II. EXPERIMENTAL

Norgestimate was a commercial reference standard, purchased from the U.S. Pharmacopeia (USP) (Lot No. G0J236), 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 0.413 891 Å from 0.5 to 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 orthorhombic unit cell having a = 11.527, b = 16.146, c = 22.265 Å, V = 4143.7 Å³, and Z = 8 using Jade (MDI, 2014). Analysis of the systematic absences suggested the space group P2₁2₁2₁, which was confirmed by successful solution and refinement of the structure. A reduced cell search in the Cambridge Structural Database (Groom et al., Reference Groom, Bruno, Lightfoot and Ward2016) combined with the chemistry “C H N O only” yielded two hits, but no structure for norgestimate. A connectivity search yielded no hits.

A norgestimate molecule was built and its conformation optimized using Spartan ‘14 (Wavefunction, 2013), and saved as a mol2 file. This 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). Using two norgestimate molecules as fragments, the structure was solved with FOX (Favre-Nicolin and Černý, Reference Favre-Nicolin and Černý2002). The minimum 2θ used was 1.5°, and the maximum sinθ/λ was 0.25 Å⁻¹.

Rietveld refinement was carried out using GSAS (Toby, Reference Toby2001; Larson and Von Dreele, Reference Larson and Von Dreele2004). Only the 1.0–20.0° portion of the pattern was included in the refinement (d _min = 1.192 Å).

A preliminary refinement yielded the initial coordinates for the density functional theory (DFT) calculation, and the final refinement was based on the DFT model. 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 4.1% to the final χ ². A single U _iso was refined for all of the ring carbon atoms, and another U _iso for the substituent heavy atoms. The hydrogen atoms were included in calculated positions, which were recalculated during the refinement. The U _iso of each hydrogen atom was constrained to be 1.3 times that of the heavy atom to which it is 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 four-term diffuse scattering function to model the Kapton capillary and any amorphous component. The final refinement of 183 variables using 18 648 observations (18 499 data points and 149 restraints) yielded the residuals R _wp = 0.0797, R _p = 0.0630, and χ ² = 1.071. The largest peak (1.23 Å from C50) and hole (1.41 Å from C26) in the difference Fourier map were 0.19 and −0.13 eÅ⁻³, respectively. The Rietveld plot is included as Figure 2.

Figure 2.

(Color online) The Rietveld plot for the refinement of norgestimate. 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 20 for 2θ > 7.0°, and by a factor of 40 for 2θ > 13.0°.

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 Le Pierre, D'Arco, Noel, Causa, Rerat and Kirtman2014). The basis sets for the H, C, N, and O atoms were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994). This was a difficult calculation, as the system was indicated to be conducting and never reached SCF convergence. A large amount of level shifting (3.0 Hartree) had to be applied. The calculation was run on 16 2.1 GHz Xeon cores (each with 6 Gb RAM) of a 304-core Dell Linux cluster at IIT (Illinois Institute of Technology), used eight k-points and the B3LYP functional, and took ~33 days.

III. RESULTS AND DISCUSSION

The refined atom coordinates of norgestimate and the coordinates from the DFT optimization are reported in the Crystallographic Information Framework files (CIFs) submitted as online Supplementary Material. The root-mean-square deviations of the non-hydrogen atoms in the norgestimate molecules are 0.226 and 0.127 Å, respectively (Figure 3). The largest differences are in the substituents. The good 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 4, and the crystal structure is presented in Figure 5.

Figure 3.

(Color online) Comparison of the refined and optimized structures of norgestimate. The Rietveld refined structure is in red, and the DFT-optimized structure is in blue. (a) Molecule 1. (b) Molecule 2.

Figure 4.

(Color online) The asymmetric unit of norgestimate, with the atom numbering. The atoms are represented by 50% probability spheroids (molecule 1, right; molecule 2, left).

Figure 5.

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

All of the bond distances, and most of the bond angles and torsion angles (the bonds and angles were restrained) 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). Only the angles C35–O49–C50 (observed = 122.9(7), optimized = 124.3, expected = 119.1(11), Z-score = 4.7), O49-C50-O51 (observed = 113.5(12), optimized = 117.2, expected = 123.6(21), Z-score = 3.0), and O49–C50–C52 (observed = 112.9(13), optimized = 121.0, expected = 110.7(22), Z-score = 4.7) and the torsion angles C35–O49–C50–O51 (observed = 159.6, optimized = −179.2, expected = 180.0) and C35–O49–C50–C52 (observed = 10.7, optimized = −0.9, expected = 0.0) are flagged as unusual. All of these unusual angles involve the acetate side chain of molecule 1. The root-mean-square displacement of the non-hydrogen atoms in the two independent molecules is 0.686 Å (Figure 6). Almost all of the differences lie in the conformation of the acetate side chains.

Figure 6.

(Color online) Comparison of the two independent molecules in the structure of norgestimate. Molecule 1 is red, and molecule 2 is green.

Norgestimate is a similar molecule to levonorgestrel acetate (Crabbé and Schlemper, Reference Crabbé and Schlemper1983; CSD Refcode CEGHOL), but has a hydroxylamine group at position 3 of Ring A of the steroid ring system instead of a carbonyl group. The conformation of molecule 1 (N1-C58) is very similar to that observed for levonorgestrel acetate, while in molecule 2 (N59-C118) the acetate is rotated by ~180°. Levonorgestrel acetate crystallizes with Z′ = 1, instead of the Z′ = 2 observed here. Norgestimate contains the hydrogen bond donor hydroxylamine group, while levonorgestrel has no hydrogen bond donors. The presence of multiple molecules in the asymmetric unit of norgestimate is correlated to the presence of hydrogen bonding.

Quantum chemical geometry optimizations (Hartree-Fock/6–31G*/water) using Spartan ’14 (Wavefunction, 2013) indicated that molecule 2 is lower in energy by 7.3 kcal mole⁻¹, consistent with its more normal conformation. Molecular mechanics conformational analyses confirmed that molecule 2 is lower in energy, and that it is the minimum energy conformation.

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

Both hydroxylimine groups form O–H⋯O hydrogen bonds to the carbonyl oxygens of the acetate groups (Table I). The hydrogen bonds link molecules of the same type (1 or 2) to chains with graph sets C(15) (Etter, Reference Etter1990; Bernstein et al., Reference Bernstein, Davis, Shimoni and Chang1995; Shields et al., Reference Shields, Raithby, Allen and Motherwell2000). The two independent chains run along the b-axis. The hydrogen bond linking molecules 2 is stronger (9.1 kcal mole⁻¹; Rammohan and Kaduk, Reference Rammohan and Kaduk2016) than the one linking molecules 1 (7.5 kcal mole⁻¹). Two other weak interactions – between the ethynyl group of molecule 2 and the hydroxylimine nitrogen of molecule 2, and the acetate methyl group of molecule 2 and the ethynyl carbon C58 of molecule 1 also apparently contribute to the crystal energy. Presumably molecule 1 is distorted to accommodate intermolecular interactions. Molecule 1 forms head-to-tail chains, which are surrounded by chains of molecule 2 (and vice versa). Norgestimate could thus be considered an inclusion compound, in which the host and guest are the same molecule.

TABLE I.

Hydrogen bonds in norgestimate.

The Bravais–Friedel–Donnay–Harker (Bravais, Reference Bravais1866; Friedel, Reference Friedel1907; Donnay and Harker, Reference Donnay and Harker1937) morphology suggests that we might expect a blocky morphology for norgestimate. A second-order spherical harmonic preferred orientation model was included in the refinement. The texture index was only 1.005, indicating that preferred orientation was not significant in this rotated capillary specimen. The powder pattern of norgestimate is included in the Powder Diffraction File as entry 00-064-1503.