Maximally localized Wannier functions: Theory and applications

The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized >Wannier functions> was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is real...

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Autores: Marzari, Nicola, Mostofi, Arash A., Yates, Jonathan R., Souza, Ivo, Vanderbilt, David
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2012
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/101941
Acceso en línea:http://hdl.handle.net/10261/101941
Access Level:acceso abierto
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spelling Maximally localized Wannier functions: Theory and applicationsMarzari, NicolaMostofi, Arash A.Yates, Jonathan R.Souza, IvoVanderbilt, DavidThe electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized >Wannier functions> was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or >Boys orbitals> as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices. © 2012 American Physical Society.Peer ReviewedAmerican Physical Society2014201420122014info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/101941reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Ingléshttp://dx.doi.org/10.1103/RevModPhys.84.1419info:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1019412026-05-22T06:33:51Z
dc.title.none.fl_str_mv Maximally localized Wannier functions: Theory and applications
title Maximally localized Wannier functions: Theory and applications
spellingShingle Maximally localized Wannier functions: Theory and applications
Marzari, Nicola
title_short Maximally localized Wannier functions: Theory and applications
title_full Maximally localized Wannier functions: Theory and applications
title_fullStr Maximally localized Wannier functions: Theory and applications
title_full_unstemmed Maximally localized Wannier functions: Theory and applications
title_sort Maximally localized Wannier functions: Theory and applications
dc.creator.none.fl_str_mv Marzari, Nicola
Mostofi, Arash A.
Yates, Jonathan R.
Souza, Ivo
Vanderbilt, David
author Marzari, Nicola
author_facet Marzari, Nicola
Mostofi, Arash A.
Yates, Jonathan R.
Souza, Ivo
Vanderbilt, David
author_role author
author2 Mostofi, Arash A.
Yates, Jonathan R.
Souza, Ivo
Vanderbilt, David
author2_role author
author
author
author
description The electronic ground state of a periodic system is usually described in terms of extended Bloch orbitals, but an alternative representation in terms of localized >Wannier functions> was introduced by Gregory Wannier in 1937. The connection between the Bloch and Wannier representations is realized by families of transformations in a continuous space of unitary matrices, carrying a large degree of arbitrariness. Since 1997, methods have been developed that allow one to iteratively transform the extended Bloch orbitals of a first-principles calculation into a unique set of maximally localized Wannier functions, accomplishing the solid-state equivalent of constructing localized molecular orbitals, or >Boys orbitals> as previously known from the chemistry literature. These developments are reviewed here, and a survey of the applications of these methods is presented. This latter includes a description of their use in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization. Wannier interpolation schemes are also reviewed, by which quantities computed on a coarse reciprocal-space mesh can be used to interpolate onto much finer meshes at low cost, and applications in which Wannier functions are used as efficient basis functions are discussed. Finally the construction and use of Wannier functions outside the context of electronic-structure theory is presented, for cases that include phonon excitations, photonic crystals, and cold-atom optical lattices. © 2012 American Physical Society.
publishDate 2012
dc.date.none.fl_str_mv 2012
2014
2014
2014
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
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dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/101941
url http://hdl.handle.net/10261/101941
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv http://dx.doi.org/10.1103/RevModPhys.84.1419
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
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