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@ARTICLE{Friedrich:21969,
      author       = {Friedrich, C. and Betzinger, M. and Schlipf, M. and
                      Blügel, S. and Schindlmayr, A.},
      title        = {{H}ybrid functionals and {GW} approximation in the {FLAPW}
                      method},
      journal      = {Journal of physics / Condensed matter},
      volume       = {24},
      issn         = {0953-8984},
      address      = {Bristol},
      publisher    = {IOP Publ.},
      reportid     = {PreJuSER-21969},
      pages        = {293201},
      year         = {2012},
      note         = {We gratefully acknowledge valuable discussions with Marjana
                      Lezaic, Gustav Bihlmayer, Mathias C. Muller, and Georg
                      Kresse, as well as financial funding by the Young
                      Investigators Group Programme of the Helmholtz Association
                      (Computational Nanoferronics Laboratory', contract
                      VH-NG-409) and by the Deutsche Forschungsgemeinschaft
                      through the Priority Program 1145.},
      abstract     = {We present recent advances in numerical implementations of
                      hybrid functionals and the GW approximation within the
                      full-potential linearized augmented-plane-wave (FLAPW)
                      method. The former is an approximation for the
                      exchange–correlation contribution to the total energy
                      functional in density-functional theory, and the latter is
                      an approximation for the electronic self-energy in the
                      framework of many-body perturbation theory. All
                      implementations employ the mixed product basis, which has
                      evolved into a versatile basis for the products of wave
                      functions, describing the incoming and outgoing states of an
                      electron that is scattered by interacting with another
                      electron. It can thus be used for representing the nonlocal
                      potential in hybrid functionals as well as the screened
                      interaction and related quantities in GW calculations. In
                      particular, the six-dimensional space integrals of the
                      Hamiltonian exchange matrix elements (and exchange
                      self-energy) decompose into sums over
                      vector–matrix–vector products, which can be evaluated
                      easily. The correlation part of the GW self-energy, which
                      contains a time or frequency dependence, is calculated on
                      the imaginary frequency axis with a subsequent analytic
                      continuation to the real axis or, alternatively, by a direct
                      frequency convolution of the Green function G and the
                      dynamically screened Coulomb interaction W along a contour
                      integration path that avoids the poles of the Green
                      function. Hybrid-functional and GW calculations are
                      notoriously computationally expensive. We present a number
                      of tricks that reduce the computational cost considerably,
                      including the use of spatial and time-reversal symmetries,
                      modifications of the mixed product basis with the aim to
                      optimize it for the correlation self-energy and another
                      modification that makes the Coulomb matrix sparse, analytic
                      expansions of the interaction potentials around the point of
                      divergence at k = 0, and a nested density and density-matrix
                      convergence scheme for hybrid-functional calculations. We
                      show CPU timings for prototype semiconductors and
                      illustrative results for GdN and ZnO.},
      keywords     = {J (WoSType)},
      cin          = {IAS-1 / PGI-1 / JARA-FIT / JARA-SIM},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IAS-1-20090406 / I:(DE-Juel1)PGI-1-20110106 /
                      $I:(DE-82)080009_20140620$ / I:(DE-Juel1)VDB1045},
      pnm          = {Grundlagen für zukünftige Informationstechnologien /
                      Helmholtz Young Investigators Group
                      (HGF-YoungInvestigatorsGroup)},
      pid          = {G:(DE-Juel1)FUEK412 /
                      G:(DE-HGF)HGF-YoungInvestigatorsGroup},
      shelfmark    = {Physics, Condensed Matter},
      typ          = {PUB:(DE-HGF)16},
      pubmed       = {pmid:22773268},
      UT           = {WOS:000306270700001},
      doi          = {10.1088/0953-8984/24/29/293201},
      url          = {https://juser.fz-juelich.de/record/21969},
}