Coupling causality and interpretable machine learning to reveal the reaction coordinate of C–N coupling with a supramolecular Cu-calix[8]arene catalyst

Supramolecular 3d transition-metal catalysts are large, flexible systems with intricate interactions, resulting in complex reaction coordinates. To capture their dynamic nature, we developed a broadly applicable, high-throughput workflow, that leverages quantum mechanics/molecular mechanics molecular dynamics (QM/MM MD) in explicit solvent, to investigate a Cu(i)-calix[8]arene-catalysed C-N coupling reaction. The system complexity and high amount of data generated from sampling the reaction requires automated analyses. To identify and quantify the reaction coordinate from noisy simulation trajectories, we applied interpretable machine learning techniques (Lasso, Random Forest, Logistic Regression) in a consensus model, alongside dimensionality reduction methods (PCA, LDA, tICA). By employing a Granger Causality model, we move beyond the traditional view of a reaction coordinate, by defining it instead as a sequence of molecular motions leading up to the reaction.