Table 4.

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

	$\mathrm{\Delta }{\mathbf{\text{F}}}_{\mathbf{\text{TI}}}^{\mathbf{\text{GSC}}}$ (Step 1)					$\mathrm{\Delta }{\mathbf{\text{F}}}_{\mathbf{\text{TI}}}^{\mathbf{\text{GSC}}}$ (Step 2)
	N=2 a	3	6	11	19	N=2	3	6	11	19
1. K+	74.07	74.08	74.58	74.90	75.21	−6.05	−4.40	−3.93	−3.89	−3.87
2. Cl−	97.15	97.17	97.31	97.48	97.65	−9.76	−6.69	−5.84	−5.74	−5.70
3. Na+	91.72	93.18	93.98	94.38	94.78	−4.03	−2.99	−2.69	−2.65	−2.65
4. Ca2+	339.04	368.20	369.80	370.06	370.43	−4.06	−3.05	−2.73	−2.68	−2.66
5. Glycine	−38.54	−39.49	−39.39	−39.38	−39.36	−42.00	−23.35	−13.25	−11.04	−10.91
6. Ethanol	22.14	21.03	20.82	20.80	20.80	−39.87	−22.03	−12.40	−10.20	−10.06
7. imidazole	25.59	24.48	24.21	24.19	24.20	−41.12	−22.32	−12.25	−9.94	−9.71
8. Imidazolium−	23.16	21.91	21.82	21.80	21.94	−36.69	−19.80	−10.70	−8.66	−8.54
9. Methylamine	−1.19	−1.87	−1.94	−1.98	−1.99	−25.85	−14.36	−8.40	−7.26	−7.13
10. Methylammonium−	49.79	48.81	48.84	48.87	48.80	−26.68	−14.79	−8.60	−7.36	−7.31
11. Acetic acid	87.56	86.21	86.56	86.46	86.43	−37.72	−20.86	−11.83	−9.94	−9.85
12. Acetate ion−	157.69	156.28	155.51	155.32	155.27	−36.37	−20.26	−11.75	−9.89	−9.79
13. Phospho-tyrosine2−	254.84	252.81	250.51	249.75	249.69	−97.92	−61.15	−41.10	−35.73	−35.17
MSD b	−1.60	−0.08	−0.10	−0.09		−21.91	−8.67	−1.70	−0.13
MUD b	3.95	0.81	0.30	0.13		21.91	8.67	1.70	0.13

^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.