Ab initio structure determination of the hygroscopic anhydrous form of α-lactose by powder X-ray diffraction

Annealing of α-lactose monohydrate at 408 K yielded a mixture of this compound with hygroscopic anhydrous α-lactose. A powder X-ray diffraction pattern of this mixture was recorded at room temperature. The starting structural model of hygroscopic α-lactose was found by a Monte Carlo simulated-annealing method. The final structure was obtained through Rietveld refinements, with soft restraints on inter­atomic bond lengths and bond angles, and crystalline energy minimization to locate the H atoms of the hydroxy groups. The crystalline cohesion is achieved by networks of O—H...O hydrogen bonds that differ from those of the monohydrate phase. The width of the Bragg peaks is interpreted by a phenomenological microstructural approach in terms of isotropic size effects and anisotropic strain effects.

S1. Experimental

Commercially available alpha-L—H2O was used for this experiment (SIGMA Company). In order to obtain the alpha-LH phase, the following procedure was used: powder of alpha-L—H2O contained in a crystallizer was annealed in an oven during 30 minutes at a given temperature T. To avoid possible rehydration, the powder was introduced in a Lindemann glass capillary then sealed rapidly for X-ray powder diffraction experiment. Attempts were done at different temperatures. For temperatures lower than 120 °C, only peaks of the alpha-L—H2O phase are present in the patterns. From 125 to 135 °C, in addition to the peaks of the alpha-L—H2O phase, new peaks appear which correspond to the ?LH phase according to Buma & Wiegers (1967). At 140 °C, the alpha-L—H2O disappears, and with the peaks of the ?LH form, there are new peaks of diffraction characterizing the alpha-LS phase (Van Kreveld, 1969). The part of the powder not used for the X-ray experiment was kept at the air contact. After a week, this powder was analysed by X-ray diffraction and only the alpha-L—H2O phase was found. This experiment confirms that the supplementary peaks correspond to the unstable hygroscopic alpha-LH phase.

Computing details

Data collection: PEAKOC; program(s) used to solve structure: FOX; program(s) used to refine structure: FULLPROF; molecular graphics: ORTEP-3; software used to prepare material for publication: SHELX97 and PARST.

Figures

	Fig. 1. : Final Rietveld plot of the hygroscopic phase of alpha-lactose. Observed data points are indicated by dots, the best-fit profile (upper trace) and the difference pattern (lower trace) are solid lines. The vertical bars correspond to the position of Bragg peaks: upper bars for alpha-LH, lower bars for alpha-L—H2O.
	Fig. 2. : Atomic numbering and molecular structure of the hygroscopic phase of alpha-lactose. The dashed bond represents the internal H bond of the molecule of lactose.
	Fig. 3. : Projection of the unit cell of the hygroscopic alpha-lactose along c*. Blue lines correspond to H bonds.
	Fig. 4. : Projection of the unit cell of the hygroscopic alpha-lactose along the twofold screw axis. Only molecules around y = 0 are drawn. Blue lines correspond to H bonds.
	Fig. 5. : Strain values on the alpha-LH phase for different directions of the lattice (black curves): a) in the monoclinic plane, b), c) and d) correspond to planes form by the twofold axis and a direction of an extreme value of the strain in the monoclinic plane (phi is the angle between the lattice parameter a and this direction): b) phi = 21.5 degrees, c) phi = 81 degrees and d) phi =142 degrees. The red curves correspond to the strain values for the commercial alphaL-H2O.

4-O-beta-D-galactopyranosyl-D-glucopyranose

Crystal data

C12H22O11	Z = 2
Mr = 342.30	F(000) = 364
Monoclinic, P21	Dx = 1.557 Mg m^−3
Hall symbol: P 2yb	Cu Kα radiation, λ = 1.540560 Å
a = 7.7795 (2) Å	µ = 1.22 mm^−1
b = 19.6931 (6) Å	T = 293 K
c = 4.90643 (11) Å	white
β = 103.6909 (15)°	cylinder, diameter 0.7 mm, ? × ? × ? mm
V = 730.32 (3) Å^3	Specimen preparation: Prepared at 293 K

Data collection

Enraf Nonius FR 590 diffractometer	Data collection mode: transmission
Radiation source: sealed X-ray tube	Scan method: Stationary detector
Quartz (curved monochromator)	Absorption correction: for a cylinder mounted on the ϕ axis ?
Specimen mounting: Lindemann glass capillary	Tmin = ?, Tmax = ?

Refinement

Rp = 2.161	Profile function: pseudo-Voigt
Rwp = 3.090	136 parameters
Rexp = 2.218	59 restraints
RBragg = 1.632
χ^2 = NOT FOUND	Background function: linear interpolation between 32 points
3946 data points	Preferred orientation correction: March-Dollase function, axis [0, 0, 1], G1 = 1.089 (4), G2 = 0
Excluded region(s): 0.291 to 8.50 : no Bragg peaks 80.00 to 114.696 : peak intensities too low

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
C1	0.3236 (10)	0.0424 (5)	0.763 (3)	0.036 (2)
C2	0.4658 (11)	0.0969 (5)	0.832 (2)	0.036 (2)
C3	0.3978 (11)	0.1444 (5)	1.025 (3)	0.036 (2)
C4	0.2173 (12)	0.1728 (5)	0.8801 (8)	0.036 (2)
C5	0.0932 (12)	0.1124 (5)	0.788 (2)	0.036 (2)
C6	−0.0800 (16)	0.1293 (7)	0.586 (4)	0.036 (2)
O1	0.4001 (16)	0.0000 (1)	0.587 (3)	0.036 (2)
O2	0.6248 (14)	0.0728 (8)	1.001 (3)	0.036 (2)
O3	0.5085 (17)	0.1997 (7)	1.140 (3)	0.036 (2)
O4	0.2244 (17)	0.2102 (8)	0.637 (2)	0.036 (2)
O5	0.1545 (13)	0.0670 (6)	0.608 (2)	0.036 (2)
O6	−0.1938 (16)	0.0721 (6)	0.559 (3)	0.036 (2)
H1	0.31410	0.01770	0.93790	0.036 (2)
H2	0.48290	0.12090	0.65910	0.036 (2)
H3	0.38150	0.11670	1.18700	0.036 (2)
H4	0.17100	0.20200	1.01520	0.036 (2)
H5	0.07080	0.08780	0.95510	0.036 (2)
H6a	−0.05790	0.14100	0.39680	0.036 (2)
H6b	−0.13570	0.16960	0.65020	0.036 (2)
HO2	0.70716	0.06547	0.87332	0.036 (2)
HO3	0.44706	0.22435	1.26435	0.036 (2)
HO4	0.17383	0.25529	0.66923	0.036 (2)
HO6	−0.27839	0.07416	0.37047	0.036 (2)
C1'	0.3291 (11)	−0.2011 (8)	0.3302 (17)	0.036 (2)
C2'	0.1633 (10)	−0.1684 (4)	0.387 (3)	0.036 (2)
C3'	0.1863 (10)	−0.0912 (4)	0.396 (3)	0.036 (2)
C4'	0.3554 (11)	−0.0699 (4)	0.612 (3)	0.036 (2)
C5'	0.5109 (10)	−0.1105 (5)	0.552 (3)	0.036 (2)
C6'	0.6885 (12)	−0.0982 (9)	0.756 (4)	0.036 (2)
O1'	0.3408 (16)	−0.1899 (8)	0.050 (2)	0.036 (2)
O2'	−0.0033 (11)	−0.1877 (7)	0.215 (3)	0.036 (2)
O3'	0.0365 (15)	−0.0597 (7)	0.461 (3)	0.036 (2)
O5'	0.4887 (13)	−0.1833 (4)	0.532 (2)	0.036 (2)
O6'	0.8254 (14)	−0.1380 (6)	0.686 (3)	0.036 (2)
H1'	0.31490	−0.25170	0.35080	0.036 (2)
H2'	0.16010	−0.18170	0.58160	0.036 (2)
H3'	0.19430	−0.07520	0.20350	0.036 (2)
H4'	0.34210	−0.07960	0.80310	0.036 (2)
H5'	0.52450	−0.09570	0.36230	0.036 (2)
H6a'	0.68200	−0.10700	0.94920	0.036 (2)
H6b'	0.72260	−0.04850	0.74470	0.036 (2)
HO1'	0.42774	−0.22535	0.02573	0.036 (2)
HO2'	0.00150	−0.16709	0.01879	0.036 (2)
HO3'	0.04068	−0.00981	0.42441	0.036 (2)
HO6'	0.86442	−0.11406	0.52733	0.036 (2)

Geometric parameters (Å, º)

C1—O1	1.427 (16)	O6—HO6	1.002
C1—O5	1.439 (13)	C1'—O1'	1.418 (14)
C1—C2	1.522 (12)	C1'—O5'	1.435 (12)
C1—H1	1.003	C1'—C2'	1.527 (14)
C2—O2	1.400 (14)	C1'—H1'	1.010
C2—C3	1.513 (14)	C2'—O2'	1.421 (13)
C2—H2	1.006	C2'—C3'	1.529 (12)
C3—O3	1.419 (15)	C2'—H2'	0.994
C3—C4	1.522 (12)	C3'—O3'	1.421 (17)
C3—H3	0.997	C3'—C4'	1.539 (13)
C4—O4	1.412 (15)	C3'—H3'	1.014
C4—C5	1.531 (11)	C4'—C5'	1.537 (14)
C4—H4	1.006	C4'—H4'	0.985
C5—O5	1.417 (13)	C5'—O5'	1.445 (12)
C5—C6	1.509 (15)	C5'—C6'	1.522 (14)
C5—H5	1.002	C5'—H5'	1.002
C6—O6	1.420 (17)	C6'—O6'	1.427 (19)
C6—H6A	1.009	C6'—H6A'	0.978
C6—H6B	0.991	C6'—H6B'	1.019
O1—C4'	1.432 (9)	O1'—HO1'	0.999
O2—HO2	1.009	O2'—HO2'	1.054
O3—HO3	0.989	O3'—HO3'	1.000
O4—HO4	0.998	O6'—HO6'	1.016
O1—C1—O5	109.7 (7)	O1'—C1'—O5'	112.8 (8)
O1—C1—C2	99.3 (7)	O1'—C1'—C2'	111.3 (9)
O5—C1—C2	113.8 (8)	O5'—C1'—C2'	113.7 (8)
O1—C1—H1	111.0	O1'—C1'—H1'	106.5
O5—C1—H1	111.9	O5'—C1'—H1'	105.6
C2—C1—H1	110.5	C2'—C1'—H1'	106.3
O2—C2—C3	103.2 (8)	O2'—C2'—C1'	118.0 (8)
O2—C2—C1	112.7 (9)	O2'—C2'—C3'	111.5 (9)
C3—C2—C1	103.4 (8)	C1'—C2'—C3'	109.1 (8)
O2—C2—H2	112.6	O2'—C2'—H2'	105.8
C3—C2—H2	111.9	C1'—C2'—H2'	106.1
C1—C2—H2	112.3	C3'—C2'—H2'	105.3
O3—C3—C2	116.9 (7)	O3'—C3'—C2'	110.1 (8)
O3—C3—C4	108.0 (9)	O3'—C3'—C4'	109.9 (8)
C2—C3—C4	110.8 (7)	C2'—C3'—C4'	111.5 (7)
O3—C3—H3	106.4	O3'—C3'—H3'	107.9
C2—C3—H3	106.9	C2'—C3'—H3'	108.3
C4—C3—H3	107.2	C4'—C3'—H3'	109.0
O4—C4—C3	111.7 (6)	O1—C4'—C5'	105.4 (6)
O4—C4—C5	107.7 (8)	O1—C4'—C3'	112.9 (7)
C3—C4—C5	107.4 (5)	C5'—C4'—C3'	108.0 (7)
O4—C4—H4	110.5	O1—C4'—H4'	110.5
C3—C4—H4	109.7	C5'—C4'—H4'	110.3
C5—C4—H4	109.8	C3'—C4'—H4'	109.7
O5—C5—C6	96.2 (7)	O5'—C5'—C6'	106.1 (10)
O5—C5—C4	113.1 (5)	O5'—C5'—C4'	116.3 (8)
C6—C5—C4	115.2 (6)	C6'—C5'—C4'	115.1 (8)
O5—C5—H5	110.7	O5'—C5'—H5'	105.3
C6—C5—H5	110.1	C6'—C5'—H5'	106.5
C4—C5—H5	110.8	C4'—C5'—H5'	106.8
O6—C6—C5	109.0 (10)	O6'—C6'—C5'	111.6 (9)
O6—C6—H6A	109.6	O6'—C6'—H6A'	110.4
C5—C6—H6A	109.6	C5'—C6'—H6A'	111.2
O6—C6—H6B	110.7	O6'—C6'—H6B'	107.3
C5—C6—H6B	110.8	C5'—C6'—H6B'	109.0
H6A—C6—H6B	107.0	H6A'—C6'—H6B'	107.2
C1—O1—C4'	111.5 (5)	C1'—O1'—HO1'	101.9
C2—O2—HO2	106.3	C2'—O2'—HO2'	102.5
C3—O3—HO3	106.6	C3'—O3'—HO3'	109.0
C4—O4—HO4	103.7	C1'—O5'—C5'	111.0 (9)
C5—O5—C1	106.5 (8)	C6'—O6'—HO6'	107.7
C6—O6—HO6	108.1
O1—C1—C2—O2	−68.2 (11)	O1'—C1'—C2'—O2'	57.1 (14)
O5—C1—C2—O2	175.2 (10)	O5'—C1'—C2'—O2'	−174.3 (10)
O1—C1—C2—C3	−178.9 (8)	O1'—C1'—C2'—C3'	−71.5 (12)
O5—C1—C2—C3	64.5 (11)	O5'—C1'—C2'—C3'	57.1 (12)
O2—C2—C3—O3	59.0 (9)	O2'—C2'—C3'—O3'	50.3 (13)
C1—C2—C3—O3	176.6 (9)	C1'—C2'—C3'—O3'	−177.6 (10)
O2—C2—C3—C4	−176.6 (8)	O2'—C2'—C3'—C4'	172.6 (9)
C1—C2—C3—C4	−59.0 (12)	C1'—C2'—C3'—C4'	−55.3 (11)
O3—C3—C4—O4	68.7 (11)	C1—O1—C4'—C5'	−150.9 (9)
C2—C3—C4—O4	−60.6 (10)	C1—O1—C4'—C3'	91.5 (11)
O3—C3—C4—C5	−173.4 (8)	O3'—C3'—C4'—O1	−69.4 (12)
C2—C3—C4—C5	57.3 (8)	C2'—C3'—C4'—O1	168.2 (9)
O4—C4—C5—O5	62.7 (10)	O3'—C3'—C4'—C5'	174.5 (10)
C3—C4—C5—O5	−57.8 (9)	C2'—C3'—C4'—C5'	52.1 (11)
O4—C4—C5—C6	−46.6 (11)	O1—C4'—C5'—O5'	−173.1 (9)
C3—C4—C5—C6	−167.1 (8)	C3'—C4'—C5'—O5'	−52.2 (12)
O5—C5—C6—O6	71.5 (12)	O1—C4'—C5'—C6'	61.9 (12)
C4—C5—C6—O6	−169.4 (9)	C3'—C4'—C5'—C6'	−177.2 (10)
O5—C1—O1—C4'	−92.3 (11)	O5'—C5'—C6'—O6'	49.6 (14)
C2—C1—O1—C4'	148.1 (9)	C4'—C5'—C6'—O6'	179.6 (11)
C6—C5—O5—C1	−179.0 (10)	O1'—C1'—O5'—C5'	72.2 (12)
C4—C5—O5—C1	60.2 (10)	C2'—C1'—O5'—C5'	−55.6 (12)
O1—C1—O5—C5	−175.7 (8)	C6'—C5'—O5'—C1'	−176.5 (10)
C2—C1—O5—C5	−65.5 (11)	C4'—C5'—O5'—C1'	54.1 (12)

Hydrogen-bond geometry (Å, º)

D—H···A	D—H	H···A	D···A	D—H···A
O2—HO2···O6^i	1.009 (19)	1.88 (2)	2.85 (2)	160.8 (13)
O3—HO3···O5′^ii	0.99 (2)	2.078 (16)	2.809 (16)	129.2 (13)
O4—HO4···O2′^iii	1.00 (2)	1.924 (19)	2.849 (19)	152.8 (15)
O6—HO6···O2^iv	1.002 (17)	1.789 (18)	2.767 (18)	164.2 (15)
O1′—HO1′···O3^v	1.00 (2)	1.81 (2)	2.74 (2)	152.7 (15)
O2′—HO2′···O6′^iv	1.054 (19)	1.953 (16)	2.800 (18)	135.0 (13)
O3′—HO3′···O5	1.00 (2)	1.873 (17)	2.697 (18)	137.6 (15)
O6′—HO6′···O3′^i	1.02 (2)	1.805 (17)	2.674 (19)	141.5 (15)

Symmetry codes: (i) x+1, y, z; (ii) −x+1, y+1/2, −z+2; (iii) −x, y+1/2, −z+1; (iv) x−1, y, z−1; (v) −x+1, y−1/2, −z+1.