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TY  - THES
AU  - Betzinger, Markus
TI  - Orbital-dependent exchange-correlation functionals in density-functional theory realized by the FLAPW method
CY  - Aachen
PB  - Publikationsserver der RWTH Aachen University
M1  - RWTH-CONV-124350
SP  - VI, 173 S. : graph. Darst.
PY  - 2011
N1  - Prüfungsjahr: 2011. - Publikationsjahr: 2012
N1  - Aachen, Techn. Hochsch., Diss., 2011
AB  - In this thesis, we extended the applicability of the full-potential linearized augmented-plane-wave (FLAPW) method, one of the most precise, versatile and generally applicable electronic structure methods 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 one-particle 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, the matrix elements of the Hamiltonian 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 4f electrons, the electronic and magnetic 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 equation for the local potential without any shape approximations for the potential. We show that a balance between the LAPW and mixed product basis is mandatory for a smooth and physical local EXX potential. The LAPW basis must be converged to an accuracy which is far beyond that for LDA or GGA calculations. We demonstrate that this is necessary to lend the LAPW basis and thus the KS wave functions and density sufficient flexibility to react adequately to the changes of the effective potential, which are described in our formalism by the MPB. If both basis sets are properly balanced, our results for C, Si, SiC, Ge, GaAs as well as solid Ne and Ar are in favorable agreement with plane-wave pseudopotential results. Because of the exceedingly large LAPW basis sets the EXX-OEP approach is computationally expensive. We propose a correction, the finite basis-set correction (FBC), for the density and wave-function response, which explicitly considers the dependence of the LAPW basis on the effective potential and which vanishes in the limit of an infinite, complete basis. For the example of ScN, we demonstrate that the FBC leads to converged potentials at much smaller LAPW basis sets and thus turns the EXX-OEP approach into a practical method. Finally, we discuss a generalization of the formalism to metals and report results for the cubic perovskites CaTiO3, SrTiO3, and BaTiO3, the transition-metal oxides MnO, FeO, and CoO as well as the metals Al, Na, and Cu.
KW  - Dichtefunktionalformalismus (SWD)
KW  - Ab-initio-Rechnung (SWD)
KW  - Elektronenstruktur (SWD)
KW  - LAPW-Methode (SWD)
KW  - Korrelationsenergie (SWD)
KW  - Störungstheorie (SWD)
LB  - PUB:(DE-HGF)11
UR  - https://publications.rwth-aachen.de/record/62853
ER  -