Orbital Specific Exchange: advancing hybrid density functional theory with geometric deep learning

One of the main challenges of hybrid Density Functional Theory (DFT) is selection of the exact-exchange fraction ($\alpha$). While state-of-the-art methods adapt $\alpha$ per molecule, they remain limited to a global scalar, ignoring that distinct electronic environments require distinct physical treatments, i.e., the optimal $\alpha$ would be different for various parts of the same molecule. We propose a generalized formalism that treats exchange mixing not as a scalar hyperparameter, but as a learnable orbital-specific interaction map. We illustrate it with OSE26 — an equivariant neural network predicting a dense mixing matrix that modulates the Hartree–Fock exchange operator. This exchange-functional implementation provides self-consistency and roto-translational energy invariance. Trained and validated on MSR-ACC-TAE and RDB7, OSE26 achieves near-chemical accuracy for reaction-barrier prediction, attaining a $\sim$1 kcal/mol MAE on RDB7 and reducing MAE by 11–56% relative to the considered baselines. This move from system-wide scalars to learnable orbital-level matrices promises a more broadly applicable hybrid-functional paradigm.