Continuous similarity measure between nonoverlapping X‐ray powder diagrams of different crystal modifications

Abstract

The problem of quantifying similarity between crystal structures is transformed into the problem of comparing the associated X‐ray powder diagrams. A smooth similarity measure between two powder diagrams, termed a “fold,” is defined. In contrast to conventional comparison methods, the introduced method is still applicable when the peaks of the spectra to be compared have no overlap. The main areas of application of the method are the construction of a molecular crystal structure when only the experimental powder diagram is available and the analysis of possible crystal packings predicted on the basis of molecular information only. A suitable empirical parameterization of the fold has been derived from a large set of experimental and force‐field‐generated crystals. The analysis of the outcome of an ab initio packing of a flexible molecule is given as an example. The algorithmic details of the method are given as a FORTRAN 77 code. © John Wiley & Sons, Inc.