Electronic-structure properties from atom-centered predictions of the electron density

TL;DR

This paper introduces a novel gradient-based machine learning approach to accurately predict electron densities of molecules and materials using atom-centered basis functions, enabling efficient energy calculations and transferability.

Contribution

It develops a gradient-based optimization method for atom-centered electron density predictions that overcomes non-orthogonality challenges and achieves high accuracy on complex datasets.

Findings

Achieves 0.1 meV/atom accuracy in total energy predictions from predicted densities.

Successfully applies the method to complex liquid water and QM9 datasets.

Enables efficient energy calculations with minimal training data.

Abstract

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multi-centered atomic basis analogous to that routinely used in density fitting approximations. However, the non-orthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex datasets, obtaining extremely accurate predictions. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark dataset, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.