TABLE 2.

Boltzmann-averaged (“mean”) conformational descriptors for free α-, β-, and γ-CD, together with literature data for crystals (Immel, 1995), with computed RMS deviations in parentheses

	Torsions			Distances			Circularity (distortion parameter)
	Φ	Ψ	Taper τ	Diagonal O1–O1′	Adjacent 2° OH–OH	Adjacent 1° OH–OH
α-cyclodextrin
Crystal	107.4	130.7	102.1	8.51	3.05	4.45	0.88
Aqueous mean (RMSD)	94.2 (6.7)	127.3 (18.2)	109.5 (12.2)	8.46 (1.12)	3.35 (0.62)	4.44 (0.19)	0.852 (0.017)
β-cyclodextrin
Crystal	110.5	127.0	100.0	9.81	2.92	4.59	0.93
Aqueous mean (RMSD)	108.3 (1.3)	116.4 (4.5)	102.6 (2.4)	9.77 (0.08)	2.89 (0.03)	4.47 (0.06)	0.980 (0.003)
γ-cyclodextrin
Crystal	110.1	129.4	104.4	11.76	2.84	4.39	0.98
Aqueous mean (RMSD)	111.6 (1.8)	125.4 (1.5)	101.5 (1.3)	11.55 (0.01)	2.82 (0.00)	4.57 (0.04)	0.996 (0.003)

See Figs. 1 and 3 and the “Structural analysis of cyclodextrins” section for definitions of the geometric parameters listed here.