Uses of anisotropic displacement parameters

Analyses of anisotropic displacement parameters give several pieces of information of interest to the chemist. 

When the determination of a crystal structure is difficult or refinement gives a strangely shaped molecule, it is possible that the molecule is disordered in a site in the crystal. This happens when the available space in the crystal is such as to accommodate two different orientations of the molecule. For example, in the crystal structure of 5-methylchrysene, -one of the two molecules in the asymmetric unit is disordered. It was difficult to solve the crystal structure until the nature of the disorder was realized. In a given site, this disordered molecule may be in one of two possible orientations. In some places in the disordered electron density map, atoms in the two orientations of the disordered molecule are near each other and their positions can be approximated (erroneously) by the use of highly anisotropic temperature parameters. The result is that the anisotropic temperature parameters on refinement do not make any sense until the nature of the disorder is understood. 

A molecule that appears to be orientationally disordered in the crystalline state is cyclohepta[ de jnaphthalene (pleiadiene), shown in Fig- 

In naphthalene and other polycyclic aromatic hydrocarbons apparent bond lengths become shorter, especially when they are more distant from the molecular center. When corrected for effects of rigid-body libration, this trend disappears. Studies of naphthalene, anthracene, and 4-hydroxybiphenyl illustrate this. In naphthalene 

FIGURE 13.16. Orientational disorder in cyclohepta[de Jnaphthalene (Ref. 73). (a) Chemical formula. Shown are a pair of molecules approximately 3,5 A apart, packing (b) head-to-tail, and (c) head-to-head. The arrangement in (c) can lead to dimerization in the solid state on exposure to X rays because of the proximity of the double bonds (indicated by a two-headed arrow). 

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