mlsanityData to 7 Oct 2026

Unifying machine learning and quantum chemistry -- a deep neural network for molecular wavefunctions

arXiv 1906.10033 ↗First posted 24 Jun 2019physics.chem-ph stat.MLcited by 73

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Abstract (arXiv)

Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for target electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.

Key facts. Cited by 73 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Jun 2019.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 11; 2022: 13; 2023: 13; 2024: 17; 2025: 11; 2026: 8.

73 papers.

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  1. 2021Equivariant message passing for the prediction of tensorial properties and molecular spectracited by 438
  2. 2022Graph neural networks for materials science and chemistrycited by 181
  3. 2021Geometric Deep Learning on Molecular Representationscited by 113
  4. 2021SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effectscited by 103
  5. 2021Provably efficient machine learning for quantum many-body problemscited by 91
  6. 2021SE(3)-equivariant prediction of molecular wavefunctions and electronic densitiescited by 67
  7. 2023Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltoniancited by 38
  8. 2022SchNetPack 2.0: A neural network toolbox for atomistic machine learningcited by 29
  9. 2022Ab-initio quantum chemistry with neural-network wavefunctionscited by 28
  10. 2023QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Moleculescited by 26
  11. 2021Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networkscited by 22
  12. 2023Improved machine learning algorithm for predicting ground state propertiescited by 22
38 more
  1. 2021Machine learning nonequilibrium electron forces for adiabatic spin dynamicscited by 17
  2. 2022Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systemscited by 16
  3. 2023Physics-inspired Equivariant Descriptors of Non-bonded Interactionscited by 13
  4. 2025Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systemscited by 13
  5. 2024Self-Consistency Training for Density-Functional-Theory Hamiltonian Predictioncited by 12
  6. 2021Audacity of huge: overcoming challenges of data scarcity and data quality for machine learning in computational materials discoverycited by 10
  7. 2024Integrating Chemistry Knowledge in Large Language Models via Prompt Engineeringcited by 10
  8. 2025Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsitycited by 10
  9. 2025High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Predictioncited by 10
  10. 2022Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulationscited by 9
  11. 2021A Leap among Quantum Computing and Quantum Neural Networks: A Surveycited by 8
  12. 2024Image Super-resolution Inspired Electron Density Predictioncited by 8
  13. 2022Transferable E(3) equivariant parameterization for Hamiltonian of molecules and solidscited by 7
  14. 2024Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Featurescited by 7
  15. 2025Learning from the electronic structure of molecules across the periodic tablecited by 7
  16. 2023Towards a Foundation Model for Neural Network Wavefunctionscited by 6
  17. 2024Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Modelscited by 6
  18. 2023GeoTMI:Predicting quantum chemical property with easy-to-obtain geometry via positional denoisingcited by 5
  19. 2023Towards Combinatorial Generalization for Catalysts: A Kohn-Sham Charge-Density Approachcited by 5
  20. 2024Explain the Black Box for the Sake of Science: the Scientific Method in the Era of Generative Artificial Intelligencecited by 5
  21. 2025Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Framescited by 5
  22. 2022Electronic-structure properties from atom-centered predictions of the electron densitycited by 4
  23. 2023Bridging Trustworthiness and Open-World Learning: An Exploratory Neural Approach for Enhancing Interpretability, Generalization, and Robustnesscited by 4
  24. 2024Reducing the Cost of Quantum Chemical Data By Backpropagating Through Density Functional Theorycited by 4
  25. 2024TraceGrad: a Framework Learning Expressive SO(3)-equivariant Non-linear Representations for Electronic-Structure Hamiltonian Predictioncited by 4
  26. 2021Implementing graph neural networks with TensorFlow-Kerascited by 3
  27. 2023Equivariant Matrix Function Neural Networkscited by 3
  28. 2024Universal Machine Learning Kohn-Sham Hamiltonian for Materialscited by 3
  29. 2024Explainable Molecular Property Prediction: Aligning Chemical Concepts with Predictions via Language Modelscited by 3
  30. 2026Transferable SCF-Acceleration through Solver-Aligned Initialization Learningcited by 3
  31. 2022Automatic Identification of Chemical Moietiescited by 2
  32. 2023Electronic excited states from physically-constrained machine learningcited by 2
  33. 2024Towards Harmonization of SO(3)-Equivariance and Expressiveness: a Hybrid Deep Learning Framework for Electronic-Structure Hamiltonian Predictioncited by 2
  34. 2024nabla2DFT: A Universal Quantum Chemistry Dataset of Drug-Like Molecules and a Benchmark for Neural Network Potentialscited by 2
  35. 2025Advancing Universal Deep Learning for Electronic-Structure Hamiltonian Prediction of Materialscited by 2
  36. 2025Towards A Transferable Acceleration Method for Density Functional Theorycited by 2
  37. 2021Predicting Quantum Potentials by Deep Neural Network and Metropolis Samplingcited by 1
  38. 2022EcoFlow: Efficient Convolutional Dataflows for Low-Power Neural Network Acceleratorscited by 1

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