Transferring Knowledge from MM to QM: A Graph Neural Network-Based Implicit Solvent Model for Small Organic Molecules

The conformational ensemble of a molecule is strongly influenced by the surrounding environment. Correctly modeling the effect of any given environment is, hence, of pivotal importance in computational studies. Machine learning (ML) has been shown to be able to model these interactions probabilistically, with successful applications demonstrated for classical molecular dynamics. While first instances of ML implicit solvents for quantum-mechanical (QM) calculations exist, the high computational cost of QM reference calculations hinders the development of a generally applicable ML implicit solvent model for QM calculations. Here, we present a novel way of developing such a general machine-learned QM implicit solvent model by transferring knowledge obtained from classical interactions to QM, emulating a QM/MM setup with electrostatic embedding and a nonpolarizable MM solvent. This has the profound advantages that neither QM/MM reference calculations nor experimental data are required for training and that the obtained graph neural network (GNN)-based implicit solvent model (termed QM-GNNIS) is compatible with any functional and basis set. QM-GNNIS is currently applicable to small organic molecules and describes 39 different organic solvents. The performance of QM-GNNIS is validated on NMR and IR experiments, demonstrating that the approach can reproduce experimentally observed trends unattainable by state-of-the-art implicit-solvent models paired with static QM calculations.