Introduction

The object of this tutorial is to guide you through the process of structure solution, using the molecule hydrochlorothiazide as an example. Tutorial 1 goes through the process in considerable detail; subsequent tutorial examples will be more concise, but will introduce other, new aspects of the structure solution process. This tutorial will take a novice user about 2 hours to complete and experienced powder crystallographers considerably less time.

Data

The data set Tutorial_1.xye is a synchrotron X-ray diffraction data set collected at 20 K on Beamline X7A of the Brookhaven National Synchrotron Light Source. The incident wavelength was 1.1294 Å and the sample was held in a 0.7 mm glass capillary.

Stage 1: Reading the data

Open DASH by double clicking on the DASH icon.

The DASH Wizard will guide you through the structure solution process, which is performed in a series of steps.

• Select View data / determine peak positions and click Next >.

• Click the Browse... button.

• Select the file Tutorial_1.xye (from, e.g. C:\Program Files\CCDC\CSD_2021\DASH\Documentation\Tutorial1\Data files) and click Open. The diffraction data will be loaded into DASH. Click Next >.

• Check that the wavelength and radiation source have been set correctly and click Next >.

• Truncate the data to a resolution of 1.75 Å and click Next >.

• The default window size setting of 100 should be good enough for this simple background. Click Next >.

Stage 2: Examining the Data

The data spans 5 to 44° 2θ. If you open the file Tutorial_1.xye in an ASCII text editor such as Wordpad you’ll see that the wavelength of 1.1294 is given on the first line.

The data consists of three columns.

1.1294
5.000 81.96 10.952
5.004 71.25 10.284
...
<bulk of data omitted for clarity>
...
43.996 69.55 3.572
44.000 68.28 3.540

Column 1 = 2θ position
Column 2 = diffracted intensity (counts)
Column 3 = estimated standard deviation of the intensity

If you zoom in on the diffracted data as it is displayed in DASH, you will see that DASH displays both the intensity and the error bars. The simplest way to zoom is to use the left mouse button. Click and hold the left mouse button and drag out a rectangle around the area that you want to zoom in on. To zoom out, simply press the Home key on the keyboard (Note that there are other ways to zoom in on the data - see the DASH User Guide for details). Try zooming in on the two peaks that lie just either side of 10° 2θ.

You can use the left and right cursor keys to move up and down the data in 2θ. Some other useful keyboard shortcuts whilst examining data are:

**Shift -**↑ : Zoom in

**Shift -**↓ : Zoom out

Ctrl - ↑ : Rescale the y-axis to the maximum in the current range

Whilst browsing the data, note the following features:

• The peak asymmetry (elongated tails to the left-hand side of the peaks) in the low angle peaks, due to axial divergence.

• The flat background indicative of a lack of amorphous content.

• The sharp peaks, indicating a good crystalline sample.

• The excellent instrumental resolution. See, for example, the doublet of peaks around 12.17° 2θ.

• The use of a small step size commensurate with the instrumental resolution and the narrow peaks, i.e. plenty of points across each peak.

• The fall-off in diffracted intensity with increasing angle due to the Lorentz effect and thermal effects.

• The increasing number of peaks per unit angle with increasing angle.

• The excellent signal to noise ratio, even at the maximum diffraction angle, i.e. peaks can still be clearly discriminated from background.

Stage 3. Fitting the Peaks to Determine the Exact Peak Positions

We need accurate estimates of the 2θ positions of the first 20 or so peaks in the diffraction pattern in order to index the diffraction data, i.e. determine the unit cell and hence the Laue class of the crystal. DASH makes this process quick and easy by fitting entire peaks accurately. It is important to emphasise that we are only interested in peak positions, not peak intensities, at this stage, so weak peaks are every bit as important in indexing as strong ones. The first peak in the diffraction pattern is at just under 7°. To fit this peak:

• Zoom in to the area around the peak.

• Sweep out an area using the right mouse button i.e. move to about 6.85° 2θ, click the right-hand mouse button and hold down as you sweep right to about 7.05° before releasing the right button. The hatched area now covers the peak and enough background either side to allow an accurate estimate of the peak parameters. If you are not happy with the area swept out (e.g. if your finger slipped as you were sweeping), simply put the cursor inside the hatched area and press the Delete key on the keyboard to remove the current selected area, then try again.

• With the cursor in the hatched area, press the Return or Enter key to fit the peak.

• The solid green line indicates the fit to the data, whilst the vertical blue line indicates the peak position. Selecting Peak Positions from the View menu shows the exact peak position:

• Do not worry if you do not have the exact same position; however, it should be very close to this value.

• Fit the next two peaks at around 9.5 and 10.3° 2θ in the same way.

• Zoom in on the doublet at 12.17° 2θ. It is clear from the shape of the peak that there are two contributing reflections here.

• Sweep out an area covering the two peaks using the right mouse button.

• Now, you need to give two initial estimates for the peak position. This is easily done by moving the cursor close to the top of the first peak and pressing 1 on the keyboard to insert the first estimate, then moving to the top of the second peak and pressing 2 to insert the second estimate.

• Then, with the cursor inside the hatched area, press Return or Enter as before to fit the two peaks. Note that the peak positions are refined from your initial estimates, in order to give the best fit to the data.

• Now, you simply repeat this until we have 20 accurate peak positions. Listed below are 2θ ranges and the number of peaks contained in them as a guide.

Region / ° 2θ	Peaks in region	Cumulative peaks
below 13.5	5	5
13.5 to 14.6	3	8
14.6 to 16.4	4	12
16.4 to 17.5	1	13
17.5 to 18.5	2	15
18.5 to 20	4	19
20 to 20.9	3	22
20.9 to 21.3	2	24

• Here are the first 24 peak positions as returned by DASH, viewed by selecting Peak Positions from the View menu:

6.9822	9.4942	10.3453	12.1847	12.2228
13.6925	13.7905	14.0003	15.2696	15.6883
15.7753	15.9581	16.8146	17.7552	18.0107
19.0501	19.1452	19.3479	19.7249	20.5468
20.6314	20.7735	21.0639	21.1688

• The only peak you might have struggled to see was the one at ~17.75° 2θ, as it is very weak.

Stage 4. Indexing

• Having selected 20 or so peaks we now want to index the pattern. There are an number of options at this point, you can choose to index the pattern using the installed version of DICVOL, use an external program (McMaille or DICVOL04) or enter known unit cell parameters. Index pattern is already selected so click Next > to index using the internal version of DICVOL.

• Ensure that all crystal systems except Triclinic are selected.

• Select Run > to run the DICVOL indexing program (See the lists of available software for powder indexing at http://www.ccp14.ac.uk/solution/indexing/).

For other Indexing Programs you can easily get the peak positions out of DASH and into a file by:

• Selecting Peak Positions from the View menu and then clicking on the word Position at the top of the column containing the peak positions. This selects the entire column.

• Use Ctrl+C to copy the entire column to the clipboard.

• Inside an appropriate editor, such as Notepad or Wordpad, use Ctrl+V to paste the column into a file.

• Save the line positions into a file with the correct format for your favourite autoindexing program.

Your indexing program should return a monoclinic unit cell of volume ~576 ų.

A typical run of DICVOL, if the selected peaks were very close to those given in the previous stage, returns a monoclinic cell, with:

a = 9.9388 Å, b = 8.49954 Å, c = 7.31875 Å, beta = 111.19°, V = 576.453 ų

Figures of merit: M(24) = 131, F(24) = 446

With figures of merit as good as these, there is little doubt that the cell has been correctly indexed. It is possible to change this cell into one with a conventional setting, but for the moment, we will proceed with the cell as it is returned by DICVOL.

Stage 5. Stop and Think

Does the cell make sense? There is a very approximate method of estimating molecular volume using 15 ų per C, N, O atom, 25 ų for Cl, S, and 5 ų per hydrogen atom. So for this molecule C₇H₄N₃O₂S₂Cl we estimate the molecular volume to be 275 ų, so 2 molecules per cell would need a volume approximately 550 ų. The DICVOL cell volume of 576 ų suggests that we have two molecules per cell, and given that the cell is monoclinic, a likely space group is P2₁, since Z = 2 for this space group.

Stage 6. Checking the Cell and Determining the Space Group

• Select the top solution from the Results from DICVOL window and import this into DASH by selecting the button next to it in the Import column. If only one solution is obtained it will be imported automatically into DASH.

• Click Next >.

You will see the data displayed as before, but this time, there are a series of tick marks at the top of the plot to indicate where the Bragg reflections corresponding to the input cell occur.

• The first thing to do is to ensure that in general, the tick marks correspond to peaks within the pattern.

• Any unaccounted for diffraction peaks are a warning that the determined unit cell might not be correct, or that there is an impurity phase present.

• A quick glance at the Tutorial_1.xye pattern shows no unaccounted for peaks, but a few excess tick marks. For example:

• The tick at just over 7.5° 2θ does not appear to correspond to anything other than background intensity, which means that it probably corresponds to a systematic absence for the true space group of the crystal.

• The tick at just over 9.5° 2θ may be another absence, although there is just a hint of a shoulder present on the stronger peak.

• We already guessed that a likely space group is P2₁, so let us see if increasing the symmetry from P2 to P2₁ eliminates likely absences whilst leaving no unaccounted for peaks.

• In the Unit Cell Parameters window select P2₁ from the Space Group pull down menu:

• Using the down arrow cursor key, move down the list, and watch the tick marks update to show the reflection positions corresponding to the currently selected space group. Alternatively, you can use the mouse to scroll down and select individual space groups.

• It’s pretty obvious that choices such as P 1 c 1 eliminate major peaks and clearly cannot be correct.

• Tick-marks with space group P 1 c 1:

• Alternatively, P 1 2₁ 1 eliminates the tick at 7.5° 2θ whilst leaving one at just over 9.5.

Tick-marks with space group P 1 2₁ 1:

• Examining the rest of the pattern, the correspondence between tick marks and peaks is excellent and we can conclude that the peak at just over 9.5° 2θ is a very weak diffraction feature of a crystal whose space group is P2₁, b axis unique.

• Click Apply in order to select the space group P2₁.

• Click Next >.

Stage 7. Extracting Intensities

Initially this is much like the indexing phase. We are aiming to model the entire diffraction pattern and so we need to be able to fit peaks. We are confident that we have a reasonably accurate cell and the correct space group. The criteria for peak fitting are slightly different from the ones used in indexing and we need to:

• Fit a number of, preferably, isolated reflections.

• Sample peaks across the pattern in order to parameterise the peak shape across the pattern.

• Ensure that any peak asymmetry is modelled at the start of the pattern.

From the Pawley Refinement Step 1: Peak Picking window select Clear Peaks. Some suitable peaks for this pattern are given below. Fit them by sweeping out areas over the peaks with the right mouse button as before in the order they are given.

Peak	Approx. Location	Note
1	6.97
2	9.49
3	14.0	1Option to Pawley refine
4	16.8
5	20.78
6	22.75	2L/parameter refine starts
7	27.8
8	31.85	3Pawley window appears

1. After three peaks have been fitted, you are given the chance to go to profile refinement directly by pressing the following icon:

or choosing Pawley Refinement from the Mode menu. Ignore this option for the moment.

2. After six peaks have been fitted, DASH has sufficient information to allow a lattice parameter (4 parameters + zero point) refinement. The results of the refinement can be seen by selecting Peak Positions from View menu. This improves the lattice constants in the majority of cases and greatly improves the starting position for the Pawley refinement.

3. After eight peaks have been fitted, DASH has determined that the peak shape has been sufficiently well defined to allow a full Pawley refinement to be performed. The Pawley Refinement Step 2 window will pop up automatically.

• In the initial Pawley refinement, only the terms describing the background and the terms corresponding to individual reflection intensities are refined, using the previously refined unit cell and zero-point.

• Select Refine; 3 cycles of least squares are performed.

• This should return figures similar to the ones below (or better).

204 reflections 9751 points Rwp = 22.25 R(exp) = 9.38 ² = 5.6

• Click Accept to accept the results of this refinement, the fit is then displayed.

• Now click in the main window and press Home to see how well the data are fitted. The (obs minus calc) plot is shown in pink and emphasises any misfit in the data. If you look closely at the data, you are likely to see something like this:

The fit is very good, but the tell-tale sinusoidal misfit indicates that the unit cell and zero point are in need of some further refinement.

• Going back to the Pawley window, note that the program has anticipated this and has flagged the unit cell and zero-point for refinement.

• Select Refine to perform a Pawley refinement for 5 cycles, in which the background, intensities, unit cell and zero point are all refined. The fit should improve to, for example:

204 reflections 9751 points Rwp = 16.2 R(exp) = 9.38 ² = 3.0

• The figures of merit have improved, so select Accept to see the improvement in the fit.

• Examine the whole profile. If you have achieved a ² of around 3, the fit to the data will be excellent. Click Save as to save the refinement results to disk as a DASH Pawley-Fit File (.sdi) called Tutorial_1.sdi.

Stage 8. Revisiting Space Group Determination

Now that Pawley fitting and refinement has been introduced it is an appropriate point to try an alternative way of determining the space group.

• Select < Back in the Pawley Refinement Step 2 window to return to the Unit Cell Parameters window. This time, select Space Group>.

• In order to furnish the space group determination program with a required set of reflections and intensities, a Pawley fit to the profile has to be obtained in the most general space group of the crystal system under study. On pressing Space Group> DASH automatically selects the correct space group.

• Select Clear Peaks from the Pawley Refinement Step 1: Peak Picking window and proceed through the Pawley fitting process as before. Once a good Pawley fit to the data has been achieved, press Run> to launch the space group determination program.

• The console window of Extinction Symbol will appear and once the calculations have finished, press Enter on the keyboard to view the results. The space group P21 should be the most probable space group found for the data and hence will be listed first with the highest probability in the right hand column of the results table:

• Close the window showing the results and press <Back in the Pawley Refinement Step 2 window. A dialogue box will pop-up asking whether the files generated during space group determination should be removed: select Yes. Now from the Space Group pull down menu select the space group determined to be the most probable (P21) and press Apply. Check the correspondence between the tick-marks and the peak positions as before.

• The correct space group has been chosen and hence a Pawley refinement should be performed in this space group. This step has already been performed previously and the .sdi file saved. Hence the structure solution process can begin.

• You can exit DASH at this point, if you wish, by selecting Exit from the File menu.

Stage 9. Molecule Construction

The crystal structure of the molecule that we are trying to solve is given below:

• You need to construct a 3D molecular description of the above molecule using your favourite modelling software and save it in pdb, mol or mol2 format.

• If you do not have a modelling package to hand, there is a model file named Tutorial_1.mol2 provided with the tutorial, taking the co-ordinates from the Cambridge Structural Database reference code HCSBTZ. If you are using this model rather than creating your own you can now skip to Stage 10.

• For the purposes of the tutorial, we’ll assume that the molecule was sketched (as indeed it was) using the freely available ISIS/Draw sketching package.

• Furthermore, we will assume the 2D to 3D conversion will be performed using a 2D to 3D structure converter package such as CORINA: https://www.molecular-networks.com/products/corina and that the molecule coordinates are saved out as e.g. Tutorial_1.mol.

Stage 10. Setting up the Structure Solution Run

• Start DASH as before and select Simulated annealing structure solution from the Wizard. Click Next >.

• Choose the option to Set up new SA runs. Click Next >.

• Browse for the DASH project file that you saved at the end of Stage 7 and Open the file that you saved, e.g. Tutorial_1.sdi.

• Click on the icon and read in the Tutorial_1.mol file, or the Tutorial_1.mol2 file.

• DASH will generate the internal format (Z-matrix) that it uses to describe the molecular conformation.

• DASH analyses the molecule and automatically selects rotatable torsions. In this case, the bond connecting the benzene ring to the SO₂NH₂ group is the only rotatable torsion in the molecule.

• The newly created Z-matrix will be automatically selected.

• Note that DASH has determined that there are 7 independent degrees of freedom to be determined if the crystal structure is to be solved i.e. 3 positional coordinates for the centre of mass of the molecule, 3 parameters describing the orientation of the molecule within the unit cell, and 1 internal torsion angle describing the molecular conformation.

• DASH now has the information it needs concerning the molecule, so click Next >.

The following menu allows you to fix or bound parameters. In this particular example, we are allowed to fix the y coordinate of the centre of mass of the molecule at any position, as P2₁ is a polar space group.

• Do this by clicking on F (short for fix) in the line corresponding to the y coordinate of the molecular fragment (y(frag1)):

• Click Next >.

The resulting Simulated Annealing Protocol window that appears need not concern us here. In most cases, the default values will suffice. See the DASH User Guide for more details. Click Next >.

The next window asks you to choose some options for the Simulated Annealing procedure. It is useful at this stage to go over some of the details.

• Hydrogens: as the scattering power of hydrogens is low, hydrogens are ignored by default to speed up the calculations. The Absorb option absorbs the electrons from the hydrogen in their riding atoms. For single crystal data, the hydrogen atoms can be taken into account explicitly during the SA.
  Note: By default hydrogens are always included during the local minimisation at the end of each simulated annealing run.
  During Rietveld refinement, hydrogen atoms are always included.

• Use crystallographic centre of mass: when selected each atom is assigned a weight of Z^-2 when the molecular centre of rotation is calculated, where Z is its number of electrons. Otherwise, no weights are applied.

• Auto local minimise: when selected, the ² of each final solution is minimised using a simplex algorithm before the solution is written out. If Use hydrogens under Auto local minimise is selected, hydrogens are included in the local minimisations of the final solutions.

• Auto align: when selected the molecules of the final solution are aligned before the solution is written out. This only applies when more than one run has been selected.

• Output .pdb: when selected the crystal structure of the final solution is written out in pdb format.

• Output .cssr: when selected the crystal structure of the final solution is written out in cssr format.

• Output .ccl: when selected the crystal structure of the final solution is written out in ccl format.

• Output .pro: when selected a file with the extension. .pro is written out which contains 2θ, the observed profile, the calculated profile for the best solution and the original ESDs. The file is written out in ASCII format and can be imported into a spreadsheet package such as Excel.

• Output .cif: when selected the crystal structure of the final solution is written out in cif format.

• Output .res: when selected the crystal structure of the final solution is written out in res format.

• Output chi-squared vs. moves: when selected, a graph of the profile ² versus moves is written out to a file in ASCII format with the extension .chi, at the end of the simulated annealing. This can be imported into a spreadsheet package such as Excel.

Note that when more than 1 simulated annealing run is requested, the above options pertain to every run. This can generate quite a number of files. Each option (except Use hydrogens) can be switched on and off while the simulated annealing is running.

• Click Solve >.

• The simulated annealing run now starts.

Stage 11. Monitoring Structure Solution Progress

Full details of all the output from the structure solution run are given in the DASH User Guide. For this tutorial, you need only watch:

• The Profile ².

• The (obs - calc) plot i.e. the difference plot, shown by default in pink.

The profile ² is on the same scale as the Pawley fit profile ² that you obtained when fitting the data in Stage 7. So, if the current profile ² is close to the value of the Pawley profile ², you’ve probably solved the structure.

DASH runs the SA process until the user intervenes by pressing one of the following buttons on the SA output panel:

• Pause - Pauses the SA run until you hit OK. This can be useful to free up the processor temporarily, as DASH is computationally intensive.

• Start next - When in a multi-run, the Start next button terminates the current run and starts the next one.

• Stop - Stops the simulated annealing run immediately and returns you to the first Simulated Annealing Protocol window.

• Click Edit to end a simulated annealing run and change parameters.

• Local minimisation - Invokes a simplex optimisation that takes the structure to the deepest minimum in the vicinity of the current best structure.

• Click View to visualise the crystal structure of the best solution obtained so far for the current run.

• Click Solutions to analyse the solutions found so far.

On a modestly specified PC (e.g. Pentium III 300 MHz) the structure solution process should take less than 30 seconds to reach a profile ² of around 12, by which point the structure is solved to a high degree of accuracy (this is an ideal value the actual number you get may differ from this).

The profile ² is 12.05, less than four times that of the Pawley profile ², i.e. solved:

Examine the difference plot:

• The fit is excellent, even at high angle.

• Remember also that we have effectively only refined a scale factor to get to this point and the structure is clearly solved.

• Click View in the Simulated Annealing Status window or on one of the buttons in the View column of the Analyse Solutions window to see that solution displayed in the 3D visualiser.

Stage 12. Examining the Output Structure

DASH can output 5 coordinate file formats describing the final answer output from simulated annealing (see the Configuration... window). Here, we assume that the project filename was Tutorial_1.sdi.

• Tutorial_1.pdb: protein data bank format file containing a Cartesian coordinate description of the SA solution.

• Tutorial_1.cssr: Cambridge Structure Search and Retrieval format file containing a fractional coordinate description of the SA solution.

• Tutorial_1.ccl: Cambridge Crystallographic Subroutine Library format file containing a fractional co-ordinate description of the SA solution.

• Tutorial_1.cif: Crystal Information File format file containing a fractional coordinate description of the SA solution.

• Tutorial_1.res: SHELX format file containing a fractional coordinate description of the SA solution.

The Mercury visualiser supplied with DASH has options to display Packing and H-bonds. Using these options your answer should look like that given below. You can see that all donors and acceptors are satisfied:

Remember that the exact location of your molecule along b depends upon where you anchored the molecule. In the above picture, the molecule was fixed at y = 0.5. The solution obtained is in excellent agreement with that reported for hydrochlorothiazide at room temperature by Dupont & Dideberg (1972).

Stage 13. Rietveld Refinement

• There are several options for Rietveld refinement in DASH including interfaces to external refinement packages and a built-in module for refinement. For the purposes of this example, to refine the structure in a meaningful manner we will use the built-in rigid-body Rietveld refinement module (see Overview of DASH in Batch/GRID Mode). This implementation uses the extracted intensities with their correlation matrix from the Pawley refinement stage and is thus limited to the resolution chosen in 2θ in Stage 1. Up to now the default setting in DASH has been used which truncated the data to 2θ of 37.65, corresponding to a resolution of 1.75 Å.

• Examination of the Pawley refinement carried out in Stage 7 will show the actual number of extracted intensities e.g. 135. The Pawley refinement result values may be examined using the View menu, and then selecting Pawley / SA. The low resolution of the data means that we cannot expect to refine coordinates of this molecule in an unconstrained manner and obtain physically reasonable values. The information is just not there!

• However, it is meaningful to fit the molecule as a sequence of rigid-body fragments, which is the meaning of the Z-matrix description. The Z-matrix consists of instructions for constructing the molecule atom-by-atom, each atom in this case being added according to the values given for a bond-length to a preceding atom, a bond-angle to two preceding atoms, and finally a torsion angle to three preceding atoms.

• In Stage 10 you ran a program which converted the Cartesian model of Stage 9 into a Z-matrix. The program further identified, by examination of the chemical atom types, that only one torsion angle should be treated as variable, namely N3:S1:C5:C6. The SA run explored the search space with all other parameters of the Z-matrix fixed, which we have seen gives a chemically sensible result in our solution. The Rietveld refinement allows variation of any of the Z-matrix parameters, for the chosen solution.

• The first stage of the Rietveld refinement is to keep all parameters fixed except the global isotropic temperature factor scale. This allows the initial guess of the Biso values for each atom in the Z-matrix to be adjusted by a global scale factor; the default values set by DASH are Biso = 3.0 for all non-hydrogens and 6.0 for hydrogens. When the scale factor, K, is refined then the Biso for each atom is simply K.Biso as input in the Z-matrix file.

• In single crystal X-ray refinement it is usual to set the value for Biso for hydrogens to about 1.25 times the parent heavy atom. In the case of powder data, for this size of molecule, there will be little observable effect if we set all H-atoms to have the same value. The starting Biso hydrogen value of 6.0 may be considered rather too large and could be adjusted to say 4.0. However the value of Biso for non-hydrogen atoms is typical for this size of molecule at room-temperature.

• Choose the first solution in the Analyse Solutions dialogue box, click on the Rietveld button then select Rigid-body Rietveld refinement and click on Next >, this will launch the following window:

• You will see that the check-box for Global isotropic temperature factor is selected, click Refine. The starting value of 1.000 with Chi-sqd 100.72 and Profile Chi-sqd 8.01 will change to 0.13902, 43.49 and 5.53 respectively. This very low value of the temperature factor scale corresponds to the unusually low data collection temperature of 20K. Keep this temperature factor fixed by deselecting the check box.

• Now switch on the check boxes marked V for the left hand column Translations and orientations by clicking the Set button below this column. This specifies refinement of the translation parameter for the molecule’s centre of mass, and the orientation of the molecule. In this space group P21 the position along the y-axis is arbitrary, so switch off the y check box, and click Refine. You will see the Chi-sqd values drop to 42.58 and 5.48, with a slight change of temperature scale to 0.13059.

• This is perhaps as far as is reasonable to refine this structure for publication. You can now output a CIF file using the Save as... button, e.g. with filename Tut1-Rietveld-Biso, and choose output file type .cif from the list of file formats.

• You can check that the Rietveld refinement is stable by allowing all torsion angles to vary; click the Set button at the bottom of the Torsions column, deselect the Global isotropic temperature factor, and clear the Translations and Orientations by using the Clear button underneath the column. There will be very little change in the parameters with almost no reduction of the Chi-sqd values.

• As a further experiment you can also switch off refinement of the Translations and Orientations, and Torsions by using the Clear button underneath each column, and deselect the Global isotropic temperature factor box. Now allow all bond angles to vary. You see a small shift in coordinates, with a small reduction in Chi-sqd to 36.82 and 5.22. You can compare this refined structure to the starting value when you entered the Rietveld window by clicking Compare. The Mercury display shows that there have been very small shifts in the coordinates (use the Zoom-in feature). The resulting coordinates are not more significant than the previous coordinates saved as the CIF file, but they do confirm that the refinement is stable, and you are in a local minimum of the Chi-sqd surface.

• Similarly you could refine all the bond-lengths, and achieve a further small reduction in Chi-sqd, but this cannot be interpreted as an improved set of coordinates for this solution. There is simply not enough data to justify these fine variations from the starting values of bond-lengths and bond-angles. Another way of looking at the calculation is that you could achieve the same low Chi-sqd values with a range of slightly different molecular models. At present you have no information of the estimated standard deviations of the coordinates.

Note: As an experiment, if you attempt to refine the Global isotropic temperature factor together with a significant number of the torsions, angles or distances then the procedure will take a considerable time to converge (e.g. 2-3 minutes), showing that the temperature factor is highly correlated with the other parameters.

• Some insight may be obtained as to how individual parameters affect the calculated Ch-sqd by manually setting any parameter value in the menu box and clicking on Calculate. This simply calculates Chi-sqd at that point, e.g. changing the bond-length C2:C7 from 1.4297 to 1.4397 typically changes Chi-sqd from 28.42 to 28.73, 4.01 to 4.03. Changing the position of a heavier atom e.g. chlorine in Cl1:C4 generally produces a larger change to Chi-sqd for a shift of 0.01 in the bond-length.

Using maximum resolution

If this were a real example of refinement of an unknown structure, you would try to refine against the maximum resolution data that the DASH intensity extraction can handle. This tutorial example so far was carried out at a resolution of 1.75 Å, using 135 extracted intensities. The current version of DASH can use a maximum of 350 reflection intensities. In order to do this you must go back to Stage 1 and read in the data with a higher truncation value in 2θ, e.g. 44.0 degrees corresponding to 1.507 Å resolution. This gives a Pawley fit of about 2.35 for 204 extracted reflections. When one runs the SA there are typically solutions with Chi-sqd about 7.04. The Rietveld refinement following the order of refinement (a) Global Temperature Factor, (b) Translations and Rotations, gives a temperature factor scale 0.211 and Chi-sqd 28.42, Profile Chi-sqd 4.01.

To refine from another SA solution

Close the Rietveld window with Close, this returns you to the main DASH window. Click on the Mode pull-down menu, then select Analyse Solutions. This returns you to the list of solutions form your last SA run. Note that if you exit completely from DASH this Analyse Solutions window is not recoverable.

References

DICVOL Program:
D. Louer & M. Louer (1972) J. Appl. Crystallogr. 5, 271-275.
A. Boultif & D. Louer (1991) J. Appl. Crystallogr. 24, 987-993.

Extinction Symbol Program:
Markvardsen, A.J., David, W.I.F., Johnson, J.C., Shankland, K. (2001) Acta Cryst., A57, 47-54

Single crystal structure (CSD Refcode HCSBTZ):
L. Dupont & O. Dideberg (1972) Acta Crystallogr. B28, 2340-2347.