% IMPORTANT: The following is UTF-8 encoded.  This means that in the presence
% of non-ASCII characters, it will not work with BibTeX 0.99 or older.
% Instead, you should use an up-to-date BibTeX implementation like “bibtex8” or
% “biber”.

@ARTICLE{Betzinger:10056,
      author       = {Betzinger, M. and Friedrich, C. and Blügel, S.},
      title        = {{H}ybrid functionals within the all-electron {FLAPW}
                      method: {I}mplementation and applications of {PBE}0},
      journal      = {Physical review / B},
      volume       = {81},
      number       = {19},
      issn         = {1098-0121},
      address      = {College Park, Md.},
      publisher    = {APS},
      reportid     = {PreJuSER-10056},
      pages        = {195117},
      year         = {2010},
      note         = {The authors gratefully acknowledge valuable discussions
                      with Gustav Bihlmayer, Martin Schlipf, Frank Freimuth,
                      Marjana Lezaic, Yuriy Mokrousov, Tatsuya Shishidou, and Arno
                      Schindlmayr as well as financial support from the HGF Young
                      Investigator Group Nanoferronics Laboratory and the Deutsche
                      Forschungsgemeinschaft through the Priority Program 1145.},
      abstract     = {We present an efficient implementation of the
                      Perdew-Burke-Ernzerhof hybrid functional PBE0 within the
                      full-potential linearized augmented-plane-wave (FLAPW)
                      method. The Hartree-Fock exchange term, which is a central
                      ingredient of hybrid functionals, gives rise to a
                      computationally expensive nonlocal potential in the
                      one-particle Schrodinger equation. The matrix elements of
                      this exchange potential are calculated with the help of an
                      auxiliary basis that is constructed from products of FLAPW
                      basis functions. By representing the Coulomb interaction in
                      this basis the nonlocal exchange term becomes a
                      Brillouin-zone sum over vector-matrixvector products. The
                      Coulomb matrix is calculated only once at the beginning of a
                      self-consistent-field cycle. We show that it can be made
                      sparse by a suitable unitary transformation of the auxiliary
                      basis, which accelerates the computation of the
                      vector-matrix-vector products considerably. Additionally, we
                      exploit spatial and time-reversal symmetry to identify the
                      nonvanishing exchange matrix elements in advance and to
                      restrict the k summations for the nonlocal potential to an
                      irreducible set of k points. Favorable convergence of the
                      self-consistent-field cycle is achieved by a nested
                      density-only and density-matrix iteration scheme. We discuss
                      the convergence with respect to the parameters of our
                      numerical scheme and show results for a variety of
                      semiconductors and insulators, including the oxides ZnO,
                      EuO, Al2O3, and SrTiO3, where the PBE0 hybrid functional
                      improves the band gaps and the description of localized
                      states in comparison with the PBE functional. Furthermore,
                      we find that in contrast to conventional local
                      exchange-correlation functionals ferromagnetic EuO is
                      correctly predicted to be a semiconductor.},
      keywords     = {J (WoSType)},
      cin          = {IFF-1 / IAS-1 / JARA-FIT / JARA-HPC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)VDB781 / I:(DE-Juel1)IAS-1-20090406 /
                      $I:(DE-82)080009_20140620$ / I:(DE-Juel1)VDB1346},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      shelfmark    = {Physics, Condensed Matter},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000278142000040},
      doi          = {10.1103/PhysRevB.81.195117},
      url          = {https://juser.fz-juelich.de/record/10056},
}