II. EXPERIMENTAL

Pemetrexed disodium heptahydrate was a commercial regent, purchased from US Pharmacopeia (Lot #F042E0), 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 0.414 533 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 = 11.732, b = 5.244, c = 21.687 Å, β = 92.7°, V = 1332.7 Å³, and Z = 2 using Jade (MDI, 2016). Analysis of the systematic absences using EXPO2014 (Altomare et al., Reference Altomare, Cuocci, Giacovazzo, Moliterni, Rizzi, Corriero and Falcicchio2013) suggested the space group P2 ₁, 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 Na O only” yielded 2 hits for MOF-706, but no structure for pemetrexed or related phases.

A pemetrexed molecule was built using Spartan ‘16 (Wavefunction, 2017), and its equilibrium conformation determined. The minimum energy conformation was more compact than is observed in the solid state. 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). Initial attempts to solve the structure (with several programs) using the pemetrexed molecule, 2 Na atoms, and 7 O atoms as fragments were unsuccessful. Under the assumption that the Na coordination was octahedral, a pemetrexed and two NaO₆ octahedra (Na-O = 2.46 Å) were used as fragments to solve the structure with FOX (Favre-Nicolin and Černý, Reference Favre-Nicolin and Černý2002). The maximum sinθ/λ used in the structure solution was 0.33 Å⁻¹. The Dynamical Occupancy Correction option indicated some overlapping oxygen atoms, but several others had to be removed manually.

Rietveld refinement was carried out using GSAS (Toby, Reference Toby2001; Larson and Von Dreele, Reference Larson and Von Dreele2004). Only the 1.0–25.0° portion of the pattern was included in the refinement (d _min = 0.957 Å), with an excluded region 1.2–1.9° 2θ to eliminate a relatively sharp peak from the Kapton capillary. 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 N1-N9/C12/C13/N15/C17 and C23-C28 portions of the molecule were restrained to be planar. The Na-O distances were not restrained. The restraints contributed 11.2% to the final χ². 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 3-term shifted Chebyshev polynomial, with a 12-term diffuse scattering function to model the Kapton capillary and any amorphous component. The final refinement of 162 variables using 23 371 observations (23 301 data points and 170 restraints) yielded the residuals Rwp = 0.0783, Rp = 0.0635, and χ ² = 1.315. The largest peak (1.54 Å from C2) and hole (1.78 Å from C17) in the difference Fourier map were 0.37 and −0.26 eÅ⁻³, respectively. The Rietveld plot is included as Figure 2. The largest errors in the fit are in the shapes of some of the low-angle peaks.

Figure 2.

(Colour online) The Rietveld plot for the refinement of pemetrexed disodium heptahydrate. The black crosses represent the observed data points, and the red line is the calculated pattern. The blue 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 3 for 2θ > 8.0°, and by a factor of 40 for 2θ > 16.0°.

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 La Pierre, D-Arco, Noël, Causà and Kirtman2014). The basis sets for the H, C, N, O, and Na atoms were those of 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 ~24 days.

III. RESULTS AND DISCUSSION

The observed powder pattern is similar to Figure 1 of US Patent Application Publication 2003/0216416 (Figure 3, digitized using UN-SCAN-IT 7.0 (Silk Scientific, 2013)) to conclude that this sample is the same “heptahydrate crystalline salt” of pemetrexed disodium as that claimed by Eli Lilly and Company (Chelius et al., Reference Chelius, Reutzel-Eden and Snorek2003). Other crystalline forms and hydrates have been reported. The refined atom coordinates of pemetrexed disodium heptahydrate and the coordinates from the density functional theory (DFT) optimization of this study are reported in the Crystallographic Information Framework attached as Supplementary Material. The root-mean-square deviation of the non-hydrogen atoms in the pemetrexed anions is 0.152 Å (Figure 4). The maximum deviation is 0.295 Å, at N9. 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 5, and the crystal structure is presented in Figure 6.

Figure 3.

(Colour online) Comparison of the powder pattern of pemetrexed disodium heptahydrate to the pattern of Figure 1 of US Patent Application 2003/0216416 for the “heptahydrate crystalline salt” of pemetrexed disodium claimed by Eli Lilly and Company.

Figure 4.

(Colour online) Comparison of the refined and optimized structures of pemetrexed disodium heptahydrate. The Rietveld refined structure is in red, and the DFT-optimized structure is in blue.

Figure 5.

(Colour online) The asymmetric unit of pemetrexed disodium heptahydrate, with the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 6.

(Colour online) The crystal structure of pemetrexed disodium heptahydrate, viewed down the b-axis.

Almost all of the bond distances, bond angles, and torsion angles in the pemetrexed anion 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 C12-C4-C3 (optimized = 107.9°, average = 112.6(12)°, Z-score = 3.96), and O49-C48-C37 (optimized = 119.7°, average = 111.5(27)°, Z-score = 3.01) are flagged as unusual. The torsion angles C25-C23-C20-C17, C26-C23-C20-C17, and O46-C45-C42-C32 are flagged as unusual. Although these lie away from the peaks in the distributions, the distributions of these torsion angles cover all possible values, and the ones here occur in the lower-probability regions of the distributions.

Each ionized carboxylate group acts as a unidentate ligand to a Na cation. The remaining five positions of the octahedral coordination spheres are occupied by water molecules. The Na51 and Na52 octahedra share an edge (the water molecules O55 and O56) to form pairs. These pairs share corners (the water molecule O59) to form chains along the b-axis. All of the water molecules are coordinated to at least one Na. The bond valence sums of Na51 and Na52 are 1.12 and 1.13, respectively. The atomic charges and Mulliken overlap populations indicate that the Na-O bonding is primarily ionic, but that the bonds have significant covalent character. The overlap populations range from 0.03 to 0.06 e.

Quantum chemical geometry optimizations (Hartree-Fock/6-31G*/water) using Spartan ‘16 (Wavefunction, 2017) indicated that the observed conformation of the pemetrexed dianion in pemetrexed disodium heptahydrate is 16.6 kcal mole⁻¹ higher in energy than a local minimum. A molecular mechanics conformational analyses indicated that the global minimum energy conformation is more compact (with parallel rings), 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 bond angle distortion terms are significant in the intramolecular deformation energy. The intermolecular energy is dominated by 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.

As expected, there is an extensive array of hydrogen bonds (Table I). All of the water molecule hydrogen atoms (H60-H73) act as hydrogen bond donors. Six of these 14 hydrogen bonds form to other water molecules. The oxygen atoms of the ionized carboxylate groups (O46, O47, O49, and O50) act as acceptors, as do the carbonyl oxygen O34 and the ring nitrogen N1. The energies of the O-H⋅⋅⋅O hydrogen bonds were calculated from the Mulliken overlap populations by the correlation in Rammohan and Kaduk (Reference Rammohan and Kaduk2017). In addition, the ring nitrogen atoms N15-H16 and N7-H8 act as hydrogen bond donors to carboxylate oxygen atom O46 and the carbonyl oxygen O6. The graph sets (Etter, Reference Etter1990; Bernstein et al., Reference Bernstein, Davis, Shimoni and Chang1995; Shields et al., Reference Shields, Raithby, Allen and Motherwell2000) for these hydrogen bonds are C1,1(17) and C1,1(4) respectively. The secondary amino group H35-H36 acts as a donor to the carbonyl oxygen O34, with graph-set C1,1(4). The primary amino group N9-H11 acts as a donor to the water molecule O57, with graph-set C1,1(20). Despite an apparently favorable geometry, the Mulliken overlap populations indicate that hydrogen H10 does not participate in a hydrogen bond.

Table I.

Hydrogen bonds in pemetrexed disodium heptahydrate.

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 653.59 Å³, 98.0% of 1/2 the unit cell volume. The molecules are thus not tightly packed. All of the significant close contacts (red in Figure 7) involve the hydrogen bonds.

Figure 7.

(Colour online) The Hirshfeld surface of pemetrexed disodium heptahydrate. 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 platy morphology for pemetrexed disodium heptahydrate, with {001} as the principal faces, or needle morphology with {010} as the long axis. A 4th-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 pemetrexed disodium heptahydrate has been submitted to ICDD for inclusion in the Powder Diffraction File.