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@PHDTHESIS{Betzinger:19392,
      author       = {Betzinger, Markus},
      title        = {{O}rbital-dependent exchange-correlation functionals in
                      density-functional theory realized by the {FLAPW} method},
      volume       = {59},
      school       = {RWTH Aachen},
      type         = {Dr. (Univ.)},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {PreJuSER-19392},
      isbn         = {978-3-89336-858-7},
      series       = {Schriften des Forschungszentrums Jülich.
                      Schlüsseltechnologien / Key Technologies},
      pages        = {VI, 173 S.},
      year         = {2011},
      note         = {Record converted from VDB: 12.11.2012; RWTH Aachen, Diss.,
                      2011},
      abstract     = {In this thesis, we extended the applicability of the
                      full-potential linearized augmented-planewave (FLAPW)
                      method, one of the most precise, versatile and generally
                      applicable electronic structuremethods for solids working
                      within the framework of density-functional theory (DFT), to
                      orbital-dependent functionals for the exchange-correlation
                      (xc) energy. In contrast to the commonly applied
                      local-density approximation (LDA) and generalized gradient
                      approximation (GGA) for the xc energy, orbital-dependent
                      functionals depend directly on the Kohn-Sham (KS) orbitals
                      and only indirectly on the density. Two different schemes
                      that deal with orbital-dependent functionals, the KS and the
                      generalized Kohn-Sham (gKS) formalism, have been realized.
                      While the KS scheme requires a local multiplicative xc
                      potential, the gKS scheme allows for a non-local potential
                      in the oneparticle Schrödinger equations. Hybrid
                      functionals, combining some amount of the orbital-dependent
                      exact exchange energy with local or semi-local functionals
                      of the density, are implemented within the gKS scheme. We
                      work in particular with the PBE0 hybrid of Perdew, Burke,
                      and Ernzerhof. Our implementation relies on a representation
                      of the non-local exact exchange potential – its
                      calculation constitutes the most time consuming step in a
                      practical calculation – by an auxiliary mixed product
                      basis (MPB). In this way, thematrix elements of
                      theHamiltonian corresponding to the non-local potential
                      become a Brillouin-zone (BZ) sum over vector-matrix-vector
                      products. Several techniques are developed and explored to
                      further accelerate our numerical scheme. We show PBE0
                      results for a variety of semiconductors and insulators. In
                      comparison with experiment, the PBE0 functional leads to
                      improved band gaps and an improved description of localized
                      states. Even for the ferromagnetic semiconductor EuO with
                      localized 4 f electrons, the electronic andmagnetic
                      properties are correctly described by the PBE0 functional.
                      Subsequently, we discuss the construction of the
                      local,multiplicative exact exchange (EXX) potential from the
                      non-local, orbital-dependent exact exchange energy. For this
                      purpose we employ the optimized effective potential (OEP)
                      method. Central ingredients of the OEP equation are the KS
                      wave-function response and the single-particle density
                      response function. A formulation in terms of a slightly
                      modified MPB enables to solve the OEP integral [...]},
      cin          = {PGI-1 / IAS-1},
      cid          = {I:(DE-Juel1)PGI-1-20110106 / I:(DE-Juel1)IAS-1-20090406},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      typ          = {PUB:(DE-HGF)11 / PUB:(DE-HGF)3},
      url          = {https://juser.fz-juelich.de/record/19392},
}