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

Viac o knihe

This thesis extends the full-potential linearized augmented-plane-wave (FLAPW) method, a highly precise and versatile electronic structure approach based on density-functional theory (DFT), to orbital-dependent functionals for exchange-correlation (xc) energy. Unlike the widely used local-density approximation (LDA) and generalized gradient approximation (GGA), orbital-dependent functionals rely directly on Kohn-Sham (KS) orbitals rather than solely on density. Two schemes for orbital-dependent functionals are realized: the KS formalism, which requires a local multiplicative xc potential, and the generalized Kohn-Sham (gKS) formalism, which accommodates a non-local potential in one-particle Schrödinger equations. Hybrid functionals, which mix orbital-dependent exact exchange energy with local or semi-local density functionals, are implemented in the gKS scheme, specifically using the PBE0 hybrid functional. The implementation involves calculating the non-local exact exchange potential through an auxiliary mixed product basis (MPB), turning the matrix elements of the Hamiltonian into a Brillouin-zone sum of vector-matrix-vector products. Various techniques are developed to enhance numerical efficiency. Results using PBE0 for different semiconductors and insulators show improved band gaps and better representation of localized states compared to experimental data. Notably, the PBE0 functional accurately describes the electronic