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Comparison and evaluation of pair distribution functions, using a similarity measure based on cross‐correlation functions
Author(s) -
Habermehl Stefan,
Schlesinger Carina,
Prill Dragica
Publication year - 2021
Publication title -
journal of applied crystallography
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.429
H-Index - 162
ISSN - 1600-5767
DOI - 10.1107/s1600576721001722
Subject(s) - pointwise , measure (data warehouse) , similarity (geometry) , mathematics , correlation , pearson product moment correlation coefficient , moment (physics) , similarity measure , cross correlation , structural similarity , probability density function , statistical physics , statistics , mathematical analysis , computer science , artificial intelligence , physics , data mining , image (mathematics) , geometry , classical mechanics
An approach for the comparison of pair distribution functions (PDFs) has been developed using a similarity measure based on cross‐correlation functions. The PDF is very sensitive to changes in the local structure, i.e. small deviations in the structure can cause large signal shifts and significant discrepancies between the PDFs. Therefore, a comparison based on pointwise differences ( e.g. R values and difference curves) may lead to the assumption that the investigated PDFs as well as the corresponding structural models are not in agreement at all, whereas a careful visual inspection of the investigated structural models and corresponding PDFs may reveal a relatively good match. To quantify the agreement of different PDFs for those cases an alternative approach is introduced: the similarity measure based on cross‐correlation functions. In this paper, the power of this application of the similarity measure to the analysis of PDFs is highlighted. The similarity measure is compared with the classical R wp values as representative of the comparison based on pointwise differences as well as with the Pearson product‐moment correlation coefficient, using polymorph IV of barbituric acid as an example.