Investigation of LDA+U and hybrid functional methods on the description of the electronic structure of YTiO₃ under high pressure

Description

Currently, there are two main methodologies for the calculation of the electronic structure and properties of crystalline solids. Known as the Hartree-Fock Method (HF) and the Density Functional Theory (DFT) methods, they are based on two different theories for the numerical solution of the many electron Schrödinger equation. Unfortunately, in highly correlated electron systems like transition metal complexes, both the HF and DFT methods have severe shortcomings. In some cases they fail to provide the correct description of the electronic structure. <p>In general, the HF method overestimates the energy band gap due to the neglect of electron correlation effects and the incorrect description of electron interactions in the unoccupied orbitals. In contrast, even though electron correlation effects are implicitly included in the density functional, DFT often underestimates the band gap due to the improper treatment of the electron self-interaction. <p> To amend these problems, two approaches have been proposed. The deficiency in the HF scheme can be corrected using a hybrid method which adds exchange correlation energy borrowed from DFT to help reduce the band gap energy and bring the predictions in better agreement with experiment. To improve DFT, the LDA+U approach, which uses a model Hubbard-like Hamiltonian including an on-site repulsion parameter U, can be employed. This method is a convenient semi-quantitative way to efficiently calculate the band gap of insulators and semiconductors.<p> In this thesis, the electronic structure of YTiO₃ under pressure is investigated using the aforementioned approaches. The performance and reliability of these methods will be examined, compared and discussed.

Tags

DFT

band structure

Hybrid Functional Method

HF

LDA+U

Additional Fields

Identifer	oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:SSU.etd-12042007-134843
Date	06 December 2007
Creators	Song, Zhe
Contributors	Tse, John S.
Publisher	University of Saskatchewan
Source Sets	Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
Language	English
Detected Language	English
Type	text
Format	application/pdf
Source	http://library.usask.ca/theses/available/etd-12042007-134843/
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