Table 2:

Ion-water binding energies (ΔE in kcal/mol) and optimum distances (d in Å) prior to (Orig¹¹) and after recalibration (vdW*) of vdW parameters against PBE0+TS. The ionwater binding energy is defined as ΔE = E_Cluster − E_Ion − nE_W, where E_Cluster, E_Ion and E_W are the energies of the cluster, ion and water following independent energy optimizations, and n is the number of water molecules in the cluster. d is the distance between the ion and the oxygen atom of water. MAE is an abbreviation for Mean Absolute Error.

Ion	# waters	PBE0+TS		Orig		vdW*
		ΔE	d	ΔE	d	ΔE	d
Na+	1	−24.7	2.23	−23.2	2.23	−25.0	2.17
	2	−47.2	2.25	−43.8	2.26	−47.2	2.20
	3	−66.1	2.27	−61.2	2.30	−65.6	2.24
	4	−81.9	2.30	−75.3	2.34	−80.6	2.28
K+	1	−18.4	2.63	−17.3	2.60	−18.0	2.57
	2	−34.8	2.67	−32.7	2.64	−34.6	2.58
	3	−49.4	2.70	−46.4	2.67	−49.1	2.60
	4	−62.1	2.72	−58.2	2.70	−61.7	2.63
MAE				6.7%	0.9%	0.7%	2.5%