Learning electron densities in the condensed phase

TL;DR

This paper presents a novel machine learning approach for accurately predicting electron densities in periodic systems, enabling efficient electronic property calculations across various materials with minimal error.

Contribution

The authors develop a local, atom-centered basis and Gaussian process regression framework for electron density prediction applicable to both isolated and periodic systems, demonstrating high accuracy and scalability.

Findings

Accurately predicts electron densities for metals, semiconductors, and molecular crystals.

Enables efficient electronic property calculations with errors around tens of meV/atom.

Successfully extrapolates from small to large systems without increased error.

Abstract

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centred auxiliary basis, which enables an accurate expansion of the all-electron density in a form suitable for learning isolated and periodic systems alike. We show that using this formulation the electron densities of metals, semiconductors and molecular crystals can all be accurately predicted using symmetry-adapted Gaussian process regression models, properly adjusted for the non-orthogonal nature of the basis. These predicted densities enable the efficient calculation of electronic properties which present errors on the order of tens of meV/atom when compared to ab initio density-functional calculations. We demonstrate the key power of this approach by using a model trained on ice unit cells containing only 4 water molecules to predict the electron densities of cells containing up to 512 molecules, and see no increase in the magnitude of the errors of derived electronic properties when increasing the system size. Indeed, we find that these extrapolated derived energies are more accurate than those predicted using a direct machine-learning model. Finally, on heterogeneous datasets SALTED can predict electron densities with errors below 4%.