TABLE I.

Computed ΔG^L→H values (in kcal/mol) and distribution overlap scores for a blocked serine in water.^a

			ΔGb					Overlap scoresc
Low	High	Constraints	M-λ TI	1-λ FEP	LRA	BAR	Staged	ΠLH	ΠHL	Overlap (%)	KHL	KLH
C36	DFTB3	Free	−18 545.3	−18 541.2	−18 545.5	…	−18 545.4	−4.04	−4.09	0.01	0.58	0.30
				(0.6)	(0.5)		(2.9/1.2)
C36	DFTB3	Frozen	…	−18 557.1	−18 559.1	−18 559.1	…	−2.03	−1.64	0.22	0.79	0.55
				(0.6)	(0.5)	…
MULL	DFTB3	Bond	…	−18 484.5	−18 485.4	−18 485.9	…	−0.89	0.34	2.01	0.95	0.70
				(0.3)	(0.2)	…
MULL	DFTB3	Frozen	…	−18 483.6	−18 483.7	−18 483.6	…	1.66	1.42	31.67	0.92	0.82
				(0.2)	(0.2)	(0.2)
DFTB3	B3LYP	Free	…	−339 808.6	−339 809.1	−339 809.0	…	−0.17	−0.68	2.75	0.73	0.43
				(0.6)	(0.5)	…

^aC36 = CHARMM36; DFTB3 = DFTB3/3OB/MM; and in MULL, the partial charges of the solute are taken as Mulliken charges from a DFTB3 calculation and held fixed during each MULL simulation.

^bM-λ TI: 11-λ window thermodynamic integration; 1-λ FEP: single window FEP based on L sampling; LRA: linear response approximation based on sampling with both end-states (L and H) windows; BAR: Bennet-Acceptance-Ratio based on the same sampling data from LRA; and Staged: staged transformation protocol introduced here. The statistical errors are estimated based on block averaging and are less than 0.1 kcal/mol for M-λ TI. For the staged transformation, the uncertainty is estimated based on 25 different choices of X₀, ${\mathbf{X}}_0^{\prime }$ combinations (see Table III for detailed data).

^cΠ_LH,HL: Eqs. (12) and (13); K_HL,LH: Eqs. (6) and (7); and Overlap %: the fraction of ΔU data points that lie in the overlapped region.