II. EXPERIMENTAL

Lubiprostone was a commercial regent, purchased from Sigma-Aldrich (Batch No. 124M4704 V), and was used as-received. The white powder was packed into a 1.5 mm diameter Kapton capillary, and rotated during the measurement at ~50 cycles s⁻¹. The powder pattern was measured at 295 K at beam line 11-BM (Lee et al., Reference Lee, Shu, Ramanathan, Preissner, Wang, Beno, Von Dreele, Ribaud, Kurtz, Antao, Jiao and Toby2008; Wang et al., Reference Wang, Toby, Lee, Ribaud, Antao, Kurtz, Ramanathan, Von Dreele and Beno2008) of the Advanced Photon Source at Argonne National Laboratory using a wavelength of 0.414163 Å from 0.5–50° 2θ with a step size of 0.001° and a counting time of 0.1 s step^–1. The pattern was indexed on a primitive triclinic unit cell with a = 9.0174, b = 10.7188, c = 12.3300 Å, α = 78.563, β = 69.684, γ = 77.312°, V = 1080.5 Å³, and Z = 2 using Jade (MDI, 2016) and N-TREOR (Altomare et al., Reference Altomare, Cuocci, Giacovazzo, Moliterni, Rizzi, Corriero and Falcicchio2013). Since lubiprostone is a chiral molecule, the space group was assumed to be P1. A reduced cell search in the Cambridge Structural Database (Groom et al., Reference Groom, Bruno, Lightfoot and Ward2016) combined with the chemistry “C H F O only” yielded no hits.

A lubiprostone molecule was built using Spartan ‘16 (Wavefunction Inc., 2017), and its equilibrium conformation determined using molecular mechanics techniques. The resulting .mol2 file was converted into a Fenske–Hall Z-matrix file using OpenBabel (O'Boyle et al., Reference O'Boyle, Banck, James, Morley, Vandermeersch and Hutchison2011). Attempts to solve the structure using FOX (Favre-Nicolin and Černý, Reference Favre-Nicolin and Černý2002) and DASH (David et al., Reference David, Shankland, van de Streek, Pidcock, Motherwell and Cole2006) were unsuccessful. During the structure solution, a Grant-in-Aid submission which became PDF entry 00-065-1086 for lubiprostone (Peng, Reference Peng2014) arrived at ICDD Headquarters, with coordinates of the non-hydrogen atoms derived from an unpublished single-crystal study. The coordinates of the hydrogen atoms were computed in Materials Studio (Dassault, 2014) and manually by assessing potential hydrogen bonding.

Rietveld refinement was carried out using GSAS (Toby, Reference Toby2001; Larson and Von Dreele, Reference Larson and Von Dreele2004). Only the 2.0–22.0° portion of the pattern was included in the refinement (d _min = 1.085 Å). All non-H bond distances and angles were subjected to restraints, based on a Mercury/Mogul Geometry Check (Bruno et al., Reference Bruno, Cole, Kessler, Luo, Motherwell, Purkis, Smith, Taylor, Cooper, Harris and Orpen2004; Sykes et al., Reference Sykes, McCabe, Allen, Battle, Bruno and Wood2011) of the molecule. The Mogul average and standard deviation for each quantity were used as the restraint parameters. The restraints contributed 12.7% to the final χ ². The displacement coefficients in the two independent molecules were constrained to be the same. A common U _iso was refined for the non-H atoms of the ring system, another U _iso for the two hydroxy oxygen atoms, another U _iso for the non-H atoms of the F-containing side chains, and another U _iso for the non-H atoms of the carboxylic acid side chains. The U _iso of each hydrogen atom was fixed at 1.3× that of the heavy atom to which it was attached. The peak profiles were described using profile function #4 (Thompson et al., Reference Thompson, Cox and Hastings1987; Finger et al., Reference Finger, Cox and Jephcoat1994), which includes the Stephens (Reference Stephens1999) anisotropic strain broadening model. The background was modeled using a three-term shifted Chebyshev polynomial, with a three-term diffuse-scattering function to model the Kapton capillary and any amorphous component. The final refinement of 200 variables using 20136 observations (20000 data points and 136 restraints) yielded the residuals R _wp = 0.0891, R _p = 0.0725, and χ² = 2.989. The largest peak (0.76 Å from C38 and hole (1.51 Å from O13) in the difference Fourier map were 0.43 and −0.50 eÅ⁻³, respectively. The Rietveld plot is included as Figure 2. The largest errors in the fit are in the shapes and positions of some of the low-angle peaks, and may reflect changes in the specimen during the measurement.

Figure 2. (Color online) The Rietveld plot for the refinement of lubiprostone. The red crosses represent the observed data points, and the green line is the calculated pattern. The magenta curve is the difference pattern, plotted at the same vertical scale as the other patterns. The vertical scale has been multiplied by a factor of 5 for 2θ > 7.0, and by a factor of 20 for 2θ > 14.7.

A density functional geometry optimization (fixed experimental unit cell) was carried out using CRYSTAL14 (Dovesi et al., Reference Dovesi, Orlando, Erba, Zicovich-Wilson, Civalleri, Casassa, Maschio, Ferrabone, De La Pierre, D-Arco, Noël, Causà and Kirtman2014). The basis sets for H, C, and O were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994), that for F was from Peintinger et al. (Reference Peintinger, Vilela Oliveira and Bredow2013). The calculation was run on eight 2.1 GHz Xeon cores (each with 6 Gb RAM) of a 304-core Dell Linux cluster at IIT, used 8 k-points and the B3LYP functional, and took ~4.3 days.

III. RESULTS AND DISCUSSION

The observed powder pattern is similar enough to Figure 3 of US Patent 8 513 441 [Figure 3, digitized using UN-SCAN-IT 7.0 (Silk Scientific, 2013)] to conclude that this sample is Polymorph B of lubiprostone. The refined atom coordinates of lubiprostone and the coordinates from the DFT optimization are reported in the CIFs attached as Supplementary Material. The root-mean-square deviation of the non-hydrogen atoms is only 0.10 Å (Figure 4). The excellent agreement between the refined and optimized structures is evidence that the experimental structure is correct (van de Streek and Neumann, Reference van de Streek and Neumann2014). This discussion uses the DFT-optimized structure. The asymmetric unit (with atom numbering) is illustrated in Figure 5, and the crystal structure is presented in Figure 6.

Figure 3. (Color online) Comparison of the powder pattern of lubiprostone to the pattern of Figure 3 of US Patent 8 513 441 for the Polymorph B of lubiprostone claimed by Alphora Research Inc.

Figure 4. (Color online) Comparison of the refined and optimized structures of lubiprostone. The Rietveld refined structure is in red, and the DFT-optimized structure is in blue.

Figure 5. (Color online) The refined molecular structures of the two independent lubiprostone molecules, with the atom numbering. The atoms are represented by 50% probability spheroids. (a) Molecule 1. (b) Molecule 2.

Figure 6. (Color online) The crystal structure of lubiprostone, viewed down the b-axis.

Almost all of the bond distances, bond angles, and torsion angles in lubiprostone fall within the normal ranges indicated by a Mercury Mogul Geometry check (Macrae et al., Reference Macrae, Bruno, Chisholm, Edington, McCabe, Pidcock, Rodriguez-Monge, Taylor, van de Streek and Wood2008). The F3-C39-C40 angle [optimized = 106.3°, average = 109.1(8)°, Z-score = 3.46] is flagged as unusual, the result of the exceptionally low uncertainty on the average. The torsion angles C23-C24-C28-C29 and C43-C44-C48-C49 are trans rather than the more-normal gauche, and the torsion angles C25-C24-C28-C29 and C45-C44-C48-C49 are gauche instead of the normal trans.

The two independent lubiprostone molecules have a similar extended conformation. The root-mean-square Cartesian displacement is 0.409 Å. The largest difference is in the conformations of the carboxyl groups. The molecules are aligned roughly along the c-axis. The hydrophobic side chains lie adjacent to each other. The result is layers of molecules parallel to the ac plane.

Quantum chemical geometry optimizations (Hartree–Fock/6-31G*/water) using Spartan ‘16 (Wavefunction Inc., 2017) indicated that the two independent molecules are within 0.5 kcal mole^–1 of each other in energy. The two molecules converge to the same local minimum. A molecular mechanics conformational analysis indicated that the observed solid-state conformation is 19.6 kcal mol^–1 higher in energy than global minimum energy conformation of an isolated molecule. In the minimum-energy conformation, the carboxylic acid side chain curls up to form a hydrogen bond to the ketone of the fused ring system. The difference shows that both hydrogen bonding and interchain interactions are important in determining the solid-state conformation.

Analysis of the contributions to the total crystal energy using the Forcite module of Materials Studio (Dassault, 2014) suggests that bond angle distortion terms are the most significant contributions to the intramolecular deformation energy, but that bond distance and torsion terms also contribute. The intermolecular energy is dominated by van der Waals attractions and electrostatic repulsions, which in this force-field-based analysis include hydrogen bonds. The hydrogen bonds are better analyzed using the results of the DFT calculation.

The two carboxylic acid groups form a ring with graph set (Etter, Reference Etter1990; Bernstein et al., Reference Bernstein, Davis, Shimoni and Chang1995; Shields et al., Reference Shields, Raithby, Allen and Motherwell2000) R2,2(8), resulting in a dimer of the two independent molecules (Table I). Each of the hydroxyl groups acts as a hydrogen bond donor to a ketone of the fused ring system. These discrete hydrogen bonds link the molecules along the b-axis. The energies of these O–H⋅⋅⋅O hydrogen bonds were calculated from the Mulliken overlap populations according to the correlation of Rammohan and Kaduk (Reference Rammohan and Kaduk2018).

Table I. Hydrogen bonds (CRYSTAL14) in lubiprostone.

The Bravais–Friedel–Donnay–Harker (Bravais, Reference Bravais1866; Friedel, Reference Friedel1907; Donnay and Harker, Reference Donnay and Harker1937) morphology suggests that we might expect blocky morphology for lubiprostone, with {001}, {010}, and {100} as principal faces. A second-order spherical harmonic preferred orientation model was included in the refinement; the texture index was only 1.0004, indicating that preferred orientation was not significant in this rotated capillary specimen. The powder pattern of lubiprostone is included in the Powder Diffraction File™ as entry 00-066-1622.