Statistical Methods for the Detection of a Centre of Symmetry in a Crystal

Summary

It is important in the determination of crystal structures to establish whether a centre of symmetry is present, since this will affect the choice of space group, the equations used for structure‐factor and electron‐density calculations? the size of the asymmetric unit, and whether molecules occupy ‘special’ or ‘general’ positions in the unit cell. As a centre of symmetry does not give rise to a systematic pattern of absent reflections in the X‐ray diffraction data, evidence for its presence or absence must be sought by other methods such as pyroelectric and piezoelectric effects, or statistical tests applied to the intensities of the X‐ray reflections. The theory underlying statistical methods applied to this problem is outlined. Practical tests suggested by several authors are reviewed. These illustrate the application of statistical methods in the field of crystallography and solid state chemistry. A computer program is described which performs the N(z)test and calculates the Wilson ratio; operating instructions and a FORTRAN IV listing are given.