate this approach with machine learning techniques, demonstrating that the forces obtained through surface integrals are sufficiently accurate to be used as training data for machine-learned potentials. This stands in contrast to forces calculated using the Hellmann-Feynman theorem, which do not offer this level of accuracy.