The numerical results for both the Na + and Cl -ions are listed in Table , where the finite-size correction term is due to the artificial effect of the Ewald potential on the free energy. The summation of the excess free energy for both solute ions with 256 solvent ion pairs is -178.5 kcal/mol, which is converged to within the standard error of the mean (SEM) of ±1.1 kcal/mol as the system size increases to 512 ion pairs. The SEM in parentheses is calculated using the block-average method (10 blocks) over the production configurations. To the best of our knowledge, this is the first prediction of the absolute solvation free energy for ions LR coupled RDF (c) Fig. The process of excess chemical potential calculation for the systems of solute Na + and Cl -ions with 256 solvent ion pairs. Panel a and panel b are for the long-ranged (LR) contributions to the solvation free energy of the solute ions Na + and Cl -, respectively. The logarithms of the distribution of interaction energies from uncoupled (right, blue) and coupled (left, black) configurations are presented with the mean value ε and standard deviation σ . The right dashed curves and the left dash-dotted curves are the Gaussian fit to both distributions. Panel c is for the packing (PK) and minus the Inner-Shell (IS) cumulative contributions for both solute ions. Along with the expansion of the cavity with(IS)/without(PK) the solute ions at the center, the coupling parameter γ increases from 0 to 1. The IS and PK contributions are listed in Table . Panel d is the distributions of interaction energy corrections ε DFTε MP2 for the solute ion with 7 and 17 solvent ion pairs. The sampling is over 400 cluster configurations carved from DFT simulation trajectories. The DFT calculation is under Periodic Boundary Conditions (PBC) in a cell of size 25.4 Å.