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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. 

Rational design of molecular chelating agents requires a detailed understanding of physicochemical ligand–metal interactions in solvent phase. Computational quantum chemistry methods should be able to provide this, but computational reports have shown poor accuracy when determining absolute binding constants for many chelating molecules. To understand why, we compare and benchmark static- and dynamics-based computational procedures for a range of monovalent and divalent cations binding to a conventional cryptand molecule: 2.2.2-cryptand ([2.2.2]). The benchmarking comparison shows that dynamics simulations using standard OPLS-AA classical potentials can reasonably predict binding constants for monovalent cations, but these procedures fail for divalent cations. We also consider computationally efficient static procedure using Kohn–Sham density functional theory (DFT) and cluster-continuum modeling that accounts for local microsolvation and pH effects. This approach accurately predicts binding energies for monovalent and divalent cations with an average error of 3.2 kcal mol −1 compared to experiment. This static procedure thus should be useful for future molecular screening efforts, and high absolute errors in the literature may be due to inadequate modeling of local solvent and pH effects. 

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.