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.

Background

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). Necessarily a centrosymmetric crystal is invariant under P and there is no absolute structure to specify.

Absolute structure is to a crystal what absolute configuration is to a molecule. However the sense is wider because absolute structure 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 object. 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. As a consequence absolute structure distinguishes between and specifies enantiomorphs of a chiral crystal structure. For achiral non-centrosymmetric crystal structures 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. In the same way that there is no absolute configuration for an achiral molecule, there is no absolute structure for a centrosymmetric crystal structure.

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.

---