II. EXPERIMENTAL

Hydrocortisone acetate was a commercial reference standard, purchased from the US Pharmacopoeia (Lot #L0L246), 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 0.413342 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 monoclinic unit cell having a = 8.852 Å, b = 13.542 Å, c = 8.871 Å, β = 101.5°, V = 1041.9 Å³, and Z = 2 using Jade (MDI, 2014). Analysis of the systematic absences suggested the space group P2₁, 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 O only” yielded eight hits, among which was ZZZGCU (Shell, Reference Shell1955), which contained no atom coordinates.

A hydrocortisone molecule was extracted from CSD entry CORTMS01 (Shikii et al., Reference Shikii, Sakamoto, Seki, Utsumi and Yamaguchi2004). The acetate group was added using Spartan ’14 (Wavefunction, 2013), and the minimum energy conformation was determined. 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). The structure was solved with FOX (Favre-Nicolin and Černý, Reference Favre-Nicolin and Černý2002). The maximum sinθ/λ used in the structure solution was 0.40 Å⁻¹.

Rietveld refinement was carried out using GSAS (Toby, Reference Toby2001; Larson and Von Dreele, Reference Larson and Von Dreele2004). Only the 2.0°–30.0° portion of the pattern was included in the refinement (d _min = 0.798 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 5.1% to the final χ ². A single U _iso was refined for all of the ring system carbon atoms, another U _iso for the ring substituent heavy atoms, and a third for the acetate 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 fixed at 0.06 Å². 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 six-term diffuse scattering function to model the Kapton capillary and any amorphous component. The final refinement of 121 variables using 28 086 observations (28 002 data points and 84 restraints) yielded the residuals R _wp = 0.0813, R _p = 0.0642, and χ ² = 2.177. The largest peak (1.33 Å from H35) and hole (1.93 Å from O28) in the difference Fourier map were 0.54 and −0.47 e(Å⁻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.

Figure 2. (Color online) The Rietveld plot for the refinement of hydrocortisone acetate. 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 4 for 2θ > 6.0°, and by a factor of 40 for 2θ > 13.1°.

A density functional geometry optimization (fixed experimental unit cell) was carried out using CRYSTAL09 (Dovesi et al., Reference Dovesi, Orlando, Civalleri, Roetti, Saunders and Zicovich-Wilson2005). The basis sets for the H, C, and O atoms were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994). The calculation was run on a 2.8 GHz PC, used eight k-points and the B3LYP functional, and took ~16 days.

III. RESULTS AND DISCUSSION

The refined atom coordinates of hydrocortisone acetate and the coordinates from the density functional theory (DFT) optimization are reported in the CIFs (Crystallographic Information Frameworks) submitted as Supplementary Material. The root-mean-square deviation of the non-hydrogen atoms in the hydrocortisone acetate molecules is only 0.066 Å (Figure 3). The largest difference is 0.119 Å, at C22. 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 4, and the crystal structure is presented in Figure 5.

Figure 3. (Color online) Comparison of the refined and optimized structures of hydrocortisone acetate. The Rietveld refined structure is in red, and the DFT-optimized structure is in blue.

Figure 4. (Color online) The asymmetric unit of hydrocortisone acetate, with the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 5. (Color online) The crystal structure of hydrocortisone acetate, viewed down the a-axis. The hydrogen bonds are indicated by dashed lines.

All of the bond distances, 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, Eddington, McCabe, Pidcock, Rodriguez-Monge, Taylor, van de Streek and Wood2008). Quantum chemical geometry optimization (Hartree–Fock/6-31G*/water) using Spartan ’14 (Wavefunction, 2013) indicated that the observed conformation of hydrocortisone acetate in the solid state is 9.4 kcal mole⁻¹ higher in energy than a local minimum energy conformation of an isolated molecule. A molecular mechanics conformational analysis indicated that the global minimum energy conformation is more compact, and thus intermolecular 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 angle, bond, and torsion distortion terms are significant in the intramolecular deformation energy. The intermolecular energy contains significant contributions from 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 hydroxyl groups form fairly strong hydrogen bonds to the ketone oxygen atom O5 (Table I). These hydrogen bonds result in chains having graph sets (Etter, Reference Etter1990; Bernstein et al., Reference Bernstein, Davis, Shimoni and Chang1995; Shields et al., Reference Shields, Raithby, Allen and Motherwell2000) C1,1(9) (H60) and C1,1(12) (H61). These chains form a three-dimensional hydrogen bond network. An intramolecular C–H···O hydrogen bond also seems to contribute to the crystal energy.

Table I. Hydrogen bonds in hydrocortisone acetate.

The volume enclosed by the Hirshfeld surface (Figure 6; Hirshfeld, Reference Hirshfeld1977; McKinnon et al., Reference McKinnon, Spackman and Mitchell2004; Spackman and Jayatilaka, Reference Spackman and Jayatilaka2009; Wolff et al., Reference Wolff, Grimwood, McKinnon, Turner, Jayatilaka and Spackman2012) is 513.44 Å³, 98.6% of 1/2 the unit-cell volume. The molecules are thus not tightly packed. The only significant close contacts (red in Figure 6) involve the hydrogen bonds.

Figure 6. (Color online) Hirshfeld surface of hydrocortisone acetate. Intermolecular contacts longer than the sums of the van der Waal's radii are colored blue, and contacts shorter than the sums of the radii are colored red. Contacts equal to the sums of radii are white.

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 hydrocortisone acetate. A fourth-order spherical harmonic preferred orientation model was included in the refinement; the texture index was 1.065, indicating that there was some preferred orientation in this rotated capillary specimen. The powder pattern of hydrocortisone acetate has been submitted to ICDD for inclusion in future releases of the Powder Diffraction File as entry 00-066-1610.