II. EXPERIMENTAL

Laboratory powder X-ray diffraction (PXRD) data were obtained at the UCL using a Stoe StadiP diffractometer in the transmission mode. The diffractometer was equipped with a copper anode operated at 40 kV and 30 mA, and an incident beam germanium monochromator (λ = 1.540 59 Å). The sample was mounted in a 0.6 mm diameter glass capillary and using a 6° linear position-sensitive detector, data were collected between 2 and 40°2θ in 0.2° steps, and re-binned to give a data-step of 0.02°. The raw data were published online (Vickers, 2008) and in the PDF (ICDD, 2013) as part of PDF entry 00-060-1211.

Pattern indexing with DICVOL06 (Boultif and Louer, Reference Boultif and Louer2004) suggested an orthorhombic unit cell with lattice parameters a = 19.7145, b = 15.0499, c = 7.6534 Å, and a cell volume of 2270.8 Å³ (M ₂₀ = 33.1, F ₂₀ = 93.9), in strong agreement with the initial assessment made at the UCL (Vickers, 2008) and tabulated in the PDF entry. Space-group determination with ChekCell (Laugier and Bochu, Reference Laugier and Bochu2000) suggested space group P2₁2₁2₁ as the most plausible option (space group Pmn2₁ was also identified based on the observed reflections, but is incompatible with chiral molecules).

A trandolapril molecule was created using fragments of the Cambridge Structural Database (CSD, Allen, Reference Allen2002) entries SIWCAC (Hausin and Codding, Reference Hausin and Codding1991) and FEFKEI (Bojarska et al., Reference Bojarska, Maniukuewicz, Sieron, Kopczacki, Walczynski and Remko2012), as illustrated in Figure 1. The molecule was prepared from the fragments using the molecular modelling software Avogadro (Hanwell et al., Reference Hanwell, Curtis, Lonie, Vandermeersch, Zurek and Hutchison2012). The molecule was converted to a Fenske–Hall Z-matrix with Open Babel (O'Boyle et al., Reference O'Boyle, Banck, James, Morley, Vandermeersch and Hutchison2011) and used to solve the structure with FOX (Favre-Nicolin and Černý, Reference Favre-Nicolin and Černý2002), using 24 sets of parallel tempering with 2 × 10⁶ trials set⁻¹. These sets yielded two solutions with cost functions of approximately 20 000 that were significantly lower than the other sets.

Initial refinement was performed using the Le Bail method with the program FullProf (Rodriguez-Carvajal, Reference Rodriguez-Carvajal2001) in order to determine the profile parameters, given the absence of an initial instrumental parameter file. The final profile parameters determined with FullProf were converted to their GSAS equivalents (Kaduk and Reid, Reference Kaduk and Reid2011) for the Rietveld refinement.

Rietveld refinement of the crystal structure was performed with the GSAS/EXPGUI program (Toby, Reference Toby2001; Larson and Von Dreele, Reference Larson and Von Dreele2004). Restraints on the bonds, angles, and planar restraints on the phenyl ring were applied using values determined by the Mogul 1.7 module of the CSD (Bruno et al., Reference Bruno, Cole, Kessler, Luo, Motherwell, Purkis, Smith, Taylor, Cooper, Harris and Orpen2004). The background was refined using a Chebyshev polynomial with 14 terms. The positions of the C, N, and O atoms were refined, while the positions of the H atoms remained fixed but were periodically optimized using Avogadro. An overall isotropic displacement parameter was refined for the C, N, and O atoms, with the H atoms constrained to 1.3 times this value. A fourth-order spherical harmonic correction (Von Dreele, Reference Von Dreele1997) was used to model preferred orientation, which yielded a small texture index (1.023).

The crystal data, data collection, and refinement details are summarized in Table I.

Table I. The crystal data, data collection, and refinement parameters obtained for trandolapril.

A density functional geometry optimization (using 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, Noel, Causa, Rerat and Kirtman2014). The basis sets for the H, C, N, and O atoms were those of Gatti et al. (Reference Gatti, Saunders and Roetti1994). The calculation was run on eight 2.1 GHz Xeon cores (each with 6 Gb RAM) of a 304-core Dell Linux cluster at the Illinois Institute of Technology (IIT), used eight k-points and the B3LYP functional, and took approximately 7 days.

III. RESULTS AND DISCUSSION

The final Rietveld refinement obtained for trandolapril is illustrated in Figure 2, while the refined atomic coordinates and density functional theory (DFT)-optimized coordinates are presented in Tables II and III, respectively. The atomic labelling used for both models is illustrated in Figure 3. The root-mean-square (RMS) difference between the Rietveld and DFT coordinates for the non-hydrogen atoms is 0.332 Å, which is towards the upper end of the range expected for correct powder structures from laboratory PXRD data (Van de Streek and Neumann, Reference Van de Streek and Neumann2014). The DFT-optimized and Rietveld refined structures are overlaid for comparison in Figure 4. The largest source of discrepancy in the heavy atoms relates to atoms C15, C18, and C19, which suggest different configurations of the octahydroindole ring, with the two molecules being diastereomers. The H53 (C18) and H56 (C20) atoms exhibit a syn configuration in the DFT-calculated molecule and an anti-configuration in the Rietveld refined molecule. To confirm the refinement results were consistent independent of the starting model, separate Rietveld refinements were performed starting with both the model obtained from FOX and the DFT solution. The Rietveld refinements obtained from both starting models yielded identical results.

Figure 2. (Color online) A plot illustrating the final Rietveld refinement of trandolapril obtained with GSAS.

Figure 3. (Color online) The molecular structure of trandolapril, illustrating the atomic labelling used in the tables.

Figure 4. (Color online) Molecular overlay of the DFT (red) and Rietveld (blue) refined crystal structures of trandolapril.

Table II. The refined crystal structure of trandolapril with lattice parameters a = 19.7685(4), b = 15.0697(4), and c = 7.6704(2) Å.

Table III. The DFT-optimized crystal structure of trandolapril calculated with fixed lattice parameters a = 19.7695, b = 15.0705, and c = 7.6706 Å.

The discrepancy between the DFT and Rietveld results may be due to the relatively low amount of powder data, with an upper 2θ limit of 40°. The pattern contains 144 reflections, and after accounting for reflection overlap (Altomare et al., Reference Altomare, Cascarano, Giacovazzo, Guagliardi, Moliterni, Burla and Polidori1995), the effective number of reflections varies between 123.8 (optimistic estimate) and 80.5 (pessimistic estimate). Using either estimate, the model is significantly underdetermined, emphasizing the importance of the restraints in the refinement and the use of DFT modelling for comparison. Given the low observation-to-parameter ratio, it is possible that the DFT model is more accurate than the Rietveld refined model. However, it has been observed by crystal energy landscape calculations (Price, Reference Price2008, Reference Price2009) that many thermodynamically plausible structures can fall within a narrow energy band of possible polymorphs (a few kJ mol⁻¹), including numerous structures, which are not observed experimentally. Different plausible structures are a trade-off between factors, including hydrogen bonding and close packing. Observed polymorphs are often metastable local energy minima that do not necessarily correspond to the most thermodynamically stable structure, due to kinetic barriers associated with crystal nucleation or growth.

The Rietveld refined structure is illustrated in Figure 5. Visually, the Rietveld fit looks excellent (Figure 2) with slight residuals in the difference plot due to the strong reflection asymmetry observed at low angles. Examination of the Rietveld refined structure with Mogul yields three angles which are unusual (z-scores greater than 3) including two angles through atom C18 (C15–C18–C19 and C15–C18–C20 with z-scores of 4.04 and 3.03, respectively). One angle is highlighted in the DFT structure (C20–N23–C24, z-score of 3.88).

Figure 5. (Color online) The crystal structure of trandolapril, viewed along to the c-axis, with the C, H, N, and O atoms coloured in grey, white, blue, and red, respectively.

The DFT results suggest minimal hydrogen bonding, tabulated in Table IV, with one prominent intermolecular bond, N28–H62···O29. The hydrogen bonds through H41 and H61 are both intramolecular. It is possible that the carboxyl group (O27) is deprotonated, yielding an additional hydrogen at N28. Zwitterionic behaviour is well documented with amino acids (Sarkar and Nahar, Reference Sarkar and Nahar2007; Tilborg et al., Reference Tilborg, Norberg and Wouters2014) and observed in both pharmaceuticals and drug delivery moieties (Jin et al., Reference Jin, Chen, Wang and Ji2014; Kostic et al., Reference Kostic, Dotsikas and Malenovic2014). Deprotonating the carboxyl group (removing H61) and adding a second H atom at N28 yields a refinement, which quickly converges with a comparable fit to the tabulated data (reduced χ ² of 2.71).

Table IV. Hydrogen bonds observed in the trandolapril structure and their parameters as determined by the DFT modelling.

In order to test whether more complete data would change the refined structure, a second data set was collected on the same diffractometer with an expanded 2θ range of 5°–60° using an 18° Dectris^® Mythen 1 K detector (data not shown). The structure was refined using the same strategy and restraints as the initial refinement, yielding a final R _wp value of 0.0328. The RMS difference between the coordinates of the non-hydrogen atoms for the two experimental refinements was <0.05 Å, suggesting only marginal change in the experimental structure with more complete data. Crystallographic information files for the Rietveld refinements of both experimental data sets and the DFT-optimized structure are included in the supplementary material.