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@ARTICLE{Friedrich:4660,
      author       = {Friedrich, C. and Schindlmayr, A. and Blügel, S.},
      title        = {{E}fficient calculation of the {C}oulomb matrix and its
                      expansion around k=0 within the {FLAPW} method},
      journal      = {Computer physics communications},
      volume       = {180},
      issn         = {0010-4655},
      address      = {Amsterdam},
      publisher    = {North Holland Publ. Co.},
      reportid     = {PreJuSER-4660},
      pages        = {347 - 359},
      year         = {2009},
      note         = {Record converted from VDB: 12.11.2012},
      abstract     = {We derive formulas for the Coulomb matrix within the
                      full-potential linearized augmented-planewave (FLAPW)
                      method. The Coulomb matrix is a central ingredient in
                      implementations of many-body perturbation theory, such as
                      the Hartree-Fock and GW approximations for the electronic
                      self-energy or the random-phase approximation for the
                      dielectric function. It is represented in the mixed product
                      basis, which combines numerical muffin-tin functions and
                      interstitial plane waves constructed from products of FLAPW
                      basis functions. The interstitial plane waves are here
                      expanded with the Rayleigh formula. The resulting algorithm
                      is very efficient in terms of both computational cost and
                      accuracy and is superior to an implementation with the
                      Fourier transform of the step function. in order to allow an
                      analytic treatment of the divergence at k = 0 in reciprocal
                      space, we expand the Coulomb matrix analytically around this
                      point without resorting to a projection onto plane waves.
                      Without additional approximations, we then apply a basis
                      transformation that diagonalizes the Coulomb matrix and
                      confines the divergence to a single eigenvalue. At the same
                      time, response matrices like the dielectric function
                      separate into head, wings, and body with the same
                      mathematical properties as in a plane-wave basis. As an
                      illustration we apply the formulas to electron-energy-loss
                      spectra (EELS) for nickel at different It vectors including
                      k = 0. The convergence of the spectra towards the result at
                      k = 0 is clearly seen. Our all-electron treatment also
                      allows to include transitions from 3s and 3p core states in
                      the EELS spectrum that give rise to a shallow peak at high
                      energies and lead to good agreement with experiment. (C)
                      2008 Elsevier B.V. All rights reserved.},
      keywords     = {J (WoSType)},
      cin          = {IFF-1 / IAS-1 / JARA-FIT / JARA-HPC},
      ddc          = {004},
      cid          = {I:(DE-Juel1)VDB781 / I:(DE-Juel1)IAS-1-20090406 /
                      $I:(DE-82)080009_20140620$ / $I:(DE-82)080012_20140620$},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      shelfmark    = {Computer Science, Interdisciplinary Applications / Physics,
                      Mathematical},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000264735800002},
      doi          = {10.1016/j.cpc.2008.10.009},
      url          = {https://juser.fz-juelich.de/record/4660},
}