II. EXPERIMENTAL

Tramadol hydrochloride, a commercial reagent, purchased from the United States Pharmacopeia (USP) (lot G0L065), 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 beamline 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 0.413 685 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 monoclinic unit cell having a = 9.678, b = 19.187, c = 9.284 Å, β = 100.6°, V = 1694.6 Å³, and Z = 4 using Jade 9.5 (MDI, 2014), which suggested the space group Cc. Since the commercial material is a racemate, the space group is reasonable, and was confirmed by successful solution and refinement of the structure. A reduced cell search in the Cambridge Structural Database (Allen, Reference Allen2002) yielded 638 hits; combining it with the chemistry “C H N O Cl only” yielded 18 hits, but no structure for tramadol hydrochloride. A name search on “tramadol” yielded 3 hits. Two of these were other salts, but one was the benzoic acid adduct of tramadol hydrochloride (AYUNUE; Siddaraju et al., Reference Siddaraju, Jasinski, Golen, Yathirajan and Raju2011). A connectivity search in the CSD yielded the structure of the acrylonitrile solvate of tramadol hydrochloride (VISQAR; Boumendjel et al., Reference Boumendjel, Taïwe, Bum, Chabrol, Beney, Sinniger, Haudecoeur, Marcourt, Challal, Queiroz, Souard, Le Borgne, Lomberget, Depaulis, Lavaud, Robins, Wolfender, Bonaz and De Waard2013).

A (1R,2R)-tramadol cation 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 and Hutchison2011). This fragment and a Cl atom were used to solve the structure with FOX (Favre-Nicolin and Černý, Reference Favre-Nicolin and Černý2002). The maximum sinθ/λ used in the solution was 0.40 Å⁻¹.

Rietveld refinement was carried out using GSAS (Larson and Von Dreele, Reference Larson and Von Dreele2004). Only the 2.0–25.0° portion of the pattern was included in the refinement (d _min = 0.95 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 1.94% to the final χ ². Isotropic displacement coefficients were refined, grouped by chemical similarity, and the Cl was refined anisotropically. 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× 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 five-term diffuse scattering function to model the Kapton capillary and any amorphous component. The final refinement of 83 variables using 23 038 observations (23002 data points and 36 restraints) yielded the residuals R _wp = 0.070, R _p = 0.057, and χ²  = 2.234. The largest peak (1.55 Å from C6) and hole (3.06 Å from O13) in the difference Fourier map were 0.53 and −0.43 eÅ⁻³, respectively. The Rietveld plot is included as Figure 2. The largest errors are in the shapes of the low-angle peaks, and may indicate subtle changes in the sample during the measurement.

Figure 2.

(Color online) The Rietveld plot for the refinement of tramadol hydrochloride. 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 10 for 2θ > 12.0° and by a factor of 40 for 2θ > 17.5°.

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, N, and O atoms were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994), and the basis set for Cl was that of Apra et al. (Reference Apra, Causa, Prencipe, Dovesi and Saunders1993). The calculation used 8 k-points and the B3LYP functional, and took ~16 days on a 3.0 GHz PC.

III. RESULTS AND DISCUSSION

The refined atom coordinates of tramadol hydrochloride are reported in Table I, and the coordinates from the density functional theory (DFT) optimization in Table II. The root-mean-square (rms) deviation of the non-hydrogen atoms is 0.064 Å, and the maximum deviation is 0.188 Å, at C22 (Figure 3). The excellent agreement between the refined and optimized structures is strong evidence that the structure is correct (van de Streek and Neumann, Reference van de Streek and Neumann2014). After this work was completed, the Bag and Reddy (Reference Bag and Reddy2014) single-crystal structure appeared. The rms difference between the experimental powder and single-crystal structures is 0.035 Å, and between the DFT and single-crystal structures is 0.053 Å; all three structures are essentially identical. The rms difference between the DFT structure and the cation in VISQAR is 0.139 Å; the cation conformation is very similar in all these structures. The discussion of the geometry 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 tramadol hydrochloride. The Rietveld refined structure is in red, and the DFT-optimized structure is in blue.

Figure 4.

(Color online) The molecular structure of tramadol hydrochloride, with the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 5.

(Color online) The crystal structure of tramadol hydrochloride, viewed down the a-axis. The hydrogen bonds are shown as dashed lines.

Table I.

Rietveld refined crystal structure of tramadol hydrochloride.

Table II.

DFT-optimized (CRYSTAL09) crystal structure of tramadol hydrochloride.

All of the bond distances, bond angles, and torsion angles fall within the normal ranges indicated by a Mercury Mogul Geometry Check (Macrae et al., Reference Macrae, Bruno, Chisholm, Edgington, McCabe, Pidcock, Rodriguez-Monge, Taylor, van de Streek and Wood2008). A quantum mechanical conformation examination (DFT/B3LYP/6-31G*/water) using Spartan ‘14 indicated that the observed conformation is ~213 kcal mole⁻¹ higher in energy than a local minimum, which differs mainly in the orientations of the dimethylammonium and methoxyphenyl portions of the molecule. A molecular mechanics force field sampling of conformational space indicated that the optimized solid-state conformation is 18.9 kcal mole⁻¹ higher in energy than the minimum-energy conformation. The energy difference indicates that hydrogen bonds and van der Waals forces contribute significantly to the crystal energy.

The conformations of the dimethylammonium and cyclohexyl portions of the cation in the current structure are similar to those in AYUNUE (Figure 6), but the orientation of the methoxyphenyl groups differ. The energies of these two cations are within 1 kcal mole⁻¹ of each other. The tramadol cation seems to have the conformational flexibility to accommodate the needs of its crystallization partners.

Figure 6.

(Color online) Comparison of the tramadol cations in the hydrochloride (this structure; blue) and tramadol hydrochloride benzoic acid adduct (AYUNUE; green).

Analysis of the contributions to the total crystal energy using the Forcite module of Materials Studio (Accelrys, 2013) suggests that the intramolecular deformation energy is dominated by bond and angle distortion terms. The intermolecular energy is dominated by electrostatic contributions, which in this force-field-based analysis include hydrogen bonds, although van der Waals repulsion is also significant. The hydrogen bonds are better analyzed using the results of the DFT calculation.

There are both N21–H45···Cl46 and O13–H27···Cl46 hydrogen bonds (Table III), which form a zigzag chain with graph set (Etter, Reference Etter1990; Bernstein et al., Reference Bernstein, Davis, Shimoni and Chang1995; Shields et al., Reference Shields, Raithby, Allen and Motherwell2000) C1,2(8) along the c-axis. We use the Mulliken overlap populations to identify real hydrogen bonds among the geometrically plausible interactions. Covalent bonds have positive overlap populations, and ionic and non-bonding interactions have small negative overlap populations. The only other positive (>0.01 e) overlap populations correspond to reasonable hydrogen bonds. We have examined more sophisticated methods of analyzing the electron density [such as Bader analysis (Bader, Reference Bader1990)], but they do not change the conclusion about whether a potential hydrogen bond is real. The chloride also acts as an acceptor in a C22–H46···Cl46 hydrogen bond (Figure 7). The ether oxygen O11 participates in two C–H···O hydrogen bonds, and the hydroxyl oxygen O13 participates in a single C–H···O hydrogen bond. Although weak, these C–H donor hydrogen bonds probably contribute significantly to the crystal energy.

Figure 7.

(Color online) Tramadol hydrochloride, showing both the hydrogen bonds and the close intermolecular contacts, as defined by Mercury. All of the C–H⋯Cl and C–H⋯O hydrogen bonds are included among the close contacts.

Table III.

Hydrogen bonds in the DFT-optimized crystal structure of tramadol hydrochloride.

The volume enclosed by the Hirshfeld surface (Figure 8; 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 417.08 Å³, 98.4% of the one-fourth of the unit-cell volume. The molecules are thus not tightly packed. The only significant close contacts (red in Figure 7) involve the hydrogen bonds.

Figure 8.

(Color online) The Hirshfeld surface of tramadol hydrochloride. Intermolecular contacts longer than the sums of the van der Waals 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 tramadol hydrochloride, with {010} as the principal faces. A second-order spherical harmonic preferred orientation model was included in the refinement; the texture index was only 1.007, indicating that preferred orientation was not significant in this rotated capillary specimen. The powder pattern of tramadol hydrochloride has been submitted to ICDD for inclusion in the PDF.