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Investigation of LDA+U and hybrid functional methods on the description of the electronic structure of YTiO<sub>3</sub> under high pressure

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 YTiO<sub>3</sub> under pressure is investigated using the aforementioned approaches. The performance and reliability of these methods will be examined, compared and discussed.

Identiferoai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:SSU.etd-12042007-134843
Date06 December 2007
CreatorsSong, Zhe
ContributorsTse, John S.
PublisherUniversity of Saskatchewan
Source SetsLibrary and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://library.usask.ca/theses/available/etd-12042007-134843/
Rightsrestricted, I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to University of Saskatchewan or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report.

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