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      • HARVEST
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      Development of Tools for the Study of Heavy-Element Containing Periodic Systems in the CRYSTAL Code and their Application

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      DESMARAIS-DISSERTATION-2020.pdf (8.276Mb)
      Date
      2020-09-17
      Author
      Desmarais, Jacques K.
      ORCID
      0000-0001-9199-1898
      Type
      Thesis
      Degree Level
      Doctoral
      Metadata
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      Abstract
      This thesis investigates the development of first-principles methods for the study of heavy-element containing periodic systems, as well as their application, in particular to crystalline lanthanide oxides. The Generalized Kohn-Sham Density Functional Theory (GKS-DFT, i.e. in which density functional approximations are built directly from KS orbitals, using so-called hybrid functionals) was shown to provide a particularly effective means to correct for self-interaction errors that plague more conventional local or semi-local formulations in a scalar-relativistic (SR) context. As such, the SR GKS-DFT scheme allowed for a detailed characterization of the electronic structure of the lanthanide sesquioxide series, and enabled (for the first time) to rationalize all known electronic and structural pressure-induced phase transitions in the prototypical strongly-correlated and mixed-valence material EuO. But the hybrid functional approach proved even more useful when developing instead fully relativistic theories and algorithms, which include not only SR effect, but also spin-dependent relativistic effects, such as spin-orbit coupling (SOC). Coincidentally, this thesis reports the first implementation for a self-consistent treatment of SOC in periodic systems with a fraction of exact non-local Fock exchange in a two- component spinor basis (2c-SCF). The numerous advantages of using such a formulation, as opposed to the more approximate treatments of previously existing implementations, are discussed. These advantages originate from the ability of the Fock exchange operator to locally rotate the magnetization of the system with respect to a starting guess configuration (local magnetic torque). In addition, the non-local Fock exchange operator permits to include in the two-electron potential the contribution of the spinors that are mapped to certain spin-blocks of the single-particle density matrix. This allows for a proper treatment of the orbital relaxation of current densities, and their coupling with the other density variables. As a result, it is shown that the lack of Fock exchange (or even its more approximate treatment in a one-component basis, as with previous implementations) from more conventional formulations of the KS-DFT means that the calculation would not allow to access the full range of time-reversal symmetry broken states. This is because, it is shown that in the absence of Fock exchange, the band structure is constrained by a sum rule, linking the one-electron energy levels at opposite points in the first Brillouin zone (kj and −kj).
      Degree
      Doctor of Philosophy (Ph.D.)
      Department
      Geological Sciences
      Program
      Geology
      Supervisor
      Pan, Yuanming; Tse, John S.; Erba, Alessandro; Civalleri, Bartolomeo
      Committee
      Ansdell, Kevin; Bowles, Richard; Ugliengo, Piero
      Copyright Date
      September 2020
      URI
      http://hdl.handle.net/10388/13055
      Subject
      ab initio methods
      rare earth elements
      lanthanides
      spin-orbit coupling
      spin-current density functional theory
      CRYSTAL program
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