II. EXPERIMENTAL

Lacosamide, a commercial reagent purchased from Carbosynth Company (Lot #FL248251201) 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 0.413 691 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 = 13.634, b = 4.799, c = 10.670 Å, β = 91.7̊, V = 679.9 Å³, and Z = 2 using Jade 9.5 (MDI, 2014). An analysis of systematic absences using EXPO2013 (Altomare et al., Reference Altomare, Cuocci, Giacovazzo, Moliterni, Rizzi, Corriero and Falcicchio2013) suggested that the space group was P2₁ (#4), which was confirmed by successful solution and refinement of the structure. Although both P2₁ and P2₁ /m have the same systematic absences, the fact that lacosamide is a chiral molecule requires the space group to be P2₁. A reduced cell search in the Cambridge Structural Database (Allen, Reference Allen2002) yielded 15 hits, but no structure for lacosamide.

A lacosamide 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). This molecule was 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. Initial positions of the active hydrogens were deduced by the analysis of potential hydrogen-bonding patterns.

Rietveld refinement was carried out using the General Structure Analysis System (GSAS, Larson and Von Dreele, Reference Larson and Von Dreele2004). Only the 1.7°–25.0° portion of the pattern was included in the refinement (d _min = 0.95 Å). The C1–H11 phenyl group was refined as a rigid body. All other non-H bond distances and angles were subjected to restraints, based on a Mercury/Mogul Geometry Check (Sykes et al., Reference Sykes, McCabe, Allen, Battle, Bruno and Wood2011; Bruno et al., Reference Bruno, Cole, Kessler, Luo, Motherwell, Purkis, Smith, Taylor, Cooper, Harris and Orpen2004) of the molecule. The Mogul average and standard deviation for each quantity were used as the restraint parameters. The restraints contributed 3.16% to the final χ ². Isotropic displacement coefficients were refined, and grouped by chemical similarity. 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 an eight-term diffuse scattering function to model the Kapton capillary and any amorphous component. The final refinement of 78 variables using 23 330 observations (23 302 data points and 28 restraints) yielded the residuals R _wp = 0.069, R _p = 0.054, and χ ² = 1.392. The largest peak (1.37 Å from C12) and hole (2.13 Å from C20) in the difference Fourier map were 0.28 and −0.26 e (Å⁻³), respectively. The Rietveld plot is included as Figure 2. The largest errors are in the shapes of some of the low-angle peaks, and may indicate subtle changes in the sample during the measurement. These features persist in a Le Bail fit of the pattern (χ ² = 1.12), especially in the strong 100 peak at low angle.

Figure 2. (Color online) The Rietveld plot for the refinement of lacosamide form I. 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 > 8.0̊, and by a factor of 40 for 2θ > 13.0̊.

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 used eight k-points and the B3LYP functional, and took ~6 days on a 3.0 GHz PC.

III. RESULTS AND DISCUSSION

The powder pattern corresponds to that of form I of lacosamide, as described by Mundorfer et al. (Reference Mundorfer, Markovic, Kosutic Hulita and Zegarac2009), so the crystal structure reported here is that of form I. The refined atom coordinates of lacosamide are reported in Table I, and the coordinates from the density functional theory (DFT) optimization in Table II. The root-mean-square deviation of the non-hydrogen atoms is 0.195 Å, and the maximum deviation is 0.302 Å, at several atoms (Figure 3). The good 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). 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 lacosamide. The Rietveld refined structure is colored red, and the DFT-optimized structure is in blue.

Figure 4. (Color online) The molecular structure of lacosamide, with the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 5. (Color online) The crystal structure of lacosamide form I, viewed down the b-axis. The hydrogen bonds are shown as dashed lines.

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, Edington, 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 ~2.6 kcal mole⁻¹ higher in energy than a local minimum. A molecular mechanics force field (MMFF) sampling of conformational space indicated that the solid-state conformation is 49.0 kcal mole⁻¹ higher in energy than the minimum energy conformation, which has a much more compact geometry. The energy difference indicates that van der Waals forces contribute significantly to the crystal energy.

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 small, and is equally distributed among bond, angle, and torsion 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 attraction is also significant. The van der Waals interactions presumably result from the parallel stacking of phenyl rings. The hydrogen bonds are better analyzed using the results of the DFT calculation.

Prominent in the crystal structure are the two hydrogen bonds N13–H26···O15 and N17–H28···O19 (Table III). Each of these forms a chain with a graph set (Etter, Reference Etter1990; Bernstein et al., Reference Bernstein, Davis, Shimoni and Chang1995; Shields et al., Reference Shields, Raithby, Allen and Motherwell2000) C1,1(4). These patterns combine into several more-complex chain and ring patterns. The hydrogen bond chains run parallel to the b-axis. Several weaker C–H···O hydrogen bonds to the ketone oxygens also contribute to the packing energy. These C–H···O extend both along the b-axis and in the ac-plane, and help link the molecules in three dimensions (Figure 6). The crystal consists of hydrophobic and hydrophilic regions.

Figure 6. (Color online) A view of the lacosamide form I structure, viewed down the a-axis to illustrate the hydrogen bonds.

The volume enclosed by the Hirshfeld surface (Figure 7; 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 342.32 Å³, 98.0% of ½ 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 7. (Color online) The Hirshfeld surface of lacosamide. 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 the 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 needle-like morphology for lacosamide form I, with <010> as the long axis, or perhaps platy morphology with {001} as the principal faces. A fourth-order spherical harmonic preferred orientation model was included in the refinement; the texture index was 1.076, indicating that preferred orientation was modest in this rotated capillary specimen. The powder pattern of lacosamide form I has been submitted to ICDD for inclusion in the PDF.