A fingerprint based metric for measuring similarities of crystalline structures

Zhu, Li; Fuhrer, Tobias; Schaefer, Bastian; Grauzinyte, Migle; Goedecker, Stefan; Amsler, Maximilian; Faraji, Somayeh; Rostami, Samare; Ghasemi, S. Alireza; Sadeghi, Ali; Wolverton, Chris

doi:10.1063/1.4940026

Title: A fingerprint based metric for measuring similarities of crystalline structures

Journal Article · Thu Jan 21 00:00:00 EST 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4940026· OSTI ID:22493662

Zhu, Li; Fuhrer, Tobias; Schaefer, Bastian; Grauzinyte, Migle; Goedecker, Stefan ^[1]; Amsler, Maximilian ^[1]; Faraji, Somayeh; Rostami, Samare; Ghasemi, S. Alireza ^[2]; Sadeghi, Ali ^[3]; Wolverton, Chris ^[4]

Department of Physics, Universität Basel, Klingelbergstr. 82, 4056 Basel (Switzerland)
Institute for Advanced Studies in Basic Sciences, P.O. Box 45195-1159, Zanjan (Iran, Islamic Republic of)
Physics Department, Shahid Beheshti University, G. C., Evin, 19839 Tehran (Iran, Islamic Republic of)
Department of Materials Science and Engineering, Northwestern University, Evanston, Illinois 60208 (United States)

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.

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OSTI ID:: 22493662

Journal Information:: Journal of Chemical Physics, Vol. 144, Issue 3; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606

Country of Publication:: United States

Language:: English

References (59)

Fast clustering of equivalent structures in crystal structure prediction Van Eijck, Bouke P.; Kroon, Jan Journal of Computational Chemistry, Vol. 18, Issue 8 https://doi.org/10.1002/(sici)1096-987x(199706)18:8<1036::aid-jcc7>3.0.co;2-u	journal	June 1997
A generalized expression for the similarity of spectra: application to powder diffraction pattern classification de Gelder, R.; Wehrens, R.; Hageman, J. A. Journal of Computational Chemistry, Vol. 22, Issue 3 https://doi.org/10.1002/1096-987x(200102)22:3<273::aid-jcc1001>3.0.co;2-0	journal	January 2001
Continuous similarity measure between nonoverlapping X-ray powder diagrams of different crystal modifications Karfunkel, H. R.; Rohde, B.; Leusen, F. J. J. Journal of Computational Chemistry, Vol. 14, Issue 10 https://doi.org/10.1002/jcc.540141002	journal	October 1993
First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties von Lilienfeld, O. Anatole International Journal of Quantum Chemistry, Vol. 113, Issue 12 https://doi.org/10.1002/qua.24375	journal	February 2013
Constructing high-dimensional neural network potentials: A tutorial review Behler, Jörg International Journal of Quantum Chemistry, Vol. 115, Issue 16 https://doi.org/10.1002/qua.24890	journal	March 2015
Gaussian approximation potentials: A brief tutorial introduction Bartók, Albert P.; Csányi, Gábor International Journal of Quantum Chemistry, Vol. 115, Issue 16 https://doi.org/10.1002/qua.24927	journal	April 2015
Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD) Saal, James E.; Kirklin, Scott; Aykol, Muratahan JOM, Vol. 65, Issue 11 https://doi.org/10.1007/s11837-013-0755-4	journal	September 2013
Diffusion of single adatoms of platinum, iridium and gold on platinum surfaces Bassett, D. W.; Webber, P. R. Surface Science, Vol. 70, Issue 1 https://doi.org/10.1016/0039-6028(78)90429-6	journal	January 1978
AFLOW: An automatic framework for high-throughput materials discovery Curtarolo, Stefano; Setyawan, Wahyu; Hart, Gus L. W. Computational Materials Science, Vol. 58 https://doi.org/10.1016/j.commatsci.2012.02.005	journal	June 2012
The Electrolyte Genome project: A big data approach in battery materials discovery Qu, Xiaohui; Jain, Anubhav; Rajput, Nav Nidhi Computational Materials Science, Vol. 103 https://doi.org/10.1016/j.commatsci.2015.02.050	journal	June 2015
USPEX—Evolutionary crystal structure prediction Glass, Colin W.; Oganov, Artem R.; Hansen, Nikolaus Computer Physics Communications, Vol. 175, Issue 11-12 https://doi.org/10.1016/j.cpc.2006.07.020	journal	December 2006
Identifying duplicate crystal structures: XtalComp, an open-source solution Lonie, David C.; Zurek, Eva Computer Physics Communications, Vol. 183, Issue 3 https://doi.org/10.1016/j.cpc.2011.11.007	journal	March 2012
CALYPSO: A method for crystal structure prediction Wang, Yanchao; Lv, Jian; Zhu, Li Computer Physics Communications, Vol. 183, Issue 10 https://doi.org/10.1016/j.cpc.2012.05.008	journal	October 2012
i-PI: A Python interface for ab initio path integral molecular dynamics simulations Ceriotti, Michele; More, Joshua; Manolopoulos, David E. Computer Physics Communications, Vol. 185, Issue 3 https://doi.org/10.1016/j.cpc.2013.10.027	journal	March 2014
Machine Learning for Quantum Mechanical Properties of Atoms in Molecules Rupp, Matthias; Ramakrishnan, Raghunathan; von Lilienfeld, O. Anatole The Journal of Physical Chemistry Letters, Vol. 6, Issue 16 https://doi.org/10.1021/acs.jpclett.5b01456	journal	July 2015
DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method ^† Aradi, B.; Hourahine, B.; Frauenheim, Th. The Journal of Physical Chemistry A, Vol. 111, Issue 26 https://doi.org/10.1021/jp070186p	journal	July 2007
Reactions of xenon with iron and nickel are predicted in the Earth's inner core Zhu, Li; Liu, Hanyu; Pickard, Chris J. Nature Chemistry, Vol. 6, Issue 7 https://doi.org/10.1038/nchem.1925	journal	April 2014
The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies Kirklin, Scott; Saal, James E.; Meredig, Bryce npj Computational Materials, Vol. 1, Issue 1 https://doi.org/10.1038/npjcompumats.2015.10	journal	December 2015
Charting the complete elastic properties of inorganic crystalline compounds de Jong, Maarten; Chen, Wei; Angsten, Thomas Scientific Data, Vol. 2, Issue 1 https://doi.org/10.1038/sdata.2015.9	journal	March 2015
The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation Woodley, Scott M.; Battle, Peter D.; Gale, Julian D. Physical Chemistry Chemical Physics, Vol. 1, Issue 10 https://doi.org/10.1039/a901227c	journal	January 1999
Minima hopping: An efficient search method for the global minimum of the potential energy surface of complex molecular systems Goedecker, Stefan The Journal of Chemical Physics, Vol. 120, Issue 21 https://doi.org/10.1063/1.1724816	journal	June 2004
How to quantify energy landscapes of solids Oganov, Artem R.; Valle, Mario The Journal of Chemical Physics, Vol. 130, Issue 10 https://doi.org/10.1063/1.3079326	journal	March 2009
The discovery of unexpected isomers in sodium heptamers by Born–Oppenheimer molecular dynamics Vásquez-Pérez, José Manuel; Martínez, Gabriel Ulises Gamboa; Köster, Andreas M. The Journal of Chemical Physics, Vol. 131, Issue 12 https://doi.org/10.1063/1.3231134	journal	September 2009
Crystal structure prediction using the minima hopping method Amsler, Maximilian; Goedecker, Stefan The Journal of Chemical Physics, Vol. 133, Issue 22 https://doi.org/10.1063/1.3512900	journal	December 2010
Atom-centered symmetry functions for constructing high-dimensional neural network potentials Behler, Jörg The Journal of Chemical Physics, Vol. 134, Issue 7 https://doi.org/10.1063/1.3553717	journal	February 2011
Commentary: The Materials Project: A materials genome approach to accelerating materials innovation Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy APL Materials, Vol. 1, Issue 1 https://doi.org/10.1063/1.4812323	journal	July 2013
Metrics for measuring distances in configuration spaces Sadeghi, Ali; Ghasemi, S. Alireza; Schaefer, Bastian The Journal of Chemical Physics, Vol. 139, Issue 18 https://doi.org/10.1063/1.4828704	journal	November 2013
Recognizing molecular patterns by machine learning: An agnostic structural definition of the hydrogen bond Gasparotto, Piero; Ceriotti, Michele The Journal of Chemical Physics, Vol. 141, Issue 17 https://doi.org/10.1063/1.4900655	journal	November 2014
Spiral chain O4 form of dense oxygen Zhu, L.; Wang, Z.; Wang, Y. Proceedings of the National Academy of Sciences, Vol. 109, Issue 3 https://doi.org/10.1073/pnas.1119375109	journal	January 2012
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502 https://doi.org/10.1088/0953-8984/21/39/395502	journal	September 2009
Ab initio random structure searching Pickard, Chris J.; Needs, R. J. Journal of Physics: Condensed Matter, Vol. 23, Issue 5 https://doi.org/10.1088/0953-8984/23/5/053201	journal	January 2011
Materials discovery via CALYPSO methodology Wang, Yanchao; Lv, Jian; Zhu, Li Journal of Physics: Condensed Matter, Vol. 27, Issue 20 https://doi.org/10.1088/0953-8984/27/20/203203	journal	April 2015
High-throughput and data mining with ab initio methods Morgan, Dane; Ceder, Gerbrand; Curtarolo, Stefano Measurement Science and Technology, Vol. 16, Issue 1 https://doi.org/10.1088/0957-0233/16/1/039	journal	December 2004
Highly optimized tight-binding model of silicon Lenosky, Thomas J.; Kress, Joel D.; Kwon, Inhee Physical Review B, Vol. 55, Issue 3 https://doi.org/10.1103/physrevb.55.1528	journal	January 1997
Transformation processes in $La Al O_{3}$ : Neutron diffraction, dielectric, thermal, optical, and Raman studies Hayward, S. A.; Morrison, F. D.; Redfern, S. A. T. Physical Review B, Vol. 72, Issue 5 https://doi.org/10.1103/physrevb.72.054110	journal	August 2005
Proposed definition of crystal substructure and substructural similarity Yang, Lusann; Dacek, Stephen; Ceder, Gerbrand Physical Review B, Vol. 90, Issue 5 https://doi.org/10.1103/physrevb.90.054102	journal	August 2014
COMPACK : a program for identifying crystal structure similarity using distances Chisholm, James Alexander; Motherwell, Sam Journal of Applied Crystallography, Vol. 38, Issue 1 https://doi.org/10.1107/s0021889804027074	journal	January 2005
Numerically stable algorithms for the computation of reduced unit cells Grosse-Kunstleve, R. W.; Sauter, N. K.; Adams, P. D. Acta Crystallographica Section A Foundations of Crystallography, Vol. 60, Issue 1 https://doi.org/10.1107/s010876730302186x	journal	December 2003
The geometry of Niggli reduction: BGAOL –embedding Niggli reduction and analysis of boundaries Andrews, Lawrence C.; Bernstein, Herbert J. Journal of Applied Crystallography, Vol. 47, Issue 1 https://doi.org/10.1107/s1600576713031002	journal	January 2014
Unexpected Stable Stoichiometries of Sodium Chlorides Zhang, W.; Oganov, A. R.; Goncharov, A. F. Science, Vol. 342, Issue 6165 https://doi.org/10.1126/science.1244989	journal	December 2013
Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems – Part II Schön, J. C.; Jansen, Martin Zeitschrift für Kristallographie - Crystalline Materials, Vol. 216, Issue 7 https://doi.org/10.1524/zkri.216.7.361.20362	journal	January 2001
A logical calculus of the ideas immanent in nervous activity McCulloch, Warren S.; Pitts, Walter Bulletin of Mathematical Biology, Vol. 52, Issue 1-2 https://doi.org/10.1007/bf02459570	journal	January 1990
Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets Chen, Ruyi; Cui, Qirui; Liao, Liyang Nature Communications, Vol. 12, Issue 1 https://doi.org/10.1038/s41467-021-23414-3	journal	May 2021
Electronic structure of AlFeN films exhibiting crystallographic orientation change from c- to a-axis with Fe concentrations and annealing effect Tatemizo, Nobuyuki; Imada, Saki; Okahara, Kizuna Scientific Reports, Vol. 10, Issue 1 https://doi.org/10.1038/s41598-020-58835-5	journal	February 2020
Unexpected Stable Stoichiometries of Sodium Chlorides Zhang, W.; Oganov, A. R.; Goncharov, A. F. Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/desy-2014-01530	text	January 2013
Machine Learning for Quantum Mechanical Properties of Atoms in Molecules Matthias, Rupp,; Raghunathan, Ramakrishnan,; Anatole, von Lilienfeld, O. American Chemical Society https://doi.org/10.5451/unibas-ep53266	text	January 2015
The Hungarian method for the assignment problem Kuhn, H. W. Naval Research Logistics Quarterly, Vol. 2, Issue 1-2, p. 83-97 https://doi.org/10.1002/nav.3800020109	journal	March 1955
The Hungarian method for the assignment problem Kuhn, H. W. Naval Research Logistics, Vol. 52, Issue 1 https://doi.org/10.1002/nav.20053	journal	February 2005
The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies Kirklin, Scott; Saal, James E.; Meredig, Bryce London : Nature Publ. Group https://doi.org/10.34657/7521	text	January 2015
How to quantify energy landscapes of solids Oganov, Artem R.; Valle, Mario arXiv https://doi.org/10.48550/arxiv.0911.3188	text	January 2009
Crystal structure prediction using the Minima Hopping method Amsler, Maximilian; Goedecker, Stefan arXiv https://doi.org/10.48550/arxiv.1007.2003	text	January 2010
Spiral Chain O4 Form of Dense Oxygen Zhu, Li; Wang, Ziwei; Wang, Yanchao arXiv https://doi.org/10.48550/arxiv.1111.2104	text	January 2011
CALYPSO: a method for crystal structure prediction Wang, Yanchao; Lv, Jian; Zhu, Li arXiv https://doi.org/10.48550/arxiv.1205.2264	text	January 2012
First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties von Lilienfeld, O. A. arXiv https://doi.org/10.48550/arxiv.1209.5033	preprint	January 2012
Conducting boron sheets formed by the reconstruction of the α-boron (111) surface Amsler, Maximilian; Botti, Silvana; Marques, Miguel A. L. arXiv https://doi.org/10.48550/arxiv.1307.0390	text	January 2013
AFLOW: An automatic framework for high-throughput materials discovery Curtarolo, Stefano; Setyawan, Wahyu; Hart, Gus L. W. arXiv https://doi.org/10.48550/arxiv.1308.5715	text	January 2013
i-PI: A Python interface for ab initio path integral molecular dynamics simulations Ceriotti, Michele; More, Joshua; Manolopoulos, David E. arXiv https://doi.org/10.48550/arxiv.1402.1045	text	January 2014
Recognizing molecular patterns by machine learning: an agnostic structural definition of the hydrogen bond Gasparotto, Piero; Ceriotti, Michele arXiv https://doi.org/10.48550/arxiv.1410.5447	text	January 2014
Gaussian Approximation Potentials: a brief tutorial introduction Bartók, Albert P.; Csányi, Gábor arXiv https://doi.org/10.48550/arxiv.1502.01366	preprint	January 2015

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