# Many-body Expansion Based Machine Learning Models for Octahedral Transition Metal Complexes

arXiv: https://arxiv.org/abs/2410.09659 · HTML: https://mlsanity.com/paper/2410.09659/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 114 references that are in the map.
- First posted on arXiv 12 Oct 2024.

## Builds on (most cited first, 9 of 9)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Convolutional Networks on Graphs for Learning Molecular Fingerprints](https://mlsanity.com/paper/1509.09292/) (2015)
- [Uncertainty Quantification Using Neural Networks for Molecular Property Prediction](https://mlsanity.com/paper/2005.10036/) (2020)
- [MT-CGCNN: Integrating Crystal Graph Convolutional Neural Network with Multitask Learning for Material Property Prediction](https://mlsanity.com/paper/1811.05660/) (2018)
- [Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles](https://mlsanity.com/paper/2106.13109/) (2021)
- [The Many-Body Expansion Combined with Neural Networks](https://mlsanity.com/paper/1609.07072/) (2016)
- [Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character Across Known Transition Metal Complex Ligands](https://mlsanity.com/paper/2205.02879/) (2022)

## Abstract (arXiv)

Graph-based machine learning models for materials properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, our molecular graph featurization method for machine learning various spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used machine learning methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary transition metal complexes, the best MBE models achieve mean absolute errors of 2.75 kcal/mol on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30-40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit mean absolute errors of 4.00 kcal/mol (i.e., a 0.73 kcal/mol reduction) on the spin-splitting energies and 0.53 eV (i.e., a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.