A universal algorithm for finding the shortest distance between systems of points

Blatov, I. A.; Kitaeva, E. V.; Шевченко, А. П.; Блатов, В. А.

doi:10.1107/s2053273319011628

Cited by 4 publications

(5 citation statements)

References 25 publications

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“…Internal coordinates (bonds lengths, bond and torsion angles) and pore dimensions (minimum and maximum diameters, shape, topology of communication). 65–70…”

Section: Topological Methods For the Description Of Reconstructive Tr...mentioning

confidence: 99%

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Topological transformations in metal–organic frameworks: a prospective design route?

et al. 2022

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“…Internal coordinates (bonds lengths, bond and torsion angles) and pore dimensions (minimum and maximum diameters, shape, topology of communication). 65–70…”

Section: Topological Methods For the Description Of Reconstructive Tr...mentioning

confidence: 99%

“…Internal coordinates (bonds lengths, bond and torsion angles) and pore dimensions (minimum and maximum diameters, shape, topology of communication). [65][66][67][68][69][70] 2. Relative placement of structural groups due to their slipping with respect to each other.…”

Section: Left)mentioning

confidence: 99%

Topological transformations in metal–organic frameworks: a prospective design route?

et al. 2022

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“…The overall order of the procedure is therefore well below , where N is the total number of atoms (see also Section ). In addition, contrary to the uniform grid proposed in ref , our approach does not require blind and massive checks on the number of grid points and their completeness in parsing the rotation space/manifold.…”

Section: Our Approachmentioning

confidence: 99%

“…Local minima are a consequence of structural symmetries; see also Figure . The authors in ref suggested an algorithm in which the space of possible rotations and reflections is discretized into a uniform grid of points. For each grid-point R , the optimal atomic assignment P B is obtained as the optimal assignment of an interstructure distance matrix with the Hungarian algorithm, which is then used to minimize rotations with SVD .…”

Section: Introductionmentioning

confidence: 99%

IRA: A Shape Matching Approach for Recognition and Comparison of Generic Atomic Patterns

Gunde

Hémeryck

Martin‐Samos

2021

J. Chem. Inf. Model.

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We propose a versatile, parameter-less approach for solving the shape matching problem, specifically in the context of atomic structures when atomic assignments are not known a priori. The algorithm Iteratively suggests Rotated atom-centered reference frames and Assignments (iterative rotations and assignments (IRA)). The frame for which a permutationally invariant set−set distance, namely, the Hausdorff distance, returns a minimal value is chosen as the solution of the matching problem. IRA is able to find rigid rotations, reflections, translations, and permutations between structures with different numbers of atoms, for any atomic arrangement and pattern, periodic or not. When distortions are present between the structures, optimal rotation and translation are found by further applying a standard singular value decompositionbased method. To compute the atomic assignments under the one-to-one assignment constraint, we develop our own algorithm, constrained shortest distance assignments (CShDA). The overall approach is extensively tested on several structures, including distorted structural fragments. The efficiency of the proposed algorithm is shown as a benchmark comparison against two other shape matching algorithms. We discuss the use of our approach for the identification and comparison of structures and structural fragments through two examples: a replica-exchange trajectory of a cyanine molecule, in which we show how our approach could aid the exploration of relevant collective coordinates for clustering the data, and a SiO 2 amorphous model, in which we compute distortion scores, and compare them with a classical strain-based potential. The source code and benchmark data are available at https://github.com/mammasmias/IterativeRotationsAssignments.

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“…Finally, crystal structures are compared (not successfully for Heusler structures [ 8 ] ) by powder diffraction patterns up to a cut off radius, which brings discontinuities similarly to other parameters. To the best of our knowledge [ 9 ] there was no distance on equivalence classes of crystal structures that satisfies all metric axioms (2.3a), (2.3b), (2.3c), and continuity (2.3d).…”

Section: Strengths and Weaknesses Of Past Approaches To A Similarity mentioning

confidence: 99%

Voronoi‐Based Similarity Distances between Arbitrary Crystal Lattices

Mosca

Kurlin

2020

Crystal Research and Technology

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This paper develops a new continuous approach to a similarity between periodic lattices of ideal crystals. Quantifying a similarity between crystal structures is needed to substantially speed up the crystal structure prediction, because the prediction of many target properties of crystal structures is computationally slow and is essentially repeated for many nearly identical simulated structures. The proposed distances between arbitrary periodic lattices of crystal structures are invariant under all rigid motions, satisfy the metric axioms and continuity under atomic perturbations. The above properties make these distances ideal tools for clustering and visualizing large datasets of crystal structures. All the conclusions are rigorously proved and justified by experiments on real and simulated crystal structures.

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A universal algorithm for finding the shortest distance between systems of points

Cited by 4 publications

References 25 publications

Topological transformations in metal–organic frameworks: a prospective design route?

Topological transformations in metal–organic frameworks: a prospective design route?

IRA: A Shape Matching Approach for Recognition and Comparison of Generic Atomic Patterns

Voronoi‐Based Similarity Distances between Arbitrary Crystal Lattices

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