Dataset analysis

The distribution of structures within the FDS, with regard to space group and DoF, was compared to that of small organic powder crystal structures (deposited at the CSD), to demonstrate that it was truly representative of the current PXRD landscape.

3.4.1.1 Space Group trends

It is well established that 80% of molecular organic compounds crystallise in one of the following five space groups: P21/c, P 1̅, P212121, P21 and C2/c (Brock and Dunitz, 1994;

Srinivasan, 1991). The FDS is broadly representative of the space group distribution in the CSD. Table 3.4 and Figure 3.3 show a good agreement between the population of space groups of organic structures in the CSD determined by PXRD and that in the FDS.

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Table 3.4 Distribution of space groups within the FDS and the CSD. *the named space group or equivalent Space Group* No. of structures

in FDS

Figure 3.3 A comparison of the relative space group distribution between the FDS (red) and the CSD (blue)

3.4.1.2 DoF trends

With increasing DoF, a pseudo-exponential decay of the number of crystal structures solved from powder data is observed. The distribution of the structural complexity within the FDS differed, with just over 50% of the structures having DoF  14, in order to satisfy the aim of improving performance in this upper range of structural complexity (Figure 3.4).

During the search for relevant crystal structures and their associated diffraction data, it was observed that the majority of IUCr published crystal structures (solved from powder data) had

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67 fewer than 15 DoF. Unsurprisingly, this appeared to be the general trend in the CSD, with approximately 70 % of the deposited organic powder crystal structures having up to 15 DoF and only just over 6% of the structures possessing more than 30 DoF. Examination of those 6% revealed these structures to be 'unusual' (e.g. peptides, glycerols, acylglycerols, etc.), falling outside the range of interest of this work and therefore not eligible for inclusion in the FDS.

However, for completeness, a single example of this complexity type was added: the 1,2,3,-tris(nonadecanoyl)glycerol (polymorph β) (B61), with the expectation that this would be an example of an intractable crystal structure. It is worth noting that whilst this example was previously solved from powder data, the starting conformation was derived from the crystal structure of -1,2,3-tris(octodecanoyl)glycerol (van Langevelde et al., 2001; Van Langevelde et al., 2000) and the addition of a CH3 group at the end of each chain. Thus the problem was reduced to one of just finding the position and orientation of the molecule in the unit cell and was (as reported) only a 6 DoF problem rather than the 49 DoF problem considered here.

3.4.1.3 Additional remarks

The resolution (minimum d-spacing) of the powder data and the number of reflections used in the Pawley refinement are two fundamental factors expected to influence both the SR and the quality of the DASH solution.

Large variations of those factors were observed within the FDS, with B3 having the lowest resolution (only 3.64 Å) and lowest number of reflections (only 19). The powder X-ray diffraction data of B3 (Figure 3.5), which was deposited by Schmidt et al. (2005), exhibits very broad peaks and was only collected to 34˚ 2θ (resolution 2.6 Å) as its main purpose was to serve as a reference for crystal structure prediction calculations. It is important to note that the DASH runs were performed using the data to only 3.64 Å because of an inability to obtain a satisfactory Pawley fit to any higher resolution using DASH. Whilst not usually a significant restriction on the ability of DASH to deal with a powder dataset, it is undoubtedly a limitation in some cases and reflects a need for some improvements in the core least-squares fitting routines in the program.

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Figure 3.4 The distribution of crystal structures plotted as a function of their DoF. The upper plot is based on the organic powder crystal structures in the CSD; the middle plot corresponds to the distribution within the FDS; and the lower plot is and overlay of the upper and middle graphs, represented as their relative distributions.

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Figure 3.5 The powder X-ray diffraction data of B3.

Due to the simplicity of B3 (only 6 DoF), its observed SR was high, but the quality of the solutions was affected, resulting in a best RMSD value of 0.281 Å. The low solution quality is clearly demonstrated in Figure 3.6 where the solved structure is visibly an offset from the true solution. However, this DASH solution was considered to be successful as the offset could be addressed by Rietveld refinement.

Figure 3.6 Overlay of the best DASH solution of B3 and the CSD deposited crystal structure (in green; CSD reference code QAMQOL). The initially minor positional shift of the molecule progressively worsens with the application of the symmetry operations. The overlay of only four molecules (rather than the default 15) is presented for clarity. Hydrogen atoms have been omitted.

On the other hand, A1 had the highest resolution of 1.17 Å and A34 the highest number of reflections (518). A1 also provided a high success rate (100%), due to the simplicity of the crystal structure. However, in this case the quality of the structure solution is also very good, with an RMSD of only 0.034 Å for the 15 molecules overlay.

2 theta

70 Shankland et al. (2002) noted that in the case of famotidine, good quality solutions could normally be found when the data resolution was better than 2.5 Å and none of the results obtained in this work with the FDS contradict this finding. It is clear from equation 1.3 that the structure factor calculation time will increase linearly with the number of reflections to be calculated. Whilst it may therefore be tempting to reduce the number of reflections in order to speed up the evaluation of each trial crystal structure, it is recommended that the above 2.5 Å resolution 'rule' is adhered to.