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In the monoclinic δ polymorph of D-mannitol, C6H14O6, both the mol­ecule and the packing have approximate twofold rotational symmetry. The P21 structure thus approximates space group C2221, and the α′ polymorph, previously reported in that space group, is almost certainly identical to the δ polymorph. However, torsion angles along the main backbone of the mol­ecule deviate from twofold symmetry by as much as 7.4 (3)° and the hydrogen-bonding pattern does not conform to the higher symmetry. The α polymorph reported here is identical to the previously reported κ polymorph, and the low-temperature structure of the β polymorph agrees well with previously reported room-temperature determinations. The range of C—O bond lengths over the three polymorphs is 1.428 (2)–1.437 (4) Å, and the range of C—C distances is 1.515 (4)–1.5406 (19) Å. The δ polymorph has the highest density of the three, both at room temperature and at 100 K.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S0108270103018961/jz1573sup1.cif
Contains datablocks global, Alpha, Beta, Delta

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270103018961/jz1573Alphasup2.hkl
Contains datablock Alpha

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270103018961/jz1573Betasup3.hkl
Contains datablock Beta

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S0108270103018961/jz1573Deltasup4.hkl
Contains datablock Delta

CCDC references: 224658; 224659; 224660

Comment top

The acyclic sugar alcohol D-mannitol, (I), is a natural product produced by various plants, algae and fungi, and is one of the classic examples of a compound which crystallizes in several polymorphs, often simultaneously (Bernstein, 2002; Berman et al., 1968). This polymorphism was first reported at least 115 years ago (Zepharovich, 1888). Understanding of the various forms is of importance to the pharmaceutical industry, because mannitol is used as an excipient in the formulation of tablets and granulated powders (Burger et al., 2000), and the polymorphs differ somewhat in their physical properties. \sch

Approximately eight polymorphs of D-mannitol have been claimed over the years, leading to much confusion in the literature. Burger et al. (2000) have summarized and correlated the various claims, and have concluded that only three, α, β, and δ, are proven to exist. Walter-Levy (1968) has reported the cell dimensions of the three, which are also designated modifications II, I, and III, respectively, by some authors. Two of the polymorphs have previously been fully characterized by crystal structure determinations at room temperature. A full structure determination of the thermodynamically most stable polymorph, β (modification I), was reported in space group P212121 by Berman et al. (1968), and was further refined by Kaminsky & Glazer (1997), including determination of the absolute configuration. Kim et al. (1968) reported the structure of a form which they designated κ, also in P212121. Its cell dimensions correspond to those of the polymorph historically designated as α (Groth, 1910; Rye & Sörum, 1952), or modification II.

Walter-Levy (1968) reported the cell dimensions and space group of a monoclinic P21 form, designated the δ form or modification III. Walter-Levy & Strauss (1972) also reported the X-ray powder diffraction pattern of the δ form. Burger et al. (2000) have studied the thermodynamic properties and compression behavior of the mannitol polymorphs. They have concluded that, although the δ polymorph is not the thermodynamically stable form, it has considerable kinetic stability and exhibits the best consolidation behavior for pharmaceutial use. The structure of the important δ form has not been reported to date, probably because high-quality single crystals are difficult to prepare. Berman et al. (1968) also reported an `α' form', and determined its structure in projection from film data in C2221. However, they report that `The crystals of the α' form were small and bladelike, and gave very elongated spots.' Based upon 13C NMR data and X-ray powder patterns, Grindley et al. (1990) concluded that the α' form and the δ form are identical. We have isolated D-mannitol from the brown alga Dictyota dichotoma by accelerated solvent extraction (Richter et al., 1996), and single crystals of the δ form were obtained directly from the extract. Their visual appearance was poor, but they yielded reasonably clean diffraction patterns and were suitable for structure determination. The structure of the δ form is reported for the first time herein. We have also prepared crystals of the α and β polymorphs from a commercial sample and have determined their structures at 100 K, that of the α form to confirm its identity with the κ form of Kim et al. (1968), and that of the β form for completeness.

The molecular structure of the α polymorph is shown in Fig. 1. While crystals were prepared from 70% ethanol, the standard method for obtaining α, it is clear that they are identical to the `κ polymorph' of Kim et al. (1968), obtained from a water-methanol solution containing boric acid. We have chosen the now-conventional c > b > a setting, rather than the b > a > c previously used. Refinement using low-temperature CCD data has led to only a slight improvement in precision versus the room-temperature data from 35 years ago. The OH groups at both ends of the molecule form C—C—C—O torsion angles of nearly 60° (Table 1), rather than being extended with the carbon chain, and the molecule has nearly C2 symmetry, with the exception of the conformations of the OH groups. The hydrogen bonding has been described fully by Kim et al. (1968).

The structure of the β polymorph is shown in Fig. 1. The torsion angles in Table 1 indicate that the conformation of the main backbone is essentially the same as that of the α form. The OH groups have different conformations and conform to a different hydrogen-bonding scheme, as has been discussed by Berman et al. (1968). Our results are in excellent agreement with the room-temperature structure of Kaminsky & Glazer (1997), with a maximum difference in any bond distance of 0.008 (3) Å (for C4—O4) and an r.m.s. difference of 0.004 Å.

The full structure of the monoclinic δ polymorph is reported here for the first time, and its structure is shown in Fig. 1. The conformation of its main backbone is very similar to those of the other two polymorphs, as can be seen from the torsion angles in Table 1. However, this conformation deviates more from local C2 molecular symmetry than do those of the α and β forms. The torsion angle about C1—C2 differs from that about C5—C6 by 7.4 (3)°, and the one about C2—C3 differs from that about C4—C5 by 6.9 (3)°. The hydrogen-bonding pattern is described in Table 4 and illustrated in Fig. 2. Prominent features of the pattern are chains in the b direction formed by single hydrogen bonds with atom O1 as donor, and triply bonded chains in the a direction, in which OH groups O2, O4, and O6 on the same molecule all serve as donors. A portion of the triply bridged chain is shown in Fig. 3. This motif is also seen in DL-mannitol (Kanters et al., 1977). Similar triply bonded chains exist in the a direction of both the α and β polymorphs of D-mannitol, but in those cases, the three donors are not all on the same molecule. The two-dimensional net formed by the single and triple chains in the δ form are crosslinked by hydrogen bonds donated by atoms O3 and O5, forming a three-dimensional network.

Fig. 2 illustrates that, not only does the molecule in the δ form have approximate twofold rotational symmetry, but the packing does also, except for the H atoms. The unit-cell transformation (−1 0 0, 1 0 2, 0 1 0) generates a C-centered cell with near-orthorhombic metric, having dimensions a = 4.899 (2), b = 8.873 (3) and c = 18.268 (6) Å, and α = β = 90° and γ = 90.67 (2)°. Thus, the structure, minus the hydroxy H atoms, conforms approximately to space group C2221, with the molecule lying on a twofold axis. This suggests that the α' form of Berman et al. (1968), described in that space group with similar cell dimensions, is the same as the δ polymorph reported here. They obtained R = 0.18 from two-dimensional film data. Transforming our monoclinic data to the C-centered setting and averaging under Laue group mmm yielded Rint = 0.135, and refinement of the structure in C2221, reproduced the results of Berman et al. (1968). For this refinement, R = 0.107, but the H atoms were not visible and the ellipsoids were not reasonable, including that of atom C3 (= C4), which became non-positive definite. A calculated X-ray powder pattern from our P21 model also matches that reported by Burger et al. (2000) for modification III, which Grindley et al. (1990) equate to both α' and δ polymorphs. Thus, it is nearly certain that α' does not exist as an orthorhombic polymorph, but is identical to δ.

We have also measured the intensity data for the δ polymorph at 300 K, and refinement of the structure to R = 0.039 confirms that it is the same at room temperature and at 100 K. Cell dimensions at 300 K are a = 4.918 (2), b = 18.263 (6) and c = 5.093 (3) Å, and β = 118.31 (2)°, which yields a density of 1.502 Mg m−3. Thus, the δ form is the most dense of the three established polymorphs at room temperature, the density of the α form being 1.471 Mg m−3 and that of the β form being 1.487 Mg m−3. The δ polymorph is also the most dense at 100 K, and is more dense than the racemic form (Kanters et al., 1977) at both room and low temperature.

We conclude that there are only three well established polymorphs of D-mannitol, α, β, and δ, that all have approximate C2 molecular symmetry, and that none have crystallographic C2 symmetry. The α form is identical to the κ form, and the δ form is identical to the α' form.

Experimental top

Crystals of the α and β polymorphs were formed by recrystallization of a commercial sample of D-mannitol (Mallinckrodt). Slow cooling of a saturated solution at 323 K in 70% ethanol yielded long flexible needles of the α polymorph after one week. Slow evaporation of an aqueous solution yielded crystals of the β polymorph. A sample of the brown alga Dictyota dichotoma was freeze dried and then extracted in an accelerated solvent extractor (Richter et al., 1996) at 313 K and 1500 psi in 1:1 methanol:methylene chloride. The crystal of the δ polymorph used for data collection formed directly from the extract.

Refinement top

H atoms on C atoms were placed in calculated positions, guided by difference maps, with C—H bond distances in the range 0.99–1.00 Å and with Uiso(H) = 1.2Ueq(C), and were thereafter treated as riding. Coordinates for the hydroxy H atoms were refined, but Uiso(H) was fixed at 1.5Ueq(O). The absolute configuration could not be established from the X-ray data, but was assigned based on the known configuration of the D enantiomer (Kaminsky & Glazer, 1997). Friedel pairs were averaged in all cases.

Computing details top

For all compounds, data collection: COLLECT (Nonius, 2000); cell refinement: DENZO and SCALEPACK; data reduction: DENZO and SCALEPACK (Otwinowski & Minor, 1997); program(s) used to solve structure: SIR97 (Altomare et al., 1999); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: ORTEP-3 for Windows (Farrugia, 1997); software used to prepare material for publication: SHELXL97.

Figures top
[Figure 1] Fig. 1. Molecular views of the three polymorphs of (I), with the atom-numbering schemes. Displacement ellipsoids are drawn at the 50% probability level and H atoms are shown as small spheres of arbitrary radii.
[Figure 2] Fig. 2. A stereoview of the unit cell of δ-D-mannitol, showing the hydrogen bonding. The view is down the approximate twofold rotation direction. The a axis is horizontal and the b axis is vertical.
[Figure 3] Fig. 3. A portion of the triply bridged hydrogen-bonded chain of δ-D-mannitol. H atoms on C atoms are not shown.
(Alpha) D-mannitol top
Crystal data top
C6H14O6F(000) = 392
Mr = 182.17Dx = 1.496 Mg m3
Orthorhombic, P212121Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2abCell parameters from 1228 reflections
a = 4.8653 (10) Åθ = 2.5–29.1°
b = 8.873 (2) ŵ = 0.14 mm1
c = 18.739 (3) ÅT = 100 K
V = 809.0 (3) Å3Needle fragment, colorless
Z = 40.50 × 0.03 × 0.02 mm
Data collection top
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
951 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.049
Graphite monochromatorθmax = 29.1°, θmin = 3.1°
ω scans with κ offsetsh = 66
8346 measured reflectionsk = 1212
1286 independent reflectionsl = 2525
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.054Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.128H atoms treated by a mixture of independent and constrained refinement
S = 1.07 w = 1/[σ2(Fo2) + (0.0685P)2]
where P = (Fo2 + 2Fc2)/3
1286 reflections(Δ/σ)max < 0.001
127 parametersΔρmax = 0.35 e Å3
0 restraintsΔρmin = 0.27 e Å3
Crystal data top
C6H14O6V = 809.0 (3) Å3
Mr = 182.17Z = 4
Orthorhombic, P212121Mo Kα radiation
a = 4.8653 (10) ŵ = 0.14 mm1
b = 8.873 (2) ÅT = 100 K
c = 18.739 (3) Å0.50 × 0.03 × 0.02 mm
Data collection top
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
951 reflections with I > 2σ(I)
8346 measured reflectionsRint = 0.049
1286 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0540 restraints
wR(F2) = 0.128H atoms treated by a mixture of independent and constrained refinement
S = 1.07Δρmax = 0.35 e Å3
1286 reflectionsΔρmin = 0.27 e Å3
127 parameters
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O10.2222 (4)0.3688 (3)0.50519 (11)0.0168 (5)
H100.091 (8)0.390 (5)0.482 (2)0.025*
O20.7367 (4)0.4175 (3)0.43556 (11)0.0168 (5)
H200.696 (7)0.332 (5)0.4505 (19)0.025*
O30.2089 (4)0.6987 (3)0.39370 (11)0.0139 (5)
H300.275 (7)0.778 (5)0.3833 (18)0.021*
O40.7222 (4)0.7196 (3)0.32185 (11)0.0142 (5)
H400.853 (8)0.707 (5)0.3458 (19)0.021*
O50.1895 (4)0.4866 (3)0.24210 (10)0.0142 (5)
H500.240 (8)0.407 (5)0.229 (2)0.021*
O60.7082 (4)0.4837 (3)0.16834 (11)0.0160 (5)
H600.837 (7)0.491 (5)0.188 (2)0.024*
C10.3746 (6)0.5061 (4)0.51429 (16)0.0167 (7)
H1A0.49430.49730.55680.020*
H1B0.24540.59060.52240.020*
C20.5494 (6)0.5394 (4)0.44927 (14)0.0135 (7)
H20.66020.63190.45940.016*
C30.3776 (6)0.5688 (4)0.38161 (15)0.0121 (6)
H30.25400.48020.37400.015*
C40.5555 (6)0.5871 (3)0.31551 (14)0.0115 (6)
H40.67630.49670.30990.014*
C50.3818 (6)0.6081 (4)0.24772 (15)0.0132 (6)
H50.27550.70400.25270.016*
C60.5557 (6)0.6191 (4)0.17989 (16)0.0154 (7)
H6A0.43420.63790.13840.019*
H6B0.68420.70520.18410.019*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0115 (9)0.0194 (12)0.0196 (11)0.0002 (9)0.0033 (9)0.0042 (9)
O20.0118 (9)0.0162 (12)0.0223 (11)0.0011 (9)0.0003 (9)0.0063 (10)
O30.0110 (9)0.0131 (12)0.0175 (11)0.0016 (9)0.0012 (8)0.0002 (9)
O40.0085 (9)0.0164 (12)0.0178 (11)0.0010 (9)0.0027 (8)0.0029 (9)
O50.0100 (9)0.0123 (11)0.0203 (11)0.0010 (9)0.0018 (8)0.0043 (10)
O60.0101 (9)0.0184 (12)0.0197 (11)0.0007 (9)0.0005 (8)0.0040 (10)
C10.0163 (13)0.0171 (17)0.0167 (15)0.0019 (13)0.0011 (11)0.0008 (13)
C20.0130 (13)0.0117 (16)0.0160 (15)0.0002 (12)0.0024 (12)0.0005 (12)
C30.0113 (12)0.0115 (16)0.0136 (13)0.0005 (11)0.0008 (11)0.0007 (12)
C40.0098 (12)0.0128 (16)0.0118 (14)0.0013 (11)0.0018 (11)0.0014 (12)
C50.0099 (12)0.0137 (16)0.0161 (14)0.0001 (11)0.0015 (12)0.0027 (12)
C60.0174 (13)0.0155 (17)0.0134 (14)0.0002 (13)0.0004 (12)0.0007 (12)
Geometric parameters (Å, º) top
O1—C11.436 (4)C1—H1A0.9900
O1—H100.79 (4)C1—H1B0.9900
O2—C21.437 (4)C2—C31.541 (4)
O2—H200.83 (4)C2—H21.0000
O3—C31.433 (4)C3—C41.520 (4)
O3—H300.80 (4)C3—H31.0000
O4—C41.434 (4)C4—C51.537 (4)
O4—H400.79 (4)C4—H41.0000
O5—C51.431 (3)C5—C61.530 (4)
O5—H500.79 (4)C5—H51.0000
O6—C61.429 (4)C6—H6A0.9900
O6—H600.73 (4)C6—H6B0.9900
C1—C21.515 (4)
C1—O1—H10106 (3)O3—C3—H3108.1
C2—O2—H20118 (3)C4—C3—H3108.1
C3—O3—H30116 (3)C2—C3—H3108.1
C4—O4—H40113 (3)O4—C4—C3110.0 (2)
C5—O5—H50120 (3)O4—C4—C5106.3 (2)
C6—O6—H60107 (4)C3—C4—C5111.9 (2)
O1—C1—C2111.1 (3)O4—C4—H4109.5
O1—C1—H1A109.4C3—C4—H4109.5
C2—C1—H1A109.4C5—C4—H4109.5
O1—C1—H1B109.4O5—C5—C6110.4 (2)
C2—C1—H1B109.4O5—C5—C4109.2 (2)
H1A—C1—H1B108.0C6—C5—C4113.0 (2)
O2—C2—C1110.7 (3)O5—C5—H5108.0
O2—C2—C3108.9 (2)C6—C5—H5108.0
C1—C2—C3113.0 (2)C4—C5—H5108.0
O2—C2—H2108.0O6—C6—C5111.0 (3)
C1—C2—H2108.0O6—C6—H6A109.4
C3—C2—H2108.0C5—C6—H6A109.4
O3—C3—C4111.7 (2)O6—C6—H6B109.4
O3—C3—C2108.5 (2)C5—C6—H6B109.4
C4—C3—C2112.3 (2)H6A—C6—H6B108.0
O1—C1—C2—O258.3 (3)O3—C3—C4—C560.9 (3)
O1—C1—C2—C364.2 (3)C2—C3—C4—C5177.0 (3)
O2—C2—C3—O3175.0 (2)O4—C4—C5—O5174.1 (2)
C1—C2—C3—O361.6 (3)C3—C4—C5—O554.0 (3)
O2—C2—C3—C451.1 (3)O4—C4—C5—C662.7 (3)
C1—C2—C3—C4174.5 (3)C3—C4—C5—C6177.2 (3)
O3—C3—C4—O457.0 (3)O5—C5—C6—O660.5 (3)
C2—C3—C4—O465.1 (3)C4—C5—C6—O662.1 (3)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H10···O2i0.79 (4)1.95 (4)2.733 (3)171 (4)
O2—H20···O1ii0.83 (4)1.97 (4)2.774 (3)162 (4)
O3—H30···O6iii0.80 (4)2.07 (4)2.812 (3)155 (3)
O4—H40···O3iv0.79 (4)1.95 (4)2.730 (3)170 (4)
O5—H50···O4v0.79 (4)1.92 (4)2.689 (3)164 (4)
O6—H60···O5iv0.73 (4)2.00 (4)2.719 (3)174 (5)
Symmetry codes: (i) x1, y, z; (ii) x+1/2, y+1/2, z+1; (iii) x+1, y+1/2, z+1/2; (iv) x+1, y, z; (v) x+1, y1/2, z+1/2.
(Beta) D-mannitol top
Crystal data top
C6H14O6F(000) = 392
Mr = 182.17Dx = 1.516 Mg m3
Orthorhombic, P212121Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ac 2abCell parameters from 1711 reflections
a = 5.5381 (10) Åθ = 2.5–34.3°
b = 8.580 (2) ŵ = 0.14 mm1
c = 16.795 (5) ÅT = 100 K
V = 798.0 (3) Å3Lath, colorless
Z = 40.37 × 0.15 × 0.05 mm
Data collection top
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
1611 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.026
Graphite monochromatorθmax = 34.3°, θmin = 2.6°
ω scans with κ offsetsh = 88
12106 measured reflectionsk = 1313
1838 independent reflectionsl = 2626
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.036Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.095H atoms treated by a mixture of independent and constrained refinement
S = 1.08 w = 1/[σ2(Fo2) + (0.0488P)2 + 0.1129P]
where P = (Fo2 + 2Fc2)/3
1838 reflections(Δ/σ)max < 0.001
127 parametersΔρmax = 0.38 e Å3
0 restraintsΔρmin = 0.25 e Å3
Crystal data top
C6H14O6V = 798.0 (3) Å3
Mr = 182.17Z = 4
Orthorhombic, P212121Mo Kα radiation
a = 5.5381 (10) ŵ = 0.14 mm1
b = 8.580 (2) ÅT = 100 K
c = 16.795 (5) Å0.37 × 0.15 × 0.05 mm
Data collection top
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
1611 reflections with I > 2σ(I)
12106 measured reflectionsRint = 0.026
1838 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0360 restraints
wR(F2) = 0.095H atoms treated by a mixture of independent and constrained refinement
S = 1.08Δρmax = 0.38 e Å3
1838 reflectionsΔρmin = 0.25 e Å3
127 parameters
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O11.0760 (2)0.61279 (13)0.44986 (6)0.0144 (2)
H1O1.064 (4)0.701 (3)0.4691 (13)0.022*
O20.55819 (18)0.61711 (13)0.46309 (7)0.0143 (2)
H2O0.411 (4)0.598 (3)0.4579 (12)0.021*
O30.83302 (19)0.27783 (13)0.36445 (6)0.0133 (2)
H3O0.987 (4)0.294 (3)0.3682 (12)0.020*
O40.32682 (18)0.28903 (13)0.36741 (6)0.01136 (19)
H4O0.385 (4)0.204 (3)0.3547 (12)0.017*
O50.61370 (18)0.49857 (13)0.20060 (6)0.0127 (2)
H5O0.766 (4)0.491 (3)0.2056 (12)0.019*
O60.09906 (18)0.49756 (13)0.21181 (6)0.0147 (2)
H6O0.164 (4)0.573 (3)0.1902 (13)0.022*
C10.9372 (3)0.50110 (17)0.49394 (8)0.0136 (3)
H1A0.91660.53850.54930.016*
H1B1.02610.40110.49590.016*
C20.6897 (2)0.47425 (16)0.45681 (8)0.0113 (2)
H20.60320.39090.48710.014*
C30.7118 (2)0.42557 (16)0.36894 (8)0.0103 (2)
H30.80890.50540.33970.012*
C40.4667 (2)0.40787 (17)0.32857 (8)0.0100 (2)
H40.37830.50880.33480.012*
C50.4879 (2)0.37379 (17)0.23879 (8)0.0109 (2)
H50.57930.27450.23080.013*
C60.2417 (2)0.36070 (18)0.19915 (8)0.0130 (3)
H6A0.26360.34430.14130.016*
H6B0.15530.26910.22090.016*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0116 (4)0.0135 (5)0.0181 (5)0.0018 (4)0.0008 (4)0.0049 (4)
O20.0097 (4)0.0128 (5)0.0204 (5)0.0010 (4)0.0005 (4)0.0070 (4)
O30.0089 (4)0.0116 (4)0.0194 (5)0.0017 (4)0.0014 (4)0.0038 (4)
O40.0093 (4)0.0109 (4)0.0139 (4)0.0009 (4)0.0011 (4)0.0013 (4)
O50.0098 (4)0.0142 (5)0.0142 (4)0.0013 (4)0.0004 (3)0.0042 (4)
O60.0104 (4)0.0142 (5)0.0195 (5)0.0008 (4)0.0001 (4)0.0049 (4)
C10.0132 (6)0.0145 (6)0.0131 (5)0.0006 (6)0.0025 (5)0.0010 (5)
C20.0116 (5)0.0109 (6)0.0113 (5)0.0000 (5)0.0003 (5)0.0019 (5)
C30.0091 (5)0.0093 (6)0.0125 (5)0.0003 (5)0.0005 (4)0.0013 (5)
C40.0091 (5)0.0106 (6)0.0103 (5)0.0002 (4)0.0000 (4)0.0007 (5)
C50.0105 (5)0.0112 (6)0.0111 (6)0.0008 (5)0.0004 (4)0.0005 (5)
C60.0121 (5)0.0142 (6)0.0128 (6)0.0007 (5)0.0012 (5)0.0001 (5)
Geometric parameters (Å, º) top
O1—C11.4342 (18)C1—H1A0.99
O1—H1O0.82 (2)C1—H1B0.99
O2—C21.4298 (18)C2—C31.5386 (18)
O2—H2O0.83 (2)C2—H21.00
O3—C31.4363 (17)C3—C41.5251 (18)
O3—H3O0.86 (2)C3—H31.00
O4—C41.4370 (17)C4—C51.5406 (19)
O4—H4O0.82 (2)C4—H41.00
O5—C51.4292 (18)C5—C61.5218 (19)
O5—H5O0.85 (2)C5—H51.00
O6—C61.4310 (18)C6—H6A0.99
O6—H6O0.82 (2)C6—H6B0.99
C1—C21.5232 (19)
C1—O1—H1O111.5 (15)O3—C3—H3109.2
C2—O2—H2O108.6 (15)C4—C3—H3109.2
C3—O3—H3O108.3 (16)C2—C3—H3109.1
C4—O4—H4O107.4 (15)O4—C4—C3110.41 (11)
C5—O5—H5O112.5 (15)O4—C4—C5110.54 (11)
C6—O6—H6O109.7 (16)C3—C4—C5112.71 (11)
O1—C1—C2111.82 (11)O4—C4—H4107.7
O1—C1—H1A109.3C3—C4—H4107.7
C2—C1—H1A109.3C5—C4—H4107.7
O1—C1—H1B109.3O5—C5—C6107.20 (11)
C2—C1—H1B109.3O5—C5—C4109.53 (11)
H1A—C1—H1B107.9C6—C5—C4111.94 (11)
O2—C2—C1107.38 (11)O5—C5—H5109.4
O2—C2—C3110.12 (11)C6—C5—H5109.4
C1—C2—C3111.24 (11)C4—C5—H5109.4
O2—C2—H2109.4O6—C6—C5111.66 (11)
C1—C2—H2109.4O6—C6—H6A109.3
C3—C2—H2109.4C5—C6—H6A109.3
O3—C3—C4107.74 (10)O6—C6—H6B109.3
O3—C3—C2109.09 (11)C5—C6—H6B109.3
C4—C3—C2112.50 (11)H6A—C6—H6B107.9
O1—C1—C2—O265.12 (13)O3—C3—C4—C564.93 (14)
O1—C1—C2—C355.43 (16)C2—C3—C4—C5174.79 (12)
O2—C2—C3—O3176.92 (10)O4—C4—C5—O5176.16 (10)
C1—C2—C3—O364.16 (14)C3—C4—C5—O559.76 (14)
O2—C2—C3—C457.42 (14)O4—C4—C5—C657.40 (15)
C1—C2—C3—C4176.34 (11)C3—C4—C5—C6178.52 (12)
O3—C3—C4—O459.22 (13)O5—C5—C6—O664.07 (14)
C2—C3—C4—O461.06 (14)C4—C5—C6—O656.06 (16)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1O···O2i0.82 (2)1.94 (2)2.7419 (16)167 (2)
O2—H2O···O1ii0.83 (2)1.87 (2)2.6801 (15)164 (2)
O3—H3O···O4iii0.86 (2)1.88 (2)2.7368 (15)168 (2)
O4—H4O···O5iv0.82 (2)2.00 (2)2.7612 (16)155 (2)
O5—H5O···O6iii0.85 (2)1.85 (2)2.6946 (14)174 (2)
O6—H6O···O3v0.82 (2)1.98 (2)2.7504 (16)155 (2)
Symmetry codes: (i) x+1/2, y+3/2, z+1; (ii) x1, y, z; (iii) x+1, y, z; (iv) x+1, y1/2, z+1/2; (v) x+1, y+1/2, z+1/2.
(Delta) D-mannitol top
Crystal data top
C6H14O6F(000) = 196
Mr = 182.17Dx = 1.524 Mg m3
Monoclinic, P21Mo Kα radiation, λ = 0.71073 Å
Hall symbol: P 2ybCell parameters from 901 reflections
a = 4.899 (2) Åθ = 2.5–27.5°
b = 18.268 (6) ŵ = 0.14 mm1
c = 5.043 (2) ÅT = 100 K
β = 118.39 (2)°Lath, colorless
V = 397.0 (3) Å30.42 × 0.12 × 0.01 mm
Z = 2
Data collection top
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
892 reflections with I > 2σ(I)
Radiation source: fine-focus sealed tubeRint = 0.021
Graphite monochromatorθmax = 27.5°, θmin = 2.5°
ω scans with κ offsetsh = 66
1534 measured reflectionsk = 2319
940 independent reflectionsl = 66
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.031Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.079H atoms treated by a mixture of independent and constrained refinement
S = 1.07 w = 1/[σ2(Fo2) + (0.0362P)2 + 0.0992P]
where P = (Fo2 + 2Fc2)/3
940 reflections(Δ/σ)max < 0.001
127 parametersΔρmax = 0.27 e Å3
1 restraintΔρmin = 0.23 e Å3
Crystal data top
C6H14O6V = 397.0 (3) Å3
Mr = 182.17Z = 2
Monoclinic, P21Mo Kα radiation
a = 4.899 (2) ŵ = 0.14 mm1
b = 18.268 (6) ÅT = 100 K
c = 5.043 (2) Å0.42 × 0.12 × 0.01 mm
β = 118.39 (2)°
Data collection top
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
892 reflections with I > 2σ(I)
1534 measured reflectionsRint = 0.021
940 independent reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0311 restraint
wR(F2) = 0.079H atoms treated by a mixture of independent and constrained refinement
S = 1.07Δρmax = 0.27 e Å3
940 reflectionsΔρmin = 0.23 e Å3
127 parameters
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
O10.6896 (4)0.53330 (9)0.8932 (4)0.0198 (4)
H1O0.732 (7)0.4904 (19)0.971 (7)0.030*
O20.1646 (4)0.61137 (9)0.9089 (3)0.0168 (4)
H2O0.017 (7)0.5820 (18)0.883 (7)0.025*
O30.5121 (4)0.67217 (9)0.4501 (4)0.0158 (3)
H3O0.385 (7)0.6533 (16)0.290 (7)0.024*
O40.0530 (3)0.74841 (9)0.4025 (3)0.0159 (3)
H4O0.201 (7)0.7265 (16)0.431 (6)0.024*
O50.7363 (3)0.81517 (9)0.8615 (4)0.0168 (4)
H5O0.770 (7)0.7954 (17)1.021 (8)0.025*
O60.2257 (4)0.89418 (9)0.9041 (4)0.0192 (4)
H6O0.078 (8)0.8711 (19)0.881 (7)0.029*
C10.3781 (5)0.53669 (12)0.6521 (5)0.0168 (5)
H1A0.25770.49520.66960.020*
H1B0.37970.53200.45720.020*
C20.2221 (5)0.60816 (12)0.6567 (5)0.0137 (4)
H20.01920.61170.46760.016*
C30.4176 (5)0.67513 (13)0.6766 (4)0.0130 (4)
H30.60920.67350.87680.016*
C40.2481 (4)0.74703 (13)0.6612 (5)0.0129 (4)
H40.22460.75160.84690.015*
C50.4173 (5)0.81441 (13)0.6344 (5)0.0134 (4)
H50.41380.81140.43480.016*
C60.2570 (5)0.88554 (12)0.6376 (5)0.0164 (5)
H6A0.37740.92720.62160.020*
H6B0.04840.88680.45920.020*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
O10.0153 (8)0.0138 (9)0.0273 (10)0.0009 (6)0.0076 (7)0.0055 (7)
O20.0174 (7)0.0173 (9)0.0181 (8)0.0048 (7)0.0103 (6)0.0015 (7)
O30.0155 (7)0.0191 (8)0.0149 (7)0.0030 (7)0.0090 (6)0.0036 (7)
O40.0113 (7)0.0165 (8)0.0170 (7)0.0011 (6)0.0044 (6)0.0032 (7)
O50.0128 (7)0.0192 (9)0.0159 (8)0.0025 (6)0.0049 (6)0.0018 (7)
O60.0211 (8)0.0163 (9)0.0241 (9)0.0049 (7)0.0140 (7)0.0053 (7)
C10.0158 (10)0.0118 (11)0.0206 (12)0.0008 (9)0.0070 (9)0.0002 (9)
C20.0141 (9)0.0117 (11)0.0144 (10)0.0010 (8)0.0062 (8)0.0022 (9)
C30.0136 (9)0.0137 (10)0.0134 (9)0.0005 (9)0.0077 (8)0.0004 (9)
C40.0122 (9)0.0112 (10)0.0141 (9)0.0015 (8)0.0052 (8)0.0006 (9)
C50.0131 (10)0.0126 (11)0.0132 (10)0.0005 (8)0.0052 (8)0.0004 (9)
C60.0192 (11)0.0133 (12)0.0179 (11)0.0013 (8)0.0099 (9)0.0005 (9)
Geometric parameters (Å, º) top
O1—C11.431 (3)C1—H1A0.99
O1—H1O0.86 (3)C1—H1B0.99
O2—C21.428 (2)C2—C31.527 (3)
O2—H2O0.86 (3)C2—H21.00
O3—C31.423 (2)C3—C41.536 (3)
O3—H3O0.82 (3)C3—H31.00
O4—C41.431 (2)C4—C51.525 (3)
O4—H4O0.90 (3)C4—H41.00
O5—C51.433 (2)C5—C61.522 (3)
O5—H5O0.82 (3)C5—H51.00
O6—C61.432 (3)C6—H6A0.99
O6—H6O0.80 (3)C6—H6B0.99
C1—C21.519 (3)
C1—O1—H1O111 (2)O3—C3—H3107.5
C2—O2—H2O110 (2)C2—C3—H3107.5
C3—O3—H3O115 (2)C4—C3—H3107.5
C4—O4—H4O113.9 (19)O4—C4—C5105.83 (17)
C5—O5—H5O114 (2)O4—C4—C3111.05 (18)
C6—O6—H6O108 (2)C5—C4—C3113.02 (16)
O1—C1—C2111.43 (18)O4—C4—H4108.9
O1—C1—H1A109.3C5—C4—H4108.9
C2—C1—H1A109.3C3—C4—H4108.9
O1—C1—H1B109.3O5—C5—C6110.81 (17)
C2—C1—H1B109.3O5—C5—C4111.67 (17)
H1A—C1—H1B108.0C6—C5—C4112.52 (17)
O2—C2—C1111.27 (18)O5—C5—H5107.2
O2—C2—C3106.96 (16)C6—C5—H5107.2
C1—C2—C3112.65 (16)C4—C5—H5107.2
O2—C2—H2108.6O6—C6—C5112.96 (17)
C1—C2—H2108.6O6—C6—H6A109.0
C3—C2—H2108.6C5—C6—H6A109.0
O3—C3—C2110.50 (17)O6—C6—H6B109.0
O3—C3—C4111.49 (17)C5—C6—H6B109.0
C2—C3—C4112.00 (16)H6A—C6—H6B107.8
O1—C1—C2—O269.4 (2)O3—C3—C4—C547.2 (2)
O1—C1—C2—C350.7 (2)C2—C3—C4—C5171.61 (17)
O2—C2—C3—O3174.05 (16)O4—C4—C5—O5173.08 (16)
C1—C2—C3—O351.5 (2)C3—C4—C5—O551.3 (2)
O2—C2—C3—C461.0 (2)O4—C4—C5—C661.6 (2)
C1—C2—C3—C4176.44 (18)C3—C4—C5—C6176.69 (17)
O3—C3—C4—O471.5 (2)O5—C5—C6—O667.7 (2)
C2—C3—C4—O452.9 (2)C4—C5—C6—O658.1 (2)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
O1—H1O···O6i0.86 (3)1.84 (3)2.697 (2)172 (3)
O2—H2O···O1ii0.86 (3)1.85 (3)2.698 (2)166 (3)
O3—H3O···O2iii0.82 (3)1.87 (3)2.676 (3)168 (3)
O4—H4O···O3ii0.90 (3)1.76 (3)2.650 (2)171 (3)
O5—H5O···O4iv0.82 (3)1.90 (3)2.705 (2)166 (3)
O6—H6O···O5ii0.80 (3)1.92 (4)2.718 (2)175 (3)
Symmetry codes: (i) x+1, y1/2, z+2; (ii) x1, y, z; (iii) x, y, z1; (iv) x+1, y, z+1.

Experimental details

(Alpha)(Beta)(Delta)
Crystal data
Chemical formulaC6H14O6C6H14O6C6H14O6
Mr182.17182.17182.17
Crystal system, space groupOrthorhombic, P212121Orthorhombic, P212121Monoclinic, P21
Temperature (K)100100100
a, b, c (Å)4.8653 (10), 8.873 (2), 18.739 (3)5.5381 (10), 8.580 (2), 16.795 (5)4.899 (2), 18.268 (6), 5.043 (2)
α, β, γ (°)90, 90, 9090, 90, 9090, 118.39 (2), 90
V3)809.0 (3)798.0 (3)397.0 (3)
Z442
Radiation typeMo KαMo KαMo Kα
µ (mm1)0.140.140.14
Crystal size (mm)0.50 × 0.03 × 0.020.37 × 0.15 × 0.050.42 × 0.12 × 0.01
Data collection
DiffractometerNonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
Nonius KappaCCD area-detector (with Oxford Cryostream)
diffractometer
Absorption correction
No. of measured, independent and
observed [I > 2σ(I)] reflections
8346, 1286, 951 12106, 1838, 1611 1534, 940, 892
Rint0.0490.0260.021
(sin θ/λ)max1)0.6840.7930.650
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.054, 0.128, 1.07 0.036, 0.095, 1.08 0.031, 0.079, 1.07
No. of reflections12861838940
No. of parameters127127127
No. of restraints001
H-atom treatmentH atoms treated by a mixture of independent and constrained refinementH atoms treated by a mixture of independent and constrained refinementH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.35, 0.270.38, 0.250.27, 0.23

Computer programs: COLLECT (Nonius, 2000), DENZO and SCALEPACK (Otwinowski & Minor, 1997), SIR97 (Altomare et al., 1999), SHELXL97 (Sheldrick, 1997), ORTEP-3 for Windows (Farrugia, 1997), SHELXL97.

Hydrogen-bond geometry (Å, º) for (Alpha) top
D—H···AD—HH···AD···AD—H···A
O1—H10···O2i0.79 (4)1.95 (4)2.733 (3)171 (4)
O2—H20···O1ii0.83 (4)1.97 (4)2.774 (3)162 (4)
O3—H30···O6iii0.80 (4)2.07 (4)2.812 (3)155 (3)
O4—H40···O3iv0.79 (4)1.95 (4)2.730 (3)170 (4)
O5—H50···O4v0.79 (4)1.92 (4)2.689 (3)164 (4)
O6—H60···O5iv0.73 (4)2.00 (4)2.719 (3)174 (5)
Symmetry codes: (i) x1, y, z; (ii) x+1/2, y+1/2, z+1; (iii) x+1, y+1/2, z+1/2; (iv) x+1, y, z; (v) x+1, y1/2, z+1/2.
Comparison of geometric parameters (Å, °) in the three polymorphs of (I) top
Atomsα polymorphβ polymorphδ polymorph
C1-O11.436 (4)1.4342 (18)1.431 (3)
C2-O21.437 (4)1.4298 (18)1.428 (2)
C3-O31.433 (4)1.4363 (17)1.423 (2)
C4-O41.434 (4)1.4370 (17)1.431 (2)
C5-O51.431 (3)1.4292 (18)1.433 (2)
C6-O61.429 (4)1.4310 (18)1.432 (3)
C1-C21.515 (4)1.5232 (19)1.519 (3)
C2-C31.541 (4)1.5386 (18)1.527 (3)
C3-C41.520 (4)1.5251 (18)1.536 (3)
C4-C51.537 (4)1.5406 (19)1.525 (3)
C5-C61.530 (4)1.5218 (19)1.522 (3)
O1-C1-C2-C364.2 (3)55.43 (16)50.7 (2)
C1-C2-C3-C4-174.5 (3)-176.34 (11)176.44 (18)
C2-C3-C4-C5177.0 (3)174.79 (12)-171.61 (17)
C3-C4-C5-C6-177.2 (3)-178.52 (12)-176.69 (17)
C4-C5-C6-O662.1 (3)56.06 (16)58.1 (2)
Hydrogen-bond geometry (Å, º) for (Beta) top
D—H···AD—HH···AD···AD—H···A
O1—H1O···O2i0.82 (2)1.94 (2)2.7419 (16)167 (2)
O2—H2O···O1ii0.83 (2)1.87 (2)2.6801 (15)164 (2)
O3—H3O···O4iii0.86 (2)1.88 (2)2.7368 (15)168 (2)
O4—H4O···O5iv0.82 (2)2.00 (2)2.7612 (16)155 (2)
O5—H5O···O6iii0.85 (2)1.85 (2)2.6946 (14)174 (2)
O6—H6O···O3v0.82 (2)1.98 (2)2.7504 (16)155 (2)
Symmetry codes: (i) x+1/2, y+3/2, z+1; (ii) x1, y, z; (iii) x+1, y, z; (iv) x+1, y1/2, z+1/2; (v) x+1, y+1/2, z+1/2.
Hydrogen-bond geometry (Å, º) for (Delta) top
D—H···AD—HH···AD···AD—H···A
O1—H1O···O6i0.86 (3)1.84 (3)2.697 (2)172 (3)
O2—H2O···O1ii0.86 (3)1.85 (3)2.698 (2)166 (3)
O3—H3O···O2iii0.82 (3)1.87 (3)2.676 (3)168 (3)
O4—H4O···O3ii0.90 (3)1.76 (3)2.650 (2)171 (3)
O5—H5O···O4iv0.82 (3)1.90 (3)2.705 (2)166 (3)
O6—H6O···O5ii0.80 (3)1.92 (4)2.718 (2)175 (3)
Symmetry codes: (i) x+1, y1/2, z+2; (ii) x1, y, z; (iii) x, y, z1; (iv) x+1, y, z+1.
 

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