# Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry

arXiv: https://arxiv.org/abs/2105.14655 · HTML: https://mlsanity.com/paper/2105.14655/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 121 references that are in the map.
- First posted on arXiv 31 May 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [Averaging Weights Leads to Wider Optima and Better Generalization](https://mlsanity.com/paper/1803.05407/) (2018)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [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)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Directional Message Passing for Molecular Graphs](https://mlsanity.com/paper/2003.03123/) (2020)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data](https://mlsanity.com/paper/1807.02547/) (2018)
- [Cormorant: Covariant Molecular Neural Networks](https://mlsanity.com/paper/1906.04015/) (2019)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics](https://mlsanity.com/paper/1707.09571/) (2017)
- [Clebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network](https://mlsanity.com/paper/1806.09231/) (2018)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [A Wigner-Eckart Theorem for Group Equivariant Convolution Kernels](https://mlsanity.com/paper/2010.10952/) (2020)
- [Kohn-Sham equations as regularizer: building prior knowledge into machine-learned physics](https://mlsanity.com/paper/2009.08551/) (2020)
- [Automated Synthetic-to-Real Generalization](https://mlsanity.com/paper/2007.06965/) (2020)
- [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 Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules](https://mlsanity.com/paper/1901.03309/) (2019)
- [Multi-task learning for electronic structure to predict and explore molecular potential energy surfaces](https://mlsanity.com/paper/2011.02680/) (2020)

## Built on by (most cited first, 30 of 30)

- [Fast, Expressive SE(n) Equivariant Networks through Weight-Sharing in Position-Orientation Space](https://mlsanity.com/paper/2310.02970/) (2023)
- [Complete and Efficient Graph Transformers for Crystal Material Property Prediction](https://mlsanity.com/paper/2403.11857/) (2024)
- [Equivariant graph neural networks for fast electron density estimation of molecules, liquids, and solids](https://mlsanity.com/paper/2112.00652/) (2021)
- [Fast Uncertainty Estimates in Deep Learning Interatomic Potentials](https://mlsanity.com/paper/2211.09866/) (2022)
- [Graph Neural Networks for Molecules](https://mlsanity.com/paper/2209.05582/) (2022)
- [CHGNet: Pretrained universal neural network potential for charge-informed atomistic modeling](https://mlsanity.com/paper/2302.14231/) (2023)
- [Higher-Order Equivariant Neural Networks for Charge Density Prediction in Materials](https://mlsanity.com/paper/2312.05388/) (2023)
- [ELECTRA: A Cartesian Network for 3D Charge Density Prediction with Floating Orbitals](https://mlsanity.com/paper/2503.08305/) (2025)
- [A Recipe for Charge Density Prediction](https://mlsanity.com/paper/2405.19276/) (2024)
- [Image Super-resolution Inspired Electron Density Prediction](https://mlsanity.com/paper/2402.12335/) (2024)
- [FeNNol: an Efficient and Flexible Library for Building Force-field-enhanced Neural Network Potentials](https://mlsanity.com/paper/2405.01491/) (2024)
- [Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Models](https://mlsanity.com/paper/2406.03794/) (2024)
- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)
- [A smooth basis for atomistic machine learning](https://mlsanity.com/paper/2209.01948/) (2022)
- [Equivariant Machine Learning Interatomic Potentials with Global Charge Redistribution](https://mlsanity.com/paper/2503.17949/) (2025)
- [High Accuracy Uncertainty-Aware Interatomic Force Modeling with Equivariant Bayesian Neural Networks](https://mlsanity.com/paper/2304.03694/) (2023)
- [Global Plane Waves From Local Gaussians: Periodic Charge Densities in a Blink](https://mlsanity.com/paper/2601.19966/) (2026)
- [Molecular Dipole Moment Learning via Rotationally Equivariant Gaussian Process Regression with Derivatives in Molecular-orbital-based Machine Learning](https://mlsanity.com/paper/2205.15510/) (2022)
- [Molecular-orbital-based Machine Learning for Open-shell and Multi-reference Systems with Kernel Addition Gaussian Process Regression](https://mlsanity.com/paper/2207.08317/) (2022)
- [Investigating the Behavior of Diffusion Models for Accelerating Electronic Structure Calculations](https://mlsanity.com/paper/2311.01491/) (2023)
- [NeuralSCF: Neural network self-consistent fields for density functional theory](https://mlsanity.com/paper/2406.15873/) (2024)
- [FreeCG: Free the Design Space of Clebsch-Gordan Transform for Machine Learning Force Fields](https://mlsanity.com/paper/2407.02263/) (2024)
- [MARA: Continuous SE(3)-Equivariant Attention for Molecular Force Fields](https://mlsanity.com/paper/2602.02671/) (2026)
- [On-the-Fly Fine-Tuning of Foundational Neural Network Potentials: A Bayesian Neural Network Approach](https://mlsanity.com/paper/2507.13805/) (2025)
- [Predictive Free Energy Simulations Through Hierarchical Distillation of Quantum Hamiltonians](https://mlsanity.com/paper/2509.10967/) (2025)
- [GDEGAN: Gaussian Dynamic Equivariant Graph Attention Network for Ligand Binding Site Prediction](https://mlsanity.com/paper/2603.19817/) (2026)
- [Closing the Prior-Posterior Loop: Self-Reflective Molecular Design with Analysis-Driven LLM Iteration](https://mlsanity.com/paper/2606.09520/) (2026)
- [DISSOLVR: An Interpretable and Fast Framework for Aqueous and Organic Solubility Prediction](https://mlsanity.com/paper/2610.02574/) (2026)
- [Equivariant Flow Matching for Electron Density Prediction](https://mlsanity.com/paper/2610.02651/) (2026)
- [Beyond DFT electronic band structures via dual-space orbital learning](https://mlsanity.com/paper/2610.19919/) (2026)

## Abstract (arXiv)

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high fidelity quantum chemical properties. OrbNet-Equi models a wide spectrum of target properties with an accuracy consistently better than standard machine learning methods and a speed orders of magnitude greater than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.