Table 3.

Accuracy of the TI method for the different numbers of λ simulations for Steps 1 and 2 of the CSC protocol in water (Figure 1a).^a The energy is in the unit of kcal/mol.

	$\mathrm{\Delta }{\mathbf{\text{F}}}_{\mathbf{\text{TI}}}^{\mathbf{\text{CSC}}}$ (Step 1)					$\mathrm{\Delta }{\mathbf{\text{F}}}_{\mathbf{\text{TI}}}^{\mathbf{\text{CSC}}}$ (Step 2)
	N=2	3	6	11	19	N=2	3	6	11	19
1. K+	77.37	74.10	73.51	73.46	73.56	−1.96	−2.01	−2.12	−2.12	−2.14
2. Cl−	99.41	95.97	94.91	94.77	94.75	13.30	−7.44	−4.12	−3.18	−2.60
3. Na+	97.78	94.60	93.86	93.79	93.67	−1.08	−1.48	−1.62	−1.62	−1.66
4. Ca2+	350.47	369.48	368.72	369.25	369.17	−0.72	−1.15	−1.29	−1.32	−1.31
5. Glycine	−46.42	−48.47	−48.92	−48.99	−48.99	11.85	−5.10	−1.82	−1.16	−0.92
6. Ethanol	13.86	12.42	12.16	12.10	12.12	−8.27	−3.83	−1.66	−1.22	−1.14
7. imidazole	16.74	15.25	14.90	14.86	14.85	−6.70	−2.64	−0.57	−0.18	−0.20
8. Imidazolium−	14.56	12.80	12.49	12.51	12.55	−5.70	−1.69	0.35	0.78	0.77
9. Methylamine	−6.74	−7.87	−8.09	−8.12	−8.12	−5.53	−2.75	−1.39	−1.02	−0.87
10. Methylammonium−	45.12	42.79	42.60	42.58	42.60	−5.53	−2.69	−1.29	−0.95	−0.85
11. Acetic acid	79.69	77.88	77.62	77.37	77.40	−9.33	−4.21	−1.68	−1.15	−1.05
12. Acetate ion−	151.13	148.02	146.84	146.72	146.49	−8.86	−4.03	−1.70	−1.23	−0.99
13. Phospho-tyrosine2−	244.52	237.72	233.78	232.90	231.83	72.26	−37.88	−22.30	18.60	−17.53
MSD b	1.97	0.99	0.19	0.10		−9.28	−3.57	−0.82	−0.19
MUD b	4.85	0.99	0.28	0.13		9.48	3.64	0.84	0.20

^aThe λ values in the N=2, 3, 6 and 11-point λ simulation results are: for N=2, λ=0 and 1; for N=3, λ=0, 0.5 and 1; for N=6, λ=0, 0.2, 0.4, 0.6, 0.8 and 1; and for N=11, λ=0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1, respectively.

^bMSD and MUD are relative to the N=19 simulation results of each step.