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@PHDTHESIS{Gerhorst:909838,
      author       = {Gerhorst, Christian-Roman},
      title        = {{D}ensity-{F}unctional {P}erturbation {T}heory within the
                      {A}ll-{E}lectron {F}ull-{P}otential {L}inearized {A}ugmented
                      {P}lane-{W}ave {M}ethod: {A}pplication to {P}honons},
      volume       = {259},
      school       = {RWTH Aachen University},
      type         = {Dissertation},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {FZJ-2022-03456},
      isbn         = {978-3-95806-649-6},
      series       = {Schriften des Forschungszentrums Jülich Reihe
                      Schlüsseltechnologien / Key Technologies},
      pages        = {xvi, 317},
      year         = {2022},
      note         = {Dissertation, RWTH Aachen University, 2022},
      abstract     = {Solids consisting of periodic lattice structures exhibit
                      vibrational modes of their atomic nuclei. In the context of
                      a quantum-mechanical description, the excitations of the
                      collective lattice vibrations are quantized and behave like
                      particles. These quasiparticles are called phonons and
                      essential for describing a diverse spectrum of central solid
                      properties and phenomena. Density-Functional Theory (DFT)
                      according to Kohn and Sham has established itself as a very
                      successful, state-of-the-art, material-specific,
                      theoretical, and computational framework. It enables us to
                      calculate the phonon modes with very high predictive power
                      from the first principles of quantum mechanics for
                      describing electrons and ions. Two different approaches to
                      obtaining phonon properties are employed: (i) the Finite
                      Displacement (FD) ansatz, where the second-order derivatives
                      of the total energy with respect to atomic displacements are
                      approximated by difference quotients that involve the forces
                      exerted on the atoms due to their finite displacement, and
                      (ii) the Density-Functional Perturbation Theory (DFPT), a
                      variational approach delivering the desired second-order
                      derivatives from linear responses to an infinitesimal
                      displacement wave. The ambition of this dissertation is to
                      pursue a DFPT beyond the common frameworks with plane-wave
                      basis functions. It is realized by means of the
                      Full-Potential Linearized Augmented Plane-Wave (FLAPW)
                      method, an all-electron electronic-structure method based on
                      muffin-tin (MT) spheres circumscribing the atomic nuclei.
                      The FLAPW method is known for providing the
                      density-functional answer to arbitrary material systems,
                      i.e., independent of which chemical element in the periodic
                      table is chosen. I report on the implementation and
                      validation of the DFPT approach within the FLAPW method in
                      terms of the newly-developed computer program juPhon. Its
                      algorithm describes the properties of phonons in harmonic
                      approximation and is based on the input of the FLEUR code,
                      which is a DFT implementation utilizing the aforementioned
                      FLAPW ansatz. In detail, I elucidate the numerical
                      challenges and show how they have been surmounted enabling
                      us to reliably set up a dynamical matrix, the associated
                      phonon energies of which are many orders of magnitude
                      smaller than the ground-state energy of a crystal. This
                      covers (i) implementing the self-consistent Sternheimer
                      equation, which determines the first-order variations of the
                      charge density as well as the effective potential due to the
                      presence of the displacement wave, and (ii) accounting for
                      the features of the LAPW basis-set. Owing to the displaced
                      atoms, the latter entails considering both Pulay basis-set
                      corrections and discontinuities at the MT-sphere surfaces in
                      the section-wise defined LAPW basis and the potentials.
                      While the Pulay terms compensate for the representation of
                      the wave functions outside the Hilbert space spanned by the
                      finite LAPW basis-set, the discontinuities require the
                      introduction of surface integral contributions. Decisive has
                      amongst others been a sustainable programming paradigm,
                      making juPhon become a complex and sophisticated testing and
                      application software. Within this thesis, I finally
                      benchmark the juPhon phonon dispersions of bulk fcc Cu, Au,
                      Al, Ne, and Ar as well as bcc Mo by comparing them with
                      respective FD computations and experimental reference data.
                      These results show a good agreement.},
      cin          = {PGI-1 / IAS-1 / JARA-FIT / JARA-HPC},
      cid          = {I:(DE-Juel1)PGI-1-20110106 / I:(DE-Juel1)IAS-1-20090406 /
                      $I:(DE-82)080009_20140620$ / $I:(DE-82)080012_20140620$},
      pnm          = {5211 - Topological Matter (POF4-521)},
      pid          = {G:(DE-HGF)POF4-5211},
      typ          = {PUB:(DE-HGF)3 / PUB:(DE-HGF)11},
      url          = {https://juser.fz-juelich.de/record/909838},
}