We first present results related to the NNIP model validation. For the LR contributions, the solute-solvent ion interaction energies calculated via AIMD and NNIP-MD simulations are shown in panel a of Fig. . Averaging over 1,000 configurations drawn from NNIP-MD simulations for the systems of one solute ion and 64 solvent ion pairs, the interaction energy of the solute Na + calculated via NNIP exhibits a 1.4 kcal/mol deviation from AIMD for the uncoupled simulation and 1.3 kcal/mol deviation for the coupled case. The deviations for the solute Cl -are -0.4 kcal/mol (uncoupled) and 0.4 kcal/mol (coupled). These values are close to chemical accuracy (∼1 kcal/mol) and indicate sufficient accuracy of the NNIP model for the free energy calculations.