The metal-ligand local mode as a descriptor for catalytic activity

We examine whether local metal-ligand vibrational modes are suitable descriptors for catalytic activity of [Cu${}_2$O${}_2$]${}^{2+}$ complexes towards CH₄ hydroxylation. The objective is to construct an active site-specific structure–activity relationship that can predict the activity for a wide range of ligand backbones. To this end, we choose N-donor ligands spanning substituted imidazoles, amines, diamines, pyridines, thiazoles, and mixed systems. We construct both linear models (or linear free energy relationships, LFERs) as well as non-linear, regression-based machine learning models using gradient boosting regression (GBR) and eXtreme Gradient Boosting (XGBoost). The LFER yields weak correlations between the descriptors and the barrier, indicating that the underlying relationship is likely not a linear one. On the other hand, GBR accurately predict barriers to within 5 kJ mol⁻¹ and yields a relationship that is transferable across several ligand backbones. The local modes constituting the active site, therefore, are suitable descriptors for catalytic activity.