Water Dipole and Quadrupole Moment Contributions to the Ion Hydration Free Energy by the Deep Neural Network Trained with Ab Initio Molecular Dynamics Data

We report a calculation scheme on water molecular dipole and quadrupole moments in the liquid phase through a Deep Neural Network (DNN) model. Employing the the Maximally Localized Wannier Functions (MLWF) for the valence electrons, we obtain the water moments through a post-process on trajectories from \textit{ab-initio} molecular dynamics (AIMD) simulations at the density functional theory (DFT) level. In the framework of the deep potential molecular dynamics (DPMD), we develop a scheme to train a DNN with the AIMD moments data. Applying the model, we calculate the contributions from water dipole and quadrupole moments to the electrostatic potential at the center of a cavity of radius 4.1 \AA\ as -3.87 V, referenced to the average potential in the bulk-like liquid region.

To unravel the ion-independent water effective local potential contribution to the ion hydration free energy, we estimate the 3rd cumulant term as -0.22 V from simulations totally over 6 ns, a time-scale inaccessible for AIMD calculations.