Systematic Improvement of Empirical Energy Functions in the Era of Machine Learning

Abstract: The impact of targeted replacement of individual terms in empirical force fields is quantitatively assessed for pure water, dichloromethane (DCM), and solvated K$^+$ and Cl$^-$ ions. For the electrostatics, point charges (PCs) and MLbased minimally distributed charges (MDCM) fitted to the molecular electrostatic potential are evaluated together with electrostatics based on the Coulomb integral. The impact of explicitly including second-order terms is investigated by adding a fragment molecular orbital (FMO)-derived polarization energy to an existing force field, in this case CHARMM. It is demonstrated that anisotropic electrostatics reduce the RMSE for water (by 1.6 kcal/mol), DCM (by 0.8 kcal/mol) and for solvated Cl$^-$ clusters (by 0.4 kcal/mol). An additional polarization term can be neglected for DCM but notably improves errors in pure water (by 1.1 kcal/mol) and in Cl$^-$ clusters (by 0.4 kcal/mol) and is key to describing solvated K$^+$, reducing the RMSE by 2.3 kcal/mol. A 12-6 Lennard-Jones functional form is found to perform satisfactorily with PC and MDCM electrostatics, but is not appropriate for descriptions that account for the electrostatic penetration energy. The importance of many-body contributions is assessed by comparing a strictly 2-body approach with self-consistent reference data. DCM can be approximated well with a 2-body potential while water and solvated K$^+$ and Cl$^-$ ions require explicit many-body corrections. The present work systematically quantifies which terms improve the performance of an existing force field and what reference data to use for parametrizing these terms in a tractable fashion for ML fitting of pure and heterogeneous systems.