DeePMD-kit provides LAMMPS support through a third-party package in order to produce classical MD simulations using the NNIP to compute the atomic interactions. In this way, large timescale simulations are accessible with quantum accuracy. We ran NVT simulations using the LAMMPS code for systems of each ion in the molten salt liquid. Following the calculation for the Na + ion hydration free energy, a cavity of radius 4.0 Å was included at the periodic box center. The variations in each contribution due to the change of the cavity size are discussed in detail in our previous calculations. We applied a Nos é-Hoover thermostat chain of length 3 to maintain a temperature of 1150 K. The system sizes were calculated following the above method. The NNIP-MD simulations were run for 1000 ps with the first 250 ps for equilibration and the subsequent 750 ps for data production. A time step of 0.5 fs was utilized and the configurations were recorded every 0.01 ps (every 20 steps).