Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method

Betzinger, Markus

Dissertation / PhD Thesis/Book

PreJuSER-19392

Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method

Betzinger, M. (Corresponding author)FZJ*

2011
Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag Jülich
ISBN: 978-3-89336-858-7

Jülich : Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag, Schriften des Forschungszentrums Jülich. Schlüsseltechnologien / Key Technologies 59, VI, 173 S. (2011) = RWTH Aachen, Diss., 2011

Please use a persistent id in citations: http://hdl.handle.net/2128/16525

Abstract: 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 [...]

Note: Record converted from VDB: 12.11.2012
Note: RWTH Aachen, Diss., 2011

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