II. EXPERIMENTAL

Sitagliptin phosphate monohydrate was commercial reagent, purchased from Sigma-Aldrich Co. LLC. (lot SLBF3906V), 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 0.413 896 Å from 0.5°2θ 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 = 6.1391, b = 9.3077, c = 38.3287 Å, V = 2190 Å³, and Z = 4 using DICVOL06 (Louër and Boultif, Reference Louër and Boultif2007). Analysis of the systematic absences in EXPO2009 (Altomare et al., Reference Altomare, Camalli, Cuocci, Giacovazzo, Moliterni and Rizzi2009) 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 (Allen, Reference Allen2002) combined with the chemistry “C H F N O P only” yielded no hits. A name search on “sitagliptin” and a connectivity search on sitagliptin yielded no hits.

A sitagliptin cation and a phosphate anion were built and their conformations optimized using Spartan ‘14 (Wavefunction, 2013), and saved as mol2 files. These files were converted into Fenske–Hall Z-matrix files using OpenBabel (O'Boyle et al., Reference O'Boyle, Banck, James, Morley, Vandermeersch and Hutchison2011). Using these two fragments, the structure was solved with DASH (David et al., Reference David, Shankland, van de Streek, Pidcock, Motherwell and Cole2006).

Rietveld refinement was carried out using GSAS (Toby, Reference Toby2001; 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 = 0.956 Å).

The C1–H8 benzene ring was refined as a rigid body. 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 1.69% to the final χ ². Isotropic displacement coefficients were refined, 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. Initial positions of the active hydrogens were deduced from an analysis of potential hydrogen-bonding patterns. 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 15-term diffuse scattering function to model the Kapton capillary and any amorphous component. The refinement yielded the residuals R _wp = 0.084, R _p = 0.068, and χ²  = 2.738. A density functional theory (DFT) calculation yielded a similar position for the sitagliptin cation, but the phosphate anion and water molecule moved ~1.4 Å along the a-axis, indicating that the structure could not be correct. Re-starting the DFT calculation assuming a different hydrogen-bonding pattern (different positions for H51 and H54) yielded a structure which was 62.4 kcal mole⁻¹ lower in energy than the original structure. This DFT result was the basis for the final refinement.

The final refinement of 113 variables using 23 072 observations (22 999 data points and 73 restraints) yielded the residuals R _wp = 0.0837, R _p = 0.0680, and χ ² = 2.702. The largest peak (1.23 Å from C12) and hole (0.16 Å from O17) in the difference Fourier map were 0.59 and −0.67 eÅ⁻³, respectively. The Rietveld plot is included as Figure 2. The largest errors are in the shapes and positions of the peaks, and may indicate subtle changes in the sample during the measurement.

Figure 2.

(Colour online) The Rietveld plot for the refinement of sitagliptin dihydrogen phosphate monohydrate. 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 5 for 2θ > 7.5°, and by a factor of 20 for 2θ > 14.0°.

The final density functional geometry optimization (fixed experimental unit cell) was carried out using CRYSTAL14 (Dovesi et al., Reference Dovesi, Saunders, Roetti, Orlando, Zicovich-Wilson, Pascale, Civalleri, Doll, Harrison, Bush, D-Arco, Llunell, Causà and Noël2014). The basis sets for the H, C, N, and O atoms were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994), the basis set for F was that of Nada et al. (Reference Nada, Catlow, Pisani and Orlando1993), and the basis set for P was that of Zicovich-Wilson et al. (Reference Zicovich-Wilson, Bert, Roetti, Dovesi and Saunders2002). 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 ~38 h.

III. RESULTS AND DISCUSSION

The powder pattern corresponds well-enough to the one reported for sitagliptin phosphate monohydrate (Cypes et al., Reference Cypes, Chen, Ferlita, Hansen, Lee, Vydra and Wenslow2005, Reference Cypes, Chen, Ferlita, Hansen, Lee, Vydra and Wenslow2008) [Figure 3(a)] to believe it is the same material. Sitagliptin phosphate monohydrate is characterized in US Patent 7,326,708 (Cypes et al., Reference Cypes, Chen, Ferlita, Hansen, Lee, Vydra and Wenslow2005). The claims define the invention chemically as a sitagliptin phosphate monohydrate, characterized by X-ray diffraction peaks at d-spacings of 7.42, 5.48, and 3.96 Å. It is further characterized by peaks at d-spacings of 6.30, 4.75, and 4.48 Å, and even further characterized by peaks with d-spacings of 5.58, 5.21, and 3.52 Å [Figure 3(b)]. Applying reasonable windows to these values, the synchrotron pattern exhibits these peaks; so we can conclude that our sample is the same material as that taught by Merck & Co. This patent is a good example of the fact that the most characteristic peaks of a compound may not be the strongest peaks in the diffraction pattern. The refined atom coordinates of sitagliptin dihydrogen phosphate monohydrate are reported in Table I, and the coordinates from the DFT optimization in Table II. The root-mean-square (rms) deviation of the non-hydrogen atoms in the sitagliptin is 0.122 Å (Figure 4), and the rms deviation of the phosphate anion is 0.054 Å. The absolute difference in the phosphate position in the unit cell is 0.185 Å. This 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 5, and the crystal structure is presented in Figure 6.

Figure 3.

(Colour online) (a) The current synchrotron pattern of sitagliptin dihydrogen phosphate monohydrate, with the pattern from US Patent 7,326,708 (re-scaled to the synchrotron wavelength). (b) The pattern of sitagliptin dihydrogen phosphate monohydrate from US Patent 7,326,708, with bars indicating the peaks which “characterize” it, “further characterize” it, and “even further characterize” it.

Figure 4.

(Colour online) Comparison of the refined and optimized structures of sitagliptin dihydrogen phosphate monohydrate. The Rietveld refined structure is in red, and the DFT-optimized structure is in blue.

Figure 5.

(Colour online) The molecular structure of sitagliptin dihydrogen phosphate monohydrate, with the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 6.

(Colour online) The crystal structure of sitagliptin dihydrogen phosphate monohydrate, viewed down the a-axis. The hydrogen bonds are shown as dashed lines.

Table I.

Rietveld refined crystal structure of sitagliptin dihydrogen phosphate monohydrate.

Table II.

DFT-optimized (CRYSTAL14) crystal structure of sitagliptin dihydrogen phosphate monohydrate.

All of the bond distances, and most of the 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). The sitagliptin cation folds so that the two planar portions are roughly parallel, and parallel stacking of rings is prominent in the structure.

A quantum mechanical conformation examination (Hartree-Fock/6-21G*/water) using Spartan ‘14 indicated that the observed conformation of the sitagliptin cation is ~13.8 kcal mole⁻¹ higher in energy than a local minimum. A molecular mechanics (MMFF) sampling of conformational space indicated that the solid state conformation is within 4.9 kcal mole⁻¹ of the minimum energy conformation. The sitagliptin cation is distorted from its minimum energy conformation to accommodate the formation of the hydrogen bonds.

Analysis of the contributions to the total crystal energy using the Forcite module of Materials Studio (Accelrys, 2013) suggests that the intramolecular deformation energy contains significant contributions from angle distortion terms, as might be expected for a fused ring system. The intermolecular energy is dominated by electrostatic contributions, 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, the ammonium group of the sitagliptin cation, the phosphate anion, and the water molecule form a network of strong hydrogen bonds (Table III). Since the ammonium cation N14 was close to the phosphate oxygens O45 and O46, it was reasonable to conclude that the oxygens O47 and O48 were protonated. One of the water molecule hydrogens forms a strong O–H···N hydrogen bond to the ring nitrogen N24. Most of these hydrogen bonds are discrete, having graph sets D1,1(2) (Etter, Reference Etter1990; Bernstein et al., Reference Bernstein, Davis, Shimoni and Chang1995; Shields et al., Reference Shields, Raithby, Allen and Motherwell2000). Many larger patterns can be identified. The result of all of these hydrogen bonds is a 2D network, parallel to the ab plane. Halfway between these hydrogen bond planes, there are planes of high fluorine density.

Table III.

Hydrogen bonds in the DFT-optimized crystal structure of sitagliptin dihydrogen phosphate monohydrate.

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 564.31 Å³, or 103.2% of 1/4 the unit-cell volume. The hydrogen bonds are thus very significant to the crystal energy. The only significant close contacts (red in Figure 7) involve the hydrogen bonds.

Figure 7.

(Colour online) The Hirshfeld surface of sitagliptin dihydrogen phosphate monohydrate. 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 sitagliptin dihydrogen phosphate monohydrate, with {002} as the principal faces. A 4th-order spherical harmonic preferred orientation model was included in the refinement; the texture index was 1.076, indicating that preferred orientation was significant in this rotated capillary specimen. The powder pattern of sitagliptin dihydrogen phosphate monohydrate has been submitted to ICDD for inclusion in the PDF as entry 00-064-1500.