Fourier Representations of Pdf's Arising in Crystallography.

A survey is given of some recent calculations of univariate and multivariate probability density functions (pdfs) of structure factors used to interpret crystallographic data. We have found that in the presence of sufficient atomic heterogeneity the frequently used approximations derived from the central limit theorem in the form of Edgeworth or Gram-Charlier series can be quite unreliable, and in these cases the more exact, but lengthier, Fourier calculations must be made.