Discovering Patterns in Molecular Interaction Energies Using Explainable Machine Learning

Abstract

The energies of molecular interactions are important in the study of the stability and behavior of metal–ligand systems, and explainable machine learning provides a way to determine which aspects of computation are responsible for the energies and patterns in data. A study of 2,418 computational records corresponding to 26 reactions of metal–ligand systems were analyzed with three density functionals and 31 basis sets. Descriptive statistics, Kruskal–Wallis test, counterpoise correction analysis, Pearson correlation and ensemble machine-learning models were used. Interactions were mostly negative, but there was considerable variation in interactions. The energies were significantly affected by the density functional and by the basis-set cardinality, the double-zeta basis sets giving more negative mean values than the triple- and quadruple-zeta basis sets. The magnitude of interaction energies was reduced by counterpoise correction; uncorrected and corrected values were well correlated, and the effects of basis-set superposition error were confirmed. Five-fold reaction-grouped cross-validation was used to evaluate Random Forest, Extra Trees and Gradient Boosting. Gradient Boosting gave the smallest prediction error, but all models were found to have negative R² values, meaning that they were not generalizable to unseen metal–ligand reactions. The computational parameters with the greatest influence were determined by permutation-based interpretation to be basis-set cardinality, basis-set identity, and density functional. In general, the explainable machine learning approach was able to capture the variation in computational drivers of interaction energy, yet molecular, geometric, and electronic descriptors are needed to achieve accurate extrapolation to new reactions.