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

## TL;DR

This paper demonstrates that molecular-orbital-based machine learning (MOB-ML) can accurately predict correlation energies across diverse organic molecules with significantly fewer training data, showing high transferability and efficiency.

## Contribution

The study introduces refined feature strategies for MOB-ML and proves its transferability and data efficiency in predicting correlation energies for a wide range of organic molecules.

## Key findings

- MOB-ML achieves chemical accuracy with three times fewer training geometries than Δ-ML.
- MOB-ML predicts energies for larger molecules with 36 times fewer training calculations.
- High transferability of MOB-ML models across different molecular sizes is demonstrated.

## Abstract

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).