TABLE III.

Ion–water binding energies (ΔE in kcal/mol) and optimum distances (d in Å) prior to (Orig^16,41 and Orig^*42,43) and after recalibration (Pol^*) of ion descriptors against PBE0+vdW. The ion–water binding energy is defined using Eq. (5), and d is the distance between the ion and the oxygen atom of water. MAE is an abbreviation for mean absolute error.

		PBE0+vdW		Orig		Orig*		Pol*
Ion	No. of waters	ΔE	d	ΔE	d	ΔE	d	ΔE	d
Li+	1	−36.0	1.82	−33.2	1.82			−36.9	1.72
	2	−66.9	1.85	−61.1	1.88			−66.9	1.78
	3	−90.6	1.89	−81.9	1.94			−88.3	1.86
	4	−107.7	1.95	−97.7	2.01			−104.1	1.93
	5	−116.6	2.06	−107.2	2.07			−112.5	1.99
	6	−125.7	2.13	−117.8	2.15			−122.6	2.10
Mg2+	1	−83.6	1.91	−78.0	1.88	−83.3		−83.6	1.84
	2	−157.1	1.93	−146.4	1.91	−155.0		−157.1	1.87
	3	−216.2	1.96	−201.2	1.96	−211.1		−215.7	1.91
	4	−263.7	1.99	−245.5	2.00	−255.7		−263.0	1.95
	5	−295.8	2.05	−276.1	2.04	−285.1		−294.8	1.99
	6	−325.5	2.09	−304.4	2.11	−312.8		−324.4	2.05
			MAE	10.0	0.02	6.5		1.4	0.05