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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 per monomer and 0.06 kcal/(mol Å) 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. NequIP trained on total energies and forces of trimers experienced much larger energy errors (at least 15 kcal/mol) 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 as valuable for modeling explicitly solvated systems with quantum-mechanical accuracy. 

Bonding energies play an essential role in describing the relative stability of molecules in chemical space. Therefore, methods employed to search chemical space need to capture the bonding behavior for a wide range of molecules, including radicals. In this work, we investigate the ability of quantum alchemy to capture the bonding behavior of hypothetical chemical compounds, specifically diatomic molecules involving hydrogen with various electronic structures. We evaluate equilibrium bond lengths, ionization energies, and electron affinities of these fundamental systems. We compare and contrast how well manual quantum alchemy calculations, i.e., quantum mechanics calculations in which the nuclear charge is altered, and quantum alchemy approximations using a Taylor series expansion can predict these molecular properties. Our results suggest that while manual quantum alchemy calculations outperform Taylor series approximations, truncations of Taylor series approximations after the second order provide the most accurate Taylor series predictions. Furthermore, these results suggest that trends in quantum alchemy predictions are generally dependent on the predicted property (i.e., equilibrium bond length, ionization energy, or electron affinity). Taken together, this work provides insight into how quantum alchemy predictions using a Taylor series expansion may be applied to future studies of non-singlet systems as well as the challenges that remain open for predicting the bonding behavior of such systems.