In crystallography the observed atomic displacement parameters are an average of millions of unit cells throughout entire volume of the crystal, and thermally induced motion over the time used for data collection. A disorder of atoms/molecules in a given structure can manifest as flat or non-spherical atomic displacement parameters in the crystal structure. Such cases of disorder are usually the result of either thermally induced motion during data collection (i.e., dynamic disorder), or the static disorder of the atoms/molecules throughout the lattice. The latter is defined as the situation in which certain atoms, or groups of atoms, occupy slightly different orientations from molecule to molecule over the large volume (relatively speaking) covered by the crystal lattice. This static displacement of atoms can simulate the effect of thermal vibration on the scattering power of the "average" atom. Consequently, differentiation between thermal motion and static disorder can be ambiguous, unless data collection is performed at low temperature (which would negate much of the thermal motion observed at room temperature).
In most cases, this disorder is easily resolved as some non-crystallographic symmetry elements acting locally on the weakly coordinating anion. The atomic site occupancies can be refined using the FVAR instruction on the different parts (see PART 1 and PART 2 in Figure 1) of the disorder, having a site occupancy factor (s.o.f.) of x and 1-x, respectively. This is accomplished by replacing 11.000 (on the F-atom lines in the “NAME.INS” file) with 21.000 or -21.000 for each of the different parts of the disorder. For instance, the "NAME.INS" file would look something like that shown in Figure 1. Note that for more heavily disordered structures, i.e., those with more than two disordered parts, the SUMP command can be used to determine the s.o.f. of parts 2, 3, 4, etc. the combined sum of which is set at s.o.f. = 1.0. These are designated in FVAR as the second, third, and fourth terms.
In small molecule refinement, the case will inevitably arise in which some kind of restraints or constraints must be used to achieve convergence of the data. A restraint is any additional information concerning a given structural feature, i.e., limits on the possible values of parameters, may be added into the refinement, thereby increasing the number of refined parameters. For example, aromatic systems are essentially flat, so for refinement purposes, a troublesome ring system could be restrained to lie in one plane. Restraints are not exact, i.e., they are tied to a probability distribution, whereas constraints are exact mathematical conditions. Restraints can be regarded as falling into one of several general types:
- Geometric restraints, which relates distances that should be similar.
- Rigid group restraints.
- Anti-bumping restraints.
- Linked parameter restraints.
- Similarity restraints.
- ADP restraints (Figure 2).
- Sum and average restraints.
- Origin fixing and shift limiting restraints.
- Those imposed upon atomic displacement parameters.
- SADI - similar distance restraints for named pairs of atoms.
- DFIX - defined distance restraint between covalently bonded atoms.
- DANG - defined non-bonding distance restraints, e.g., between F atoms belonging to the same PART of a disordered BF4-.
- FLAT - restrains group of atoms to lie in a plane.
- DELU - rigid bond restraints (Figure 2).
- SIMU - similar ADP restraints on corresponding Uij components to be approximately equal for atoms in close proximity (Figure 2).
- ISOR - treat named anisotropic atoms to have approximately isotropic behavior (Figure 2).
- EADP - equivalent atomic displacement parameters.
- AFIX - fitted group; e.g., AFIX 66 would fit the next six atoms into a regular hexagon.
- HFIX - places H atoms in geometrically ideal positions, e.g., HFIX 123 would place two sets of methyl H atoms disordered over two sites, 180° from each other.
