DASH : a program for crystal structure determination from powder diffraction data

computer programs Journal of

Applied Crystallography

DASH: a program for crystal structure determination from powder diffraction data

ISSN 0021-8898

Received 7 April 2006 Accepted 11 October 2006

William I. F. David,a* Kenneth Shankland,a Jacco van de Streek,b Elna Pidcock,b W. D. Samuel Motherwellb and Jason C. Coleb a

ISIS Facility, CCLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK, and bCambridge Crystallographic Data Centre, 12 Union Road, Cambridge CB2 1EZ, UK. Correspondence e-mail: [email protected]

# 2006 International Union of Crystallography Printed in Great Britain – all rights reserved

DASH is a user-friendly graphical-user-interface-driven computer program for solving crystal structures from X-ray powder diffraction data, optimized for molecular structures. Algorithms for multiple peak fitting, unit-cell indexing and space-group determination are included as part of the program. Molecular models can be read in a number of formats and automatically converted to Z-matrices in which flexible torsion angles are automatically identified. Simulated annealing is used to search for the global minimum in the space that describes the agreement between observed and calculated structure factors. The simulated annealing process is very fast, which in part is due to the use of correlated integrated intensities rather than the full powder pattern. Automatic minimization of the structures obtained by simulated annealing and automatic overlay of solutions assist in assessing the reproducibility of the best solution, and therefore in determining the likelihood that the global minimum has been obtained.

1. Introduction As computers have increased in speed over the past decade, crystal structure determination from powder diffraction data (SDPD) has become a feasible alternative if the conditio sine qua non of singlecrystal analysis, namely the existence of a suitable single crystal, cannot be met (Shankland & David, 2002). DASH (Fig. 1) is a computer program intended primarily for the structure determination of organic and organometallic molecular materials from X-ray powder diffraction (XRPD) data alone, in cases where the molecular connectivity of the material being studied is known. The first use of DASH was recorded in 1998 with the publication of the crystal structures of capsaicin, thiothixene and promazine hydrochloride from synchrotron XRPD data (David et al., 1998). DASH was a logical development of the GAP program described a year earlier (Shankland, David & Csoka, 1997), which utilized a genetic-algorithm-based approach to structure determination from XRPD data.

Providing a user-friendly graphical user interface (GUI) in order to allow non-expert users to utilize SDPD routinely has been one of the major driving forces behind DASH developments since the public release of version 1.0 in April 2001.

2. Overview of the graphical user interface SDPD is an inherently sequential process with each step depending on the outcome of the previous steps. This type of process is well suited to implementation in the form of a ‘Wizard’ (as seen in many GUI-driven programs) and it is this approach that is taken in DASH. By separating the structure determination task into a series of manageable steps, the user is able to concentrate fully on one specific step at a time. Positive feedback from users indicates that the DASH GUI is considered to be very easy to use. An example of one such Wizard dialogue window is shown in Fig. 2. Crucially, the user can

Figure 1 The main DASH window displaying a laboratory XRPD pattern of a caffeine– acetic acid (1:1) co-crystal. The co-crystal was exclusively obtained via solid-state grinding; a single crystal could not therefore be grown (Trask et al., 2005).

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Figure 2 The background-subtraction dialogue window of the DASH Wizard.

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computer programs preview the outcome of actions and decisions before accepting the current settings and moving to the next step. At every stage, the user can rewind to previous dialogue windows by pressing ‘Back’ (which acts as an ‘undo’ mechanism) and because the dialogue windows remember the settings that the user entered previously, clicking ‘Next’ provides the corresponding ‘redo’ mechanism. This design allows the user to experiment with their data and explore the capabilities of DASH without tedious and repetitive entry of parameters and settings. Although the Wizard structure of the GUI is intended to make the process as fast and as easy as possible, the user is not restricted to operating via the Wizard; SDPD is by no means a fully automated process and users are recommended to read the comprehensive documentation that is provided with DASH. In the documentation, particular attention is given to how to collect good quality XRPD data at the outset of the analysis, as this crucially underpins the whole process of SDPD and its likelihood of success.

3. Program description 3.1. Loading and preparing the diffraction pattern

A variety of plain-text and binary file formats can be read, including .asc (Rigaku), .cpi (Sietronics), .mdi (Materials Data Inc.), .raw (Bruker and Stoe), .rd /.sd (Philips), .udf, .uxd, .x01 (Bede) and .xye. The data must have been measured with a monochromatic X-ray source. Standard uncertainties (s.u.’s) are explicitly taken into account throughout the whole of the structure solution process, starting from the point where the data are initially read. Explicit s.u.’s are necessary in order to ensure that the relative errors of the raw data points do not change when their intensities are modified. There are three important cases where the intensities of the raw data points need to be modified: (i) Background subtraction. (ii) Synchrotron data. As a result of the beam decay, the incoming flux on a synchrotron is not constant during the measurement of the powder pattern. This has to be corrected for by scaling all data points to correspond to a fixed incoming flux, and recalculating the s.u.’s accordingly. (iii) Variable count time (VCT) data collection (Shankland, David & Sivia, 1997).

For diffraction data from a laboratory instrument without VCT, the s.u. of each data point is calculated as the square root of the number of raw counts, i.e. only errors due to counting statistics are considered. Synchrotron data, after correction for beam decay, must be presented in the .xye file format, which contains an extra column listing the s.u. of each data point. For VCT data from a Bruker .raw file, DASH automatically scales and combines the individual data ranges and calculates the proper s.u.’s. Once XRPD data have been read in, the next step is for the user to decide which part of the data to use for structure solution. Typically, ˚ resolution (Shankland data are considered to approximately 1.75 A & David, 2002), which is sufficient for SDPD (provided that a directspace method is used) and which avoids the problem of dealing with the increasing number of overlapping reflections and the decreasing intensities at higher 2
values. Although it is possible to determine the background signal of the powder pattern while the peak intensities are being fitted in a Pawleytype refinement, this tends to lead to linear dependencies, and, as a result, numerical instabilities. The numerical stability of the Pawleytype refinement can be improved by first subtracting the background in a separate step using a very flexible and robust algorithm published by Bru¨ckner (2000) or a modified version of that algorithm (David & Sivia, 2001). 3.2. Indexing and manual space-group determination

Indexing (determining the unit-cell parameters) is performed with a version of DICVOL91 (Boultif & Loue¨r, 1991) that, with permission, has been integrated within DASH at the source-code level. Indexing relies on obtaining accurate peak positions, which can be a challenge for asymmetric or partially overlapping peaks. DASH incorporates a highly flexible and robust multiple-peak fitting routine based on an asymmetry-corrected Voigt peak shape that allows easy and accurate determination of peak positions, even for cases where visual determination is difficult (Fig. 3). The list of peak positions can also be copied and used as input for other indexing programs. Knowledge of the unit-cell parameters enables the generation of markers in the diffraction data where reflections are expected to occur and thus permits identification of reflections that have negligible intensity. DASH gives the user the ability to scroll easily through a list of possible space groups that are consistent with the determined crystal system, updating the markers against the data in

Figure 3 Peak positions of asymmetric (a), noisy (b) and partially overlapping (c) peaks can be determined accurately by using the peak fitting functionality in DASH. Experimental data points are shown in red, the fitted peaks in green; the fitted peak positions are indicated with vertical blue lines. The high accuracy of the peak positions increases the probability of successful unit-cell indexing. Note that due to peak asymmetry, the peak positions do not correspond to the peak maxima.

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computer programs real time. This allows manual selection of the most likely space group, but is, of course, highly subjective, and the automated probabilistic method built into DASH (Markvardsen et al., 2001), which is discussed in more detail in x3.3, is preferred. 3.3. Pawley refinement

Pawley refinement (Pawley, 1981) is a well recognized way of fitting an XRPD profile in the absence of a full structural model. Armed with only a unit cell and crystal system, the XRPD pattern can be fitted by allowing parameters such as background, peak shape, lattice constants and reflection intensities to vary in a least-squares procedure. The end result is a set of profile parameters that can be carried over to a Rietveld refinement, but of course, a list of correlated integrated reflection intensities is also obtained. Within DASH, the Pawley refinement step serves three purposes: (a) as a means of confirming the determined unit cell and crystal system, (b) as a prerequisite to probabilistic space-group determination, and (c) as a prerequisite to high-speed global optimization of trial molecular structures. The list of correlated integrated intensities is central to the latter two uses. In the case of space-group determination, the Pawley fit is performed in a space group that has no systematic absences (typically P2 for monoclinic, P222 for orthorhombic) and the list of extracted intensities is then analysed to generate a table of extinction systems ranked in order of the probability that they explain the observed data. In the case of structure determination, the Pawley fit is performed in the correct space group and DASH then works directly with the extracted correlated integrated intensities rather than with the original XRPD profile. As direct-space methods of structure determination involve the evaluation (via a comparison of calculated and observed intensities) of a great many trial structures, this approach conveys obvious speed advantages. When a new best fit to the correlated integrated intensity data has been obtained, a full diffraction pattern is calculated and displayed for the user to monitor the progress of structure solution. Care has also been taken in performing these profile calculations rapidly; typically a full diffraction profile calculation is only 3–10 times slower than the equivalent correlated integrated intensities calculation. Note too that because the correlations are included, this procedure is formally equivalent to using a fit to the whole pattern (David, 2004). The goodness of fit of the Pawley refinement is reported as the Pawley 2, which is the square of the ratio of the weighted profile R factor and the expected profile R factor; it is the measure of the best pattern fit possible with optimized unit-cell, space-group and peakshape parameters. This Pawley 2 also serves as the ‘yardstick’ against which the final structure determination is to be compared (see x4 below).

but (by default) are not included in structure-factor calculations as (generally) they contribute little to the overall scattering and simply serve to reduce the speed at which structure factors are calculated. Up to 32 Z-matrices of different chemical species can be entered in the asymmetric unit, while the combined number of atoms is currently limited to 150. We have found that the average atomic volumes as published by Hofmann (2002) in conjunction with the unit-cell volume are useful in determining the number of molecules (Z-matrices) in the unit cell. A global optimization method (simulated annealing; see e.g. Aarts & Korst, 1988; Van Laarhoven & Aarts 1987) is used to determine the crystal structure that best matches the experimental data by adjusting molecular positions and orientations, as well as any flexible torsion angles that may be present. These adjustable parameters represent the degrees of freedom of the search problem, and in SDPD, it is the number of degrees of freedom rather than the number of atoms that dictates the success rate of finding the global minimum. With reasonable diffraction data, crystal structures with up to 15 degrees of freedom can normally be solved routinely with DASH, and structures with up to 28 degrees of freedom have been solved. For any given degree of freedom, the user has three options regarding the range of values to be explored by the simulated annealing algorithm. The parameter can be fixed at a user-specified value, restricted to a user-specified interval or left to explore its full range of possible values (Fig. 4). Torsion angles and fractional coordinates with unrestricted ranges of 0 to 360 and 0.0 to 1.0, respectively, are given special treatment to eliminate continuity problems near the boundaries. Likewise, quaternions as opposed to Euler angles are used to describe the orientations of the Z-matrices, because of the discontinuity problems associated with the latter. More specialized control of particular degrees of freedom is also available; see xx3.4.2 and 3.4.3. As a global optimization method, simulated annealing has the advantage of being both effective and of possessing relatively few algorithm control variables. The majority of these variables can be set automatically, rendering it ideal for routine use by non-experts. A thorough investigation of the influence of the DASH simulated annealing control parameters upon the SDPD process can be found elsewhere (Shankland et al., 2002). If the presence of preferred orientation is suspected, a March– Dollase preferred orientation correction (Dollase, 1986) can be included for a fixed direction during the simulated annealing and the extent of the preferred orientation annealed as an additional parameter.

3.4. Structure solution by simulated annealing

Direct-space methods of structure determination are particularly appropriate for XRPD data as the generation of trial crystal structures (with associated calculated reflection intensities) from an initial molecular model incorporates a tremendous amount of prior chemical knowledge that is conventionally denied to ab initio methods. Of course, the exact chemical composition of the contents of the unit cell must be known before this approach can be applied. In DASH, every molecular model is expressed as a Z-matrix (Shankland, 2005) which defines the three-dimensional molecular geometry in terms of bond lengths, valence angles and torsion angles. Hydrogen atoms are normally included in the Z-matrix description

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Figure 4 The ‘Parameter Bounds’ window of the DASH Wizard that allows control over the degrees of freedom that are to be explored by the global optimization technique. The y translation of the Z-matrix has been fixed at 12. A trimodal constraint has been placed on the N3:S1:C5:C6 torsion angle (highlighted in red) to restrict the search space to three 60 intervals centred at 0 and 120 .

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computer programs 3.4.1. Z-matrix generation. There are two common pitfalls associated with the generation of Z-matrices for SDPD purposes, both stemming from the fact that there is no unique way to derive a Zmatrix from a set of atomic coordinates. The first is that the definition of flexible torsion angles within the Z-matrix must ensure that it correctly describes the independent rotation of connected rigid groups (Shankland, 2005). The second is that, unless special care is taken, the Z-matrix definition gives rise to adverse dependencies in which small changes in certain torsion angles result in large changes in the resultant atomic coordinates (Shankland et al., 2002). Accordingly, it is not possible (or appropriate) to use a Z-matrix generated by an arbitrary molecular modelling program and DASH comes with a Z-matrix generator that first locates all flexible torsion angles and then generates the Z-matrix starting from the centre of the molecule and building up the Z-matrix, working outwards. A flexible torsion angle is defined as any torsion angle involving four contiguous atoms where the bond between the two central atoms is a single bond that is not part of a ring system, and where the two central atoms are bonded to each other and to at least one other non-hydrogen atom; this definition therefore avoids counting a methyl group as a group that can rotate. The centre of the molecule is defined as an appropriate atom lying close to the centre of mass of the molecule. Zmatrices can be generated from molecular models stored in .mol, .mol2, .pdb, .res and .cif formats. DASH handles all elements up to and including lawrencium, atomic number 103. 3.4.2. Crystallographic constraints. DASH implements two types of crystallographic constraints: positional and rotational. Positional constraints give the ability to fix the x, y or z coordinates of any Zmatrix, e.g. to fix the xyz location of a fragment in P1, or to fix an atom at a special position. The simplest rotational constraint is that for a Z-matrix consisting of a single atom where no rotational degrees of freedom need to be optimized: a case that is automatically recognized by DASH. More sophisticated rotational constraints are possible; these include the constraining of a molecule to a mirror plane and the constraining of rotations to an axis perpendicular to a mirror plane or to an axis of rotation. When restricting rotations to a single axis, the two-dimensional analogues of quaternions are used to avoid the discontinuities that would otherwise occur in the regions near 0 and 360 , i.e. instead of being parameterized by means of a single variable ’, the rotation is parameterized by means of two variables q0 = cos(’) and q1 = sin(’). Occupancies of atomic sites are used as supplied by the user, allowing disorder to be modelled and enabling atoms to occupy special positions. For an example of a disordered crystal structure solved with DASH, see Dinnebier, Schweiger et al. (2000). 3.4.3. Torsion-angle constraints and use of CSD data via Mogul. To increase the efficacy of DASH and to extend the utility of DASH to flexible molecules with a large number of degrees of freedom, reduction of the search space may be achieved by applying constraints to torsion angles. Mogul (Bruno et al., 2004), a library of intramolecular geometries obtained from the analysis of organic crystal structures within the Cambridge Structural Database (CSD; Allen, 2002), provides quick and easy access to ‘probability distributions’ for bond lengths, bond angles and torsion angles. Subscribers to the CSD can access Mogul torsion-angle distributions by clicking on a button within the DASH interface (Fig. 4). A simple classification of the torsion-angle distribution as unimodal, bimodal or trimodal is performed by DASH and initial torsion-angle ranges are provided for guidance. These torsion-angle ranges serve as recommendations only and are customizable by the user. Reduction of search space through the application of modal torsion-angle ranges has been shown to increase the success rate of structure solution for a J. Appl. Cryst. (2006). 39, 910–915

number of pharmaceutically relevant molecules (Florence et al., 2005).

4. Assessing the solutions In theory, an infinitely long simulated annealing run should find the global minimum, at least within the limitations of the model supplied by the user. However, a better, more pragmatic strategy is to perform multiple simulated annealing runs of a more finite duration. Simulated annealing is a stochastic process and thus each run can result in a different solution corresponding to a different minimum. The user must decide if the best solution found by DASH corresponds to the global minimum. The two most obvious indicators of a successful structure solution are a visual assessment of the goodness of fit between the experimental and simulated powder pattern (Fig. 5) and the ratio ‘profile 2/Pawley 2’, where the Pawley 2 is as defined in x3. For a promising solution, this ratio should generally be less than 5 (the smaller, the better), although this value is system dependent; for the fit shown in Fig. 5 the ratio is 5.30/2.47 ’ 2. Visualization of the crystal structure to assess if it is chemically reasonable is a further step in deciding if the solution is indeed the global minimum. Hydrogen bonds and short contacts can be visualized with the program Mercury (Macrae et al., 2006), which is bundled with DASH for that purpose. In the three checks described so far, the best solution has been considered in isolation. A final check involves comparing it against the other simulated annealing solutions to assess reproducibility and this comparison can be done conveniently by means of several options in the DASH GUI (Fig. 6). The simplex optimization that is performed automatically at the end of each simulated annealing run

Figure 5 Fit to the experimental powder pattern of the best simulated annealing solution for the caffeine–acetic acid (1:1) co-crystal from Fig. 1. The measured pattern (red), calculated pattern (blue), difference profile (magenta) and cumulative profile 2 (black) are shown. Tick marks at the top of the pattern indicate peak positions allowed by the unit-cell parameters and space group.

Figure 6 The ‘Analyse Solutions’ window of the DASH Wizard showing the options available to examine the simulated annealing solutions. See text for explanation. Note that solutions numbered 1, 2, 8, 9 and 10 are not visible.

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Figure 7 Overlay of ten DASH solutions of chlorpropamide to assess reproducibility. In this particular case, most simulated annealing runs resulted in the same minimum, which is a strong indication that it is the global minimum. In one run, shown in red, the rigid and electron-rich part of the molecule was located successfully, but the flexible tail was not. This points to a local minimum, as is confirmed by its higher profile and intensity 2.

facilitates comparison. As shown in Fig. 6, simplex minimization has optimized the five best solutions to an identical minimum in both profile and intensity 2 space. Any subset of solutions can be selected and visualized simultaneously in Mercury to assess similarities and differences. The solutions share the same unit cell and space group, and can therefore be written out to a single file; when viewed in Mercury, the solutions then appear overlaid (Fig. 7). It is not necessary to have a licensed version of Mercury for this overlay functionality to work. Even though the unit cell and space group are fixed, identical crystal structures returned from separate structure solution runs can look very different due to, for example, certain allowed translations of the centres of mass of the molecules. To aid the comparison of structures returned from multiple simulated annealing runs, an algorithm has been written that standardizes the presentation of the solutions. By applying all permutations of allowed shifts and the inversion operation (dependent on the space group) all possible configurations of the asymmetric unit are generated. Arbitrary but consistent selection of one of these configurations (here we choose the configuration that yields the shortest distance between the cell origin and a molecular centre residing between 0.0 and 1.0 on all axes) allows the standardization of the asymmetric unit without reference to any other solution structure. Hence solutions of the same structure, obtained from different simulated annealing runs, will be presented in the same configuration. This standardization cannot be applied to systems with more than one Z-matrix in the asymmetric unit. Further options shown in Fig. 6 include the ability to save the full set of solutions to a single file in a DASH-specific format, enabling the user to return to previous results for further analysis at any time. This, in combination with the option to resume the simulated annealing from where it was stopped, makes it possible to interrupt the simulated annealing temporarily. When the simulated annealing is resumed, the new solutions are appended to the existing ones. If a solution is thought to be partially correct, it can be used as the starting point for a new series of simulated annealing runs by selecting the corresponding ‘Restart’ button. Every simulated annealing run in that case is initialized with the values of the solution chosen.

5. Rietveld refinement After structure solution, Rietveld refinement (Rietveld, 1967, 1969) can be applied to the best solution before publication. Rigid-body Rietveld refinement as implemented in DASH can be invoked for any solution via the appropriate ‘Rietveld’ button (Fig. 6). However,

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DASH was mainly developed for structure solution rather than for Rietveld refinement, and solved structures can be transferred into dedicated Rietveld refinement packages via several output options, with .res and .cif files being the most common. The DASH Z-matrix serves as a convenient starting point for the generation of a series of restraints that can be utilized in subsequent Rietveld refinement. Equally, the Z-matrix can be used as the starting point for setting up a rigid-body refinement. Any powder diffraction pattern read into DASH, including automatically processed VCT files, can be written out in .xye format, which can be read by all major Rietveld refinement packages.

6. Use of single-crystal data Using additional chemical knowledge in the form of a molecular model to compensate for limitations in the diffraction data is not restricted to powder diffraction data. At least two other applications are possible: (a) to compensate for the low completeness of singlecrystal diffraction data due to shading in high-pressure diffraction experiments, and (b) to compensate for the overlap of single-crystal diffraction data caused by twinning. To deal with the first case, DASH has the ability to read in single-crystal diffraction data from a standard hkl file; twinned single-crystal data can be dealt with by converting the data to a powder diffraction pattern.

7. Examples of application DASH has been used to solve a range of molecular crystal structures from laboratory and synchrotron X-ray powder diffraction data. A study of how DASH performs with laboratory data on a selection of 35 organic molecules of varying complexity has been published previously (Florence et al., 2005). Several examples of organometallic crystal structures solved with DASH from powder data have been published by Dinnebier et al.; see for example (Dinnebier, Wagner et al., 2000) for the crystal structure of [(C5H4BMe2)2Fe]-4,40 -bipyridine polymer. The crystal structure of 2-fluorophenol solved with DASH from incomplete high-pressure single-crystal data (0.36 GPa) has been published by Oswald et al. (2005).

8. Program design, environment and future development DASH is available for Intel-compatible 32-bit processors running under Windows Me, Windows 2000 or Windows XP. The program was originally written in Fortran77, but has now been converted to Fortran90, and all additions since version 1.0 have been written in Fortran90. The GUI was programmed using the Winteracter library (Interactive Software Services Ltd, 2000). A version of DASH suitable for deployment on large-scale grid-type computing networks is under development.

9. Documentation and availability DASH is fully documented, and there are several tutorials. DASH is a commercial program available from the Cambridge Crystallographic Data Centre (CCDC, http://www.ccdc.cam.ac.uk/) and comes with full support for technical and scientific queries. Readers interested in the functionality DASH provides should contact [email protected]; a fully functional evaluation copy is available on request for those interested in purchase. J. Appl. Cryst. (2006). 39, 910–915

computer programs Magnus Kessler and Anders Markvardsen are gratefully acknowledged for their contributions to parts of the program.

References Aarts, E. & Korst, J. (1988). Simulated Annealing and Boltzmann Machines: a Stochastic Approach to Combinatorial Optimization and Neural Computing. Chichester: John Wiley. Allen, F. H. (2002). Acta Cryst. B58, 380–388. Boultif, A. & Loue¨r, D. (1991). J. Appl. Cryst. 24, 987–993. Bru¨ckner, S. (2000). J. Appl. Cryst. 33, 977–979. Bruno, I. J., Cole, J. C., Kessler, M., Luo, J., Motherwell, W. D. S., Purkis, L. H., Smith, B. R., Taylor, R., Cooper, R. I., Harris, S. E. & Orpen, A. G. (2004). J. Chem. Inf. Comput. Sci. 44, 2133–2144. David, W. I. F. (2004). J. Appl. Cryst. 37, 621–628. David, W. I. F., Shankland, K. & Shankland, N. (1998). Chem. Commun. pp. 931–932. David, W. I. F. & Sivia, D. S. (2001). J. Appl. Cryst. 34, 318–324. Dinnebier, R. E., Schweiger, M., Bildstein, B., Shankland, K., David, W. I. F., Jobst, A. & Van Smaalen, S. (2000). J. Appl. Cryst. 33, 1199–1207. Dinnebier, R. E., Wagner, M., Peters, F., Shankland, K. & David, W. I. F. (2000). Z. Anorg. Allg. Chem. 626, 1400–1405. Dollase, W. A. (1986). J. Appl. Cryst. 19, 267–272. Florence, A. J., Shankland, N., Shankland, K., David, W. I. F., Pidcock, E., Xu, X., Johnston, A., Kennedy, A. R., Cox, P. J., Evans, J. S. O., Steele, G., Cosgrove, S. D. & Frampton, C. S. (2005). J. Appl. Cryst. 38, 249–259.

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Hofmann, D. W. M. (2002). Acta Cryst. B58, 489–493. Interactive Software Services Ltd (2000). Winteracter version 3.0, Interactive Software Services Ltd, Huntington, UK, http://www.winteracter.com/iss/. Macrae, C. F., Edgington, P. R., McCabe, P., Pidcock, E., Shields, G., Taylor, R., Towler, M. & Van de Streek, J. (2006). J. Appl. Cryst. 39, 453–457. Markvardsen, A. J., David, W. I. F., Johnson, J. C. & Shankland, K. (2001). Acta Cryst. A57, 47–54. Oswald, I. D. H., Allan, D. R., Motherwell, W. D. S. & Parsons, S. (2005). Acta Cryst. B61, 69–79. Pawley, G. S. (1981). J. Appl. Cryst. 14, 357–361. Rietveld, H. M. (1967). Acta Cryst. 22, 151–152. Rietveld, H. M. (1969). J. Appl. Cryst. 2, 65–71. Shankland, K. (2005). IUCr Commission Crystallogr. Comput. Newsl. No. 5, pp. 92–102. Shankland, K. & David, W. I. F. (2002). Structure Determination from Powder Diffraction Data, edited by W. I. F. David, K. Shankland, L. B. McCusker & C. Baerlocher. Oxford University Press. Shankland, K., David, W. I. F. & Csoka, T. (1997). Z. Kristallogr. 212, 550– 552. Shankland, K., David, W. I. F. & Sivia, D. S. (1997). J. Mater. Chem. 7, 569– 572. Shankland, K., McBride, L., David, W. I. F., Shankland, N. & Steele, G. (2002). J. Appl. Cryst. 35, 443–454. Trask, A. V., Van de Streek, J., Motherwell, W. D. S. & Jones, W. (2005). Cryst. Growth Design, 5, 2233–2241. Van Laarhoven, P. J. & Aarts, E. H. (1987). Simulated Annealing: Theory and Applications. Dordrecht: Kluwer Academic Publishers.

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