Application of the overlap integral in X-ray diffraction powder pattern recognition

Lawton, Stephen L.; Bartell, Lawrence S.

doi:10.1017/s088571560001410x

Cited by 8 publications

(4 citation statements)

References 16 publications

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“…In the present article, it is shown that there is a simple relationship between the conventional criterion based on squared differences, the Pearson product‐moment correlation coefficient2 and the overlap integral described by Lawton and Bartell3—who define a measure for the similarity of powder diffraction patterns on an absolute scale—when these criteria are written in terms of the correlation function. With respect to the correlation function, the drawback of these criteria is that they only consider one point (the value at the origin) from the auto‐ and crosscorrelation functions and neglect the information that is present in the remainder of the auto‐ and crosscorrelation functions.…”

Section: Introductionmentioning

confidence: 84%

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A generalized expression for the similarity of spectra: application to powder diffraction pattern classification

2001

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ABSTRACT:A generalized expression is given for the similarity of spectra, based on the normalized integral of a weighted crosscorrelation function. It is shown that various similarity and dissimilarity criteria previously described in literature can be written as special cases of this general expression. A new similarity criterion, based on this generalized expression, is introduced. The benefits of this criterion are that it properly recognizes shifted but otherwise similar details in spectra and that the resulting similarity measure is normalized. Moreover, the criterion can easily be adapted to specific properties of spectra resulting from various analytical methods. The new criterion is applied to the classification of a series of crystal structures of cephalosporin complexes, based on comparison of their calculated powder diffraction patterns. The results are compared with those obtained using previously described criteria.

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Section: Introductionmentioning

confidence: 84%

“…The Pearson product‐moment correlation coefficient is closely related to the overlap integral S αβ that is described by Lawton and Bartell 3. In principle, the method they propose is based on peak positions (lines) deduced from powder diagrams.…”

Section: Pointwise Similarity and Dissimilarity Criteriamentioning

confidence: 99%

A generalized expression for the similarity of spectra: application to powder diffraction pattern classification

2001

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“…A further advantage of powder-based indices is that they identify structurally related compounds (conformational phases, isomorphous systems) as similar. 26 De Gelder et al's powder-based index using cross-correlation functions, 26 based on similar previously proposed measures, [31][32][33] is a very popular powder-based index. 19,[34][35][36][37][38] Comparing an in silico crystal structure with an experimental pattern using a powder-based index requires overcoming two difficulties.…”

Section: Introductionmentioning

confidence: 99%

Powder-Diffraction-Based Structural Comparison for Crystal Structure Prediction without Prior Indexing

Otero de la Roza

2024

Preprint

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The objective of crystal structure prediction (CSP) is to predict computationally the thermodynamically stable crystal structure of a compound from its stoichiometry or its molecular diagram. Crystal similarity indices measure the degree of similarity between two crystal structures, and are essential in CSP because they are used to identify duplicates. In addition, powder-based indices, which are based on comparing X-ray diffraction patterns, also allow the use of experimental X-ray powder diffraction data to inform the CSP search. Powder-assisted CSP presents two unique difficulties: i) the experimental and computational structures are not entirely comparable because the former is subject to thermal expansion from lattice vibrations, and ii) experimental patterns present features (noise, background contribution, varying peak shapes, etc.) that are not easily predictable computationally. In this work, we present a powder-based similarity index (GPWDF) based on a modification of de Gelder et al.'s index using cross-correlation functions that can be calculated analytically. Based on GPWDF, we also propose a variable-cell similarity index (VC-GPWDF) that assigns a high similarity score to structures that differ only by a lattice deformation and takes advantage of the analytical derivatives of GPWDF with respect to the lattice parameters. VC-GPWDF can be used to identify similarity between: two computational structures generated using different methods, a computational and a experimental structure, and two experimental structures measured under different conditions (e.g. different temperature and pressure). In addition, VC-GPWDF can also be used to compare crystal structures with experimental patterns in combination with an automatic pre-processing step. The proposed similarity indices are simple, efficient, and fully automatic. They require no indexing of the experimental pattern or a guess of the space group, account for deformations caused by varying experimental conditions, give meaningful results even when the experimental pattern is of very poor quality, and have a cost does not increase with the flexibility of the molecular motif.

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“…The applicability of different similarity measures depends on the characteristics of the spectra that are being evaluated, e.g., NMR, [1,2,3], infrared, [4], UV/Vis, [5] or x-ray diffraction. [6,7,8] First-row transition metal systems, with their near-degenerate 3d electron levels, are prominent examples of systems with close-lying electronic states. This can lead to difficulties in calculating both electronic ground states and reaction pathways.…”

Section: Introductionmentioning

confidence: 99%

Quantifying similarity for spectra with a large number of overlapping transitions: Examples from soft X-ray spectroscopy

et al. 2020

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Application of the overlap integral in X-ray diffraction powder pattern recognition

Cited by 8 publications

References 16 publications

A generalized expression for the similarity of spectra: application to powder diffraction pattern classification

A generalized expression for the similarity of spectra: application to powder diffraction pattern classification

Powder-Diffraction-Based Structural Comparison for Crystal Structure Prediction without Prior Indexing

Quantifying similarity for spectra with a large number of overlapping transitions: Examples from soft X-ray spectroscopy

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