Kernel-Based Minimal\nDistributed Charges: A Conformationally\nDependent ESP-Model for Molecular Simulations

A kernel-based method (kernelized minimal distributed\ncharge model\n(kMDCM)) to represent the molecular electrostatic potential (ESP)\nin terms of off-center point charges is introduced. The positions\nof the charges adapt to the molecular geometry and allow the description\nof intramolecular charge flow. Using Gaussian kernels and atom–atom\ndistances as the features, the ESPs for water and methanol are shown\nto improve by at least a factor of 2 compared with point charge models\nfit to an ensemble of structures. The conformationally fluctuating\nmolecular dipole moment of water is reproduced almost twice as accurately\nusing kMDCM compared with static PCs, despite not fitting to the dipole\ndirectly. The role of hyperparameters in the kernelization is investigated\nand their implication on model performance and simulation stability\nis discussed. Combining kMDCM for the electrostatics and reproducing\nkernels for the bonded terms allows energy-conserving simulations\nof 2000 water molecules with periodic boundary conditions on the nanosecond\ntime scale. These MD simulations sample geometries outside the training\nset but remain stable, which demonstrates the robustness of the model\nand its implementation.