# Overcoming the Barrier of Orbital-Free Density Functional Theory for Molecular Systems Using Deep Learning

arXiv: https://arxiv.org/abs/2309.16578 · HTML: https://mlsanity.com/paper/2309.16578/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 129 references that are in the map.
- First posted on arXiv 28 Sep 2023.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [A Survey of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [E(n) Equivariant Graph Neural Networks](https://mlsanity.com/paper/2102.09844/) (2021)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Tensor field networks: Rotation- and translation-equivariant neural networks for 3D point clouds](https://mlsanity.com/paper/1802.08219/) (2018)
- [E(3)-Equivariant Graph Neural Networks for Data-Efficient and Accurate Interatomic Potentials](https://mlsanity.com/paper/2101.03164/) (2021)
- [SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks](https://mlsanity.com/paper/2006.10503/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Efficient and Accurate Estimation of Lipschitz Constants for Deep Neural Networks](https://mlsanity.com/paper/1906.04893/) (2019)
- [Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs](https://mlsanity.com/paper/2206.11990/) (2022)
- [Learning Local Equivariant Representations for Large-Scale Atomistic Dynamics](https://mlsanity.com/paper/2204.05249/) (2022)
- [TorchMD-NET: Equivariant Transformers for Neural Network based Molecular Potentials](https://mlsanity.com/paper/2202.02541/) (2022)
- [Frame Averaging for Invariant and Equivariant Network Design](https://mlsanity.com/paper/2110.03336/) (2021)
- [Generalization in Deep Learning](https://mlsanity.com/paper/1710.05468/) (2017)
- [Artificial Intelligence for Science in Quantum, Atomistic, and Continuum Systems](https://mlsanity.com/paper/2307.08423/) (2023)
- [Machine Learning of coarse-grained Molecular Dynamics Force Fields](https://mlsanity.com/paper/1812.01736/) (2018)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [Benchmarking Graphormer on Large-Scale Molecular Modeling Datasets](https://mlsanity.com/paper/2203.04810/) (2022)
- [Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics](https://mlsanity.com/paper/2009.08551/) (2020)
- [Learning Iterative Reasoning through Energy Minimization](https://mlsanity.com/paper/2206.15448/) (2022)
- [Towards Predicting Equilibrium Distributions for Molecular Systems with Deep Learning](https://mlsanity.com/paper/2306.05445/) (2023)
- [DeePKS: a comprehensive data-driven approach towards chemically accurate density functional theory](https://mlsanity.com/paper/2008.00167/) (2020)
- [Orbital-free Bond Breaking via Machine Learning](https://mlsanity.com/paper/1306.1812/) (2013)
- [KineticNet: Deep learning a transferable kinetic energy functional for orbital-free density functional theory](https://mlsanity.com/paper/2305.13316/) (2023)
- [Variational principle to regularize machine-learned density functionals: the non-interacting kinetic-energy functional](https://mlsanity.com/paper/2306.17587/) (2023)

## Built on by (most cited first, 13 of 13)

- [Self-Consistency Training for Density-Functional-Theory Hamiltonian Prediction](https://mlsanity.com/paper/2403.09560/) (2024)
- [AI-driven inverse design of materials: Past, present and future](https://mlsanity.com/paper/2411.09429/) (2024)
- [Learning Equivariant Non-Local Electron Density Functionals](https://mlsanity.com/paper/2410.07972/) (2024)
- [Physical Consistency Bridges Heterogeneous Data in Molecular Multi-Task Learning](https://mlsanity.com/paper/2410.10118/) (2024)
- [Surrogate Functionals for Machine-Learned Orbital-Free Density Functional Theory](https://mlsanity.com/paper/2604.20458/) (2026)
- [Learning the Kohn-Sham map with neural operators for quasi-linear scaling density functional theory](https://mlsanity.com/paper/2608.23895/) (2026)
- [NeuralSCF: Neural network self-consistent fields for density functional theory](https://mlsanity.com/paper/2406.15873/) (2024)
- [Self-Refining Training for Amortized Density Functional Theory](https://mlsanity.com/paper/2506.01225/) (2025)
- [Enhancing molecular dynamics with equivariant machine-learned densities](https://mlsanity.com/paper/2604.24563/) (2026)
- [Stable and Accurate Orbital-Free DFT Powered by Machine Learning](https://mlsanity.com/paper/2503.00443/) (2025)
- [Position: The Inevitable Transition to Machine Learning in Quantum Chemistry](https://mlsanity.com/paper/2607.18281/) (2026)
- [Electron-Density-Informed Molecular Property Prediction Using Surrogate Functionals](https://mlsanity.com/paper/2610.13649/) (2026)
- [All-electron machine-learned orbital-free density functional for periodic CHNO systems](https://mlsanity.com/paper/2610.17975/) (2026)

## Abstract (arXiv)

Orbital-free density functional theory (OFDFT) is a quantum chemistry formulation that has a lower cost scaling than the prevailing Kohn-Sham DFT, which is increasingly desired for contemporary molecular research. However, its accuracy is limited by the kinetic energy density functional, which is notoriously hard to approximate for non-periodic molecular systems. Here we propose M-OFDFT, an OFDFT approach capable of solving molecular systems using a deep learning functional model. We build the essential non-locality into the model, which is made affordable by the concise density representation as expansion coefficients under an atomic basis. With techniques to address unconventional learning challenges therein, M-OFDFT achieves a comparable accuracy with Kohn-Sham DFT on a wide range of molecules untouched by OFDFT before. More attractively, M-OFDFT extrapolates well to molecules much larger than those seen in training, which unleashes the appealing scaling of OFDFT for studying large molecules including proteins, representing an advancement of the accuracy-efficiency trade-off frontier in quantum chemistry.