Cited by 2,572Machine Learning in Materials ScienceAdvanced Chemical Physics StudiesAdvanced Physical and Chemical Molecular Interactions

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On representing chemical environments

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Bartók, Albert P., Kondor, Risi, Csányi, Gábor·2013·Physical Review B

DOI 10.1103/physrevb.87.184115

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Abstract

We review some recently published methods to represent atomic neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave numbers are used to expand the atomic neighborhood density function. Using the example system of small clusters, we quantitatively show that this expansion needs to be carried to higher and higher wave numbers as the number of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.

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Authors: Bartók, A. P., Kondor, R., & Csányi, G.
Affiliations: University of Cambridge (GB)
University of Chicago (US)
ORCID: Bartók, Albert P.
Kondor, Risi
Venue: Physical Review B
Publisher: American Physical Society (APS)
Published: 2013-05-28
Volume: 87
Issue: 18
ISSN: 1098-0121 (ISSN-L)
1550-235X
DOI: 10.1103/physrevb.87.184115
OpenAlex: W2029413789
Cited by: 2,572
References: 60
Citations by year: 2026: 292 · 2025: 350 · 2024: 367 · 2023: 365 · 2022: 303 · 2021: 270 · 2020: 257 · 2019: 163 · 2018: 105 · 2017: 48 · 2016: 19 · 2015: 11 · 2014: 13 · 2013: 4
FWCI: 7.07
Type: journal article
Language: en
Open access: green
arxiv.org
Licence: link.aps.org/licenses/aps-default-license (vor)
Locations: Physical Review B (publishedVersion)
arXiv (Cornell University) (submittedVersion)
Cambridge University Engineering Department Publications Database (submittedVersion)
arXiv (Cornell University)
Funders: Engineering and Physical Sciences Research Council (EP/K014560/1)
Topics: Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
Keywords: potential energy surface fitting, basis function expansion, silicon clusters, small clusters

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