Modeling molecular ensembles with gradient-domain machine learning force fields

Gradient-domain machine learning (GDML) force fields have shown excellent accuracy, data efficiency, and applicability for molecules with hundreds of atoms, but the employed global descriptor limits transferability to ensembles of molecules. Many-body expansions (MBEs) should provide a rigorous procedure for size-transferable GDML by training models on fundamental n-body interactions. We developed many-body GDML (mbGDML) force fields for water, acetonitrile, and methanol by training 1-, 2-, and 3-body models on only 1000 MP2/def2-TZVP calculations each. Our mbGDML force field includes intramolecular flexibility and intermolecular interactions, providing that the reference data properly describes these effects. We also compare this mbGDML approach to GAP, SchNet, and NequIP potentials. Energy and force predictions of clusters containing up to 20 molecules are within 0.38 kcal/mol per monomer of reference supersystem calculations. This deviation partially arises from the restriction of the mbGDML model to 3-body interactions. Given these approximations, our automated mbGDML training schemes also resulted in fair agreement with reference radial distribution functions (RDFs) of bulk solvents. These results highlight mbGDML as valuable for modeling explicitly solvated systems with quantum-mechanical accuracy.