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 adequately describe these effects. Energy and force predictions of clusters containing up to 20 molecules are within 0.38 kcal mol-1 per monomer and 0.06 kcal (mol angstrom)-1 per atom of reference supersystem calculations. This deviation partially arises from the restriction of the mbGDML model to 3-body interactions. GAP and SchNet in this MBE framework achieved similar accuracies but occasionally had abnormally high errors up to 17 kcal mol-1. NequIP trained on total energies and forces of trimers experienced much larger energy errors (at least 15 kcal mol-1) as the number of monomers increased-demonstrating the effectiveness of size transferability with MBEs. 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's value for modeling explicitly solvated systems with quantum-mechanical accuracy. Gradient-domain machine learning (GDML) force fields show excellent accuracy, data efficiency, and applicability for molecules, and a many-body approach opens the possibility of increased transferability to molecular ensembles.