Table 2.

The properties of alkali cations, halide anions and divalent cations with Drude polarizable models.

Ion	Umina	dminb	ΔHc	rmax	gmax	rmin	gmin	Nc	Dd	ΔGe	ΔΔGf
Li+	−35.9 (−35.2)	1.91 (1.87)	−35.6 (−34.0,−34.0)	2.02	12.50	2.56	0.00	4.0	1.30 (1.03)	−120.5	−24.2 (−23.8~-26.2)
Na+	−24.6 (−24.3)	2.25 (2.26)	−24.4 (−24.0,−25.0)	2.38	7.42	3.24	0.20	5.6	1.58 (1.33)	−96.3	−17.3 (−16.7~−17.7)
K+	−17.9 (−17.8)	2.62 (2.64)	−17.6 (−17.9,−18.1)	2.74	4.80	3.56	0.45	6.9	2.20 (1.98)	−78.6	−5.2 (−4.9~−5.4)
Rb+	−15.7 (−16.1)	2.79 (2.79)	−15.2 (−15.9,−16.0)	2.90	4.04	3.80	0.62	8.1	2.44 (2.07)	−73.7	−7.1 (−5.5~−7.7)
Cs+	−13.3 (−14.1)	3.05 (2.99)	−12.5 (−13.7, —)	3.16	3.25	4.10	0.75	9.7	2.56 (2.06)	−66.5
F−	−23.5 (−25.9)	2.53 (2.44)	−23.2 (−23.3,−23.3)	2.72	4.77	3.34	0.37	5.5	1.33 (1.48)	−108.0	−30.0 (−13.4~−30.6)
Cl−	−14.0 (−14.4)	3.09 (3.11)	−13.7 (−13.1,−14.4)	3.16	3.15	3.78	0.72	6.5	1.82 (2.03)	−78.4	−6.5 (−3.3~−6.9)
Br−	−12.4 (−12.7)	3.26 (3.26)	−11.9 (−12.6,−13.0)	3.28	2.70	3.96	0.75	6.8	1.85 (2.08)	−71.6	−8.5 (−7.7~−11.1)
I−	−10.2 (−10.6)	3.56 (3.50)	−9.7 (−10.2,−10.5)	3.50	2.28	4.16	7.13	7.1	2.02 (2.05)	−63.1
Zn2+	−100.0 (−96.3)	1.82 (1.86)	−99.4 (−103.1)	2.14	17.2	3.08	0.0	6.0	0.61 (0.70)	−460.2	−90.3 (−107.6)
Mg2+	−89.4 (−77.9)	1.86 (1.93)	−89.0 (−81.8)	2.06	19.0	2.72	0.0	6.0	0.82 (0.71)	−447.2	−77.3 (−77.7~−80.3)
Ca2+	−55.6 (−54.9)	2.18 (2.25)	−55.1 (−56.5)	2.28	16.9	2.76	0.0	6.0	0.96 (0.79)	−369.9	−32.7 (−29.8~32.9)
Sr2+	−45.2 (−40.6)	2.30 (2.52)	−44.7 (−)	2.42	11.9	3.20	0.0	7.2	0.96 (0.79)	−337.2	−27.2 (−27.9~31.1)
Ba2+	−37.7 (−34.0)	2.56 (2.73)	−37.3 (−)	2.68	10.4	3.30	0.1	8.2	0.97 (0.85)	−310.0

^aThe reference binding energy in parentheses U_min of monovalent monohydrates are taken from various sources: ²⁹ Li⁺; ⁷³ Na⁺; ⁷⁴ K⁺; ⁷⁵ Rb⁺; ⁷⁴ Cs⁺; ⁷⁴ F⁻; ⁷⁶ Cl⁻; ⁷⁶ Br⁻; ⁷⁶ I⁻; ⁷⁶ The reference values for divalent were obtained with MP2 calculations with basis set 6-311++G(3df,3pd) for hydrogen, oxygen, Mg²⁺, Ca²⁺, and Zn²⁺ and LANL2DZ pseudopotential and associated basis set for Sr²⁺ and Zn²⁺. The energies are in kcal/mol.

^bThe reference distance in parentheses R_min of the alkali cations are taken from various sources ²⁹ while those of the halide anions are taken from. ⁷⁶ The reference values for divalent cations were obtained from MP2 calculations (See a for details). The distances are in Å.

^cThe reference enthalpies in parentheses ΔH for the monovalent monohydrates are taken from the experimental studies. ⁷¹,⁷² The reference enthalpies in parentheses ΔH for the divalent monohydrates are taken from the theoretical study. ⁸⁷ The enthalpies are in kcal/mol.

^dThe experimental self diffusion coefficients are taken from the Handbook of Chemistry and Physics. ⁹⁵ The self diffusion coefficients are in 10⁻⁵cm²/s.

^eThe real hydration free energies ΔG^real in kcal/mol are obtained from the intrinsic free energies from periodic boundary conditions (PBC) simulations corrected with the phase potential and entropy related contributions.

^fThe experimental hydration free energy differences in kcal/mol for the monovalent ions are taken from, ⁷²,⁷⁸-⁸³ while those for the divalent ions are taken from. ⁸⁰,⁸²,⁸³ The entry for Zn²⁺ is defined as $\Delta G_{\mathrm{hydr}}^{\mathrm{real}}\left({\mathrm{Zn}}^{2+}\right)-\Delta G_{\mathrm{hydr}}^{\mathrm{real}}\left({\mathrm{Ca}}^{2+}\right)$.