TABLE 2.

Results in kcal/mol for energy and free energy components and their difference (Δ) between the free and bound microstates for R_tmpl=12 and R_water=13Å^#

	Eloop-temp	Eloop -loop	$F_{\text{water}}^{\text{TI}}(\text{ch})$	$F_{\text{water}}^{\text{TI}}(\text{LJ})$	Eloop	$F_{\text{water}}^{\text{TI}}$	Fsum	Etotal
Nwater= 80 ρwater= 0.0170 ns=40
Free	−52	−46	−67	27	−98	−40	−138	−1207
Bound	−128	−10	−48	17	−138	−31	−169	−1246
Δ1	76 (1)	−36 (1)	−19 (1)	10 (1)	40 (1)	−9 (1)	31(1)	39 (1)
Nwater =100 ρwater= 0.0217 ns=40
Free	−50	−45	−71	37	−95	−34	−129	−1389
Bound	−128	−10	−48	27	−138	−21	−159	−1435
Δ1	78 (1)	−35 (1)	−23 (1)	10 (1)	43 (1)	−13 (1)	30 (1)	46 (3)
Nwater =120 ρwater= 0.0261 ns=40
Free	−102	−25	−63	57	−127	−6	−133	−1646
Bound	−128	−10	−50	41	−138	−9	−147	−1653
Δ2	26 (1)	−15 (1)	−13 (2)	16 (1)	11 (2)	3 (3)	14 (2)	7 (1)
Nwater =140 ρwater= 0.0304 ns=80
Free	−75	−34	−76	99	−109	23	−86	−1788
Bound	−118	−5	−50	95	−123	45	−78	−1791
Δ3	43 (1)	−29 (1)	−26 (1)	4 (1)	14 (1)	−22 (1)	−8 (2)	3 (3)
Nwater =160 ρwater= 0.0348 ns=80 double integration
Free	−77	−10	−81	123	−87	42	−45	−1981
Bound	−121	−1	−53	131	−122	78	−44	−1962
Δ3	44 (1)	−9 (2)	−28 (1)	−8 (1)	35 (1)	−36 (2)	−1 (2)	−19 (5)
Nwater =180 ρwater= 0.0391 ns=80 double integration
Free	−71	−37	−84	148	−108	64	−44	−2155
Bound	−119	1	−48	127	−118	79	−39	−2160
Δ3	48 (1)	−38 (1)	−36 (1)	21 (4)	10 (1)	−15 (4)	−5 (4)	5 (2)

^#The energies, E_loop-tmpl, E_loop-loop , their sum, E_loop, and the total energy, E_total are defined in eq 1.$F_{\text{water}}^{\text{TI}}(\text{ch})\text{and}{F}_{\text{water}}^{\text{TI}}(\text{LJ})$ are free energies calculated by thermodynamic integration, where the charges and Lennard-Jones interactions, respectively, are gradually eliminated; they and their sum, $F_{\text{water}}^{\text{TI}}$ are defined in eq 21. $F_{\text{sum}}=E_{\text{loop}}+F_{\text{water}}^{\text{TI}}$ is the total free energy (without the contribution of the loop entropy, S_loop). Δ is the difference, free – bound. N_water is the number of capped water molecules. P_water=N_water/[2π(R_water)³/3] is the density of water (in Å⁻³ units) in the hemisphere defined by the radius, R_water. n_s is the sample size. Statistical errors, s/(n_s)^1/2, where s is the standard deviation, are smaller than 2.5 and 1.5 kcal/mol for E_total and the other quantities, respectively. The errors in Δ appear in parenthesis, e.g., −46 (2) =−46±2; thus, the 2 kcal/mol in this example is the difference between the value which appears in the table and the value obtained for a smaller sample size, n_s: ¹for n_s=20; ²for n_s=17; ³for n_s=40. Double integration means that the MD simulation at each TI step is doubled - it is 40 ps for each λ_i step.