This title appears in the Scientific Report :
2011
Please use the identifier:
http://hdl.handle.net/2128/16525 in citations.
Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method
Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method
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...
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Personal Name(s): | Betzinger, Markus (Corresponding author) |
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Contributing Institute: |
Quanten-Theorie der Materialien; IAS-1 Quanten-Theorie der Materialien; PGI-1 |
Imprint: |
Jülich
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag
2011
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Physical Description: |
VI, 173 S. |
Dissertation Note: |
RWTH Aachen, Diss., 2011 |
ISBN: |
978-3-89336-858-7 |
Document Type: |
Book Dissertation / PhD Thesis |
Research Program: |
Grundlagen für zukünftige Informationstechnologien |
Series Title: |
Schriften des Forschungszentrums Jülich. Schlüsseltechnologien / Key Technologies
59 |
Subject (ZB): | |
Link: |
OpenAccess |
Publikationsportal JuSER |
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 [...] |