# Molecular-orbital-based Machine Learning for Open-shell and Multi-reference Systems with Kernel Addition Gaussian Process Regression

arXiv: https://arxiv.org/abs/2207.08317 · HTML: https://mlsanity.com/paper/2207.08317/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 92 references that are in the map.
- First posted on arXiv 17 Jul 2022.

## Builds on (most cited first, 23 of 23)

- [MoleculeNet: A Benchmark for Molecular Machine Learning](https://mlsanity.com/paper/1703.00564/) (2017)
- [SchNet: A continuous-filter convolutional neural network for modeling quantum interactions](https://mlsanity.com/paper/1706.08566/) (2017)
- [Equivariant message passing for the prediction of tensorial properties and molecular spectra](https://mlsanity.com/paper/2102.03150/) (2021)
- [Fast and Uncertainty-Aware Directional Message Passing for Non-Equilibrium Molecules](https://mlsanity.com/paper/2011.14115/) (2020)
- [Molecular Graph Convolutions: Moving Beyond Fingerprints](https://mlsanity.com/paper/1603.00856/) (2016)
- [Spherical Message Passing for 3D Graph Networks](https://mlsanity.com/paper/2102.05013/) (2021)
- [Deep Reinforcement Learning for De-Novo Drug Design](https://mlsanity.com/paper/1711.10907/) (2017)
- [Deep neural network solution of the electronic Schr"odinger equation](https://mlsanity.com/paper/1909.08423/) (2019)
- [SpookyNet: Learning Force Fields with Electronic Degrees of Freedom and Nonlocal Effects](https://mlsanity.com/paper/2105.00304/) (2021)
- [By-passing the Kohn-Sham equations with machine learning](https://mlsanity.com/paper/1609.02815/) (2016)
- [OrbNet: Deep Learning for Quantum Chemistry Using Symmetry-Adapted Atomic-Orbital Features](https://mlsanity.com/paper/2007.08026/) (2020)
- [Deep learning for molecular design - a review of the state of the art](https://mlsanity.com/paper/1903.04388/) (2019)
- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [Solving the electronic Schr"odinger equation for multiple nuclear geometries with weight-sharing deep neural networks](https://mlsanity.com/paper/2105.08351/) (2021)
- [Predicting molecular dipole moments by combining atomic partial charges and atomic dipoles](https://mlsanity.com/paper/2003.12437/) (2020)
- [Multi-fidelity machine-learning with uncertainty quantification and Bayesian optimization for materials design: Application to ternary random alloys](https://mlsanity.com/paper/2006.00139/) (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)
- [Regression-clustering for Improved Accuracy and Training Cost with Molecular-Orbital-Based Machine Learning](https://mlsanity.com/paper/1909.02041/) (2019)
- [Molecular Energy Learning Using Alternative Blackbox Matrix-Matrix Multiplication Algorithm for Exact Gaussian Process](https://mlsanity.com/paper/2109.09817/) (2021)
- [Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space](https://mlsanity.com/paper/2204.09831/) (2022)
- [Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery](https://mlsanity.com/paper/2205.02967/) (2022)
- [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)

## Built on by (most cited first, 1 of 1)

- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)

## Abstract (arXiv)

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML (KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H10 chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML (KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, GDB-13-T) and open-shell (QMSpin) molecules.