Table 3.

Free energy of water (in kcal∕mol) calculated with thermodynamic integration (TI) for the open and closed loops.^a

	$F_{\mathrm{water}}^{\mathrm{TI}}$(ch)			$F_{\mathrm{water}}^{\mathrm{TI}}$(LJ)		$F_{\mathrm{water}}^{\mathrm{TI}}$
Window (ps)	Open	Closed	δ (Å2)	Open	Closed	Open	Closed	ΔFwater
20	–54.4	–117.2	0.5	∞	∞	∞	∞	–
			2.0	45.2	32.6	–9.2	–84.6	75.4
			3.0	41.6	30.1	–12.8	–87.1	74.3
40	−53.4	−116.2	2.0	46.5	34.9	−6.9	−81.3	74.4
Errors	±1.0	±0.8		±0.6	±0.4	±1.0	±0.9	±1.3

^a$F_{\mathrm{water}}^{\mathrm{TI}}$(ch) and $F_{\mathrm{water}}^{\mathrm{TI}}$(LJ) were obtained by eliminating the loop-water electrostatic (charge) and Lennard Jones (LJ) interactions, respectively; $F_{\mathrm{water}}^{\mathrm{TI}}$ is their sum [Eq. 17]. Each integration is based on 22 windows, where the (best) results for windows of 40 ps are bold-faced. δ defines the soft-core LJ potentials [Eq. 21]. ΔF_water [Eq. 18] is the difference in the water free energy between the open and closed configurations. “Errors” stand for statistical errors [(standard deviation)∕40^1∕2].