# DeepDFT: Neural Message Passing Network for Accurate Charge Density Prediction

arXiv: https://arxiv.org/abs/2011.03346 · HTML: https://mlsanity.com/paper/2011.03346/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2020.

## Built on by (most cited first, 12 of 12)

- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids](https://mlsanity.com/paper/2112.00652/) (2021)
- [Higher-Order Equivariant Neural Networks for Charge Density Prediction in Materials](https://mlsanity.com/paper/2312.05388/) (2023)
- [Equivariant Neural Operator Learning with Graphon Convolution](https://mlsanity.com/paper/2311.10908/) (2023)
- [ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitals](https://mlsanity.com/paper/2503.08305/) (2025)
- [Gaussian Plane-Wave Neural Operator for Electron Density Estimation](https://mlsanity.com/paper/2402.04278/) (2024)
- [Image Super-resolution Inspired Electron Density Prediction](https://mlsanity.com/paper/2402.12335/) (2024)
- [Towards Combinatorial Generalization for Catalysts: A Kohn-Sham Charge-Density Approach](https://mlsanity.com/paper/2310.18702/) (2023)
- [Electronic-structure properties from atom-centered predictions of the electron density](https://mlsanity.com/paper/2206.14087/) (2022)
- [Self-consistent Validation for Machine Learning Electronic Structure](https://mlsanity.com/paper/2402.10186/) (2024)
- [ED-DiT: Physics-Guided Diffusion Pretraining for Transferable Molecular Representations from Electron Density](https://mlsanity.com/paper/2608.03260/) (2026)
- [E3STO: Orbital Inspired SE(3)-Equivariant Molecular Representation for Electron Density Prediction](https://mlsanity.com/paper/2410.06119/) (2024)

## Abstract (arXiv)

We introduce DeepDFT, a deep learning model for predicting the electronic charge density around atoms, the fundamental variable in electronic structure simulations from which all ground state properties can be calculated. The model is formulated as neural message passing on a graph, consisting of interacting atom vertices and special query point vertices for which the charge density is predicted. The accuracy and scalability of the model are demonstrated for molecules, solids and liquids. The trained model achieves lower average prediction errors than the observed variations in charge density obtained from density functional theory simulations using different exchange correlation functionals.