Approaches for machine learning intermolecular interaction energies and application to energy components from symmetry adapted perturbation theory

Accurate prediction of intermolecular interaction energies is a fundamental challenge in electronic structure theory due to their subtle character and small magnitudes relative to total molecular energies. Symmetry adapted perturbation theory (SAPT) provides rigorous quantum mechanical means for computing such quantities directly and accurately, but for a computational cost of at least $O(N5)$⁠, where N is the number of atoms. Here, we report machine learned models of SAPT components with a computational cost that scales asymptotically linearly, $O(N)$⁠. We use modified multi-target Behler–Parrinello neural networks and specialized intermolecular symmetry functions to address the idiosyncrasies of the intermolecular problem, achieving 1.2 kcal mol⁻¹ mean absolute errors on a test set of hydrogen bound complexes including structural data extracted from the Cambridge Structural Database and Protein Data Bank, spanning an interaction energy range of 20 kcal mol⁻¹. Additionally, we recover accurate predictions of the physically meaningful SAPT component energies, of which dispersion and induction/polarization were the easiest to predict and electrostatics and exchange–repulsion are the most difficult.