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##### Hybrid functional with selfconsistent density-dependent mixing

**Authors**: Thorsten Aull

**Ref.**: Master thesis, Martin-Luther University of Halle-Wittenberg (2018)

**Abstract**: In this thesis we want to derive a system-dependent mixing parameter for hybrid functionals
that can be used in a self-consistent manner. We begin with a brief introduction to DFT
in the next chapters. Starting with the Hartree-Fock approximation, which was one of the earliest, to some extent successful, attempts to calculate the energy of a fermionic system.
In the third chapter the fundamentals of DFT and three different ways of approximating the
exchange-correlation energy functional (Local Density Approximation, Generalized Gradient
Approximation and global hybrid functionals) are explained. After this, fundamentals of the
program VASP, which we used to compute the band gaps, densities and mixing parameters,
are presented. In chapter five we are going to investigate the limit of the density-dependent
mixing parameter introduced by Marques et al. and derive as well as test a new approach
for a selfconsistent density-dependent mixing parameter for PBE0 and HSE06. In the following, we will present and discuss for four selected structures (silicon, diamond, germanium
and gallium arsenide) the results for the equilibrium lattice constant and the bulk modulus.
Finally, we conclude the thesis with a summary in chapter six.