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Absolute structure

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.

Absolute structure is 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 positions of 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).

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. An important aspect, mentioned in the definition above, of the determination of absolute structure is the physical characterization of the crystal. Without this information an independent worker would be unable to know with adequate precision what sample had been used and its orientation in order to repeat and check the absolute-structure determination. The physical characterization may take the form of suitable physical or morphological measurements on the crystal itself or even, in some circumstances, of measurements on a solution made from the single crystal.

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 configuration from absolute structure

One must first have a valid absolute-structure determination see Flack parameter. The most stringent requirement in order to deduce the absolute configuration of the molecules composing a crystal from an absolute-structure determination is that the crystal structure be composed of enantiopure (chiral) molecules. Experimental evidence should be provided of the enantiopurity of the crystal or of the bulk. Some necessary but not-sufficient requirements are easier to apply. The crystal structure should be chiral. A chiral crystal structure displays a space group that only contains translations, pure rotations and screw rotations, and does not contain any reflections, inversions, rotoinversions or glide reflections. Another necessary but not-sufficient condition is that the crystal structure contains chiral molecules.