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Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method
von Markus BetzingerIn 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.
(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.