Corrections for the interaction energy of the solute ion (Na⁺ or Cl⁻) with solvent ion pairs (7 and 17). The correction is referenced to the MP2 calculation using the Psi4 quantum chemistry package. In parenthesis is the SEM. In the square bracket is the standard deviation σ of the sampling. The configurations are carved out from a CP2K simulation trajectory without a cavity around the solute ion. The DFT calculations are implemented via the CP2K package. The MP2 and the first two DFT calculations are for the isolated systems. The subsequent two DFT calculations are under Periodic Boundary Condition (PBC) in the simulation cell of size 16.0 Å and 25.4 Å, respectively. The row number 5 shows the dispersion correction of D2 contributions. The PBC effects on the corrections are presented in the last two rows.

	Na+ 07	Cl− 07	Na+ 17	Cl− 17
0) MP2	0.0	0.0	0.0	0.0
1) DFT	−1.9(0.5)[2.3]	−0.7(0.4)[3.5]	−3.1(0.4)[4.7]	−1.9(0.4)[3.9]
2) DFT + D2	−8.7(0.6)[2.8]	−6.5(0.5)[3.5]	−10.4(0.5)[5.3]	−7.9(0.3)[4.8]
3) DFT + D2 PBC 16.0	−15.9(0.6)[4.2]	10.8(0.5)[4.4]	−31.3(0.6)[9.6]	23.6(0.7)[7.0]
4) DFT + D2 PBC 25.4	−10.5(0.6)[2.8]	−2.5(0.4)[3.5]	−16.7(0.5)[3.4]	0.0(0.4)[3.4]
5) D2, (2)-(1)	−6.8(0.8)	−5.8(0.6)	−7.3(0.6)	−6.0(0.5)
6) PBC 16.0,(3)-(2)	−7.2(0.8)	17.3(0.7)	−20.9(0.8)	31.5(0.8)
7) PBC 25.4,(4)-(2)	−1.8(0.8)	4.0(0.6)	−6.3(0.7)	7.9(0.5)