The following steps describe a general procedure used to collect data with any type of single crystal instrument. The order of the steps after collecting the data is not crucial. Selection of an appropriate crystal and alignment of the crystal on the instrument must be carefully performed in order to get the best results from the data.

• Select and mount crystal.
• Align center of mass of crystal to the center of the goniometer arcs. Always check that the crosshairs on the microscope or video camera are properly aligned either by rotating the sample by 180 ^o or by checking the crosshairs with a known, aligned sample.
• Locate and center several diffraction maxima. With a point detector instrument this is accomplished by measuring the positions of spots on a film or by using a search algorithm. With area detector data, threshhold a short series of data frames.
• Index diffraction spots; refine cell parameters; check for higher metric symmetry in cell parameters.
• Determine data collection parameters; collect data. Be sure to collect both the Laue-unique and Friedel-related data for non-centrosymmteric space groups.
• Reduce the data (apply background, profile (spot-shape), Lorentz, polarization and scaling corrections).
• Determine precise cell parameters.
• Collect appropriate information for an absorption correction. When possible, index the faces of the crystal for an analytical absorption correction. Programs (chi90) are available to determine the best reflections for collecting psi scan data with point detector instruments. A highly redundant set of data collected with an area detector is sufficient for an empirical absorption correction.
• Apply an absorption correction to the data. This step is sometimes delayed until complete information about the empirical formula is available (after structure solution and partial refinement). back to top

For many of the more common space groups, the systematic absences uniquely determine the space group. However, for a large number of less common space groups, there are two or more possible space groups that will match the absences. In these cases, the possiblespace groups are usually tried beginning with the highest symmetry space group until the structure is determined.

• The cell parameters are tested for possible higher metric symmetry. The Laue symmetry is determined by the comparing the intensities of symmetry equivalent data for the various possible crystal symmetries.
• The systematic absence conditions appropriate for the given Laue group are tested to determine cell centering, glide planes and screw axes.
• A statistical test is performed to test for a center of symmetry.
• From the previous tests a list of possible space groups is found.

There are several ways to solve the crystal structure of a small molecule. The most common method used today is called direct methods. Another series of common methods used today are based on the Patterson technique, which require one or more "heavy atoms" be present in the structure. Heavy atom methods will not be discussed here. The modes of using a direct methods program for solving a crystal structure are very dependent on the program itself. However, all direct methods programs do fail when a severe error is made in the choice of space group or when an incomplete set of data are collected. Also, direct methods are rarely sucessful when fewer than half of the data are observed in shells out to about 1.0 Å resolution.

The following steps describe ways to solve a crystal structure using George Sheldrick's SHELXS program. This program generates random phase sets, and then refines these phase sets using phase annealing and tangent formula methods. Correct phase sets typically have small (< 0.2) values for R(alpha), small (<-0.5) values for N(qual), and small(<0.2) values for R(E). Higher values for the previous statistics may give a correct solution, depending on the quality of the intensity data. The program choses the phase set with the smallest combined figure of merit (lowest R(alpha) and N(qual)) to compute a single E map. The following steps should be tried, usually in this order until the structure is solved.

• Try the default TREF instruction.
• If there are < 20 phase relations per reflection then lower the E-value cutoff, and retry a simple TREF run.
• If several phase sets have similar low values for R(alpha) and N(qual), and have different values for the signs of the seminvariant phases, then try computing the maps for different phase sets using TREF -nnnn where nnnn is the number of the phase set.
• Try a larger number of phase sets, e.g. TREF 2000.
• The algorithm in SHELXS for solving noncentrosymmetric structures is more powerful than the algorithm for solving centrosymmetric structures. If the space group is centrosymmetric, then try to solve the structure in related noncentrosymmetric space group. For example, if the original space group is P2₁/c, then try solving the structure in P2₁. Once the structure is solved and partially refined in the lower symmetry space group, locate the symmetry element(s) of the higher symmetry space group, and move the structure so that the symmetry element(s) are at the appropriate locations for the higher symmetry space group.
• Check the manual for other parameters that may be changed for your specific problem.
• Be sure that the space group is correct and that the data are corrected for any systematic errors such as absorption. If the average I / s(I) is less than 5.0 increase the intensities by one or more of the following:
• Collect data on a larger crystal.
• Collect data at low temperature.
• Collect data with a brighter source, preferably with copper radiation.
• Collect data with an area detector.

The steps to complete and refine a crystal structure are somewhat dependent on the program(s) being used for refinement and Fourier map generation. There are two important principles for all refinement methods. First, the model must be chemically reasonable. Second, the answer is in the data. The data will often tell you through the difference map and the analysis of variance what changes should be made to improve the model. Be very careful when adding atoms to the model that are not seen in a difference map. The steps listed below are deliberately conservative, i.e., they are designed for poor quality data sets. For good quality (average I / s > 12) data sets, least squares refinements usually converge rapidly and many of these steps can be combined.

The SHELXL refinement program from Prof. George M. Sheldrick (or one of its variants) is used in our laboratory. The following steps include special comments for this program.

• Translate or rotate the coordinates of all groups in the structure until the centroids of the groups are within one unit cell (centroid coordinates between 0.0 and 1.0).
• If the space group is polar (the origin is not defined in one more directions by the space group operators), then define the origin by either holding the appropriate coordinate(s) of a heavy atom fixed or by restraining all coordinates in the polar axis to sum to a constant value. The latter "floating origin" approach is described by H. D. Flack and D. Schwarzenbach (1988) Acta Cryst. A44 499-506, and is used in Prof. Sheldrick's SHELXL program.
• For atoms sitting on special positions in the space group apply the appropriate constraints to hold these atoms on the respective special positions. Usually this requires that one or more coordinates are held fixed. The SHELXL program automatically constrains atoms at (or very near) special positions. Change the occupancies of these atoms to have values equal to the ratio of the # of symmetry operators for the special position to the # of symmetry operators in the space group. The occupancies are automatically adjusted by Prof. Sheldrick's program.
• Assign reasonable isotropic displacement parameters to all atoms. For room temperature data sets of organic or organometallic compounds these displacement parameters should be in the range of U = 0.03 to 0.05. Low temperature data for these types of compounds typically have displacement parameters in the range 0.02 to 0.04. Structures with strong bonding networks, such as minerals, usually have displacement parameters in the range 0.001 to 0.02. If the intensity data are weak (average I / s < 10), fix the displacement parameters for all atoms of first row elements.
• Refine the structure using a reasonable weighting scheme. For programs that refine on F, unit weights are suitable in the early stages of refinement, but statistical weights should be used for any final refinement cycles. For programs that refine on F², statistical weights should be used for all cycles of refinement. For the SHELXL program begin with "WGHT 0.08" for structures with no heavy atoms and "WGHT 0.08 100.0" for structures with heavy metal atoms.
• Begin the structure factor, least-squares, Fourier map calculations.
• From a difference map, add non-hydrogen atoms to the model that have chemically-reasonable bond distances and angles. Repeat the structure factor, least squares refinement, and Fourier map calculations until all non-hydrogen atoms are located and until the positional parameters have converged (all shift/error ratios are < 0.1). To achieve convergence may require that rigid group or distance restraints be applied to poorly determined regions of the structure.
• Use the difference map as a guide for the following steps in refinement. It is usually best to refine to convergence before beginning the following stage.
• Refine any heavy atoms with anisotropic displacement parameters. Atoms on special positions may require constraints on the parameters. These constraints are automatically applied in the SHELXL program.
• Locate and refine the positions of the hydrogen atoms. For many hydrogen atoms, it is possible to simply calculate the positions from known geometry. If hydrogren atom positions are to be refined, be sure that their final positions represent chemically-reasonable geometry.
• Refine the isotropic displacement parameters of the light, non-hydrogen atoms that were fixed in the early stages of refinement.
• Regions of the structure exhibiting disorder (more than one orientation for a given group) should be carefully modeled. The occupancies of the atoms in each orientation must be given equivalent values. Often the geometry of the disordered atoms must be restrained to give chemically reasonable values. The displacement parameters should be initially set at reasonable fixed isotropic values. As the model converges, the displacement parameters may be refined isotropically and finally anisotropically (often with restraints).
• Be careful not to over model the structure. Do not add unnecessary parameters in the search for a lower R value.
• Include a secondary extinction correction in the model, if needed. Secondary extinction is a multiple diffraction problem that shows up as reduced measured intensities especially for the strong, low scattering angle data. This effect is more pronounced in data from larger crystals. Often empirical absorption corrections at least partially correct for secondary extinction.
• If the space group is noncentrosymmetric, check the absolute structure for correct handedness and for possible twinning. The best test for correct absolute structure is the Flack test (H. D. Flack (1983) Acta Cryst., A39 876-881). If the wrong absolute structure was chosen, the correct absolute structure is usually obtained by inverting through the center of the unit cell. When the space group is one of 11 pairs of enantiomorph space groups (e.g. P3₁ | P3₂) then the operators must also be changed to enantimorph space group. Finally, there are 7 high symmetry space groups that must be inverted through some other point than through the origin. These space groups are listed in E. Parthe and L. M. Gelato (1984) Acta Cryst. A40, 169-183, C. Bernardinelli and H. D. Flack (1985) Acta Cryst. A41, 500-511, and the SHELXL manual.
• Refine all appropriate non-hydrogen atoms with anisotropic displacement parameters. If the displacement parameters for some of these atoms become "non-positive definite", then carefully consider the model. Is the correct hybridization being used for all nearby atoms? If the correct hybridizations are being used, then try modifying the displacement parameters to correct the npd problem and apply restraints to the displacement parameters to force a chemically-reasonable result. Check the difference map for the appearance of peaks that may indicate the need to use a disorder model.
• Refine the structure to full convergence (all shift / error ratios are < 0.05). Check the analysis of variance and list of worst fitting reflections for outliers and the difference map for large peaks or valleys.

Completed crystal structures must pass the following tests.

1. The model must be chemically reasonable. Similar bonds should have similar geometries and match literature values.
2. The structure should be refined to convergence, that is the maximum shift/error ratio should be < 0.05. All non-hydrogen atoms should be refined with anisotropic displacement parameters provided that there are at least 10 data per parameter. Lower data-to-parameter ratios indicate that either the data were not collected to a high enough scattering angle, or that Friedel-related (or equivalent) data were not collected for a structure in a noncentrosymmetric space group.
3. There should be no atoms with displacement parameters that are "non-positive definite". The displacement parameters should be checked for signs of systematic error. For example, ellipsoids of several heavy atoms aligned in one direction may indicate the need for a better absorption correction.
4. Non-centrosymmetric space groups should be refined with the correct absolute structure.
5. The weighting scheme should be adjusted so as to produce nearly constant values for the variances as functions of intensity and resolution and the goodness of fit should have a value around 1.0.
6. There should be no peaks with strong intensities in a list of "worst-fitting data."
7. The final difference map should have no abnormally high peaks or low valleys.

Most journals that accept crystal structures require the following information in the crystal structure report.

• Data collection
• Source of sample and conditions of crystallization.
• Habit, color, and dimensions of the crystal.
• Formula, formula weight.
• Unit cell parameters and volume with esds. The number of data and theta range of data used to determine the cell parameters.
• Crystal type and space group.
• Z, density, and absorption coefficient.
• Instrument and temperature of data collection and cell parameter determination.
• Structure solution
• # of data collected, # unique[R(int)].
• Method and program used for structure solution.
• Absorption correction details.
• Structure refinement
• Method and program for refinement.
• # of data refined, # restraints, # parameters.
• Weighting scheme.
• R1(observed data), wR2(all data), S values.
• Final maximum shift/error.
• Final maximum and minimum of difference electron density map.
• Tables and figures
• Postional parameters and isotropic or equivalent displacement parameters.
• Bond distances, angles, and torsion angles.
• Anisotropic displacement parameters.
• Structure factor tables (often required for review but discarded by the journal).
• Torsion angles(optional).
• Least-squares planes(optional).
• Hydrogen bond geometry(optional).
• A labelled figure showing the displacement ellipsoids.
• A packing diagram showing relevant intermolecular interactions.