Analytical gradients for molecular-orbital-based machine learning

Molecular-orbital-based machine learning (MOB-ML) enables the prediction of accurate correlation energies at cost obtaining molecular orbitals. Here, we present derivation, implementation, and numerical demonstration MOB-ML analytical nuclear gradients, which are formulated in a general Lagrangian framework to enforce orthogonality, localization, Brillouin constraints on The gradient is with respect regression technique (e.g., Gaussian process or neural networks) MOB feature design. We show that gradients highly compared other ML methods ISO17 dataset while only being trained for hundreds molecules thousands methods. also shown yield optimized structures computational evaluation comparable density-corrected density functional theory calculation.