Absolute structure

Definition

The spatial arrangement of the atoms of a physically identified non-centrosymmetric crystal and its description by way of unit-cell dimensions, space group, and representative coordinates of all atoms.

Interpretation as an orientation

Absolute structure is a specification of the orientation of a non-centrosymmetric crystal structure under the operation of inversion through a point otherwise known as parity (P). A centrosymmetric crystal structure is invariant under P and there is no absolute structure to specify. For a chiral crystal structure, which is necessarily non-centrosymmetric, absolute structure distinguishes between and specifies enantiomorphs of the crystal structure. For an achiral non-centrosymmetric crystal structure there are no enantiomorphs and the inversion-related crystal structures may be brought into coincidence by translation and pure rotation. In this case the inversion is always equivalent to a pure rotation.

Physical origin of absolute structure

The need for special treatment of absolute structure in crystal-structure analysis arises from two phenomena. The first of these is that the point-group symmetry of a crystalline lattice of translations is always centrosymmetric regardless of whether the point symmetry of the crystal structure itself is centrosymmetric or non-centrosymmetric. Consequently the positionsof the Bragg reflections on a diffractogram from a single crystal are always arranged centrosymmetrically. Thus one can only distinguish a non-centrosymmetric crystal structure from its inversion-related image by referring to the intensities of the Bragg reflections. The second factor concerns the intensity distribution on a diffractogram from a non-centrosymmetric crystal structure. This tends to be approximately centrosymmetric because the electron density is real (see Friedel's Law).

Absolute structure versus absolute configuration

Absolute structure is to a crystal what absolute configuration is to a molecule. However the sense of absolute structure is wider because it applies to any non-centrosymmetric crystal structure whether it is chiral or achiral. Both absolute structure and absolute configuration describe certain aspects of the spatial arrangement of the atoms in their respective objects. However the object, its symmetry and the method of its specification are different. The table compares the two cases.

                Absolute Structure        Absolute Configuration
Property       spatial  arrangement        spatial  arrangement
Content               atoms                       atoms
Object               crystal                     molecule
Symmetry        non-centrosymmetric               chiral
Specification     crystallographic            stereochemical
                    space group                    CIP
                  cell dimensions
                 atomic coordinates

Whereas absolute configuration distinguishes between and specifies enantiomers (chiral molecules of opposite hand), absolute structure does the same for inversion-related models of the crystal structure. In the same way that there is no absolute configuration for an achiral molecule, there is no absolute structure for a centrosymmetric crystal structure.

Determination of absolute structure

The most common way of determining the absolute structure of a non-centrosymmetric crystal by way of X-ray diffraction is to exploit the intensity differences between inversion-related Bragg reflections h k l and -h -k -l by way of the Flack parameter.

Related chemical terms

The IUPAC Basic Terminology of Stereochemistry contains definitions of related chemical terms of use to the crystallographer, viz: absolute configuration, chiral, chirality, chirality sense, enantiomer, enantiomerically pure, enantiomorph, racemate, racemic, racemic conglomerate and relative configuration.

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