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Molecular Geometry |
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Molecular Geometry |
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Molecular Geometry
The determination of a crystal structure by diffraction has several objectives: Obviously the most immediate concern is the arrangement of atoms in three-dimensional space. From the symmetry and coordinates of the atoms within the unit cell one can determine the coordination and bonding of the individual atoms. In order to do this, one needs to be able to calculate interatomic distances (or bond lengths), interatomic angles (or bond angles), torsion angles, distances between planes of atoms, and so on. It is of fundamental importance to be able to calculate these values given a set of atomic coordinates and the symmetry, i.e. space group, of a particular material, and it is very useful if these values can be calculated automatically at the end of each stage in the refinement process. This provides us with an additional tool to follow the progress of the refinement.
As a case study for the next few pages, we will use the coordinates of
sulphur hexafluoride §,
the structure of which was shown
earlier.
At 5 K, the space group is C2/m with
| Atom | Site Symmetry | x | y | z | |
|---|---|---|---|---|---|
| S(1) | 2a | 2/m | 0 | 0 | 0 |
| S(2) | 4i | m | 0.6677(5) | 0 | 0.581(1) |
| F(1) | 4i | m | 0.0687(2) | 0 | 0.2817(6) |
| F(2) | 8j | 1 | 0.0646(1) | -0.1350(3) | -0.1202(4) |
| F(3) | 4i | m | 0.7469(2) | 0 | 0.3675(6) |
| F(4) | 4i | m | 0.5903(2) | 0 | 0.7996(6) |
| F(5) | 8j | 1 | 0.7255(2) | -0.1348(3) | 0.7583(4) |
| F(6) | 8j | 1 | 0.6096(2) | 0.1353(3) | 0.4102(4) |
From the information provided above, tables of bond lengths and angles, intermolecular distances, together with estimated deviations on these variables can all be calculated. The next few pages attempt to explain how this is done in practice.
§
Zeitschrift fü Kristallographie, 1988, 184, 123.
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| © Copyright 1997-2006. Birkbeck College, University of London. | Author(s): Jeremy Karl Cockcroft |