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

arXiv: https://arxiv.org/abs/2206.14087 · HTML: https://mlsanity.com/paper/2206.14087/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 8 of 8)

- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions](https://mlsanity.com/paper/1906.10033/) (2019)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Machine learning for electronically excited states of molecules](https://mlsanity.com/paper/2007.05320/) (2020)
- [Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties](https://mlsanity.com/paper/2109.12083/) (2021)
- [Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles](https://mlsanity.com/paper/2003.12437/) (2020)
- [DeepDFT: Neural Message Passing Network for Accurate Charge Density Prediction](https://mlsanity.com/paper/2011.03346/) (2020)
- [A deep neural network for molecular wave functions in quasi-atomic minimal basis representation](https://mlsanity.com/paper/2005.06979/) (2020)

## Built on by (most cited first, 4 of 4)

- [ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitals](https://mlsanity.com/paper/2503.08305/) (2025)
- [Image Super-resolution Inspired Electron Density Prediction](https://mlsanity.com/paper/2402.12335/) (2024)
- [NeuralSCF: Neural network self-consistent fields for density functional theory](https://mlsanity.com/paper/2406.15873/) (2024)
- [Enhancing molecular dynamics with equivariant machine-learned densities](https://mlsanity.com/paper/2604.24563/) (2026)

## Abstract (arXiv)

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.