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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.