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<p>Using field theoretical methods models of strongly correlated electrons have been investigated. Application to electronic structure calculations has been made.</p><p>In this thesis an attempt is made to build a bridge between first-principle band structure calculations and a theory of systems with strongly correlated electrons, by making use of perturbation theory from the atomic limit. Analyzing the total non-relativistic Hamiltonian leads to the basic model of strongly correlated systems, the Hubbard-Anderson model. In this thesis these basic models have been tested. Conclusions on delocalization and many-body aspects have been extracted from the solutions. Specifically for the lanthanides a separation of the f-system into two subsystems has resolved the discrepancy between calculated equilibrium volumes and experimental ones. The calculations are done within the Hubbard-I approximation, where it is possible to define renormalized fermion operators. The calculation is a true many-body calculation.</p><p>Using perturbation theory a set of self consistent equations has been formulated, and solved, for praseodymium metal using the periodical Anderson model. The solution shows a self consistent decrease of the Hubbard U, and delocalization of the f-shell, when crucial parameters of the model are changed. The most salient feature of the models for strongly correlated electrons is the transfer of spectral weight from one energy region to another by adjusting pressure or other external parameters. The effects come from kinematic interactions that are important for strongly correlated systems.</p><p>Investigations of the degenerate Hubbard model applied to the metal to insulator transition has also been made. When the degeneracy is considered, the transition to the metallic state occurs at smaller Coulomb energies. </p><p>The validity of the Fermi liquid description for strongly correlated electrons has also been studied. The results show that the general behavior of the Fermi liquid state is quite robust.</p>

Using field theoretical methods models of strongly correlated electrons have been investigated. Application to electronic structure calculations has been made. In this thesis an attempt is made to build a bridge between first-principle band structure calculations and a theory of systems with strongly correlated electrons, by making use of perturbation theory from the atomic limit. Analyzing the total non-relativistic Hamiltonian leads to the basic model of strongly correlated systems, the Hubbard-Anderson model. In this thesis these basic models have been tested. Conclusions on delocalization and many-body aspects have been extracted from the solutions. Specifically for the lanthanides a separation of the f-system into two subsystems has resolved the discrepancy between calculated equilibrium volumes and experimental ones. The calculations are done within the Hubbard-I approximation, where it is possible to define renormalized fermion operators. The calculation is a true many-body calculation. Using perturbation theory a set of self consistent equations has been formulated, and solved, for praseodymium metal using the periodical Anderson model. The solution shows a self consistent decrease of the Hubbard U, and delocalization of the f-shell, when crucial parameters of the model are changed. The most salient feature of the models for strongly correlated electrons is the transfer of spectral weight from one energy region to another by adjusting pressure or other external parameters. The effects come from kinematic interactions that are important for strongly correlated systems. Investigations of the degenerate Hubbard model applied to the metal to insulator transition has also been made. When the degeneracy is considered, the transition to the metallic state occurs at smaller Coulomb energies. The validity of the Fermi liquid description for strongly correlated electrons has also been studied. The results show that the general behavior of the Fermi liquid state is quite robust.

Intermolecular potential energy functions for CO2 have been developed from first principles for use in heterogeneous systems, including one with explicit polarization. The intermolecular potentials have been expressed in a transferable form and parameterized from nearly exact electronic structure calculations. Models with and without explicit many-body polarization effects, known to be important in simulation of interfacial processes, are constructed. The models have been validated on pressure-density isotherms of bulk CO2 and adsorption in three metal-organic framework (MOF) materials. The present models appear to offer advantages over high quality fluid/liquid state potentials in describing CO2 interactions in interfacial environments where sorbates adopt orientations not commonly explored in bulk fluids. Thus, the nonpolar CO2-PHAST and polarizable CO2-PHAST* potentials are recommended for materials/interfacial simulations.

In electronic structure calculations the computational cost is of great importance because large systems can contain a huge number of electrons. One effective method to make such calculations is by density matrix purification. Although, the cost for this method is relatively low compared to other existing methods there is room for improvements. In this paper one method proposed by Emanuel Rubensson and one method proposed by Jaehoon Kim &amp; Yousung Jung was compared to each other with respect to efficiency, simplicity and robustness. Both are improved methods to compute the density matrix by accelerated polynomial expansion. Rubensson’s method consists of two different algorithms and results showed that both performed better than Kim &amp; Jung’s method in terms of efficiency, which is the property both methods directs their main focus on. The major differences between them was identified in terms of adaptivity. The methods require different inputs that demands separate levels of knowledge about the system. Kim &amp; Jung’s method which require less knowledge can however benefit efficiency-wise from more information in order to optimize the algorithm for the system. Results also showed that both methods were stable, but since they only were tested with arbitrarily assumed input arguments no conclusion about their general stability could be drawn.

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Thermoelectric semiconductors can convert temperature differences into electricity or electricity into temperature differences. This offers great potential for the use of wasted heat or cooling. These materials can be used in a variety of fields, from healthcare to space exploration. The effectiveness of the materials is evaluated by their thermoelectric properties such as the Seebeck coefficient, electrical conductivity, and thermal conductivity. The aim of this PhD thesis is to investigate the electronic structure using first-principle methods for potential thermoelectric applications. Materials of interest include Copper and Tin based ternary /quaternary compounds, and monolayers of SnS2, SnSe2 and Janus SnSSe. Density functional theory, ab initio molecular dynamics and Boltzmann transport theory are used to study the electronic and phonon transport properties. In the first part of the thesis, electronic structure calculations were performed on both monoclinic and disordered cubic forms of Cu2SnS3(CTS). The impact of structural disorder on thermoelectric properties was examined through these simulations. The results, obtained through first-principle calculations, revealed the existence of band tails in the electronic density of states for the disordered structure, and low-lying optical modes in the disordered cubic structure. This was found to be caused by a significant variation in Sn bonding, leading to strong anharmonicity as measured by the Grüneisen parameter. The findings from the first principle calculations were supported by Nuclear inelastic scattering experiments. Furthermore, the effect of grain size on Cu2SnS3 was studied using first-principles calculations on various ordered and disordered surfaces. The density of states (DOS) revealed that the surface of CTS is conductive due to the presence of dangling bonds. Furthermore, calculations of the formation energy showed that the stoichiometric CTS, Cu-vacant and Cu-rich systems are energetically more favourable, while the formation of Sn-vacant and Sn-rich systems is less likely. In the subsequent study, the impact of Ag substitution at the Sn site at various concentrations was investigated. The Fermi level for Ag-substituted systems was found to lie deep within the valence band, with the shift of the Fermi level inside the valence band increasing with substitution increasing the carrier concentration. The incorporation of Ag into the system decreases the root mean squared displacement of the other cations and anions, which reduces the scattering of phonons and thereby increases the lattice thermal conductivity. A comparative study of various polymorphs of CTS, Cu2ZnSnS4 and Cu2ZnSnSe4 was done. Ab-initio molecular dynamics was performed on CTS, CZTS and CZTSe. The root mean squared displacement value for the disordered polymorph was higher than for the ordered phase, indicating increased static disorder. This corresponds to the static (temperature-independent) distortion of the crystalline lattice due to the disorder of the cations and is associated with higher anharmonicity and bond inhomogeneity in the disordered phase, which is then directly responsible for the ultra-low thermal conductivity. In the final part of the thesis, thermoelectric properties of dichalcogenide monolayer of SnS2, SnSe2 and Janus SnSSe was performed. Density functional theoretical calculations points out the hexagonal Janus SnSSe monolayer as a potential high-performing thermoelectric material. Results for the Janus SnSSe monolayer show an ultra-low thermal conductivity originating from the low group velocity of the low-lying optical modes, leading to superior zT values of 0.5 and 3 at 300 K and 700 K for the p-type doping, respectively. The successful calculation of properties for materials shows that the computational work done in this thesis can be used for further research into thermoelectricity.

Developments are made on the quantum Monte Carlo methods towards increasing the precision and the stability of the non fixed-node projector calculations of fermions. In the first part of the developments, the wavefunction correction scheme, which was developed to increase the precision of the diusion Monte Carlo (DMC) method, is applied to non fixed-node DMC to increase the precision of such fermion calculations which do not have nodal error. The benchmark calculations indicate a significant decrease of statistical error due to the usage of the correction scheme in such non fixed-node calculations. The second part of the developments is about the modifications of the wavefunction correction scheme for having a stable non fixed-node DMC algorithm for fermions. The minus signed walkers of the non fixed-node calculations are avoided by these modifications in the developed stable algorithm. However, the accuracy of the method decreases, especially for larger systems, as a result of the discussed modifications to overcome the sign instability.

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