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

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      Zhe_Song_Thesis_200712.pdf (2.638Mb)
      Date
      2007-12-06
      Author
      Song, Zhe
      Type
      Thesis
      Degree Level
      Masters
      Metadata
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      Abstract
      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. 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. 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. 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.
      Degree
      Master of Science (M.Sc.)
      Department
      Physics and Engineering Physics
      Program
      Physics and Engineering Physics
      Supervisor
      Tse, John S.
      Copyright Date
      December 2007
      URI
      http://hdl.handle.net/10388/etd-12042007-134843
      Subject
      DFT
      band structure
      Hybrid Functional Method
      HF
      LDA+U
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