II. EXPERIMENTAL

Vardenafil hydrochloride trihydrate was a commercial reagent, purchased from Sigma Aldrich (European Pharmacopoeia ID #009DE2), 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 0.414163 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 beamline staff reported substantial darkening of the specimen and change of intensities during the measurement, indicating beam damage. A low-angle shoulder on the lowest angle peak indicated the presence of an unidentified impurity phase.

The pattern was indexed on a monoclinic unit cell with a = 34.775, b = 11.568, c = 14.693 Å, β = 93.32°, V = 5900.8 Å³, and Z = 8 using DICVOL as incorporated into FOX (Favre-Nicolin and Černý, Reference Favre-Nicolin and Černý2002). Analysis of potential space groups suggested C2/c, which was confirmed by successful solution and refinement. Indexing using N-TREOR (Altomare et al., Reference Altomare, Cuocci, Giacovazzo, Moliterni, Rizzi, Corriero and Falcicchio2013) yielded a primitive triclinic cell corresponding to the reduced cell of the C-centered monoclinic lattice. 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, O, S, and Cl yielded no hits. The vardenafil cation was built using Spartan ‘16 (Wavefunction, 2017) and saved as a mol2 file. The structure was solved with DASH (David et al., Reference David, Shankland, van de Streek, Pidcock, Motherwell and Cole2006) using a vardenafil cation, a chlorine atom, and three oxygen atoms as fragments.

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). The region 1.4–1.7°, which includes a peak from the Kapton capillary, was also excluded. 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 fused ring system C3–C11 and the phenyl ring C17–22 were restrained to be planar. The restraints contributed 5.6% to the final χ ². The hydrogen atoms were included in calculated positions, which were recalculated during the refinement using Materials Studio (Dassault, 2016). Positions of the active hydrogens were derived by analysis of potential hydrogen bonding patterns. A common U _iso was refined for the non-H atoms of the fused-ring system, another U_iso for the methyl and ethyl groups attached to the five-membered ring, another for the phenyl ring, another U_iso for the ethyl substituent on the phenyl ring, another U_iso for the two sulfone oxygen atoms, another U_iso for the C₄N₂ saturated ring, another U_iso for the ethyl substituent on the C₄N₂ saturated ring, and a common U_iso for the water molecules. The chlorine atom Cl68 was refined anisotropically. The U_iso for 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 three-term diffuse scattering function to model the Kapton capillary and any amorphous component.

The final refinement of 137 variables using 23 800 observations (23 701 data points and 99 restraints) yielded the residuals R _wp = 0.1429, R _p = 0.1118, and χ ² = 10.32. The largest peak (1.43 Å from C22) and hole (1.63 Å from C33) in the difference Fourier map were 0.84 and −0.80 eÅ⁻³, respectively. The Rietveld plot is included as Figure 2. The largest errors in the fit are in the positions, shapes, and intensities of some of the strong, low-angle peaks, reflecting beam damage.

Figure 2.

(Color online) The Rietveld plot for the refinement of vardenafil hydrochloride trihydrate. 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 > 8.0°, and by a factor of 20 for 2θ > 15.0°.

A density functional geometry optimization (fixed experimental unit cell) was carried out using VASP (Kresse and Furthmüller, Reference Kresse and Furthmüller1996). The calculation used the GGA-PBE functional, a plane wave cut-off energy of 400.0 eV, and a k-point spacing of 0.5 Å⁻¹ leading to a 3 × 3 × 1 mesh. The calculation was carried out on 16 2.4 GHz processors (each with 4 Gb RAM) of a 64-processor HP Proliant DL580 Generation 7 Linux cluster at North Central College, and took ~10.3 h. A density functional geometry optimization was also 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, and O atoms were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994), and the basis sets for S and Cl 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, using 8 k-points and the B3LYP functional, and took ~96 h.

III. RESULTS AND DISCUSSION

The experimental powder pattern of vardenafil hydrochloride trihydrate matches Figure 3 of US patent 8 841 446 B2 (Serno et al., Reference Serno, Grunenberg, Ohm, Bellinghausen, Vollers and Henck2014; Bayer) well enough to conclude that the material studied here is the same as that used by Bayer to formulate the coated tablets claimed in that patent (Figure 4).

Figure 3.

(Color Online) Comparison of the synchrotron powder diffraction pattern to the laboratory X-ray powder diffraction pattern of US Patent 8 841 446 (Serno et al., Reference Serno, Grunenberg, Ohm, Bellinghausen, Vollers and Henck2014; Bayer). The literature pattern (measured using CuKα radiation) was digitized using UN-SCAN-IT (Silk Scientific, 2013), and re-scaled to the synchrotron wavelength of 0.414163 Å using Jade 9.8 (MDI, 2017).

Figure 4.

(Color Online) Comparison of the CRYSTAL14- (blue) and VASP-optimized (purple) structures of vardenafil hydrochloride trihydrate.

The refined atom coordinates of vardenafil hydrochloride trihydrate and the coordinates from the DFT optimizations are reported in the CIFs attached as Supplementary Material. The optimized structures from VASP and CRYSTAL14 are compared in Figure 5. The structures are almost identical. The RMSD is only 0.0722 Å. The major difference is in the orientation of the methyl group C15. This discussion concentrates on the CRYSTAL-optimized structure. Comparison of the experimental and optimized structures shows that the root-mean-square Cartesian displacement of the non-hydrogen atoms in the vardenafil cations is 0.1956 Å (Figure 6). The largest deviations are in the ethyl and propyl side chains. These are the regions of the molecule with the largest displacement coefficients. We cannot rule out the possibility of disorder of these side chains. 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). The asymmetric unit (with atom numbering) is illustrated in Figure 7, and the crystal structure is presented in Figure 8.

Figure 5.

(Color Online) Comparison of the refined and optimized (CRYSTAL14) structures of the cation in vardenafil hydrochloride trihydrate. The Rietveld refined structure is in red, and the DFT-optimized structure is in blue.

Figure 6.

(Color Online) The asymmetric unit of vardenafil hydrochloride trihydrate, with the atom numbering. The atoms are represented by 50% probability spheroids.

Figure 7.

(Color Online) The crystal structure of vardenafil hydrochloride trihydrate, viewed down the b-axis.

Figure 8.

(Color Online) Comparison of the atomic charges from CRYSTAL14 and VASP (Bader change transfer).

The fused ring system and the phenyl ring are nearly co-planar; the interplanar angle between them is 6.0°. Two intramolecular hydrogen bonds (N10–H1⋯O23 and C22–H49⋯N8) help determine this conformation. These planes stack along the c-axis. The side chains of these ring systems have a large U_iso and are neighbors in the stacks. Along the a-axis, these stacks are separated by hydrophilic layers of chloride, water molecules, and the positively charged nitrogen atoms of the vardenafil cation (N32 is the protonated nitrogen).

The two DFT calculations we performed yielded two measures of the atomic charges: the “default” atomic charges from CRYSTAL14 and the Bader analysis (charge transfer) from VASP (Figure 3). In general, the Bader analysis yields larger absolute values for the atomic charges. For the C atoms, there is a reasonable trend (r ² = 0.72), but there are outliers. The Bader analysis yields large positive charges for the ketone carbon C11 and C3 and C9, which are located between two N atoms. For C21 (adjacent to the S atom), CRYSTAL14 indicates a positive charge, while the Bader analysis yields a negative charge. The agreement between the two charges is excellent for H bound to C. Both methods indicate that the hydrogen atoms in the water molecules, as well as the proton H2 bound to N32, are more positive than the hydrogens bound to C; the Bader analysis yields more-positive charges. Both analyses indicate that the O charges are in the order: SO₂ > C=O > H₂O. The N atoms are also negatively charged, but the Bader analysis yields a much lower charge for N4, which accepts a hydrogen bond from a water molecule. The agreement between the two charges is good for Cl, but the Bader analysis yields a much more positive S atom.

Almost all of the bond distances and all 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 S26–O27 and S26–O28 distances of 1.492 and 1.493 Å [average = 1.431(12), Z-score = 5.00 and 5.07] are flagged as unusual. The experimental average is probably shorter than the true internuclear distance because of the large electron density in the S=O double bonds. The S26–N29 distance of 1.683 Å [average = 1.630(14), Z-score = 3.73] was also flagged as unusual.

Quantum chemical geometry optimizations (DFT/6-31G*/water) using Spartan ‘16 (Wavefunction, 2017) indicated that the observed conformation of vardenafil in vardenafil hydrochloride trihydrate is 65.2 kcal mole⁻¹ higher in energy than the local minimum energy conformation. The geometrical differences are small, and lie mainly in the conformation of the saturated ring. Molecular mechanics conformational analysis indicated that the global minimum energy conformation (−2.4 kcal mol⁻¹) is only slightly lower in energy than this local minimum. The small energy differences indicate that intermolecular interactions contribute to determining the solid-state conformation.

Analysis of the contributions to the total crystal energy using the Forcite module of Materials Studio (Dassault, 2016) suggests that angle, bond, and torsion distortion terms are significant in the intramolecular deformation energy, as might be expected from a fused ring system. The intermolecular energy contains significant contributions from van der Waals 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.

Hydrogen bonds are prominent in the crystal structure (Table I). As expected, the protonated nitrogen atom N32 forms a strong hydrogen bond to the chloride anion Cl68. The water molecules form a hexagon, making hydrogen bonds with themselves, as well as Cl68 and the ring nitrogen atom N4. These discrete hydrogen bonds form a cluster, and there is no extended hydrogen bond network. There are many C–H⋯Cl, C–H⋯O, and C–H⋯N hydrogen bonds, which (although individually weak) contribute significantly to the crystal energy.

Table I.

Hydrogen bonds (CRYSTAL14) in vardenafil hydrochloride trihydrate.

^a Intramolecular.

The volume enclosed by the Hirshfeld surface (Figure 9; Hirshfeld, Reference Hirshfeld1977; Turner, et al., Reference Turner, McKinnon, Wolff, Grimwood, Spackman, Jayatilaka and Spackman2017) is 726.27 Å³, 98.44% of 1/8 the unit-cell volume. The molecules are thus not tightly packed. All of the significant close contacts (red in Figure 9) involve the hydrogen bonds.

Figure 9.

(Color Online) The Hirshfeld surface of vardenafil hydrochloride trihydrate. 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 vardenafil hydrochloride trihydrate, with {200} as the principal faces. A fourth-order spherical harmonic preferred orientation model was included in the refinement; the texture index was 1.0582, indicating that preferred orientation was present in this rotated capillary specimen. The powder pattern of vardenafil hydrochloride trihydrate from this synchrotron data set is included in the Powder Diffraction File^™ as entry 00-066-1620.