Kohn-Sham accuracy from orbital-free density functional theory via $\Delta$-machine learning

TL;DR

This paper introduces a $$-machine learning approach that significantly enhances the accuracy of orbital-free DFT calculations, enabling efficient and precise molecular dynamics simulations of complex materials.

Contribution

The authors develop a $$-machine learning model that corrects orbital-free DFT energies and forces to match Kohn-Sham accuracy, improving efficiency and robustness.

Findings

The model improves orbital-free DFT accuracy by over two orders of magnitude.

It outperforms MLFFs based solely on Kohn-Sham DFT in accuracy.

Application to molten Al-Si shows no Si atom aggregation, consistent with previous studies.

Abstract

We present a $\Delta$-machine learning model for obtaining Kohn-Sham accuracy from orbital-free density functional theory (DFT) calculations. In particular, we employ a machine learned force field (MLFF) scheme based on the kernel method to capture the difference between Kohn-Sham and orbital-free DFT energies/forces. We implement this model in the context of on-the-fly molecular dynamics simulations, and study its accuracy, performance, and sensitivity to parameters for representative systems. We find that the formalism not only improves the accuracy of Thomas-Fermi-von Weizs{\"a}cker (TFW) orbital-free energies and forces by more than two orders of magnitude, but is also more accurate than MLFFs based solely on Kohn-Sham DFT, while being more efficient and less sensitive to model parameters. We apply the framework to study the structure of molten Al$_{0.88}$Si$_{0.12}$, the results suggesting no aggregation of Si atoms, in agreement with a previous Kohn-Sham study performed at an order of magnitude smaller length and time scales.