Kernel-Based Minimal Distributed Charges: A Conformationally Dependent ESP-Model for Molecular Simulations

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