Structural parameters: Analysis of results

Abstract

The results of an X-ray structure analysis are coordinates of the individual, chemically identified atoms in each unit cell, the space group (which gives equivalent positions), and displacement parameters that may be interpreted as indicative of molecular motion and/or disorder. Such data obtained from crystal structure analyses may be incorporated into a CIF or mmCIF (Crystallographic Information File or Macromolecular Crystallographic Information File). These ensure that the results of crystal structure analyses are usefully archived. There are many checks that the crystallographer can make to ensure that the CIF or mmCIF file is correctly informative. For example, the automated validation program PLATON (Spek, 2003) checks that all data reported are up to the standards required for publication by the International Union of Crystallography. It does geometrical calculations on the structure, illustrates the results, finds if any symmetry has been missed, investigates any twinning, and checks if the structure has already been reported. We now review the ways in which these atomic parameters can be used to obtain a three-dimensional vision of the entire crystal structure. When molecules crystallize in an orthorhombic, tetragonal, or cubic unit cell it is reasonably easy to build a model using the unit-cell dimensions and fractional coordinates, because all the interaxial angles are 90◦. However, the situation is more complicated if the unit cell contains oblique axes and it is often simpler to convert the fractional crystal coordinates to orthogonal coordinates before calculating molecular geometry. The equations for doing this for bond lengths, interbond angles, and torsion angles are presented in Appendix 12. If the reader wishes to compute interatomic distances directly, this is also possible if one knows the cell dimensions (a, b, c, ∝ , β , γ ,), the fractional atomic coordinates (x, y, z for each atom), and the space group.