I. INTRODUCTION
Cephalexin monohydrate (trade names Aristosporin, Keflex) is a first-generation β-lactam cephalosporin antibiotic. It kills Gram-positive and some Gram-negative bacteria by disrupting the growth of the bacterial cell wall. Cephalexin monohydrate is used to treat respiratory, urinary tract, bone, and skin bacterial infections by preventing bacteria from forming cell walls that surround each cell. It works similarly to other cephalosporins but can be taken orally. The IUPAC name (CAS Registry number 23325-78-2) is (6R,7R)-7-[[(2R)-2-amino-2-phenylacetyl]amino]-3-methyl-8-oxo-5-thia-1-azabicyclo[4.2.0]oct-2-ene-2-carboxylic acid hydrate. A two-dimensional molecular diagram (without H2O) is shown in Figure 1.
Figure 1. The molecular structure of cephalexin.
Indexed powder patterns of cephalexin monohydrate are contained in the Powder Diffraction File (Gates-Rector and Blanton, Reference Gates-Rector and Blanton2019), entries 00-040-1653 (Sonneveld, Reference Sonneveld1989; space group Im) and 00-045-1537 (Jenkins and Stevenson, Reference Jenkins and Stevenson1990; space group P21/m). A star-quality pattern generated from the synchrotron data set of this paper is present as entry 00-065-1417. A star-quality pattern of cephalexin dihydrate is contained in PDF entry 00-040-1652 (Sonneveld, Reference Sonneveld1989; space group Im), and a primary pattern calculated from a 150 K crystal structure is contained in the PDF-4/Organics database as entry 02-084-1771 (Kennedy et al., Reference Kennedy, Okoth, Sheen, Sherwood, Teat and Vrcelj2003). Powder data for cephalexin monohydrate are reported in US Patent 3,862,186 (Silvestri, Reference Silvestri1975; Bristol-Myers). Powder patterns for cephalexin monohydrate, dihydrate, and several solvates are reported in Pfeiffer et al. (Reference Pfeiffer, Yang and Tucker1970). Several of these patterns, as well as patterns for cephalexin hydrochloride derivatives, are contained in the PDF.
This work was carried out as part of a project (Kaduk et al., Reference Kaduk, Crowder, Zhong, Fawcett and Suchomel2014) to determine the crystal structures of large-volume commercial pharmaceuticals and include high-quality powder diffraction data for these pharmaceuticals in the Powder Diffraction File.
II. EXPERIMENTAL
Cephalexin monohydrate was a commercial reagent, purchased from United States Pharmacopeial Convention (Lot #K0J198), 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 Hz. 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 0.413693 Å from 0.5° to 50° 2θ with a step size of 0.001° and a counting time of 0.1 s/step.
The pattern was indexed on a monoclinic unit cell with a = 16.7522, b = 11.9187, c = 27.0468 Å, β = 107.031°, V = 5163.45 Å3, and Z = 12 using DICVOL06 (Louër and Boultif, Reference Louër and Boultif2007). Analysis of the systematic absences using EXPO2013 (Altomare et al., Reference Altomare, Cuocci, Giacovazzo, Moliterni, Rizzi, Corriero and Falcicchio2013) suggested the space group I2. Indexing the pattern using Jade 9.5 (MDI, 2014) yielded the equivalent C-centered cell, which was used for the structure solution and refinement, as the β angle was closer to 90°.
A reduced cell search in the Cambridge Structural Database (Groom et al., Reference Groom, Bruno, Lightfoot and Ward2016) yielded three hits but no cephalexin structures. A name search on “cephalexin” yielded the structure of cephalexin dihydrate (Kennedy et al., Reference Kennedy, Okoth, Sheen, Sherwood, Teat and Vrcelj2003; Refcode BEBNIG), as well as the structure of a bis(cephalexin) β-naphthol 5.5 hydrate (Kemperman et al., Reference Kemperman, de Gelder, Dommerholt, Raemakers-Franken, Klunder and Zwanenburg1999; Refcode GUCSEC).
After several attempts to solve the structure using Monte Carlo-simulated annealing techniques with multiple programs failed to yield plausible results, a different strategy was used. We noted that the lattice parameters were not very different from those of BEBNIG. The BEBNIG lattice parameters were changed to those of the current C-centered monoclinic cell, the (disordered) water molecules were removed, and the structure was optimized using the Forcite module of Materials Studio (Dassault Systèmes, 2014). A successful refinement was begun from this model. It might be said that the structure was solved by “isomorphous replacement”.
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 = 0.955 Å); no significant peaks were observed at higher angles. The three C6H5 phenyl rings were refined as rigid bodies. All other 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 5.6% to the final χ 2. The initial refinement did not include the three water molecules. The locations of the oxygen atom were established by successive difference Fourier maps. The initial positions of the active hydrogen atoms were derived based on potential hydrogen bonding patterns. The U iso were grouped by chemical similarity, and the Ui so in the three independent cephalexin molecules were constrained to be identical. The hydrogen atoms were included in calculated positions, which were recalculated during the refinement. The U iso of the hydrogen atoms were constrained to be 1.3× that of the heavy atom to which they are 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 seven-term diffuse scattering function to model the Kapton capillary and any amorphous component. The refinement of 225 variables using 24003 observations and 252 restraints yielded the residuals R wp = 0.0879, R p = 0.0707, and χ2 = 2.772. The largest peak (2.33 Å from N13c) and hole (1.86 Å from C29c) in the difference Fourier map were 0.45 and −0.33 eÅ−3, respectively. The Rietveld plot is included as Figure 2. The largest errors are in the shapes and positions of some 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 cephalexin monohydrate. The red crosses represent the observed data points, and the magenta line is the difference (observed – calculated) pattern. The vertical scale has been multiplied by a factor of 5× for 2θ > 7.0°, and by a factor of 40× for 2θ > 13.0°.
A density functional geometry optimization (fixed experimental unit cell) was carried out using VASP (Kresse and Furthmüller, Reference Kresse and Furthmüller1996) through the MedeA graphical interface (Materials Design, 2016). 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. The calculation used the GGA-PBE functional, a plane wave cutoff energy of 400.0 eV, and a k-point spacing of 0.5 Å−1 leading to a 3 × 3 × 1 mesh, and took ~8.4 days. A single-point calculation on the VASP-optimized structure 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, and O atoms were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994), and the basis set for S was that 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 ~37 h.
III. RESULTS AND DISCUSSION
The synchrotron powder pattern of this study matches those of PDF entries 00-040-1653 and 00-045-1537 (Figure 3) and that of Pfeiffer et al. (Reference Pfeiffer, Yang and Tucker1970) well enough (Figure 4) to conclude that all four samples contain the same crystalline phase, and thus that this pattern is representative of material in commerce. The powder pattern of cephalexin monohydrate is very different from that of the reported dihydrate (Figure 5).
Figure 3. (Color online) Comparison of this pattern of cephalexin monohydrate (red) (PDF entry 00-065-1417, converted to CuKα wavelength) to the other patterns of this compound reported in PDF entries 00-040-1653 (blue sticks) and 00-045-1537 (green sticks).
Figure 4. (Color online) Comparison of this synchrotron pattern of cephalexin monohydrate to that reported by Pfeiffer et al. (Reference Pfeiffer, Yang and Tucker1970) converted to the synchrotron wavelength of 0.413693 Å.
Figure 5. (Color online) Comparison of this pattern of cephalexin monohydrate (red) (PDF entry 00-065-1417, converted to CuKα wavelength) to the pattern of cephalexin dihydrate (blue) from PDF entry 02-084-1771 (Kennedy et al., Reference Kennedy, Okoth, Sheen, Sherwood, Teat and Vrcelj2003).
The refined atom coordinates of cephalexin monohydrate and the coordinates from the DFT optimization have been deposited with ICDD. The root-mean-square Cartesian displacement of the non-hydrogen atoms in the Rietveld-refined and DFT-optimized structures of the three independent cephalexin molecules are 0.135, 0.163, and 0.226 Å (Figures 6–8). The good agreement provides evidence that the experimental structure is correct (van de Streek and Neumann, Reference van de Streek and Neumann2014). This discussion concentrates on the DFT-optimized structure. The asymmetric unit (with atom numbering) is illustrated in Figure 9, and the crystal structure is presented in Figure 10.
Figure 6. (Color online) Comparison of the Rietveld-refined (red) and VASP-optimized (blue) structures of molecule a of cephalexin monohydrate. The rms Cartesian displacement is 0.135 Å.
Figure 7. (Color online) Comparison of the Rietveld-refined (red) and VASP-optimized (blue) structures of molecule b of cephalexin monohydrate. The rms Cartesian displacement is 0.163 Å.
Figure 8. (Color online) Comparison of the Rietveld-refined (red) and VASP-optimized (blue) structures of molecule c of cephalexin monohydrate. The rms Cartesian displacement is 0.226 Å.
Figure 9. (Color online) The asymmetric unit of cephalexin monohydrate, with the atom numbering. The atoms are represented by 50% probability spheroids.
Figure 10. (Color online) The crystal structure of cephalexin monohydrate viewed down the b-axis.
The crystal structure is characterized by alternating layers of hydrogen bonds and van der Waals contacts parallel to the bc-plane. The water molecules occur in clusters (Figure 11), occupying one of the apparent voids (probe radius in Mercury decreased to 1.0 Å). The general arrangement of the cephalexin molecules is similar in the monohydrate and dihydrate structures (Figure 12), but the differences in the lattice parameters and structural details cause the powder patterns to be very different.
Figure 11. (Color online) Voids in the structure of cephalexin monohydrate after the water molecules are removed. The probe radius was 1.0 Å.
Figure 12. (Color online) Comparison of the crystal structures of cephalexin monohydrate and cephalexin dihydrate. The Mercury Structure Overlay tool was used to fit the positions of all 12 sulfur atoms in the unit cell.
All of the bond distances, angles, and torsion angles fall within the normal ranges indicated by a Mercury Mogul Geometry check (Macrae et al., Reference Macrae, Sovago, Cottrell, Galek, McCabe, Pidcock, Platings, Shields, Stevens, Towler and Wood2020). The three independent cephalexin molecules exhibit different conformations (Figures 13–15) with root-mean-square Cartesian displacements of a/b = 0.434, a/c = 0.719, and b/c = 0.332 Å, respectively.
Figure 13. (Color online) Comparison of cephalexin molecule a (green) and molecule b (orange). The rms Cartesian displacement is 0.434 Å.
Figure 14. (Color online) Comparison of cephalexin molecule b (orange) and molecule c (purple). The rms Cartesian displacement is 0.719 Å.
Figure 15. (Color online) Comparison of cephalexin molecule a (green) and molecule c (purple). The rms Cartesian displacement is 0.332 Å.
Quantum chemical geometry optimization of the cephalexin molecules (DFT/B3LYP/6-31G*/water) using Spartan ‘18 (Wavefunction, Inc., 2018) indicated that molecules a and b are within 0.1 kcal mol−1 of each other in energy, and that molecule c is 76.6 kcal mol−1 higher in energy. A molecular mechanics conformational analysis indicated that the minimum-energy conformation is much more compact than the observed ones, with the ammonium and carboxylate groups folded toward each other. Intermolecular interactions are thus important in determining the observed conformations.
Analysis of the contributions to the total crystal energy using the Forcite module of Materials Studio (Dassault, 2014) suggests that angle distortion terms dominate the intramolecular deformation energy, as might be expected in a fused-ring system. The intermolecular energy is dominated by electrostatic repulsions, which in this force-field-based analysis include cation coordination and hydrogen bonds. The hydrogen bonds are better analyzed using the results of the DFT calculation.
Hydrogen bonds are important in the crystal structure (Table I). Five of the six protons in the water molecules act as donors in O–H⋯O hydrogen bonds. The energies of these hydrogen bonds were calculated using the correlation of Rammohan and Kaduk (Reference Rammohan and Kaduk2018). The hydrogen atom H128 acts as a donor to two different phenyl ring carbon atoms, to form bifurcated O–H⋯C hydrogen bonds. Each cephalexin molecule is a zwitterion, containing an ammonium group (N13a, b, and c) and carboxylate groups (C26, O27, O28). As expected, the ammonium ions form N–H⋯O hydrogen bonds to carboxylate groups and water molecules, as well as to the carbonyl groups O15. The energies of these N–H⋯O hydrogen bonds were calculated using the correlation of Wheatley and Kaduk (Reference Wheatley and Kaduk2019). Methyl, methylene, and methyne groups participate in a variety of weak interactions involving phenyl ring carbon atoms, sulfur atoms, and carboxylate groups, forming C–H⋯C, C–H⋯S, and C–H⋯O hydrogen bonds. Two phenyl ring hydrogen atoms also act as donors in C–H⋯S hydrogen bonds.
TABLE I. Hydrogen bonds (CRYSTAL14) in cephalexin monohydrate.
The volume enclosed by the Hirshfeld surface (Figure 16; Hirshfeld, Reference Hirshfeld1977; Turner, et al., Reference Turner, McKinnon, Wolff, Grimwood, Spackman, Jayatilaka and Spackman2017) is 1278.47 Å3, 98.97% of 1/4 the unit cell volume. The packing density is thus fairly typical. All of the significant close contacts (red in Figure 16) involve the hydrogen bonds. The volume/non-hydrogen atom is 17.2 Å3.
Figure 16. (Color online) The Hirshfeld surface of cephalexin 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 Gatti, Saunders and Roetti1866; Friedel, Reference Friedel1907; Donnay and Harker, Reference Donnay and Harker1937) morphology suggests that we might expect blocky morphology for cephalexin monohydrate, with {001} as the principal faces. A fourth-order spherical harmonic model for preferred orientation was incorporated into the refinement. The texture index was only 1.027, indicating that the preferred orientation was slight in this rotated capillary specimen. The powder pattern of cephalexin monohydrate from this synchrotron data set is included in the Powder Diffraction File as entry 00-065-1417.
IV. DEPOSITED DATA
The Crystallographic Information Framework (CIF) files containing the results of the Rietveld refinement (including the raw data) and the DFT geometry optimization were deposited with the ICDD. The data can be requested at info@icdd.com.
ACKNOWLEDGEMENTS
Use of the Advanced Photon Source at Argonne National Laboratory was supported by the U. S. Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE-AC02-06CH11357. This work was partially supported by the International Centre for Diffraction Data. We thank Lynn Ribaud and Saul Lapidus for their assistance in the data collection, and Andrey Rogachev for the use of computing resources at IIT.
CONFLICTS OF INTEREST
The authors have no conflicts of interest to declare.
