Maximally localized Wannier functions for entangled energy bands

Ivo Souza, Nicola Marzari, David Vanderbilt

Research output: Contribution to journalArticle

747 Scopus citations


We present a method for obtaining well-localized Wannier-like functions (WF's) for energy bands that are attached to or mixed with other bands. The present scheme removes the limitation of the usual maximally localized WF's method [N. Marzari and D. Vanderbilt, Phys. Rev. B 56, 12 847 (1997)] that the bands of interest should form an isolated group, separated by gaps from higher and lower bands everywhere in the Brillouin zone. An energy window encompassing N bands of interest is specified by the user, and the algorithm then proceeds to disentangle these from the remaining bands inside the window by filtering out an optimally connected N-dimensional subspace. This is achieved by minimizing a functional that measures the subspace dispersion across the Brillouin zone. The maximally localized WF's for the optimal subspace are then obtained via the algorithm of Marzari and Vanderbilt. The method, which functions as a postprocessing step using the output of conventional electronic-structure codes, is applied to the s and d bands of copper, and to the valence and low-lying conduction bands of silicon. For the low-lying nearly-free-electron bands of copper we find WF's which are centered at the tetrahedral-interstitial sites, suggesting an alternative tight-binding parametrization.

Original languageEnglish (US)
Article number035109
Pages (from-to)351091-3510913
Number of pages3159823
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
StatePublished - Jan 15 2002

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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