The electronic structure of perfect and defective perovskite crystals [Elektronische Ressource] : ab initio hybrid functional calculations / by Sergejs Piskunovs

The electronic structure of perfect anddefective perovskite crystals: Ab initiohybrid functional calculationsPh.D. ThesisPresented to the Department of Physicsof the University of Osnabruc¨ kbySergejs PiskunovsThesis Advisor: Prof. Dr. Gunnar BorstelOctober 2003Contents1 Introduction 12 Basic perovskite crystals: Strontium, Barium, and Lead Titanates 3Introduction................................ 32.1 Experimentalresults........................... 52.1.1 Bulkcrystals ........................... 52.1.2 Impuritydefectsinperovskites ................. 92.1.3 Surfaces..............................102.2 Previoustheoreticalresults........................142.2.1 Bulkperovskites .........................142.2.2 Point defects: SrTiO:Fe.....................1632.2.3 Calculationsonsurfaces.....................172.3 Motivation.................................183 DFT/HF formalism and methodology 21Introduction213.1 DFTformalism..............................23.1.1 Schr¨odingerequation.......................23.1.2 Total energy through the density matrices . . . . . . . . . . . 243.1.3 Hohenberg-Kohntheorems....................263.1.4 Energyfunctional.........................273.1.5 Localdensityapproximation...................293.1.6 Generalizedgradientapproximation...............33.1.7 Hybridexchangefunctionals.333.1.8 Spin-density functional theory . . . . . . . . . . . . . . . . . . 35CONTENTS ii3.2 Practical implementation of DFT/HF calculation scheme . .