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@PHDTHESIS{Klppelberg:283574,
      author       = {Klüppelberg, Daniel Aaron},
      title        = {{F}irst-principle investigation of displacive response in
                      complex solids},
      volume       = {119},
      school       = {RWTH Aachen},
      type         = {Dr.},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {FZJ-2016-01888},
      isbn         = {978-3-95806-123-1},
      series       = {Schriften des Forschungszentrums Jülich. Reihe
                      Schlüsseltechnologien / Key Technologies},
      pages        = {XI, 177 S.},
      year         = {2016},
      note         = {RWTH Aachen, Diss., 2015},
      abstract     = {In this work, we discuss two approaches to calculate phonon
                      spectra of crystals within the all-electron full-potential
                      linearized augmented-plane-wave (FLAPW) method. This method
                      is one of the most precise implementations of Kohn-Sham (KS)
                      density functional theory(DFT) due to the inclusion of all
                      electrons into the calculation and the use of the full
                      potential, i.e., no shape approximations are applied to the
                      potential. The calculation of phonons requires the
                      force-constant matrix (FCM). The FCM is the second-order
                      derivative of the KS total energy with respect to two atomic
                      displacements. Its Fourier transform yields the dynamical
                      matrix (DM). The eigenvalues of the DM are thesquares of the
                      phonon frequencies. Its eigenvectors are the polarization
                      vectors. The first approach to calculate phonons is the
                      nite-displacement (FD) method. In this method, the FCM is
                      obtained from displacing one atom at a time from
                      equilibrium, calculating the forces on all atoms, and
                      dividing by the displacement amplitude. This is repeated for
                      each atom and for each spatial direction. In practice, the
                      number of calculations reduces signicantly by exploiting the
                      symmetry of the crystal lattice. The FCM is transformed to
                      the DM and the phonon energies and polarization vectors are
                      extracted. A drawback of this approach is given by the
                      necessity to use supercells. The phonon frequencies are only
                      correct for phonons whose wave vector $\textit{q}$ is
                      commensurable with the lattice. Hence, to correctly
                      calculate phonon frequencies at small wave vectors, large
                      super cells are needed, because the displacement pattern of
                      such phonons repeats only after many instances of the
                      primitive unit cell. Since the FD procedure relies on an
                      analytical derivation of the total energy followed by a
                      numerical one, precise forces are necessary. Otherwise, the
                      FCM is not symmetric, forexample. We present a reformulation
                      of the FLAPW force formalism which includes the whole unit
                      cell into the calculation of the atomic force contribution
                      from the core states and which incorporates additional terms
                      to deal with the slight discontinuity of the LAPW basis
                      functions and the quantities derived from them. The
                      improvement of the force precision is demonstrated by the
                      study of different criteria. We then present phonon spectra
                      for Al, MgO, GaAs, and EuTiO$_{3}$ obtained by the FD method
                      from forces calculated in the FLAPW approach using our
                      reformulation. The second approach to calculate phonon
                      spectra is density functional perturbation theory(DFPT). In
                      DFPT, the second-order derivative of the KS total energy is
                      directly calculated via perturbation theory. DFPT allows the
                      determination of phonon frequencies at arbitrary wave
                      vectors $\textit{q}$ from calculations involving the
                      primitive unit cell, only, by treating a phonon of this wave
                      vector as the perturbation. The first-order changes of the
                      basis functions, the electronic density, and the potential
                      have to be obtained from the Sternheimer equation, which is
                      the linearized Schrodinger equation. Additionally, the
                      second-order changes of the external potential, the ion-ion
                      energy, and the LAPW basis functions are required. We
                      provide formulas which explicitly include adjustments of the
                      general DFPT approach when used in conjunction with the
                      FLAPW method. These adjustments include Pulay terms, the
                      correct treatment of the core state contribution, and
                      surface terms which are analogous to those within the force
                      formalism.},
      cin          = {PGI-1 / IAS-1},
      cid          = {I:(DE-Juel1)PGI-1-20110106 / I:(DE-Juel1)IAS-1-20090406},
      pnm          = {142 - Controlling Spin-Based Phenomena (POF3-142) / 143 -
                      Controlling Configuration-Based Phenomena (POF3-143)},
      pid          = {G:(DE-HGF)POF3-142 / G:(DE-HGF)POF3-143},
      typ          = {PUB:(DE-HGF)11 / PUB:(DE-HGF)3},
      url          = {https://juser.fz-juelich.de/record/283574},
}