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

arXiv: https://arxiv.org/abs/1906.10033 · HTML: https://mlsanity.com/paper/1906.10033/

## Key facts

- Cited by 73 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jun 2019.

## Built on by (most cited first, 30 of 73)

- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [Provably efficient machine learning for quantum many-body problems](https://mlsanity.com/paper/2106.12627/) (2021)
- [SE(3)-equivariant prediction of molecular wavefunctions and electronic densities](https://mlsanity.com/paper/2106.02347/) (2021)
- [Efficient and Equivariant Graph Networks for Predicting Quantum Hamiltonian](https://mlsanity.com/paper/2306.04922/) (2023)
- [Ab-initio quantum chemistry with neural-network wavefunctions](https://mlsanity.com/paper/2208.12590/) (2022)
- [SchNetPack 2.0: A neural network toolbox for atomistic machine learning](https://mlsanity.com/paper/2212.05517/) (2022)
- [QH9: A Quantum Hamiltonian Prediction Benchmark for QM9 Molecules](https://mlsanity.com/paper/2306.09549/) (2023)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [Machine learning nonequilibrium electron forces for adiabatic spin dynamics](https://mlsanity.com/paper/2112.12124/) (2021)
- [Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systems](https://mlsanity.com/paper/2201.00798/) (2022)
- [Physics-inspired Equivariant Descriptors of Non-bonded Interactions](https://mlsanity.com/paper/2308.13208/) (2023)
- [Enhancing the Scalability and Applicability of Kohn-Sham Hamiltonians for Molecular Systems](https://mlsanity.com/paper/2502.19227/) (2025)
- [Self-Consistency Training for Density-Functional-Theory Hamiltonian Prediction](https://mlsanity.com/paper/2403.09560/) (2024)
- [Efficient and Scalable Density Functional Theory Hamiltonian Prediction through Adaptive Sparsity](https://mlsanity.com/paper/2502.01171/) (2025)
- [High-order Equivariant Flow Matching for Density Functional Theory Hamiltonian Prediction](https://mlsanity.com/paper/2505.18817/) (2025)
- [Audacity of huge: overcoming challenges of data scarcity and data quality for machine learning in computational materials discovery](https://mlsanity.com/paper/2111.01905/) (2021)
- [Integrating Chemistry Knowledge in Large Language Models via Prompt Engineering](https://mlsanity.com/paper/2404.14467/) (2024)
- [Accurate Machine Learned Quantum-Mechanical Force Fields for Biomolecular Simulations](https://mlsanity.com/paper/2205.08306/) (2022)
- [A Leap among Quantum Computing and Quantum Neural Networks: A Survey](https://mlsanity.com/paper/2107.03313/) (2021)
- [Transferable E(3) equivariant parameterization for Hamiltonian of molecules and solids](https://mlsanity.com/paper/2210.16190/) (2022)
- [Image Super-resolution Inspired Electron Density Prediction](https://mlsanity.com/paper/2402.12335/) (2024)
- [Towards a Foundation Model for Neural Network Wavefunctions](https://mlsanity.com/paper/2303.09949/) (2023)
- [Towards Symbolic XAI -- Explanation Through Human Understandable Logical Relationships Between Features](https://mlsanity.com/paper/2408.17198/) (2024)
- [Learning from the electronic structure of molecules across the periodic table](https://mlsanity.com/paper/2510.00224/) (2025)
- [Infusing Self-Consistency into Density Functional Theory Hamiltonian Prediction via Deep Equilibrium Models](https://mlsanity.com/paper/2406.03794/) (2024)
- [Efficient Prediction of SO(3)-Equivariant Hamiltonian Matrices via SO(2) Local Frames](https://mlsanity.com/paper/2506.09398/) (2025)

## 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.