# A Universal Density Matrix Functional from Molecular Orbital-Based Machine Learning: Transferability across Organic Molecules

arXiv: https://arxiv.org/abs/1901.03309 · HTML: https://mlsanity.com/paper/1901.03309/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2019.

## Built on by (most cited first, 9 of 9)

- [Informing Geometric Deep Learning with Electronic Interactions to Accelerate Quantum Chemistry](https://mlsanity.com/paper/2105.14655/) (2021)
- [OrbitAll: A Unified Quantum Mechanical Representation Deep Learning Framework for All Molecular Systems](https://mlsanity.com/paper/2507.03853/) (2025)
- [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)
- [Machine learning for accuracy in density functional approximations](https://mlsanity.com/paper/2311.00196/) (2023)
- [Representing local protein environments with machine learning force fields](https://mlsanity.com/paper/2505.23354/) (2025)
- [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)
- [Delta-ML Ensembles for Selecting Quantum Chemistry Methods to Compute Intermolecular Interactions](https://mlsanity.com/paper/2511.17753/) (2025)

## Abstract (arXiv)

We address the degree to which machine learning can be used to accurately and transferably predict post-Hartree-Fock correlation energies. Refined strategies for feature design and selection are presented, and the molecular-orbital-based machine learning (MOB-ML) method is applied to several test systems. Strikingly, for the MP2, CCSD, and CCSD(T) levels of theory, it is shown that the thermally accessible (350 K) potential energy surface for a single water molecule can be described to within 1 millihartree using a model that is trained from only a single reference calculation at a randomized geometry. To explore the breadth of chemical diversity that can be described, MOB-ML is also applied to a new dataset of thermalized (350 K) geometries of 7211 organic models with up to seven heavy atoms. In comparison with the previously reported Delta-ML method, MOB-ML is shown to reach chemical accuracy with three-fold fewer training geometries. Finally, a transferability test in which models trained for seven-heavy-atom systems are used to predict energies for thirteen-heavy-atom systems reveals that MOB-ML reaches chemical accuracy with 36-fold fewer training calculations than Delta-ML (140 versus 5000 training calculations).