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Continuous similarity measure between nonoverlapping X‐ray powder diagrams of different crystal modifications
Author(s) -
Karfunkel H.R.,
Rohde B.,
Leusen F.J.J.,
Gdanitz R.J.,
Rihs G.
Publication year - 1993
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.540141002
Subject(s) - similarity (geometry) , fortran , measure (data warehouse) , diagram , crystal (programming language) , set (abstract data type) , crystal structure , ab initio , basis (linear algebra) , field (mathematics) , similitude , computer science , crystallography , chemistry , mathematics , geometry , physics , data mining , image (mathematics) , pure mathematics , quantum mechanics , artificial intelligence , database , programming language , operating system
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.