A fingerprint based metric for measuring similarities of crystalline structures

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

doi:10.1063/1.4940026

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

Abstract

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. In this paper, 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. Finally, 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.

Authors:

Zhu, Li ^[1]; Amsler, Maximilian ^[2]; Fuhrer, Tobias ^[1]; Schaefer, Bastian ^[1]; Faraji, Somayeh ^[3]; Rostami, Samare ^[3]; Ghasemi, S. Alireza ^[3];

^[4]; Grauzinyte, Migle ^[1]; Wolverton, Chris ^[5]; Goedecker, Stefan ^[1]

Univ. of Basel (Switzerland). Dept. of Physics
Univ. of Basel (Switzerland). Dept. of Physics; Northwestern Univ., Evanston, IL (United States). Dept. of Materials Science and Engineering
Inst. for Advanced Studies in Basic Sciences, Zanjan (Iran)
Shahid Beheshti Univ., Tehran (Iran). Physics Dept.
Northwestern Univ., Evanston, IL (United States). Dept. of Materials Science and Engineering

Publication Date:: Thu Jan 21 00:00:00 EST 2016

Research Org.:: Northwestern Univ., Evanston, IL (United States); Univ. of Basel (Switzerland)

Sponsoring Org.:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Swiss National Science Foundation (SNSF)

OSTI Identifier:: 1469171

Alternate Identifier(s):: OSTI ID: 1235591

Grant/Contract Number:: FG02-07ER46433; AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 144; Journal Issue: 3; Journal ID: ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; carbides; theoretical computer science; symmetry functions; electronic noise; machine learning; chemical elements; perovskites; classical statistical mechanics; crystal structure; potential energy surfaces

Citation Formats


                    Zhu, Li, Amsler, Maximilian, Fuhrer, Tobias, Schaefer, Bastian, Faraji, Somayeh, Rostami, Samare, Ghasemi, S. Alireza, Sadeghi, Ali, Grauzinyte, Migle, Wolverton, Chris, and Goedecker, Stefan. A fingerprint based metric for measuring similarities of crystalline structures.  United States: N. p., 2016. 
Web.  doi:10.1063/1.4940026.

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                    Zhu, Li, Amsler, Maximilian, Fuhrer, Tobias, Schaefer, Bastian, Faraji, Somayeh, Rostami, Samare, Ghasemi, S. Alireza, Sadeghi, Ali, Grauzinyte, Migle, Wolverton, Chris, & Goedecker, Stefan. A fingerprint based metric for measuring similarities of crystalline structures.  United States.  https://doi.org/10.1063/1.4940026

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                    Zhu, Li, Amsler, Maximilian, Fuhrer, Tobias, Schaefer, Bastian, Faraji, Somayeh, Rostami, Samare, Ghasemi, S. Alireza, Sadeghi, Ali, Grauzinyte, Migle, Wolverton, Chris, and Goedecker, Stefan. Thu .  
"A fingerprint based metric for measuring similarities of crystalline structures".  United States.  https://doi.org/10.1063/1.4940026.  https://www.osti.gov/servlets/purl/1469171.

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@article{osti_1469171,

  title        = {A fingerprint based metric for measuring similarities of crystalline structures},

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

  abstractNote = {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. In this paper, 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. Finally, 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.},

  doi          = {10.1063/1.4940026},

  journal      = {Journal of Chemical Physics},

  number       = 3,

  volume       = 144,

  place        = {United States},

  year         = {Thu Jan 21 00:00:00 EST 2016},

  month        = {Thu Jan 21 00:00:00 EST 2016}

}

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A fingerprint based metric for measuring similarities of crystalline structures

Journal Article Zhu, Li ; Fuhrer, Tobias ; Schaefer, Bastian ; ... - Journal of Chemical Physics

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.more »« less
https://doi.org/10.1063/1.4940026
Metrics for measuring distances in configuration spaces

Journal Article Sadeghi, Ali ; Ghasemi, S. Alireza ; Schaefer, Bastian ; ... - Journal of Chemical Physics

In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD betweenmore »« less
https://doi.org/10.1063/1.4828704
A biology-informed similarity metric for simulated patches of human cell membrane

Journal Article Bhatia, Harsh ; Thiagarajan, Jayaraman J. ; Anirudh, Rushil ; ... - Machine Learning: Science and Technology

Complex scientific inquiries rely increasingly upon large and autonomous multiscale simulation campaigns, which fundamentally require similarity metrics to quantify ‘sufficient’ changes among data and/or configurations. However, subject matter experts are often unable to articulate similarity precisely or in terms of well-formulated definitions, especially when new hypotheses are to be explored, making it challenging to design a meaningful metric. Furthermore, the key to practical usefulness of such metrics to enable autonomous simulations lies in in situ inference, which requires generalization to possibly substantial distributional shifts in unseen, future data. Here, we address these challenges in a cancer biology application and developmore »« less
https://doi.org/10.1088/2632-2153/ac8523

Full Text Available
Establishing metrics to quantify spatial similarity in spherical and red blood cell distributions

Journal Article Roychowdhury, Sayan ; Draeger, Erik W. ; Randles, Amanda - Journal of Computational Science

As computational power increases and systems with millions of red blood cells can be simulated, it is important to note that varying spatial distributions of cells may affect simulation outcomes. Since a single simulation may not represent the ensemble behavior, many different configurations may need to be sampled to adequately assess the entire collection of potential cell arrangements. In order to determine both the number of distributions needed and which ones to run, we must first establish methods to identify well-generated, randomly placed cell distributions and to quantify distinct cell configurations. We utilize metrics to assess (1) the presence ofmore »« less
https://doi.org/10.1016/j.jocs.2023.102060
EI_MS_ML

Software Mitchell, Joshua ; USDOE Laboratory Directed Research and Development

The unambiguous identification of compounds from their electron ionization mass (EI-MS) spectra remains a significant unsolved problem in the field of metabolomics and analytical chemistry as a whole. Typically EI-MS spectra are compared using various mathematical operations that convert the spectral similarity or differences into a distance-like metric that roughly approximates the similarity of any two spectra. A commonly used metric for this is the cosine similarity metric which has values close to one for very similar spectra and a value of zero for very dissimilar spectra; however, no metric is perfect. Due to the prevalence of structurally-similar compounds suchmore »« less
https://doi.org/10.11578/dc.20231103.3

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

Abstract

Citation Formats

Recognizing molecular patterns by machine learning: An agnostic structural definition of the hydrogen bond journal, November 2014

CALYPSO: A method for crystal structure prediction journal, October 2012

Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels journal, July 1929

Projector augmented-wave method journal, December 1994

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules text, January 2015

DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method † journal, July 2007

The discovery of unexpected isomers in sodium heptamers by Born–Oppenheimer molecular dynamics journal, September 2009

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials journal, September 2009

Ab initio random structure searching journal, January 2011

On representing chemical environments journal, May 2013

From ultrasoft pseudopotentials to the projector augmented-wave method journal, January 1999

The Electrolyte Genome project: A big data approach in battery materials discovery journal, June 2015

i-PI: A Python interface for ab initio path integral molecular dynamics simulations journal, March 2014

Crystal structure prediction using the Minima Hopping method text, January 2010

Diffusion of single adatoms of platinum, iridium and gold on platinum surfaces journal, January 1978

The Hungarian method for the assignment problem journal, March 1955

Novel Structural Motifs in Low Energy Phases of LiAlH 4 journal, May 2012

Unexpected Stable Stoichiometries of Sodium Chlorides journal, December 2013

Gaussian Approximation Potentials: a brief tutorial introduction preprint, January 2015

The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies journal, December 2015

The Hungarian method for the assignment problem journal, February 2005

Electronic structure of AlFeN films exhibiting crystallographic orientation change from c- to a-axis with Fe concentrations and annealing effect journal, February 2020

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set journal, October 1996

Unexpected Stable Stoichiometries of Sodium Chlorides text, January 2013

Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems – Part II journal, January 2001

Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets journal, May 2021

Metrics for measuring distances in configuration spaces journal, November 2013

A logical calculus of the ideas immanent in nervous activity journal, January 1990

CALYPSO: a method for crystal structure prediction text, January 2012

Minima hopping: An efficient search method for the global minimum of the potential energy surface of complex molecular systems journal, June 2004

High-throughput and data mining with ab initio methods journal, December 2004

Low-density silicon allotropes for photovoltaic applications journal, July 2015

Materials discovery via CALYPSO methodology journal, April 2015

Charting the complete elastic properties of inorganic crystalline compounds journal, March 2015

Crystal structure prediction via particle-swarm optimization journal, September 2010

AFLOW: An automatic framework for high-throughput materials discovery text, January 2013

i-PI: A Python interface for ab initio path integral molecular dynamics simulations text, January 2014

Crystal Structure of Cold Compressed Graphite journal, February 2012

Conducting Boron Sheets Formed by the Reconstruction of the α -Boron (111) Surface journal, September 2013

USPEX—Evolutionary crystal structure prediction journal, December 2006

Recognizing molecular patterns by machine learning: an agnostic structural definition of the hydrogen bond text, January 2014

Reactions of xenon with iron and nickel are predicted in the Earth's inner core journal, April 2014

Atom-centered symmetry functions for constructing high-dimensional neural network potentials journal, February 2011

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules journal, July 2015

How to quantify energy landscapes of solids journal, March 2009

The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies text, January 2015

Spiral Chain O4 Form of Dense Oxygen text, January 2011

Gaussian approximation potentials: A brief tutorial introduction journal, April 2015

How to quantify energy landscapes of solids text, January 2009

Bond-orientational order in liquids and glasses journal, July 1983

Conducting boron sheets formed by the reconstruction of the α-boron (111) surface text, January 2013

Commentary: The Materials Project: A materials genome approach to accelerating materials innovation journal, July 2013

Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD) journal, September 2013

Identifying duplicate crystal structures: XtalComp, an open-source solution journal, March 2012

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties preprint, January 2012

AFLOW: An automatic framework for high-throughput materials discovery journal, June 2012

Constructing high-dimensional neural network potentials: A tutorial review journal, March 2015

The geometry of Niggli reduction: SAUC – search of alternative unit cells journal, January 2014

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties journal, February 2013

Continuous similarity measure between nonoverlapping X-ray powder diagrams of different crystal modifications journal, October 1993

Crystal structure prediction using the minima hopping method journal, December 2010

Spiral chain O4 form of dense oxygen journal, January 2012

The Cambridge Structural Database: a quarter of a million crystal structures and rising journal, May 2002

The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation journal, January 1999

Unsupervised machine learning in atomistic simulations, between predictions and understanding text, January 2019

Insightful classification of crystal structures using deep learning journal, July 2018

Using symmetry to elucidate the importance of stoichiometry in colloidal crystal assembly journal, May 2019

Comparing molecules and solids across structural and alchemical space journal, January 2016

Unsupervised discovery of solid-state lithium ion conductors journal, November 2019

From DFT to machine learning: recent approaches to materials science–a review journal, May 2019

Quantifying similarity of pore-geometry in nanoporous materials journal, May 2017

Perspective: Machine learning potentials for atomistic simulations journal, November 2016

Unsupervised discovery of solid-state lithium ion conductors journal, November 2019

Distinguishing Metal–Organic Frameworks journal, January 2018

Quantifying similarity of pore-geometry in nanoporous materials journal, May 2017

Optimized symmetry functions for machine-learning interatomic potentials of multicomponent systems journal, September 2018

Navigating at Will on the Water Phase Diagram journal, December 2017

Recognizing molecular patterns by machine learning: An agnostic structural definition of the hydrogen bond
journal, November 2014

CALYPSO: A method for crystal structure prediction
journal, October 2012

Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels
journal, July 1929

Projector augmented-wave method
journal, December 1994

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
text, January 2015

DFTB+, a Sparse Matrix-Based Implementation of the DFTB Method ^†
journal, July 2007

The discovery of unexpected isomers in sodium heptamers by Born–Oppenheimer molecular dynamics
journal, September 2009

QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009

Ab initio random structure searching
journal, January 2011

On representing chemical environments
journal, May 2013

From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999

The Electrolyte Genome project: A big data approach in battery materials discovery
journal, June 2015

i-PI: A Python interface for ab initio path integral molecular dynamics simulations
journal, March 2014

Crystal structure prediction using the Minima Hopping method
text, January 2010

Diffusion of single adatoms of platinum, iridium and gold on platinum surfaces
journal, January 1978

The Hungarian method for the assignment problem
journal, March 1955

Novel Structural Motifs in Low Energy Phases of ${LiAlH}_{4}$
journal, May 2012

Unexpected Stable Stoichiometries of Sodium Chlorides
journal, December 2013

Gaussian Approximation Potentials: a brief tutorial introduction
preprint, January 2015

The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies
journal, December 2015

The Hungarian method for the assignment problem
journal, February 2005

Electronic structure of AlFeN films exhibiting crystallographic orientation change from c- to a-axis with Fe concentrations and annealing effect
journal, February 2020

Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996

Unexpected Stable Stoichiometries of Sodium Chlorides
text, January 2013

Determination, prediction, and understanding of structures, using the energy landscapes of chemical systems – Part II
journal, January 2001

Reducing Dzyaloshinskii-Moriya interaction and field-free spin-orbit torque switching in synthetic antiferromagnets
journal, May 2021

Metrics for measuring distances in configuration spaces
journal, November 2013

A logical calculus of the ideas immanent in nervous activity
journal, January 1990

CALYPSO: a method for crystal structure prediction
text, January 2012

Minima hopping: An efficient search method for the global minimum of the potential energy surface of complex molecular systems
journal, June 2004

High-throughput and data mining with ab initio methods
journal, December 2004

Low-density silicon allotropes for photovoltaic applications
journal, July 2015

Materials discovery via CALYPSO methodology
journal, April 2015

Charting the complete elastic properties of inorganic crystalline compounds
journal, March 2015

Crystal structure prediction via particle-swarm optimization
journal, September 2010

AFLOW: An automatic framework for high-throughput materials discovery
text, January 2013

i-PI: A Python interface for ab initio path integral molecular dynamics simulations
text, January 2014

Crystal Structure of Cold Compressed Graphite
journal, February 2012

Conducting Boron Sheets Formed by the Reconstruction of the $α$ -Boron (111) Surface
journal, September 2013

USPEX—Evolutionary crystal structure prediction
journal, December 2006

Recognizing molecular patterns by machine learning: an agnostic structural definition of the hydrogen bond
text, January 2014

Reactions of xenon with iron and nickel are predicted in the Earth's inner core
journal, April 2014

Atom-centered symmetry functions for constructing high-dimensional neural network potentials
journal, February 2011

Machine Learning for Quantum Mechanical Properties of Atoms in Molecules
journal, July 2015

How to quantify energy landscapes of solids
journal, March 2009

The Open Quantum Materials Database (OQMD): assessing the accuracy of DFT formation energies
text, January 2015

Spiral Chain O4 Form of Dense Oxygen
text, January 2011

Gaussian approximation potentials: A brief tutorial introduction
journal, April 2015

How to quantify energy landscapes of solids
text, January 2009

Bond-orientational order in liquids and glasses
journal, July 1983

Conducting boron sheets formed by the reconstruction of the α-boron (111) surface
text, January 2013

Commentary: The Materials Project: A materials genome approach to accelerating materials innovation
journal, July 2013

Materials Design and Discovery with High-Throughput Density Functional Theory: The Open Quantum Materials Database (OQMD)
journal, September 2013

Identifying duplicate crystal structures: XtalComp, an open-source solution
journal, March 2012

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties
preprint, January 2012

AFLOW: An automatic framework for high-throughput materials discovery
journal, June 2012

Constructing high-dimensional neural network potentials: A tutorial review
journal, March 2015

The geometry of Niggli reduction: SAUC – search of alternative unit cells
journal, January 2014

First principles view on chemical compound space: Gaining rigorous atomistic control of molecular properties
journal, February 2013

Continuous similarity measure between nonoverlapping X-ray powder diagrams of different crystal modifications
journal, October 1993

Crystal structure prediction using the minima hopping method
journal, December 2010

Spiral chain O4 form of dense oxygen
journal, January 2012

The Cambridge Structural Database: a quarter of a million crystal structures and rising
journal, May 2002

The prediction of inorganic crystal structures using a genetic algorithm and energy minimisation
journal, January 1999

Unsupervised machine learning in atomistic simulations, between predictions and understanding
text, January 2019

Insightful classification of crystal structures using deep learning
journal, July 2018

Using symmetry to elucidate the importance of stoichiometry in colloidal crystal assembly
journal, May 2019

Comparing molecules and solids across structural and alchemical space
journal, January 2016

Unsupervised discovery of solid-state lithium ion conductors
journal, November 2019

From DFT to machine learning: recent approaches to materials science–a review
journal, May 2019

Quantifying similarity of pore-geometry in nanoporous materials
journal, May 2017

Perspective: Machine learning potentials for atomistic simulations
journal, November 2016

Unsupervised discovery of solid-state lithium ion conductors
journal, November 2019

Distinguishing Metal–Organic Frameworks
journal, January 2018

Quantifying similarity of pore-geometry in nanoporous materials
journal, May 2017

Optimized symmetry functions for machine-learning interatomic potentials of multicomponent systems
journal, September 2018

Navigating at Will on the Water Phase Diagram
journal, December 2017

Surface reconstructions and premelting of the (100) CaF ₂ surface
journal, January 2019

Local invertibility and sensitivity of atomic structure-feature mappings
preprint, January 2021

Local invertibility and sensitivity of atomic structure-feature mappings
journal, January 2021