Master Degree / Yüksek Lisans Tezleri
Permanent URI for this collectionhttps://hdl.handle.net/11147/3008
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Master Thesis Quantum Monte Carlo Study of the Multi-Orbital Anderson Model Including the Su(2) Invariant Hund's Coupling(Izmir Institute of Technology, 2018) Öztarhan, Gökhan; Bulut, NejatIn this study, an SU(2) invariant multi-orbital Anderson impurity model is discussed to obtain the electronic properties of metalloproteins. Metalloproteins are organic molecules containing transition metal atoms. They have important roles in the chemical reactions taking place in organisms. The electronic properties of metalloproteins can be modeled by an effective Anderson impurity model. The effective Anderson impurity model can be studied with the quantum Monte Carlo algorithm developed by Hirsch and Fye (1986). In the quantum Monte Carlo simulations of the Anderson impurity model so far, only the longitudinal component of the Hund’s coupling term which arises from the Coulomb interactions between the 3d orbitals is taken into account. Spin-flip and pairhopping terms (the transverse terms of the Hund’s coupling) are not considered. They are required to make the Hamiltonian SU(2) invariant, which is related to the spin rotations, so that the Hamiltonian is more realistic. The treatment of the transverse Hund’s coupling with the Hirsch-Fye algorithm has been difficult because of the problems encountered in the Trotter decomposition. Instead, a series expansion method was developed by Sakai et al. (2006). Here, we combine the Hirsch-Fye quantum Monte Carlo algorithm with the series expansion method to study the SU(2) invariant multi-orbital Anderson impurity model. Therefore, we present results from quantum Monte Carlo simulations with the new algorithm.Master Thesis Investigation of the Electronic Structure of the Ruthenium Dyes Used in Solar Cells by Combining Hartree-Fock Theory With the Quantum Monte Carlo Technique(Izmir Institute of Technology, 2015) Berkman, Irmak Çağlar; Bulut, NejatThe Haldane-Anderson model is constructed to describe the electronic properties of a system where a transition-metal impurity atom is added into a semiconductor host material. The electric and magnetic properties of the ruthenium-based dyes are investigated by using Haldane-Anderson model in this study. Because ruthenium-based dyes are semiconductor and ruthenium atom is a transition metal and its 4d orbitals are considered as impurities for dye molecules. Density Functional Theory (DFT) and Hartree-Fock Theory (HF) was used to obtain the Haldane-Anderson model parameters of the ruthenium-based dyes. Multi-orbital Hirsch-Fye Quantum Monte Carlo (HFQMC) algorithm was used to investigate effect of onsite Coulomb interactions of impurity 4d orbitals. Firstly, the Anderson model parameters are calculated by using Hartree-Fock and Density Functional Theory. After that, the occupation numbers of 4d orbitals and the all orbital occupancies of the dye molecules are obtained by using the Hirsch-Fye Quantum Monte Carlo algorithm and the magnetization of 4d orbitals are calculated. Finally, physical meaning of our results are discussed.Master Thesis Mapping of the Electronic Structure of Metalloproteins Onto Multi-Orbital Anderson Model Using the Density Functional Theory(Izmir Institute of Technology, 2013) Kandemir, Zafer; Bulut, NejatIn this thesis, an effective Haldane-Anderson model is constructed in order to describe the electronic properties of a system where a the transition-metal impurity atom is added into a semiconductor host material. Metalloenzymes and metalloproteins are proteins which contain a transition metal. Vitamin B12 is a metalloenzyme which contains a cobalt (Co) atom. The vitamin B12 exhibits semiconducting properties due to the presence of a semiconductor gap in the electronic density of states. Thus, we argue that the electronic properties of vitamin B12 can be studied within the framework of the Haldane- Anderson model. In this thesis, firstly, the electronic structure of vitamin B12, which is known as cyanocobalamin, is obtained by using the Density Functional Theory (DFT) via the Gaussian program. By using the DFT results, the energies of the host and the 3d orbitals, and the hybridization terms between them are calculated. The final Haldane- Anderson Hamiltonian is obtained by adding the onsite Coulomb repulsion at the impurity 3d orbitals. The Haldane-Anderson Hamiltonian which has been constructed in this way from the DFT results can be studied by using the exact techniques many-body physics such as quantum Monte Carlo. Perturbative mean-field treats can also be used to study this Hamiltonian. Hence, the DFT calculations presented in this thesis represent the first step of thorough investigation of metalloproteins using these techniques of many-body physics.