research papers\(\def\hfill{\hskip 5em}\def\hfil{\hskip 3em}\def\eqno#1{\hfil {#1}}\)

IUCrJ
ISSN: 2052-2525

On the correlation between hydrogen bonding and melting points in the inositols

aInstitute for Inorganic and Analytical Chemistry, Goethe-University, Max-von-Laue-Str. 7, 60438 Frankfurt am Main, Germany, and bDepartment of Pharmacy, University of Copenhagen, Universitetsparken 2, 2100 Copenhagen, Denmark
*Correspondence e-mail: jacco.vandestreek@sund.ku.dk

Edited by A. D. Bond, University of Copenhagen, Denmark (Received 28 June 2013; accepted 25 September 2013; online 18 October 2013)

Inositol, 1,2,3,4,5,6-hexahydroxycyclohexane, exists in nine stereoisomers with different crystal structures and melting points. In a previous paper on the relationship between the melting points of the inositols and the hydrogen-bonding patterns in their crystal structures [Simperler et al. (2006[Simperler, A., Watt, S. W., Bonnet, P. A., Jones, W. & Motherwell, W. D. S. (2006). CrystEngComm, 8, 589-600.]). CrystEngComm 8, 589], it was noted that although all inositol crystal structures known at that time contained 12 hydrogen bonds per molecule, their melting points span a large range of about 170 °C. Our preliminary investigations suggested that the highest melting point must be corrected for the effect of molecular symmetry, and that the three lowest melting points may need to be revised. This prompted a full investigation, with additional experiments on six of the nine inositols. Thirteen new phases were discovered; for all of these their crystal structures were examined. The crystal structures of eight ordered phases could be determined, of which seven were obtained from laboratory X-ray powder diffraction data. Five additional phases turned out to be rotator phases and only their unit cells could be determined. Two previously unknown melting points were measured, as well as most enthalpies of melting. Several previously reported melting points were shown to be solid-to-solid phase transitions or decomposition points. Our experiments have revealed a complex picture of phases, rotator phases and phase transitions, in which a simple correlation between melting points and hydrogen-bonding patterns is not feasible.

1. Introduction

The term inositol, 1,2,3,4,5,6-hexahydroxycyclohexane, denotes a class of compounds whose basis is provided by the nine stereoisomers in Fig. 1[link] (for the nomenclature and numbering of cyclitoles, refer to Dawson et al., 1973[Dawson, M. C., Hoffmann-Ostenhof, O., Klyne, W. & Posternak, T. (1973). Pure Appl. Chem. 37, 285-297.]; Parthasarathy & Eisenberg, 1991[Parthasarathy, R. & Eisenberg, F. II Jr (1991). Inositol Phosphates and Derivatives, edited by A. B. Reitz, ACS Symposium Series, Vol. 463, ch. 1. Washington: ACS Publications.]). All inositol isomers exhibit the same chemical composition, C6H12O6, but each of them with its own configuration. Four of them [myo-, scyllo-, D-(+)-chiro and L-(−)-chiro-inositol] occur in nature, the remaining five (cis-, epi-, allo-, neo- and muco-inositol) have synthetic origins. All of them could be synthesized and described in the past and their syntheses optimized in recent years (Posternak, 1951[Posternak, T. (1951). Bull. Soc. Chim. Biol. 33, 1041-1058.]; Angyal, 1957[Angyal, S. J. (1957). Q. Rev. Chem. Soc. 11, 212-226.]; Angyal & McHugh, 1957[Angyal, S. J. & McHugh, D. J. (1957). J. Chem. Soc. pp. 3682-3691.]; Angyal & Hickman, 1971[Angyal, S. J. & Hickman, R. J. (1971). Carbohydr. Res. 20, 97-104.]; Angyal et al., 1995[Angyal, S. J., Odier, L. & Tate, M. E. (1995). Carbohydr. Res. 266, 143-146.]; Chung & Kwon, 1999[Chung, S. K. & Kwon, Y. U. (1999). Bioorg. Med. Chem. Lett. 9, 2135-2140.]). D-(+)-chiro- and L-(−)-chiro-inositol are enantiomers, and their crystal structures can be expected to be mirror images, with identical thermodynamic properties such as melting points.

[Figure 1]
Figure 1
Inositol stereoisomers and molecular symmetry numbers σ.

Our interest in the inositols was sparked by a paper by Simperler et al. (2006[Simperler, A., Watt, S. W., Bonnet, P. A., Jones, W. & Motherwell, W. D. S. (2006). CrystEngComm, 8, 589-600.]) concerning the correlation of the melting points of the inositols with the hydrogen-bonding patterns in their crystal structures. In all the inositol crystal structures known at that time, each inositol molecule was connected to its neighbours by 12 hydrogen bonds. Based on the simple criterion of counting hydrogen bonds, the melting points would therefore be expected to be fairly similar. Surprisingly, the melting points reported in the paper by Simperler et al. span a large range from 180 to 350 °C. In particular, scyllo-inositol had a significantly higher melting point than the remaining inositols, whereas the melting point of allo-inositol was significantly lower. We noticed that the explanations for each of these two anomalous melting points could be found in the literature.

The excellent paper by Wei (1999[Wei, J. (1999). Ind. Eng. Chem. Res. 38, 5019-5027.]) describes how high molecular symmetry gives rise to elevated melting points in homologous series of compounds. In brief, molecules of high point-group symmetry – high symmetry number, σ, to be precise – benefit less from the rotational degrees of freedom that become available upon melting, and as such resist melting and have higher melting points; it is an entropy effect that follows from statistical thermodynamics. The symmetry number σ corresponds to the order of the point group if only proper rotations and the identity are counted. Wei's paper offers an explanation and quantification of Carnelley's rule, published in 1882 (Carnelley, 1882a[Carnelley, T. (1882a). Philos. Mag. 13, 112-130.],b[Carnelley, T. (1882b). Philos. Mag. 13, 180-193.]). The remarkable melting point behaviour observed in other series of isomeric or homologous compounds (Joseph et al., 2011[Joseph, S., Sathishkumar, R., Mahapatra, S. & Desiraju, G. R. (2011). Acta Cryst. B67, 525-534.]; Podsiadło et al., 2012[Podsiadło, M., Bujak, M. & Katrusiak, A. (2012). CrystEngComm, 14, 4496-4500.]) may also be explained by this effect.

All inositols in the Simperler paper have σ = 1 or σ = 2, with the exception of scyllo-inositol, which has σ = 6. The connection between the high melting point of scyllo-inositol and its high molecular symmetry was mentioned earlier by Orloff (1954[Orloff, H. D. (1954). Chem. Rev. 54, 347-447.]). The higher melting point of scyllo-inositol is therefore as expected based on its higher molecular symmetry. Calculation of the corrected melting point – the melting point scyllo-inositol would have in the absence of molecular symmetry – requires the value of the enthalpy of melting, Hm.

The significantly lower melting point of allo-inositol can also be explained: in the paper that reports the crystal structure and its melting point of 180 °C (Bonnet et al., 2006a[Bonnet, A., Jones, W. & Motherwell, W. D. S. (2006a). Acta Cryst. E62, o2578-o2579.]), another paper is cited that reports a melting point of 310 °C for allo-inositol (Tschamber et al., 1992[Tschamber, T., Backenstrass, F., Fritz, H. & Streith, J. (1992). Helv. Chim. Acta, 75, 1052-1060.]), essentially the same as neo- (315 °C) and epi-inositol (304 °C). It appears that allo-inositol exhibits polymorphism, and the change at 180 °C may well refer to a phase transition to another polymorph rather than to a melting point.

After allo-inositol, the second lowest melting point in the Simperler paper was reported for myo-inositol, at 225 °C. Interestingly, 1 year after the Simperler paper, Khan et al. (2007[Khan, U., Qureshi, R. A., Saeed, S. & Bond, A. D. (2007). Acta Cryst. E63, o530-o532.]) reported a new polymorph for myo-inositol, with unknown melting point. This leaves room for speculation that perhaps the new polymorph has a higher melting point.

That would leave L-(−)-chiro-inositol and its enantiomer D-(+)-chiro-inositol as the only remaining inositols with a slightly lower melting point than the other inositols. Because D-(+)- and L-(−)-chiro-inositol are the only inositols that are chiral, they are the only inositols that cannot pack in a space group with an inversion centre or a glide plane – two symmetry elements that are known to lead to efficient packing (Kitaigorodskii, 1961[Kitaigorodskii, A. I. (1961). Organic Chemical Crystallography. New York: Consultants Bureau.]). It is therefore to be expected that a racemic mixture of L-(−)-chiro-inositol and D-(+)-chiro-inositol is able to crystallize in a structure with a more stable packing and it may therefore have a melting point that is more in line with the other inositols.

For cis-inositol, only the crystal structure of a monohydrate has been published (Freeman et al., 1996[Freeman, H. C., Langs, D. A., Nockolds, C. E. & Oh, Y. L. (1996). Aust. J. Chem. 49, 413-424.]); we are not aware of a published melting point for cis-inositol.

We therefore set out to fill these gaps. Specifically, we wanted to find the high-melting polymorph of allo-inositol, to determine Hm for scyllo-inositol (to calculate its corrected melting point), to determine the melting point of the second polymorph of myo-inositol and to determine the crystal structures and melting points of rac-chiro-inositol and cis-inositol.

2. Experimental

2.1. Materials and crystallization

We denote the compounds by numbers (see Fig. 1[link]) and the crystal phases by capital letters, e.g. 7-A, 7-B and 7-C for the three polymorphs of myo-inositol.

D-(+)-chiro-Inositol (D-1·1/3H2O), L-(−)-chiro-inositol (L-1·1/3H2O), cis-inositol (5), allo-inositol (6) and myo-inositol (7) were purchased from Sigma Aldrich (≥ 98.0%), whereas scyllo-inositol (2) was purchased from TCI Europe (≥ 98.0%). All materials were used as received without further purification. The prices of the compounds allowed only small quantities to be purchased, which in turn hampered the growing of sizeable single crystals. The crystal structure determinations in this paper were therefore achieved using X-ray powder diffraction data, but the compounds are readily crystallized and for those phases stable at room temperature, single crystals can almost certainly be grown given sufficient starting material.

rac-chiro-Inositol (rac-1) was prepared by dissolving 30 mg of each enantiomer in 3 ml water. The solution was left to evaporate at room temperature and a white powder precipitated after ca 5 d.

2.2. X-ray powder diffraction (XRPD) and temperature-dependent X-ray powder diffraction (T-XRPD)

Temperature-dependent X-ray powder diffraction data were recorded on a Stoe Stadi-P diffractometer with a Ge(111) monochromator (Cu Kα1 radiation, λ = 1.5406 Å). For temperature regulation and detection, two different systems were used, depending on their application. For phase identification at temperatures up to 500 °C, a HUBER heater device 670.3 equipped with a high-temperature controller HTC 9634 and an imaging-plate position-sensitive detector (IP-PSD) were used. The heating rate was 5 °C min−1 for the mixture 5-B + 5-C, 3 °C min−1 for all other phases. Due to the limited 2θ range of 2–40° that is possible for this system, these measurements were not suitable for Pawley refinement or Rietveld refinement. Powder diffraction patterns for Pawley refinement (phases D-1-B, L-1-B, 5-B and 6-B) or Rietveld refinement (phases rac-1, D-1-A, 5-A, 5-D, 5-E and 7-C) were measured in transmission mode in a 0.7 mm diameter glass capillary from 2.0 to 80.0° in 2θ with 0.01° steps, using a linear position-sensitive detector and an Oxford Cryosystems 700 Series Cryostream, equipped with a Cryostream Plus controller. Each measurement lasted approximately 15 h. Compound 7-C crystallizes in plates and was therefore additionally measured with amorphous SiO2 in a 2:1 ratio to minimize preferred orientation. The patterns were recorded at 25 (2) °C for rac-1, D-1-A, 5-A, 5-E and 7-C, at 135 (2) °C for 5-D, at 200 (2) °C for 5-B and 6-B, and at 227 (2) °C for D-1-B, L-1-B and the mixture of 5-B + 5-C. The software package WinXPOW (Stoe & Cie, 2005[Stoe & Cie (2005). WinXPOW, Version 2.23. Stoe and Cie, Darmstadt, Germany.]) was used for data acquisition.

2.3. Structure determination from X-ray powder diffraction data

The structure of D-1-A was derived from the known crystal structure of its enantiomer, L-1-A [Cambridge Structural Database (CSD; Allen, 2002[Allen, F. H. (2002). Acta Cryst. B58, 380-388.]) reference code FOPKOK, Jeffrey & Yeon, 1987[Jeffrey, G. A. & Yeon, Y. (1987). Carbohydr. Res. 159, 211-216.]]. The crystal structures of rac-1, 5-A, 5-D, 5-E and 7-C were solved from laboratory X-ray powder diffraction data using real-space methods within the program DASH3.1 (David et al., 2006[David, W. I. F., Shankland, K., Van de Streek, J., Pidcock, E., Motherwell, W. D. S. & Cole, J. C. (2006). J. Appl. Cryst. 39, 910-915.]). The structures were subsequently refined by the Rietveld method using the program TOPAS-Academic4.1 (Coelho, 2007[Coelho, A. A. (2007). TOPAS-Academic, Version 4.1. Coelho Software, Brisbane, Australia.]).

To aid the indexing process and the determination of the space group, the expected volume of an inositol molecule in the solid state was calculated by averaging the molecular volumes of all known inositol crystal structures that had been determined from single-crystal data, yielding 184 ± 5 Å3 at room temperature.

For indexing and structure solution, the powder patterns were truncated to a real-space resolution of about 2.5 Å. The backgrounds were subtracted with a Bayesian high-pass filter (David & Sivia, 2001[David, W. I. F. & Sivia, D. S. (2001). J. Appl. Cryst. 34, 318-324.]). Peak positions for indexing were obtained by fitting approximately 20 manually selected peaks with an asymmetry-corrected full-Voigt function (Thompson et al., 1987[Thompson, P., Cox, D. E. & Hastings, J. B. (1987). J. Appl. Cryst. 20, 79-83.]; Finger et al., 1994[Finger, L. W., Cox, D. E. & Jephcoat, A. P. (1994). J. Appl. Cryst. 27, 892-900.]). The powder patterns could be indexed with monoclinic lattices for rac-1 and 5-A and orthorhombic lattices for 5-D, 5-E and 7-C without ambiguity using the program DICVOL91 (Boultif & Louër, 1991[Boultif, A. & Louër, D. (1991). J. Appl. Cryst. 24, 987-993.]) with the corresponding figures of merit (de Wolff, 1968[Wolff, P. M. de (1968). J. Appl. Cryst. 1, 108-113.]; Smith & Snyder, 1979[Smith, G. S. & Snyder, R. L. (1979). J. Appl. Cryst. 12, 60-65.]) M(20) = 25.1 and F(20) = 57.0 for rac-1, M(20) = 45.8 and F(20) = 88.8 for 5-A, M(17) = 39.1 and F(17) = 61.9 for 5-D, M(20) = 25.5 and F(20) = 42.1 for 5-E and M(20) = 35.8 and F(20) = 66.1 for 7-C, and unit-cell volumes of 713.03 Å3 for rac-1, 743.02 Å3 for 5-A, 1466.88 Å3 for 5-D, 1442.97 Å3 for 5-E and 721.24 Å3 for 7-C after Pawley fit (Pawley, 1981[Pawley, G. S. (1981). J. Appl. Cryst. 14, 357-361.]). With an expected molecular volume of 184 Å3, these volumes correspond to 4, 4, 8, 8 and 4 molecules in the unit cell for rac-1, 5-A, 5-D, 5-E and 7-C, respectively. The close agreement of the indexed unit-cell volumes with the expected unit-cell volumes is another indication that the lattices did not contain further water or other solvent molecules. Using Bayesian statistical analysis (Markvardsen et al., 2001[Markvardsen, A. J., David, W. I. F., Johnson, J. C. & Shankland, K. (2001). Acta Cryst. A57, 47-54.]), the space groups were determined to be P21/c for rac-1, P21/n for 5-A, Pbca for 5-D, P212121 for 5-E and Pca21 for 7-C. Pawley refinements were then applied to extract integrated intensities and their correlations.

For structure solution, the starting molecular geometry for rac-1 was taken from the single-crystal structure of the known polymorph of L-chiro-inositol (L-1-A) (CSD reference code FOPKOK; Jeffrey & Yeon, 1987[Jeffrey, G. A. & Yeon, Y. (1987). Carbohydr. Res. 159, 211-216.]), for 5-A, 5-D and 5-E from cis-inositol monohydrate (5·H2O) (CSD reference code TAZMOW; Freeman et al., 1996[Freeman, H. C., Langs, D. A., Nockolds, C. E. & Oh, Y. L. (1996). Aust. J. Chem. 49, 413-424.]) and for 7-C from polymorph B 7-B (CSD reference code MYINOL01; Khan et al., 2007[Khan, U., Qureshi, R. A., Saeed, S. & Bond, A. D. (2007). Acta Cryst. E63, o530-o532.]). The crystal structures were solved without any problems.

After structure solution, Rietveld refinements were performed. All C atoms in each compound were assigned one global isotropic displacement parameter, as were all O atoms. The isotropic displacement parameter of the H atoms was constrained to be 1.2 times the global isotropic parameter of the parent atom. The preferred orientation in 7-C could not be eliminated and a March–Dollase (Dollase, 1986[Dollase, W. A. (1986). J. Appl. Cryst. 19, 267-272.]) preferred orientation correction was therefore applied. A Mogul (Bruno et al., 2004[Bruno, I. J., Cole, J. C., Kessler, M., Luo, J., Motherwell, W. D. S., Purkis, L. H., Smith, B. R., Taylor, R., Cooper, R. I., Harris, S. E. & Orpen, A. G. (2004). J. Chem. Inf. Comput. Sci. 44, 2133-2144.]) geometry check of the refined crystal structures shows that all z-scores for all bond lengths and all angles are lower than 2.0.

The positions of the H atoms were determined by running short molecular dynamics simulations with the COMPASS force field (Sun, 1998[Sun, H. (1998). J. Phys. Chem. B, 102, 7338-7364.]) in Materials Studio (Accelrys, 2011[Accelrys (2011). Materials Studio, Version 6.0. Accelrys, Inc. San Diego, USA.]) and quenching at regular intervals. The hydrogen-bonding pattern with the lowest energy was transferred to the experimental crystal structure and subsequently energy-minimized using dispersion-corrected density functional theory (Perdew et al., 1996[Perdew, J. P., Burke, K. & Ernzerhof, M. (1996). Phys. Rev. Lett. 77, 3865-3868.]; Grimme, 2006[Grimme, S. (2006). J. Comput. Chem, 27, 1787-1799.]), with the positions of the non-H atoms and the unit cell fixed. In cis-inositol monohydrate, single-crystal analysis showed the H atoms involved in intramolecular hydrogen bonds to be disordered (Freeman et al., 1996[Freeman, H. C., Langs, D. A., Nockolds, C. E. & Oh, Y. L. (1996). Aust. J. Chem. 49, 413-424.]). Our short molecular dynamics simulations show that it is highly likely that the H atoms involved in intramolecular hydrogen bonds in the high-temperature phase 5-D, and probably also in 5-E, are also disordered.

2.4. Thermal analysis (DSC and TGA)

Differential scanning calorimetry (DSC) measurements were performed on a SETARAM (DSC 131) device. For each measurement, about 10 to 15 mg of the sample was filled into an Al crucible and measured at a rate of 1 °C min−1 under an N2 atmosphere. The given values for the temperatures are onset and offset values for the corresponding heating and cooling processes. Thermogravimetric analyses (TGA) were performed on a SETARAM (TGA 92) device. For each measurement, about 15 to 20 mg of the samples was filled into an Al2O3 (corundum) crucible and measured at a rate of 1 °C min−1 under an N2 atmosphere.

2.5. Elemental analysis (EA)

Elemental analyses (CH) were carried out on an Elementar (vario MICRO cube) elemental analyzer. For each measurement, about 1 to 4 mg of the sample were placed into a Sn vessel and measured at 1150 °C under a He atmosphere with the addition of O2 during the measurement. The results are included in the supporting information.

3. Results and discussion

3.1. Overview

Thirteen new phases were found. The crystal structures of all eight ordered phases could be determined, of which seven were determined from laboratory X-ray powder diffraction data. The remaining five phases turned out to be rotator phases and only their unit cells could be determined. Melting points and phase-transition temperatures were recorded for investigated phases. An overview of the results is given in Tables 1[link] and 2[link].

Table 1
Overview of the polymorphs (not including hydrates) of the inositols and their phase transition temperatures

Isomer Phase ρ (g cm−3) Space group Tm (°C) ΔHt (J g−1) Type of phase transition Reference
D-(+)-chiro D-1-A 1.60 P21 201 181.9 Conversion to 1-B This work
D-(+)-chiro D-1-B 1.50 F*** 245 17.0 Melting This work
L-(−)-chiro L-1-A 1.60 P21 202 191.0 Conversion to 1-B Jeffrey & Yeon (1987[Jeffrey, G. A. & Yeon, Y. (1987). Carbohydr. Res. 159, 211-216.])
L-(−)-chiro L-1-B 1.50 F*** 246 16.4 Melting This work
racemic rac-1 1.69 P21/c 250 243.1 Melting This work
scyllo 2-A 1.57 P21/c 358§ 263.1 Decomposition Yeon (2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.]), Day et al. (2006[Day, G. M., Van de Streek, J., Bonnet, A., Burley, J. C. & Jones, W. (2006). Cryst. Growth Des. 6, 2301-2307.])
scyllo 2-B 1.66 [P\bar 1] 360§ Yeon (2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.]), Day et al. (2006[Day, G. M., Van de Streek, J., Bonnet, A., Burley, J. C. & Jones, W. (2006). Cryst. Growth Des. 6, 2301-2307.])
neo 3 1.70 [P\bar 1] 315 Melting Yeon (2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.])
muco 4 1.65 P21/c 290 Melting Craig & James (1979[Craig, D. C. & James, V. J. (1979). Cryst. Struct. Commun. 8, 629-633.])
cis 5-A 1.61 P21/n 152 136.8 Conversion to 5-B This work
cis 5-B 1.51 P3**/P6**†† 215 > 3.6‡‡ Conversion to 5-C This work
cis 5-C 1.47 F*** 351 313.6 Decomposition This work
cis 5-D 1.63 Pbca 156 93.6 Conversion to 5-B This work
cis 5-E 1.66 P212121 57 12.5 Conversion to 5-D This work
allo 6-A 1.68 P21/n 184 197.2 Conversion to 6-B Bonnet et al. (2006a[Bonnet, A., Jones, W. & Motherwell, W. D. S. (2006a). Acta Cryst. E62, o2578-o2579.])
allo 6-B 1.50 F*** 319 23.04 Melting This work
myo 7-A 1.58 P21/c 225 242.7 Melting Rabinovich & Kraut (1964[Rabinovich, I. N. & Kraut, J. (1964). Acta Cryst. 17, 159-168.])
myo 7-B 1.65 Pna21 Khan et al. (2007[Khan, U., Qureshi, R. A., Saeed, S. & Bond, A. D. (2007). Acta Cryst. E63, o530-o532.])
myo 7-C 1.66 Pca21 170 −31.8 Conversion to 7-A This work
epi 8 1.66 P21/c 304 Melting Jeffrey & Kim (1971[Jeffrey, G. A. & Kim, H. S. (1971). Acta Cryst. B27, 1812-1817.])
†Rotator phase, cubic, space group unknown, see text.
‡Onset/offset melting point from DSC measurements in this publication.
§Melting points of 2-A and 2-B given as 360 °C by Yeon (2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.]); we observed decomposition at 358 °C for 2-A.
¶See Simperler et al. (2006[Simperler, A., Watt, S. W., Bonnet, P. A., Jones, W. & Motherwell, W. D. S. (2006). CrystEngComm, 8, 589-600.]).
††Rotator phase, hexagonal, space group unknown, see text.
‡‡Conversion is incomplete.

Table 2
Crystallographic data for the structures determined from X-ray powder diffraction data

  rac-1 D-1-A 5-A 5-D 5-E 7-C
Crystal data
Chemical formula C6H12O6 C6H12O6 C6H12O6 C6H12O6 C6H12O6 C6H12O6
Mr 180.16 180.16 180.16 180.16 180.16 180.16
Crystal system, space group Monoclinic, P21/c Monoclinic, P21 Monoclinic, P21/n Orthorhombic, Pbca Orthorhombic, P212121 Orthorhombic, Pca21
Temperature (K) 293 293 293 408 293 293
a (Å) 10.1435 (6) 6.86637 (11) 11.58792 (19) 14.1313 (2) 14.01476 (14) 11.8577 (3)
b (Å) 8.1542 (4) 9.12272 (14) 12.2101 (2) 11.0757 (2) 11.03782 (11) 7.01486 (16)
c (Å) 8.6239 (4) 6.21914 (10) 5.25364 (10) 9.36191 (18) 9.33193 (12) 8.68032 (19)
α (°) 90 90 90 90 90 90
β (°) 92.3556 (15) 106.5963 (6) 90.5649 (7) 90 90 90
γ (°) 90 90 90 90 90 90
V3) 712.70 (7) 373.338 (10) 743.30 (2) 1465.27 (5) 1443.58 (3) 722.03 (3)
Vmol3) 178 187 186 183 180 181
Z 4 2 4 8 8 4
Radiation type Cu Kα1, λ = 1.54056 Å
μ (mm−1) 1.33 1.27 1.28 1.30 1.31 1.31
Specimen shape, size (mm) Cylinder, 10 × 0.7 Cylinder, 10 × 0.7 Cylinder, 10 × 0.7 Cylinder, 10 × 0.7 Cylinder, 10 × 0.7 Cylinder, 10 × 0.7
             
Data collection
Diffractometer Stoe Stadi-P diffractometer
Specimen mounting Glass capillary
Data collection mode Transmission
Scan method Step
2θ values (°) 2θmin = 2.0, 2θmax = 79.99, 2θstep = 0.01
             
Refinement
Rwp 0.0577 0.0329 0.0408 0.0356 0.0331 0.04336
Rp 0.0411 0.0252 0.0304 0.0259 0.0244 0.0326
Rexp 0.0198 0.0239 0.0302 0.0274 0.0274 0.0369
Rwp 0.1235 0.0787 0.0827 0.0816 0.0686 0.1021
Rp 0.1024 0.0793 0.0779 0.0758 0.0611 0.1117
Rexp 0.0423 0.0571 0.0613 0.0628 0.0567 0.0870
χ2 8.510 1.896 1.825 1.687 1.464 1.378
No. of data points 7800 7800 7800 7800 7800 7599
No. of parameters 102 69 64 65 90 65
No. of restraints 66 66 66 66 132 66
H-atom treatment Calculated Calculated Calculated Calculated Calculated Calculated
Rwp, Rp and Rexp denote the values after background subtraction.
‡Calculated by molecular dynamics followed by energy-minimization with DFT-D (see text).

3.2. chiro-Inositols (1)

chiro-Inositol (1) exists in two enantiomers, D-(+)- and L-(−)-chiro-inositol. Both pure enantiomers and the racemate, rac-1, were investigated.

3.2.1. D-(+)- and L-(−)-chiro-inositols

The crystals initially obtained for D-(+)-chiro-inositol turned out to be a 1/3 hydrate, D-1·1/3H2O, as determined by single-crystal analysis. Hydrates are also known for cis-inositol (Freeman et al., 1996[Freeman, H. C., Langs, D. A., Nockolds, C. E. & Oh, Y. L. (1996). Aust. J. Chem. 49, 413-424.]) and for myo-inositol (Bonnet et al., 2006b[Bonnet, A., Jones, W. & Motherwell, W. D. S. (2006b). Acta Cryst. E62, o2902-o2904.]; CSD reference code MYTOLD01). DSC analysis of D-1·1/3H2O shows a broad­ened endothermic signal with an onset at about 74 °C resulting from the loss of water and conversion of the 1/3 hydrate to the known anhydrate (D-1-A) (Jeffrey & Yeon, 1987[Jeffrey, G. A. & Yeon, Y. (1987). Carbohydr. Res. 159, 211-216.]). The TGA curve shows a mass loss of about 2.98% between 83 and 93 °C corresponding to a loss of approximately 0.3 water molecules per D-(+)-chiro-inositol molecule (Fig. 2[link]).

[Figure 2]
Figure 2
Combined DSC (red) and TGA (black) traces of the 1/3 hydrate of D-(+)-chiro-inositol (D-1·1/3H2O) measured from 20 to 400 °C.

In the DSC, three further endothermic signals could be observed; the first sharp peak at 201 °C resulting from a phase transition to the high-temperature polymorph, (D-1-B), the second sharp peak at 245 °C from melting and a third broad signal between 281 and 337 °C resulting from decomposition. The enthalpy of the phase transition at 201 °C is remarkably large, whereas the melting enthalpy at 245 °C is remarkably small. This is because the high-temperature phase (D-1-B) is a rotator phase (see §3.9[link]) and the major part of the melting process takes place at 201 °C, with only the translational order of the centres of mass of the molecules remaining. This translational order is then lost when the final melting takes place at 245 °C.

The phases were identified by measuring T-XRPD patterns before and after the phase transitions (see Fig. 3[link]).

[Figure 3]
Figure 3
Temperature-dependent X-ray powder diffraction traces of D-(+)-chiro-inositol (D-1) at 25, 100 and 210 °C showing the phase transitions from the 1/3 hydrate (black) (D-1·1/3H2O) to the anhydrate (red) (D-1-A) and to the high-temperature polymorph (blue) (D-1-B).

The DSC and TGA curves and the XRPD patterns of L-1 are the same as for its enantiomer D-1.

The crystal structures of the two 1/3 hydrates, L-1·1/3H2O and D-1·1/3H2O, will not be discussed in this paper, and this paper therefore only reports and discusses 11 of the 13 new phases.

The crystal structure of the room-temperature phase L-1-A was determined by Jeffrey & Yeon (1987[Jeffrey, G. A. & Yeon, Y. (1987). Carbohydr. Res. 159, 211-216.]). The enantiomeric crystal structure of D-1-A was established by Rietveld refinement (see the supporting information for full details). The molecules are connected to their neighbours by 12 hydrogen bonds (as determined with Mercury; Macrae et al., 2008[Macrae, C. F., Bruno, I. J., Chisholm, J. A., Edgington, P. R., McCabe, P., Pidcock, E., Rodriguez-Monge, L., Taylor, R., Van de Streek, J. & Wood, P. A. (2008). J. Appl. Cryst. 41, 466-470.]). Each —OH group acts as a donor and as an acceptor for one intermolecular hydrogen bond each, resulting in a three-dimensional network.

D-1-A does not rehydrate upon cooling to room temperature. The reversibility of the melting process and of the transition from 1-A to 1-B was not investigated. For structural investigations of the high-temperature rotator phases L-1-B and D-1-B, see §3.9[link].

3.2.2. Racemic chiro-inositol

The DSC analysis of rac-chiro-inositol, rac-1, shows only one endothermic signal at 250 °C from melting, which is 4–5 °C higher than for the pure enantiomers. Decomposition occurs as a broad signal between 308 and 344 °C. The TGA curve shows no mass loss before melting (see Fig. 4[link]).

[Figure 4]
Figure 4
Combined DSC (red) and TGA (black) traces of rac-chiro-inositol (rac-1) measured from 20 to 400 °C showing the melting of rac-1 at 250 °C.

The crystal structure of rac-1 (see Fig. 5[link]) was determined from powder diffraction data (the Rietveld refinement plot is shown in the supporting information). The compound crystallizes in the space group P21/c with one molecule in the asymmetric unit. Each molecule is connected to the other molecules through 12 hydrogen bonds. In contrast to D-1-A and L-1-A, one O atom (O3) accepts two hydrogen bonds, while another (O2) accepts none.

[Figure 5]
Figure 5
Crystal structure of racemic chiro-inositol (rac-1). Space group P21/c, view along the b axis (a axis shown in red, c axis shown in blue). Hydrogen bonds are indicated as dashed blue lines, H atoms have been omitted for clarity.

3.3. scyllo-Inositol (2)

DSC analysis of 2-A shows only one sharp endothermic signal at 358 °C resulting from decomposition. TGA measurements show no mass loss or gain until 330 °C. Further heating results in decomposition (see Fig. 6[link]).

[Figure 6]
Figure 6
Combined DSC (red) and TGA (black) traces of scyllo-inositol (2-A) measured from 20 to 500 °C showing the decomposition of 2-A at 358 °C.

To determine the unknown melting point of the second reported polymorph of scyllo-inositol (2-B, Yeon, 2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.]; Day et al., 2006[Day, G. M., Van de Streek, J., Bonnet, A., Burley, J. C. & Jones, W. (2006). Cryst. Growth Des. 6, 2301-2307.]), a sample of pure 2-B had to be prepared. Whereas samples of 100% 2-A can be routinely obtained, 2-B always crystallizes in the presence of 2-A (Yeon, 2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.]; Day et al., 2006[Day, G. M., Van de Streek, J., Bonnet, A., Burley, J. C. & Jones, W. (2006). Cryst. Growth Des. 6, 2301-2307.]). Repeated attempts to crystallize 2-B using crystallization experiments from methanol/water as indicated in the publication of Day et al. failed to reproduce the polymorph. Vapour diffusion experiments were performed by dissolving 50, 40 and 30 mg samples of 2-A in 3 ml water using an ultrasonic bath. The solutions were filtered using a filter paper with a porosity under 2.7 µm and filled into vials. The first set of solutions (containing 50, 40 and 30 mg dissolved in 3 ml water) were deposited without a lid into screw-top jars containing 10 ml methanol. In order to minimize the diffusion velocity of methanol into the solutions containing scyllo-inositol, the second set of vials was closed with snap-on lids perforated with a 0.9 mm cannula. Additionally, antisolvent crystallization experiments were performed by dissolving scyllo-inositol in the same manner as for the vapour diffusion experiments. Afterwards, portions of about 7 ml methanol were added, at first fast to each of the first set of experiments using a syringe and then slowly by placing methanol carefully over the solution containing scyllo-inositol to yield a two-phase system. In each experiment, different ratios of 2-A and 2-B were obtained, but these experiments also failed to produce pure 2-B. We were therefore not able to determine the melting point of 2-B. The DSC measurements of the mixtures of 2-A and 2-B showed two separate but barely resolved events, with onsets at about 359 and 364 °C.

The crystal structures of both polymorphs were reported by Yeon (2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.]); CSD reference codes EFURIH01 and EFURIH02 for 2-A and 2-B, respectively.

3.4. neo-Inositol (3) and muco-inositol (4)

The crystal structures of neo-inositol (3) and muco-inositol (4) were reported by Yeon (2001[Yeon, Y. (2001). Korean J. Crystallogr. 12, 150-156.]; CSD reference code YEPNOW01) and Craig & James (1979[Craig, D. C. & James, V. J. (1979). Cryst. Struct. Commun. 8, 629-633.]; CSD reference code MUINOS), respectively. For their melting points, see Simperler et al. (2006[Simperler, A., Watt, S. W., Bonnet, P. A., Jones, W. & Motherwell, W. D. S. (2006). CrystEngComm, 8, 589-600.]). Considering the number of new phases discovered in our relatively straightforward heating experiments, it must be assumed that additional experiments on neo- and muco-inositol (not considered in our experiments) will reveal additional phases.

3.5. cis-Inositol (5)

DSC analysis of 5-A shows a sharp endothermic signal at 152 °C resulting from the phase transition to a high-temperature form 5-B. Furthermore, 5-B shows a phase transition to another high-temperature form labelled as 5-C. As was the case for D-1-B, the high value of the phase transition enthalpy from 5-A to 5-B is due to the fact that 5-B and 5-C are rotator phases. Upon further heating, a simultaneous melting/decomposition process occurs at 350 °C (Fig. 7[link]).

[Figure 7]
Figure 7
Combined DSC (red) and TGA (black) traces of cis-inositol (5-A) measured from 20 to 400 °C showing the phase transition of polymorph 5-A to 5-B at 152 °C and 5-B to 5-C at 215 °C until melting/decomposition of 5-C at 350 °C.

For identification of the polymorphs, T-XRPD patterns were measured before and after the phase transitions as shown in Fig. 8[link]. The XRPD patterns show that the transition from 5-B to 5-C at 215 °C is incomplete, resulting in a mixture of 5-B and 5-C. However, the newly appearing peaks in 5-C have a very different peak width (as measured by the full width at half maximum) than the peaks from 5-B, which indicates that 5-C is a true separate phase.

[Figure 8]
Figure 8
Temperature-dependent X-ray powder diffraction traces of cis-inositol (5) at 20, 200 and up to 227 °C showing the phase transition of polymorph 5-A (black) to the first high-temperature polymorph 5-B (red) to the second high-temperature polymorph 5-C (blue). The asterisks (green) denote new reflections caused by polymorph 5-C.

When polymorph 5-B is cooled from 200 °C to room temperature, it does not convert back to 5-A, but forms two new polymorphs: at 141 °C form 5-B transforms to 5-D, which at 57 °C converts to form 5-E (Fig. 9[link]). Therefore, it can be assumed that 5-D is an additional high-temperature form of cis-inositol. To identify the polymorphic forms that appeared during DSC measurement, T-XRPD patterns were recorded as shown in Fig. 10[link].

[Figure 9]
Figure 9
DSC trace of cis-inositol measured from 200 °C down to room temperature showing the phase transition of polymorph 5-B to 5-D at 141 °C and 5-D to 5-E at 57 °C.
[Figure 10]
Figure 10
Temperature-dependent X-ray powder diffraction traces of cis-inositol (5) at 200, 135 and down to 20 °C showing the phase transitions of polymorph 5-B (black) to polymorph 5-D (red) to polymorph (5-E) (blue). 5-D and 5-E can be indexed with the same unit cell; the asterisks (green) denote the reflections that are visible in 5-E but that are systematic absences in 5-D.

These transformations are reversible: upon heating, 5-E changes back to 5-D at 57 °C, to 5-B at 156 °C and to 5-C at 215 °C, which finally shows a melting/decomposition point at 351 °C (Fig. 11[link]). For the identification of the polymorphs occurring during the DSC measurement, T-XRPD patterns were measured before and after the phase transitions as shown in Fig. 12[link]. After all T-XRPD measurements, a final rapid cooling process from 227 to 20 °C led to a conversion of polymorph 5-C to 5-E. The TGA curves show no mass loss or gain during these heating and cooling processes, except at the melting/decomposition points.

[Figure 11]
Figure 11
DSC trace of cis-inositol (5) measured from 20 up to 400 °C showing the phase transition of polymorph 5-E back to 5-D at 57 °C, 5-D back to 5-B at 156 °C and 5-B to 5-C at 215 °C until melting/decomposition of 5-C at 351 °C.
[Figure 12]
Figure 12
Temperature-dependent X-ray powder diffraction traces of cis-inositol (5) at 20, 135, 200 and up to 227 °C showing the phase transitions of 5-E (black) to polymorph 5-D (red) to polymorph 5-B (blue) and finally to a mixture of polymorphs 5-B and 5-C (green).

The crystal structures of the ordered phases 5-A, 5-D and 5-E were solved and refined from laboratory X-ray powder diffraction data. The Rietveld plots are shown in the supporting information.

In 5-A, each molecule forms one intramolecular hydrogen bond and ten intermolecular hydrogen bonds (five as donors, five as acceptors; Fig. 13[link]).

[Figure 13]
Figure 13
Crystal structure of 5-A. Space group P21/n, view along the c axis (a axis shown in red, b axis shown in green). Hydrogen bonds are indicated as dashed blue lines, H atoms have been omitted for clarity.

5-D is a high-temperature polymorph that only exists above 57 °C and that converts to 5-E on cooling. The crystal structures of 5-D and 5-E are very similar and share the same unit-cell parameters. The phase transition corresponds to the loss of the inversion symmetry to lower the space-group symmetry from Pbca, Z′ = 1 to one of its maximum subgroups P212121, Z′ = 2 (see overlay in Fig. 14[link]). In 5-D and 5-E, each molecule forms one intramolecular and ten intermolecular hydrogen bonds.

[Figure 14]
Figure 14
Overlay of the crystal structures of 5-D (red, Pbca, Z′ = 1) and 5-E (blue, P212121, Z′ = 2). View approximately along the c axis (a axis shown in red, b axis shown in green, c axis shown in blue), H atoms have been omitted for clarity.

Interestingly, the C3v-symmetrical cis-inositol (σ = 3) has five different polymorphs, of which two are rotator phases, the first even at quite a low temperature (156 °C). In contrast, the D3d-symmetrical scyllo-inositol (σ = 6) exhibits neither a rotator phase nor any other phase transition up to its decomposition at 355 °C.

The crystal structure of cis-inositol monohydrate (5·H2O) was determined by Freeman et al. (1996[Freeman, H. C., Langs, D. A., Nockolds, C. E. & Oh, Y. L. (1996). Aust. J. Chem. 49, 413-424.]). This inositol phase is the only previously reported inositol phase with less than 12 hydrogen bonds per molecule. 5·H2O crystallizes in P21/c with two molecules in the asymmetric unit; one molecule forms 11 hydrogen bonds, the other only ten.

3.6. allo-Inositol (6)

DSC analysis of allo-inositol shows a sharp endothermic signal with a minimum at about 184 °C resulting from the phase transition from polymorph 6-A to the high-temperature polymorph 6-B. Two further endothermic signals could be observed; the first onset at 319 °C resulting from melting of polymorph 6-B and the second sharp endothermic signal at 334 °C resulting from decomposition. 6-B is another rotator phase, again explaining the unusually high enthalpy of the transition from 6-A to 6-B (Fig. 15[link]).

[Figure 15]
Figure 15
DSC trace of allo-inositol measured from 20 up to 400 °C showing the phase transition of polymorph 6-A to 6-B at 184 °C, melting of 6-B at 319 °C and decomposition at 334 °C.

T-XRPD measurements were performed before and after the phase transition as observed in the DSC (Fig. 15[link]), see Fig. 16[link].

[Figure 16]
Figure 16
Temperature-dependent X-ray powder diffraction traces of allo-inositol (6) at 20, 170 and 200 °C showing the phase transition of polymorph 6-A (black and red), which is stable up to the minimum 170 °C, to polymorph 6-B at 200 °C (blue).

The crystal structure of the room-temperature phase 6-A was determined by Bonnet et al. (2006a[Bonnet, A., Jones, W. & Motherwell, W. D. S. (2006a). Acta Cryst. E62, o2578-o2579.]; CSD reference code IFAKAC); for the rotator phase 6-B see §3.9[link].

3.7. myo-Inositol (7)

We redetermined the melting point of polymorph 7-A using DSC measurement (Fig. 17[link]). The crystal structure of 7-A was published by Rabinovich & Kraut (1964[Rabinovich, I. N. & Kraut, J. (1964). Acta Cryst. 17, 159-168.]; CSD reference code MYINOL).

[Figure 17]
Figure 17
DSC trace of myo-inositol (7) measured from 20 up to 400 °C showing its melting point of polymorph 7-A at 225 °C and its decomposition between 306 and 363 °C.

To determine the unknown melting point of the second reported polymorph of myo-inositol (7-B, Khan et al., 2007[Khan, U., Qureshi, R. A., Saeed, S. & Bond, A. D. (2007). Acta Cryst. E63, o530-o532.]; CSD reference code MYINOL01), a sample of 7-B had to be prepared. Repeated attempts to crystallize 7-B including crystallizations from ethanol/ethyl acetate 60:40 as indicated in the publication of Khan et al. and additional solvent-assisted grinding experiments failed to reproduce the polymorph. The authors of the paper were contacted, but the sample was no longer available. We were therefore not able to determine the melting point of 7-B.

Although we did not obtain 7-B, we could observe a third polymorph of myo-inositol (7-C) during thermal analyses on polymorph 7-A. Polymorph 7-C was obtained during DSC measurements by heating 7-A to 280 °C until 7-A had melted completely. During the cooling down process to 20 °C, 7-C crystallizes from the melt at 189 °C and is stable at 20 °C (Fig. 18[link]). It appears that a slow cooling rate yields form 7-C from the melt, whereas a fast cooling rate yields form 7-A from the melt.

[Figure 18]
Figure 18
DSC trace of myo-inositol (7) measured from 280 down to 20 °C showing the transformation from the melt to polymorph 7-C at 189 °C.

Heating 7-C to 280 °C, at 170 °C it transforms back to 7-A, which melts at 225 °C (see Fig. 19[link]); this transition is reproducible.

[Figure 19]
Figure 19
DSC trace of myo-inositol (7) measured from 20 up to 280 °C showing the phase transition of 7-C back to 7-A at 170 °C, and the melting point of polymorph 7-A at 225 °C.

T-XRPD measurements with the HUBER heater device and an imaging-plate position-sensitive detector were performed before and after the phase transitions observed in the DSC measurements (Fig. 20[link]).

[Figure 20]
Figure 20
Temperature-dependent X-ray powder diffraction traces of myo-inositol (7) at 20 up to 280 down to 20 and up to 200 °C showing the melt of polymorph 7-A (black and red), recrystallization to 7-C (blue) and phase transition back to 7-A (green).

A final cool-down of the melt shown in Fig. 19[link] led to the recrystallization of polymorph 7-A (see Fig. S13[link] in the supporting information).

At room temperature, 7-C slowly converts to 7-A over time. See the supporting information for further information.

The crystal structure of 7-C was solved from laboratory X-ray powder diffraction data using real-space methods. The Rietveld refinement is shown in the supporting information.

The new polymorph of myo-inositol (7-C) crystallizes in Pca21 with one molecule in the asymmetric unit. Each molecule is connected to the other molecules through 12 hydrogen bonds (Fig. 21[link]).

[Figure 21]
Figure 21
Crystal structure of 7-C. Space group Pca21, view along the b axis (a axis shown in red, c axis shown in blue). Hydrogen bonds are indicated as dashed blue lines, H atoms have been omitted for clarity.

3.8. epi-Inositol (8)

The crystal structure of epi-inositol (8) was determined by Jeffrey & Kim (1971[Jeffrey, G. A. & Kim, H. S. (1971). Acta Cryst. B27, 1812-1817.]; CSD reference code EPINOS). For the melting point, see Simperler et al. (2006[Simperler, A., Watt, S. W., Bonnet, P. A., Jones, W. & Motherwell, W. D. S. (2006). CrystEngComm, 8, 589-600.]). Considering the number of new phases discovered in our relatively straightforward heating experiments, it must be assumed that additional experiments on epi-inositol, not considered in our experiments, will reveal additional phases.

3.9. Rotator phases

The peak positions and intensities in the X-ray powder patterns of D-1-B, L-1-B, 5-C and 6-B are the same, and it must therefore be assumed that these phases – though consisting of chemically different molecules – are isostructural. The patterns contain only six peaks, which can be indexed with an orthorhombic, a tetragonal, a hexagonal or a cubic unit cell; these unit cells all have unit-cell parameters in common. Only the unit-cell volume of the cubic unit cell is chemically sensible, with the other unit-cell volumes being smaller than the volume of a single inositol molecule at room temperature. The volume of the cubic unit cell is 800 Å3 (a = 9.3 Å) and based on the systematic absences, it must be F-centred; this yields a plausible molecular volume of 200 Å3, which is about 8% larger than the molecular volume in the room-temperature phases. The Pawley refinements can be found in the supporting information.

We conclude from the unusually high space-group symmetry, the low densities, the high temperatures at which these phases occur and the high enthalpies for the transitions between the ordered phases to these high-temperature phases that these structures are rotator phases. That also explains how the crystal structures of three chemically different species can be isostructural.

The X-ray powder pattern of 5-B consists of only nine reflections. The powder pattern could be indexed by a hexagonal cell without ambiguity (a = 6.575, c = 10.580 Å); the unit-cell volume is 396.05 Å3, corresponding to Z = 2. The Pawley refinement can be found in the supporting information.

As was the case for D-1-B, L-1-B, 5-C and 6-B, we conclude from the unusually high space-group symmetry, the low density, the high temperature at which this phase occurs and from the high transition energy between 5-A and 5-B, that 5-B is also a rotator phase.

3.10. Calculation of corrected melting points

Equation (4) in the paper by Wei (1999[Wei, J. (1999). Ind. Eng. Chem. Res. 38, 5019-5027.])

[T_{\rm{m}}^{'} = {{{T_{\rm{m}}}} \over {\displaystyle 1 + {{R\ln ({\rm{\sigma }}){T_{\rm{m}}}} \over {{H_{\rm{m}}}}}}} \eqno(1)]

allows the calculation of corrected melting points: the melting point a compound would have if it had no internal symmetry. It is these corrected melting points that should be correlated with e.g. lattice energies, densities or number of hydrogen bonds. In equation (1)[link], [T{\,}'_{\rm m}] is the corrected melting point, Tm is the experimental melting point, Hm is the melting enthalpy and σ is the molecule's symmetry number. Because of the observed polymorphism, it would be incorrect to speak of `the' melting point for an inositol: each polymorph has its own Tm, Hm and Tm′, just like each polymorph has its own hydrogen-bonding pattern and lattice energy.

The quantitative evaluation of the corrected melting points through equation (1)[link] is hampered by several problems:

  • (1) The definition of the molecular symmetry number σ in equation (1)[link] assumes that the molecules are rigid. In our values for σ, we have ignored the flexible H atoms of the hydroxyl groups [a more rigorous calculation of σ for flexible molecules has been published (Gilson & Irikura, 2010[Gilson, M. K. & Irikura, K. K. (2010). J. Phys. Chem. B, 114, 16304-16317.]), but this is beyond the scope of this paper].

  • (2) Many polymorphs show phase transitions below their melting point, in which case Tm and Hm cannot be measured directly (see Fig. 22[link]). In principle, these values can be derived from other experimental data (Yu, 1995[Yu, L. (1995). J. Pharm. Sci. 84, 966-974.]), but this has not been attempted in the current paper.

  • (3) scyllo-Inositol and cis-inositol decompose before melting.

  • (4) The correction that is applied is based on the assumption that the molecules in the liquid phase can rotate freely whereas those in the solid state do not rotate at all, causing the large difference in rotational entropy between the solid and the liquid phase. The rotator phases D-1-B, L-1-B, 5-B, 5-C and 6-B, however, clearly violate this assumption.

[Figure 22]
Figure 22
Virtual melting point Tm,A of phase A: the Gibbs free energies of phase A, phase B and the liquid as a function of temperature are shown. Phase A is the most stable phase at low temperature, and when the temperature increases phase A converts to phase B before melting. Tm,A and Hm,A cannot be measured directly (at ambient pressure), but Tm,A must lie between TA→B and Tm,B. The temperature dependence of the Gibbs free energies is represented as straight lines for clarity, in reality these lines are curved. A similar situation occurs when a phase decomposes before melting. The most stable phase at each temperature is shown in bold.

Given these complications, we are not able to give a rigorous quantitative analysis of the melting points of the inositols. The only corrected melting point that can be calculated with the current data is that of rac-chiro-inositol (rac-1), for which Tm′ = 221 °C.

4. Conclusions

The aims of this work were to find the high-melting polymorph of allo-inositol (6-B), to determine Hm of scyllo-inositol (2-A), to determine the melting point of the second polymorph of myo-inositol (7-B) and to determine the crystal structures and corrected melting points of rac-chiro-inositol (rac-1) and cis-inositol (5).

We were able to identify the high-melting polymorph of allo-inositol (6-B) as a rotator phase, establish its unit cell and measure its melting point. HA→B and Hm,B were also measured. scyllo-Inositol (2-A) decomposes before melting, and we were therefore not able to measure Hm. The second known polymorph (2-B) could not be reproduced in pure form. The second polymorph of myo-inositol (7-B) proved elusive. A third polymorph was discovered (7-C), but it converts to the known first polymorph (7-A) before melting. Although Hm,A was measured, myo-inositol has no molecular symmetry and its melting point remains at 225 °C. We were able to solve the crystal structure of rac-chiro-inositol and to measure Hm and Tm to determine its corrected melting point as 221 °C. The phase behaviour of cis-inositol turned out to be unexpectedly complex. Five polymorphs were identified; for three of these (5-A, 5-D and 5-E), the crystal structures were solved from XRPD data, the remaining two structures are rotator phases (5-B and 5-C). cis-Inositol decomposes before melting. Additionally, we established that the phase behaviour and crystal structures of L-chiro-inositol and D-chiro-inositol are the same, as expected.

Including hydrates and rotator phases, and counting enantiomers separately, 13 new phases are reported in this paper, bringing the total number of known phases for the inositols to 24, of which four are hydrates and five are rotator phases.

Our experiments have revealed a complex picture of phases, rotator phases and phase transitions, in which a simple correlation between melting points and hydrogen-bonding patterns is not feasible. A thorough discussion of the melting points of these 24 phases requires future work to determine the virtual melting points.

CCDC deposition numbers: 891302–891305, 891307 and 891309.

Supporting information


Computing details top

For all compounds, data collection: WINXPOW (Stoe & Cie, 2005); cell refinement: TOPAS Academic 4.1 (Coelho, 2007); data reduction: DASH 3.1 (David et al., 2006); program(s) used to solve structure: DASH 3.1 (David et al., 2006); program(s) used to refine structure: TOPAS Academic 4.1 (Coelho, 2007); molecular graphics: Mercury (Macrae et al., 2008).

Figures top
[Figure 1]
[Figure 2]
[Figure 3]
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[Figure 5]
[Figure 6]
[Figure 7]
[Figure 8]
[Figure 9]
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[Figure 18]
[Figure 19]
[Figure 20]
[Figure 21]
[Figure 22]
cis-1,2,3,4,5,6-cyclohexanehexol (5-A) top
Crystal data top
C6H12O6F(000) = 384.0
Mr = 180.16alternate setting of space-group P21/c
Monoclinic, P21/nDx = 1.610 Mg m3
a = 11.58792 (19) ÅCu Kα1 radiation, λ = 1.54056 Å
b = 12.2101 (2) ŵ = 1.28 mm1
c = 5.25364 (10) ÅT = 293 K
β = 90.5649 (7)°white
V = 743.30 (2) Å3cylinder, 10 × 0.7 mm
Z = 4
Data collection top
STOE Stadi-P
diffractometer
Data collection mode: transmission
Radiation source: sealed x-ray tubeScan method: step
primary focussing Ge 1112θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Specimen mounting: 0.7mm glass capillary
Refinement top
Least-squares matrix: full with fixed elements per cycle64 parameters
Rp = 0.07866 restraints
Rwp = 0.0830 constraints
Rexp = 0.061H-atom parameters not refined
χ2 = 1.825Weighting scheme based on measured s.u.'s
7800 data points(Δ/σ)max = 0.001
Excluded region(s): noneBackground function: Chebyshev function with 20 terms
Profile function: Fundamental ParametersPreferred orientation correction: none
Crystal data top
C6H12O6V = 743.30 (2) Å3
Mr = 180.16Z = 4
Monoclinic, P21/nCu Kα1 radiation, λ = 1.54056 Å
a = 11.58792 (19) ŵ = 1.28 mm1
b = 12.2101 (2) ÅT = 293 K
c = 5.25364 (10) Åcylinder, 10 × 0.7 mm
β = 90.5649 (7)°
Data collection top
STOE Stadi-P
diffractometer
Scan method: step
Specimen mounting: 0.7mm glass capillary2θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Data collection mode: transmission
Refinement top
Rp = 0.078χ2 = 1.825
Rwp = 0.0837800 data points
Rexp = 0.06164 parameters
RBragg = ?66 restraints
R(F) = ?H-atom parameters not refined
R(F2) = ?
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C10.28779 (9)0.75361 (9)0.1126 (2)0.02213
H1'0.323830.833120.054950.02656
O10.28150 (12)0.74816 (14)0.3813 (2)0.02817
H10.303580.820090.452210.02656
C20.36888 (9)0.66349 (9)0.0023 (2)0.02213
H2'0.380640.683480.199980.02656
O20.47975 (10)0.66851 (13)0.1181 (2)0.02817
H20.469290.661660.302570.02656
C30.31524 (9)0.54969 (9)0.0122 (2)0.02213
H3'0.373700.493940.090120.02656
O30.30578 (11)0.51237 (11)0.2691 (2)0.02817
H30.344870.440540.290550.02656
C40.19976 (9)0.54954 (9)0.1302 (2)0.02213
H4'0.219120.582570.320920.02656
O40.15454 (13)0.44217 (10)0.1530 (2)0.02817
H40.071750.444770.201580.02656
C50.11491 (9)0.62963 (9)0.0105 (2)0.02213
H5'0.034690.632540.124450.02656
O50.08204 (11)0.59585 (13)0.2425 (2)0.02817
H50.149540.556480.313380.02656
C60.16628 (9)0.74511 (9)0.0089 (2)0.02213
H6'0.169050.775130.205450.02656
O60.08837 (12)0.81296 (10)0.1285 (3)0.02817
H60.080290.780440.298840.02656
Geometric parameters (Å, °) top
C1—H1'1.100O3—H30.993
C1—O11.416 (2)C4—H4'1.105
C1—C21.562 (2)C4—O41.416 (2)
C1—C61.544 (1)C4—C51.527 (2)
O1—H10.987O4—H40.991
C2—H2'1.100C5—H5'1.101
C2—O21.417 (2)C5—O51.446 (2)
C2—C31.523 (1)C5—C61.531 (1)
O2—H20.981O5—H50.988
C3—H3'1.104C6—H6'1.097
C3—O31.430 (2)C6—O61.426 (2)
C3—C41.527 (2)O6—H60.984
H1'—C1—O1109.8C3—C4—H4'105.01
H1'—C1—C2106.74C3—C4—O4111.4 (1)
H1'—C1—C6107.02C3—C4—C5111.25 (9)
O1—C1—C2111.9 (1)H4'—C4—O4109.8
O1—C1—C6110.7 (1)H4'—C4—C5106.08
C2—C1—C6110.42 (9)O4—C4—C5112.9 (1)
C1—O1—H1108.6C4—O4—H4110.4
C1—C2—H2'106.42C4—C5—H5'109.90
C1—C2—O2110.87 (9)C4—C5—O5111.9 (1)
C1—C2—C3112.50 (9)C4—C5—C6109.90 (9)
H2'—C2—O2106.5H5'—C5—O5106.3
H2'—C2—C3106.85H5'—C5—C6107.43
O2—C2—C3113.2 (1)O5—C5—C6111.3 (1)
C2—O2—H2107.5C5—O5—H5105.7
C2—C3—H3'107.06C1—C6—C5114.67 (9)
C2—C3—O3110.98 (9)C1—C6—H6'109.37
C2—C3—C4109.90 (9)C1—C6—O6109.34 (9)
H3'—C3—O3108.43C5—C6—H6'108.52
H3'—C3—C4107.46C5—C6—O6106.85 (9)
O3—C3—C4112.8 (1)H6'—C6—O6107.9
C3—O3—H3110.5C6—O6—H6107.0
cis-1,2,3,4,5,6-cyclohexanehexol (5-D) top
Crystal data top
C6H12O6F(000) = 768.00
Mr = 180.16standard setting
Orthorhombic, PbcaDx = 1.633 Mg m3
a = 14.1313 (2) ÅCu Kα1 radiation, λ = 1.54056 Å
b = 11.0757 (2) ŵ = 1.30 mm1
c = 9.36191 (18) ÅT = 293 K
V = 1465.27 (5) Å3white
Z = 8cylinder, 10 × 0.7 mm
Data collection top
STOE Stadi-P
diffractometer
Data collection mode: transmission
Radiation source: sealed x-ray tubeScan method: step
primary focussing Ge 1112θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Specimen mounting: 0.7mm glass capillary
Refinement top
Least-squares matrix: full with fixed elements per cycle65 parameters
Rp = 0.07666 restraints
Rwp = 0.0820 constraints
Rexp = 0.063H-atom parameters not refined
χ2 = 1.687Weighting scheme based on measured s.u.'s
7800 data points(Δ/σ)max = 0.001
Excluded region(s): noneBackground function: Chebyshev function with 20 terms
Profile function: Fundamental ParametersPreferred orientation correction: none
Crystal data top
C6H12O6V = 1465.27 (5) Å3
Mr = 180.16Z = 8
Orthorhombic, PbcaCu Kα1 radiation, λ = 1.54056 Å
a = 14.1313 (2) ŵ = 1.30 mm1
b = 11.0757 (2) ÅT = 293 K
c = 9.36191 (18) Åcylinder, 10 × 0.7 mm
Data collection top
STOE Stadi-P
diffractometer
Scan method: step
Specimen mounting: 0.7mm glass capillary2θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Data collection mode: transmission
Refinement top
Rp = 0.076χ2 = 1.687
Rwp = 0.0827800 data points
Rexp = 0.06365 parameters
RBragg = ?66 restraints
R(F) = ?H-atom parameters not refined
R(F2) = ?
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C10.11053 (9)0.81674 (11)0.14857 (12)0.03337
H1'0.101030.719790.127480.04004
O10.11967 (13)0.87432 (13)0.01386 (14)0.04678
H10.136970.958620.035750.04004
C20.20024 (9)0.83473 (10)0.23915 (12)0.03337
H2'0.192790.778540.335720.04004
O20.28047 (12)0.78799 (13)0.16547 (15)0.04678
H20.292700.831530.07460.04004
C30.21254 (8)0.96468 (10)0.28828 (13)0.03337
H3'0.271380.966360.366100.04004
O30.23660 (11)1.04196 (13)0.17062 (16)0.04678
H30.215931.126000.187630.04004
C40.12422 (9)1.00414 (10)0.37124 (12)0.03337
H4'0.118000.942370.463220.04004
O40.13406 (14)1.12253 (12)0.42465 (14)0.04678
H40.093171.181210.375700.04004
C50.03470 (9)0.99313 (10)0.28353 (12)0.03337
H5'0.026661.012260.353460.04004
O50.03580 (10)1.07669 (13)0.16512 (17)0.04678
H50.023511.072580.110260.04004
C60.02533 (9)0.86356 (11)0.23176 (13)0.03337
H6'0.016080.803810.325160.04004
O60.05579 (10)0.85770 (15)0.14193 (17)0.04678
H60.110490.851520.207070.04004
Geometric parameters (Å, °) top
C1—H1'1.100O3—H30.988
C1—O11.419 (2)C4—H4'1.103
C1—C21.538 (2)C4—O41.410 (2)
C1—C61.525 (2)C4—C51.513 (2)
O1—H10.987O4—H40.983
C2—H2'1.103C5—H5'1.107
C2—O21.424 (2)C5—O51.444 (2)
C2—C31.521 (2)C5—C61.520 (2)
O2—H20.993O5—H50.984
C3—H3'1.106C6—H6'1.104
C3—O31.436 (2)C6—O61.423 (2)
C3—C41.534 (2)O6—H60.987
H1'—C1—O1106.9C3—C4—H4'106.46
H1'—C1—C2109.0C3—C4—O4111.4 (1)
H1'—C1—C6109.1C3—C4—C5112.49 (9)
O1—C1—C2110.9 (1)H4'—C4—O4107.9
O1—C1—C6111.9 (1)H4'—C4—C5107.88
C2—C1—C6109.0 (1)O4—C4—C5110.5 (1)
C1—O1—H1105.3C4—O4—H4113.0
C1—C2—H2'107.47C4—C5—H5'108.57
C1—C2—O2110.0 (1)C4—C5—O5110.9 (1)
C1—C2—C3112.55 (9)C4—C5—C6108.78 (9)
H2'—C2—O2105.5H5'—C5—O5109.9
H2'—C2—C3107.28H5'—C5—C6107.51
O2—C2—C3113.5 (1)O5—C5—C6111.2 (1)
C2—O2—H2112.1C5—O5—H5111.2
C2—C3—H3'107.5C1—C6—C5114.5 (1)
C2—C3—O3111.0 (1)C1—C6—H6'107.1
C2—C3—C4109.26 (9)C1—C6—O6108.6 (1)
H3'—C3—O3108.5C5—C6—H6'108.9
H3'—C3—C4105.87C5—C6—O6107.6 (1)
O3—C3—C4114.3 (1)H6'—C6—O6110.2
C3—O3—H3111.6C6—O6—H6105.6
cis-1,2,3,4,5,6-cyclohexanehexol (5-E) top
Crystal data top
C6H12O6F(000) = 768.0
Mr = 180.16standard setting
Orthorhombic, P212121Dx = 1.658 Mg m3
a = 14.01476 (14) ÅCu Kα1 radiation, λ = 1.54056 Å
b = 11.03782 (11) ŵ = 1.31 mm1
c = 9.33193 (12) ÅT = 293 K
V = 1443.58 (3) Å3white
Z = 8cylinder, 10 × 0.7 mm
Data collection top
STOE Stadi-P
diffractometer
Data collection mode: transmission
Radiation source: sealed x-ray tubeScan method: step
primary focussing Ge 1112θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Specimen mounting: 0.7mm glass capillary
Refinement top
Least-squares matrix: full with fixed elements per cycle90 parameters
Rp = 0.061132 restraints
Rwp = 0.0690 constraints
Rexp = 0.057H-atom parameters not refined
χ2 = 1.464Weighting scheme based on measured s.u.'s
7800 data points(Δ/σ)max = 0.001
Excluded region(s): noneBackground function: Chebyshev function with 20 terms
Profile function: Fundamental ParametersPreferred orientation correction: none
Crystal data top
C6H12O6V = 1443.58 (3) Å3
Mr = 180.16Z = 8
Orthorhombic, P212121Cu Kα1 radiation, λ = 1.54056 Å
a = 14.01476 (14) ŵ = 1.31 mm1
b = 11.03782 (11) ÅT = 293 K
c = 9.33193 (12) Åcylinder, 10 × 0.7 mm
Data collection top
STOE Stadi-P
diffractometer
Scan method: step
Specimen mounting: 0.7mm glass capillary2θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Data collection mode: transmission
Refinement top
Rp = 0.061χ2 = 1.464
Rwp = 0.0697800 data points
Rexp = 0.05790 parameters
RBragg = ?132 restraints
R(F) = ?H-atom parameters not refined
R(F2) = ?
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C1A0.38767 (13)0.82385 (18)0.3621 (2)0.02099
H1A'0.401430.726920.381690.02519
O1A0.3670 (2)0.8753 (2)0.5001 (2)0.02995
H1A0.340820.955830.474830.02519
C2A0.30109 (13)0.83564 (16)0.2622 (2)0.02099
H2A'0.317420.783000.164210.02519
O2A0.21927 (18)0.7849 (2)0.3292 (3)0.02995
H2A0.161310.807400.271300.02519
C3A0.28551 (13)0.96709 (18)0.21354 (19)0.02099
H3A'0.227120.966790.134780.02519
O3A0.25919 (15)1.0409 (3)0.3349 (3)0.02995
H3A0.283121.124480.321810.02519
C4A0.37579 (13)1.01526 (17)0.1407 (2)0.02099
H4A'0.390310.957360.046850.02519
O4A0.36037 (15)1.13805 (19)0.0976 (3)0.02995
H4A0.317631.140410.013230.02519
C5A0.46161 (14)1.01141 (16)0.23920 (19)0.02099
H5A'0.525951.036650.177140.02519
O5A0.4460 (3)1.0935 (2)0.3532 (2)0.02995
H5A0.503691.100160.413600.02519
C6A0.47698 (13)0.87927 (17)0.2930 (2)0.02099
H6A'0.490990.823950.195960.02519
O6A0.55796 (15)0.8776 (2)0.3841 (2)0.02995
H6A0.568740.793530.415430.02519
C1B0.97075 (13)0.97495 (16)0.3017 (2)0.02099
H1B'1.026780.982860.385330.02519
O1B0.98914 (19)1.0593 (2)0.1902 (3)0.02995
H1B1.046101.037810.135370.02519
C2B0.87372 (13)0.99719 (18)0.3763 (2)0.02099
H2B'0.870810.931310.465430.02519
O2B0.8692 (2)1.11549 (19)0.4332 (2)0.02995
H2B0.824241.124000.515040.02519
C3B0.78870 (14)0.96725 (17)0.27964 (19)0.02099
H3B'0.723970.979010.345830.02519
O3B0.7808 (3)1.0456 (2)0.1550 (2)0.02995
H3B0.786131.131810.183300.02519
C4B0.79385 (13)0.83290 (16)0.2392 (2)0.02099
H4B'0.796840.781340.340390.02519
O4B0.71109 (18)0.7943 (3)0.1609 (2)0.02995
H4B0.656960.803950.227050.02519
C5B0.88707 (13)0.80575 (18)0.1576 (2)0.02099
H5B'0.892300.707390.137310.02519
O5B0.88647 (19)0.8641 (2)0.0187 (2)0.02995
H5B0.871370.949990.037930.02519
C6B0.97369 (13)0.84327 (17)0.24883 (19)0.02099
H6B'0.973010.783860.343320.02519
O6B1.05941 (15)0.8265 (3)0.1693 (2)0.02995
H6B1.064780.742010.133360.02519
Geometric parameters (Å, °) top
C1A—H1A'1.102C1B—H1B'1.111
C1A—O1A1.437 (3)C1B—O1B1.419 (3)
C1A—C2A1.536 (3)C1B—C2B1.548 (3)
C1A—C6A1.535 (3)C1B—C6B1.535 (3)
O1A—H1A0.990O1B—H1B0.977
C2A—H2A'1.107C2B—H2B'1.105
C2A—O2A1.421 (3)C2B—O2B1.411 (3)
C2A—C3A1.536 (3)C2B—C3B1.531 (3)
O2A—H2A1.006O2B—H2B0.994
C3A—H3A'1.100C3B—H3B'1.105
C3A—O3A1.443 (3)C3B—O3B1.454 (3)
C3A—C4A1.531 (3)C3B—C4B1.532 (3)
O3A—H3A0.989O3B—H3B0.990
C4A—H4A'1.103C4B—H4B'1.103
C4A—O4A1.430 (3)C4B—O4B1.436 (3)
C4A—C5A1.514 (3)C4B—C5B1.542 (3)
O4A—H4A0.989O4B—H4B0.984
C5A—H5A'1.107C5B—H5B'1.104
C5A—O5A1.414 (3)C5B—O5B1.447 (3)
C5A—C6A1.558 (3)C5B—C6B1.540 (3)
O5A—H5A0.989O5B—H5B0.988
C6A—H6A'1.110C6B—H6B'1.099
C6A—O6A1.418 (3)C6B—O6B1.424 (3)
O6A—H6A0.985O6B—H6B0.994
H1A'—C1A—O1A105.6H1B'—C1B—O1B109.6
H1A'—C1A—C2A108.7H1B'—C1B—C2B107.0
H1A'—C1A—C6A108.3H1B'—C1B—C6B106.3
O1A—C1A—C2A110.5 (2)O1B—C1B—C2B112.7 (2)
O1A—C1A—C6A112.6 (2)O1B—C1B—C6B112.4 (2)
C2A—C1A—C6A110.8 (2)C2B—C1B—C6B108.6 (1)
C1A—O1A—H1A102.5C1B—O1B—H1B111.9
C1A—C2A—H2A'107.1C1B—C2B—H2B'105.5
C1A—C2A—O2A109.7 (2)C1B—C2B—O2B110.9 (2)
C1A—C2A—C3A111.8 (1)C1B—C2B—C3B112.6 (2)
H2A'—C2A—O2A108.9H2B'—C2B—O2B108.9
H2A'—C2A—C3A106.3H2B'—C2B—C3B105.8
O2A—C2A—C3A112.8 (2)O2B—C2B—C3B112.7 (2)
C2A—O2A—H2A108.6C2B—O2B—H2B113.9
C2A—C3A—H3A'107.5C2B—C3B—H3B'106.5
C2A—C3A—O3A109.7 (2)C2B—C3B—O3B113.7 (2)
C2A—C3A—C4A110.0 (1)C2B—C3B—C4B108.5 (2)
H3A'—C3A—O3A109.6H3B'—C3B—O3B108.3
H3A'—C3A—C4A108.6H3B'—C3B—C4B106.9
O3A—C3A—C4A111.3 (2)O3B—C3B—C4B112.5 (2)
C3A—O3A—H3A110.0C3B—O3B—H3B110.6
C3A—C4A—H4A'107.7C3B—C4B—H4B'106.9
C3A—C4A—O4A109.2 (2)C3B—C4B—O4B112.0 (2)
C3A—C4A—C5A112.2 (2)C3B—C4B—C5B110.5 (1)
H4A'—C4A—O4A110.7H4B'—C4B—O4B108.3
H4A'—C4A—C5A108.6H4B'—C4B—C5B106.9
O4A—C4A—C5A108.5 (2)O4B—C4B—C5B112.0 (2)
C4A—O4A—H4A109.9C4B—O4B—H4B105.7
C4A—C5A—H5A'108.8C4B—C5B—H5B'109.4
C4A—C5A—O5A108.4 (2)C4B—C5B—O5B110.6 (2)
C4A—C5A—C6A109.4 (1)C4B—C5B—C6B110.0 (1)
H5A'—C5A—O5A111.0H5B'—C5B—O5B106.5
H5A'—C5A—C6A107.0H5B'—C5B—C6B107.9
O5A—C5A—C6A112.3 (2)O5B—C5B—C6B112.4 (2)
C5A—O5A—H5A110.5C5B—O5B—H5B105.4
C1A—C6A—C5A113.3 (2)C1B—C6B—C5B114.3 (2)
C1A—C6A—H6A'105.5C1B—C6B—H6B'107.9
C1A—C6A—O6A113.3 (2)C1B—C6B—O6B108.2 (2)
C5A—C6A—H6A'106.1C5B—C6B—H6B'106.1
C5A—C6A—O6A108.4 (2)C5B—C6B—O6B110.0 (2)
H6A'—C6A—O6A109.9H6B'—C6B—O6B110.4
C6A—O6A—H6A108.2C6B—O6B—H6B111.2
cis-1,2,3,5-trans-4,6-cyclohexanehexol (7-C) top
Crystal data top
C6H12O6F(000) = 384.0
Mr = 180.16standard setting
Orthorhombic, Pca21Dx = 1.657 Mg m3
a = 11.8577 (3) ÅCu Kα1 radiation, λ = 1.54056 Å
b = 7.01486 (16) ŵ = 1.31 mm1
c = 8.68032 (19) ÅT = 293 K
V = 722.03 (3) Å3white
Z = 4cylinder, 10 × 0.7 mm
Data collection top
STOE Stadi-P
diffractometer
Data collection mode: transmission
Radiation source: sealed x-ray tubeScan method: step
primary focussing Ge 1112θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Specimen mounting: 0.7mm glass capillary
Refinement top
Least-squares matrix: full with fixed elements per cycle65 parameters
Rp = 0.11266 restraints
Rwp = 0.1020 constraints
Rexp = 0.087H-atom parameters not refined
χ2 = 1.378Weighting scheme based on measured s.u.'s
7800 data points(Δ/σ)max = 0.001
Excluded region(s): noneBackground function: Chebyshev function with 20 terms
Profile function: Fundamental ParametersPreferred orientation correction: preferred orientation correction in direction [001] = 0.84459 with March-Dollase formula (Dollase, 1986)
Crystal data top
C6H12O6V = 722.03 (3) Å3
Mr = 180.16Z = 4
Orthorhombic, Pca21Cu Kα1 radiation, λ = 1.54056 Å
a = 11.8577 (3) ŵ = 1.31 mm1
b = 7.01486 (16) ÅT = 293 K
c = 8.68032 (19) Åcylinder, 10 × 0.7 mm
Data collection top
STOE Stadi-P
diffractometer
Scan method: step
Specimen mounting: 0.7mm glass capillary2θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Data collection mode: transmission
Refinement top
Rp = 0.112χ2 = 1.378
Rwp = 0.1027800 data points
Rexp = 0.08765 parameters
RBragg = ?66 restraints
R(F) = ?H-atom parameters not refined
R(F2) = ?
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C10.00262 (14)0.9090 (3)0.3548 (2)0.01979
H1'0.043460.876530.243630.02375
O10.0503 (2)1.0792 (3)0.4185 (2)0.01979
H10.112001.122380.347930.02375
C20.12206 (16)0.9434 (3)0.3225 (2)0.01979
H2'0.130601.062700.241340.02375
O20.1748 (2)0.9933 (3)0.4659 (2)0.01979
H20.238401.080820.448490.02375
C30.17469 (14)0.7627 (3)0.2522 (2)0.01979
H3'0.128240.733530.144760.02375
O30.29092 (17)0.8003 (4)0.2131 (2)0.01979
H30.295520.867360.111770.02375
C40.16077 (14)0.5881 (3)0.35284 (19)0.01979
H4'0.211970.599750.458220.02375
O40.1976 (2)0.4265 (3)0.2652 (2)0.01979
H40.267630.380270.313740.02375
C50.03700 (15)0.5617 (3)0.4014 (2)0.01979
H5'0.010190.516870.297920.02375
O50.0300 (3)0.4199 (3)0.5187 (2)0.01979
H50.017700.294030.469860.02375
C60.01911 (16)0.7426 (3)0.4610 (2)0.01979
H6'0.016000.776840.575270.02375
O60.13798 (16)0.7124 (3)0.4758 (3)0.01979
H60.153790.644970.574190.02375
Geometric parameters (Å, °) top
C1—H1'1.104O3—H30.999
C1—O11.432 (3)C4—H4'1.101
C1—C21.524 (3)C4—O41.433 (3)
C1—C61.500 (2)C4—C51.538 (2)
O1—H11.001O4—H40.986
C2—H2'1.099C5—H5'1.104
C2—O21.436 (3)C5—O51.427 (3)
C2—C31.539 (2)C5—C61.523 (3)
O2—H20.985O5—H50.990
C3—H3'1.102C6—H6'1.103
C3—O31.444 (3)C6—O61.431 (3)
C3—C41.513 (2)O6—H60.994
H1'—C1—O1109.7C3—C4—H4'111.1
H1'—C1—C2107.3C3—C4—O4107.5 (2)
H1'—C1—C6108.6C3—C4—C5111.1 (1)
O1—C1—C2108.8 (2)H4'—C4—O4109.4
O1—C1—C6111.1 (2)H4'—C4—C5107.9
C2—C1—C6111.3 (1)O4—C4—C5109.9 (2)
C1—O1—H1107.7C4—O4—H4106.9
C1—C2—H2'109.1C4—C5—H5'107.2
C1—C2—O2107.5 (2)C4—C5—O5109.6 (2)
C1—C2—C3109.7 (1)C4—C5—C6114.2 (1)
H2'—C2—O2109.3H5'—C5—O5110.6
H2'—C2—C3109.6H5'—C5—C6107.0
O2—C2—C3111.6 (2)O5—C5—C6108.2 (2)
C2—O2—H2110.6C5—O5—H5108.9
C2—C3—H3'106.6C1—C6—C5112.5 (1)
C2—C3—O3109.3 (2)C1—C6—H6'109.5
C2—C3—C4113.2 (1)C1—C6—O6107.4 (2)
H3'—C3—O3108.2C5—C6—H6'108.8
H3'—C3—C4106.5C5—C6—O6109.7 (2)
O3—C3—C4112.8 (2)H6'—C6—O6108.9
C3—O3—H3110.2C6—O6—H6109.5
cis-1,2,4-trans-3,5,6-cyclohexanehexol (D-1-A) top
Crystal data top
C6H12O6F(000) = 192.0
Mr = 180.16standard setting
Monoclinic, P21Dx = 1.603 Mg m3
a = 6.86637 (11) ÅCu Kα1 radiation, λ = 1.54056 Å
b = 9.12272 (14) ŵ = 1.27 mm1
c = 6.21914 (10) ÅT = 293 K
β = 106.5963 (6)°white
V = 373.34 (1) Å3cylinder, 10 × 0.7 mm
Z = 2
Data collection top
STOE Stadi-P
diffractometer
Data collection mode: transmission
Radiation source: sealed x-ray tubeScan method: step
primary focussing Ge 1112θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Specimen mounting: 0.7mm glass capillary
Refinement top
Least-squares matrix: full with fixed elements per cycle69 parameters
Rp = 0.07966 restraints
Rwp = 0.0790 constraints
Rexp = 0.057H-atom parameters not refined
χ2 = 1.896Weighting scheme based on measured s.u.'s
7800 data points(Δ/σ)max = 0.001
Excluded region(s): noneBackground function: Chebyshev function with 20 terms
Profile function: Fundamental ParametersPreferred orientation correction: none
Crystal data top
C6H12O6V = 373.34 (1) Å3
Mr = 180.16Z = 2
Monoclinic, P21Cu Kα1 radiation, λ = 1.54056 Å
a = 6.86637 (11) ŵ = 1.27 mm1
b = 9.12272 (14) ÅT = 293 K
c = 6.21914 (10) Åcylinder, 10 × 0.7 mm
β = 106.5963 (6)°
Data collection top
STOE Stadi-P
diffractometer
Scan method: step
Specimen mounting: 0.7mm glass capillary2θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Data collection mode: transmission
Refinement top
Rp = 0.079χ2 = 1.896
Rwp = 0.0797800 data points
Rexp = 0.05769 parameters
RBragg = ?66 restraints
R(F) = ?H-atom parameters not refined
R(F2) = ?
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C10.35945 (18)0.69483 (13)0.59938 (19)0.01252
H1'0.255640.764770.474410.01502
O10.55526 (19)0.7185 (2)0.5719 (2)0.01634
H10.654270.643620.653330.01502
C20.29135 (18)0.53525 (12)0.54482 (18)0.01252
H2'0.294980.511560.372630.01502
O20.4292 (2)0.43890 (17)0.69835 (19)0.01634
H20.435200.347350.611700.01502
C30.07687 (18)0.51256 (13)0.56518 (19)0.01252
H3'0.040070.395090.543030.01502
O30.06101 (19)0.59722 (16)0.3918 (3)0.01634
H30.177660.534020.316950.01502
C40.07224 (16)0.55493 (13)0.8014 (2)0.01252
H4'0.178120.482410.921590.01502
O40.12653 (18)0.54379 (14)0.8281 (3)0.01634
H40.148550.439060.858890.01502
C50.13658 (18)0.71364 (13)0.8561 (2)0.01252
H5'0.025010.784300.739020.01502
O50.13849 (18)0.7467 (2)1.0813 (2)0.01634
H50.032800.688821.121680.01502
C60.34732 (19)0.74488 (13)0.83170 (18)0.01252
H6'0.462290.687490.965520.01502
O60.3847 (3)0.89994 (15)0.8481 (2)0.01634
H60.450760.922881.008290.01502
Geometric parameters (Å, °) top
C1—H1'1.097O3—H30.989
C1—O11.419 (2)C4—H4'1.102
C1—C21.537 (2)C4—O41.425 (2)
C1—C61.540 (2)C4—C51.524 (2)
O1—H10.994O4—H40.994
C2—H2'1.100C5—H5'1.102
C2—O21.437 (2)C5—O51.429 (2)
C2—C31.528 (2)C5—C61.524 (2)
O2—H21.001O5—H50.986
C3—H3'1.101C6—H6'1.102
C3—O31.439 (2)C6—O61.436 (2)
C3—C41.528 (2)O6—H60.992
H1'—C1—O1105.8C3—C4—H4'108.0
H1'—C1—C2107.4C3—C4—O4112.2 (1)
H1'—C1—C6107.1C3—C4—C5111.8 (1)
O1—C1—C2110.9 (1)H4'—C4—O4110.2
O1—C1—C6112.0 (1)H4'—C4—C5109.0
C2—C1—C6113.2 (1)O4—C4—C5105.5 (1)
C1—O1—H1111.6C4—O4—H4107.1
C1—C2—H2'108.1C4—C5—H5'107.8
C1—C2—O2109.4 (1)C4—C5—O5109.9 (1)
C1—C2—C3110.47 (9)C4—C5—C6112.2 (1)
H2'—C2—O2109.5H5'—C5—O5109.5
H2'—C2—C3110.2H5'—C5—C6109.0
O2—C2—C3109.3 (1)O5—C5—C6108.4 (1)
C2—O2—H2105.9C5—O5—H5109.6
C2—C3—H3'108.3C1—C6—C5110.2 (1)
C2—C3—O3108.0 (1)C1—C6—H6'110.4
C2—C3—C4109.3 (1)C1—C6—O6107.6 (1)
H3'—C3—O3110.5C5—C6—H6'109.4
H3'—C3—C4107.4C5—C6—O6109.4 (1)
O3—C3—C4113.2 (1)H6'—C6—O6109.8
C3—O3—H3108.1C6—O6—H6107.5
rac-chiro-1,2,3,4,5,6-cyclohexanehexol (rac-1) top
Crystal data top
C6H12O6Z = 4
Mr = 180.16F(000) = 384.0
Monoclinic, P21/cDx = 1.679 Mg m3
a = 10.1435 (6) ÅCu Kα1 radiation, λ = 1.54056 Å
b = 8.1542 (4) ŵ = 1.33 mm1
c = 8.6239 (4) ÅT = 293 K
β = 92.3556 (15)°white
V = 712.70 (7) Å3cylinder, 10 × 0.7 mm
Data collection top
STOE Stadi-P
diffractometer
Data collection mode: transmission
Radiation source: sealed x-ray tubeScan method: step
primary focussing Ge 1112θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Specimen mounting: 0.7mm glass capillary
Refinement top
Least-squares matrix: full with fixed elements per cycle102 parameters
Rp = 0.10266 restraints
Rwp = 0.1240 constraints
Rexp = 0.042H-atom parameters not refined
RBragg = 2.417Weighting scheme based on measured s.u.'s
χ2 = 8.509(Δ/σ)max = 0.001
7800 data pointsBackground function: Chebyshev function with 15 terms
Excluded region(s): nonePreferred orientation correction: none
Profile function: Fundamental Parameters
Crystal data top
C6H12O6V = 712.70 (7) Å3
Mr = 180.16Z = 4
Monoclinic, P21/cCu Kα1 radiation, λ = 1.54056 Å
a = 10.1435 (6) ŵ = 1.33 mm1
b = 8.1542 (4) ÅT = 293 K
c = 8.6239 (4) Åcylinder, 10 × 0.7 mm
β = 92.3556 (15)°
Data collection top
STOE Stadi-P
diffractometer
Scan method: step
Specimen mounting: 0.7mm glass capillary2θmin = 2.0°, 2θmax = 79.99°, 2θstep = 0.01°
Data collection mode: transmission
Refinement top
Rp = 0.102χ2 = 8.509
Rwp = 0.1247800 data points
Rexp = 0.042102 parameters
RBragg = 2.41766 restraints
R(F) = ?H-atom parameters not refined
R(F2) = ?
Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
C20.69423 (17)0.3490 (2)0.8530 (2)0.06013
C30.60787 (18)0.4791 (2)0.7741 (2)0.06013
C10.83555 (19)0.4096 (2)0.8779 (2)0.06013
O20.7001 (3)0.2091 (3)0.7565 (3)0.06013
H2'0.655730.319440.967530.07215
C40.66655 (19)0.5382 (2)0.6232 (2)0.06013
O30.4774 (2)0.4189 (3)0.7487 (3)0.06013
H3'0.601910.585710.852380.07215
C60.88933 (17)0.4629 (2)0.7254 (2)0.06013
O10.8407 (4)0.5407 (3)0.9861 (3)0.06013
H1'0.896570.306780.922800.07215
H20.630090.129170.777010.07215
C50.80745 (19)0.5975 (2)0.6539 (2)0.06013
O40.5840 (3)0.6665 (3)0.5569 (3)0.06013
H4'0.669850.435710.540090.07215
H30.456340.329390.832520.07215
O61.0208 (2)0.5225 (4)0.7433 (3)0.06013
H6'0.885470.355980.646900.07215
H10.889550.507591.084820.07215
O50.8581 (4)0.6331 (3)0.5049 (3)0.06013
H5'0.810100.708510.727490.07215
H40.565990.645130.443700.07215
H61.070270.486440.651550.07215
H50.849950.753440.484500.07215
Geometric parameters (Å, °) top
C2—C31.519 (2)C4—O41.443 (3)
C2—C11.523 (3)C4—H4'1.102
C2—O21.415 (3)O3—H31.055
C2—H2'1.104C6—C51.494 (2)
C3—C41.531 (3)C6—O61.422 (3)
C3—O31.420 (3)C6—H6'1.104
C3—H3'1.104O1—H11.004
C1—C61.508 (2)C5—O51.433 (3)
C1—O11.419 (3)C5—H5'1.105
C1—H1'1.103O4—H41.001
O2—H20.985O6—H60.998
C4—C51.522 (3)O5—H51.000
C3—C2—C1111.0 (1)C3—C4—H4'109.7
C3—C2—O2109.7 (2)C5—C4—O4111.3 (2)
C3—C2—H2'109.6C5—C4—H4'107.5
C1—C2—O2106.4 (2)O4—C4—H4'108.9
C1—C2—H2'108.1C3—O3—H3110.3
O2—C2—H2'112.0C1—C6—C5110.9 (1)
C2—C3—C4111.3 (1)C1—C6—O6112.0 (2)
C2—C3—O3110.1 (2)C1—C6—H6'107.6
C2—C3—H3'108.7C5—C6—O6107.3 (2)
C4—C3—O3111.7 (2)C5—C6—H6'108.8
C4—C3—H3'107.8O6—C6—H6'110.3
O3—C3—H3'107.0C1—O1—H1111.0
C2—C1—C6110.0 (1)C4—C5—C6109.9 (1)
C2—C1—O1110.3 (2)C4—C5—O5106.1 (2)
C2—C1—H1'108.3C4—C5—H5'111.1
C6—C1—O1110.6 (2)C6—C5—O5107.8 (2)
C6—C1—H1'107.9C6—C5—H5'111.4
O1—C1—H1'109.7O5—C5—H5'110.4
C2—O2—H2112.3C4—O4—H4109.9
C3—C4—C5110.3 (1)C6—O6—H6108.2
C3—C4—O4109.0 (2)C5—O5—H5109.1

Acknowledgements

Dr S. X. M. Boerrigter is gratefully acknowledged for bringing to our attention the paper by J. Wei (1999). Dr I. B. Rietveld is gratefully acknowledged for helpful discussions on the interpretation of virtual corrected melting points. The Lundbeck Foundation (Denmark) is gratefully acknowledged for financial support (grant No. R49-A5604).

Funding information

Funding for this research was provided by: Lundbeck Foundation (Denmark) (award No. R49-A5604).

References

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