The Kohn-Sham density functional theory (KS-DFT) finds an approximate solution for the many-electron problem for the ground state energy and density by solving the self-consistent one-electron Schr\"{o}dinger equations. KS-DFT would be an exact theory if we could find the precise form of exchange-correlation energy $(E_{xc})$. However, this would not be computationally feasible. The density functional approximations (DFAs) are designed to be exact in the limit of uniform densities. They require a parametrization of the correlation energy per electron $(\varepsilon_c)$ of the uniform electron gas (UEG). These DFAs take the parametrizations of correlation energy as their input since the exact analytical form of $\varepsilon_c$ is still unknown. Almost all the DFAs of higher rungs of Jacob's ladder employ an additional function on top of $\varepsilon_c$ for approximating their correlation energy. Exchange energies in these DFAs are also approximated by applying an enhancement factor to the exchange energy per electron of the UEG. Exchange-correlation energy is the glue that holds the atoms and molecules together. The correlation energy is an important part of ``nature's glue" that binds one atom to another, and it changes significantly when the bonding of the molecule changes. It is a measure of the effect of Coulomb repulsion due to electronic mutual avoidance and is necessarily negative. We compared three parametrizations of the correlation energy per electron of the uniform electron gas to the original and the corrected density parameter interpolation (DPI), which is almost independent of QMC input, and with the recent QMC of Spink \textit{et al.}, which extends the Ceperley-Alder results to fractional spin polarization and higher densities or smaller Seitz radius $r_s$. These three parametrizations are Perdew-Zunger or PZ 1981, Vosko-Wilk-Nusair or VWN 1980, and Perdew-Wang or PW 1992. The three parametrizations (especially the sophisticated PW92) are closer to the constraint satisfying DPI and are very close to the high-density limit rather than the QMC results of Spink \textit{et al.}. These DFAs suffer from self-interaction error (SIE) which arises due to an imperfect cancellation of self-Hartree energy by self-exchange-correlation energy of a single fully occupied orbital. The self-interaction correction (SIC) method introduced by Perdew and Zunger (PZ) in 1981 to remove the SIE encounters a size-extensivity problem when applied to the Kohn-Sham (KS) orbitals. Hence, we make use of Fermi L\"owdin orbitals (FLO) for applying the PZ-SIC to the density functional approximations (DFAs). FLOs are the unitary transformation of the KS orbitals localized at the Fermi orbital descriptor (FOD) positions and then orthonormalized using L\"owdin's symmetric method. The PZ-SIC makes any approximation exact only in the region of one-electron density and no correction if applied to the exact functional. But it spoils the slowly varying (in space) limits of the uncorrected approximate functionals, where those functionals are right by construction. Hence, scaling of PZ-SIC is required such that it remains intact in the region of one-electron density and scales down in the region of many-electron densities. The PZ-SIC improves the performance of DFAs for the properties that involve significant SIE, as in stretched bond situations, but overcorrects for equilibrium properties where SIE is insignificant. This overcorrection is often reduced by LSIC, local scaling of the PZ-SIC to the local spin density approximation (LSDA). We propose a new scaling factor to use in an LSIC-like approach that satisfies an additional important constraint: the correct coefficient of Z in the asymptotic expansion of the $E_{xc}$ for atoms of atomic number Z, which is neglected by LSIC. LSIC and LSIC+ are scaled by functions of the iso-orbital indicator $z_{\sigma}$ that distinguishes one-electron regions from many-electron regions. LSIC+ applied to LSDA works better than LSDA-LSIC and the Perdew, Burke, and Ernzerhof (PBE) generalized gradient approximation (GGA) and gives comparable results to the strongly constrained and appropriately normed (SCAN) meta-GGA in predicting the total energies of atoms, atomization energies, barrier heights, ionization potentials, electron affinities, and bond-length of molecules. LSDA-LSIC and LSDA-LSIC+ both fail to predict interaction energies involving weaker bonds, in sharp contrast to their earlier successes. It is found that more than one set of localized SIC orbitals can yield a nearly degenerate energetic description of the same multiple covalent bonds, suggesting that a consistent chemical interpretation of the localized orbitals requires a new way to choose their Fermi orbital descriptors. A spurious correction to the exact functional would be found unless the self-Hartree and exact self-exchange-correlation terms of the PZ-SIC energy density were expressed in the same gauge. Therefore, LSIC and LSIC+ are applied only to LSDA since only LSDA has the exchange-correlation (xc) energy density in the gauge of the Hartree energy density. The transformation of energy density that achieves the Hartree gauge for the exact xc functional can be applied to approximate functionals. The use of this compliance function guarantees that scaled-down self-interaction correction (sdSIC) will make no spurious non-zero correction to the exact functional and transforms the xc energy density into the Hartree gauge. We start from the interior scaling of PZ-SIC and end at exterior scaling after the gauge transformation. SCAN-sdSIC evaluated on SCAN-SIC total and localized orbital densities is applied to the highly accurate SCAN functional, which is already much better than LSDA. Hence, the predictive power of SCAN-sdSIC is much better, even though it is scaled by $z_\sigma$ too. It provides good results for several ground state properties discussed here, including the interaction energy of weakly bonded systems. SCAN-sdSIC leads to an acceptable description of many equilibrium properties, including the dissociation energies of weak bonds. However, sdSIC fails to produce the correct asymptotic behavior $-\frac{1}{r}$ of xc potential. The xc potential as seen by the outermost electron will be $\frac{-X_{HO}^{sd}}{r}$ where HO labels the highest occupied orbital and hence doesn't guarantee a good description of charge transfer. The optimal SIC that remains to be developed might be PZ-SIC evaluated on complex Fermi-L\"owdin orbitals (with nodeless orbital densities) and Fermi orbital descriptors chosen to minimize a measure of the inhomogeneity of the orbital densities. / Physics

Modeling and analysing materials with theoretical tools is of great use when finding new systems for applications, for example, semiconductors with point defects can be used for quantum applications, like single photon emitters. One important aspect to consider symmetry, which can yield useful information about the properties of a system. To perform symmetry analysis, a code was developed that takes the orbitals of atomic structures, as calculated with Density Functional Theory simulations, as input. Specifically, the orbitals of molecules, and defects in solids are in focus. The symmetry analysis code calculates overlap of orbitals and their symmetry transformed counterpart, maps these overlaps to characters, finds the irreducible representations, and also finds which optical transitions are allowed. The code was tested on CH4 and SF6 molecules, and the divacancy defect in 4H-SiC. The symmetry analysis is performed easily and produces results that coincide well with other theoretical results. Furthermore, symmetry matrices can be approximated to be integer matrices, and the wave functions can be approximated with less accurate plane wave expansions by reducing the cutoff energy, and thus reducing the number of plane waves. These approximations shorten the calculation time and do not compromise the accuracy of the overlap. The code automates the symmetry analysis and is intended to be used in a high-throughput manner. / <p>2021-10-12          </p><p>The student thesis was first published online. </p><p>2022-02-25          </p><p>The student thesis was updated with an errata list which is downloadable from the permanent link.</p>

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

No description available.

The design of series-loaded resonant converters using the state of the art SiC power transistorsis investigated in the thesis. SiC devices are chosen as they offer lower switching losses comparedto conventional Si based devices A very detailed study about the working and differentmodes of operation of the resonant converter is carried out. The thesis further explains how thehigh speed switching capabilities of the SiC devices remain untapped owing to the presence ofstray inductances in the switch-snubber layout. A comparison of all the commercially availableSiC devices are carried out to find the most suitable switch for the resonant converter. Thethesis also carries out a very detailed step by step design of the circuit and the PCB layout forthe resonant converter. Two different layouts are proposed and then compared for their strayinductance and power losses. Finally, based on the experiments the thesis validates the suitabilityof using discrete SiC power transistors in place of power modules. / Utformningen av serie-belastade resonansomvandlare med hjälp av toppmoderna SiC högeffekttransistorernaundersöks i denna avhandlingen. SiC-enheter väljs eftersom de erbjuderlägre switch-förluster jämfört med konventionella Si-baserade enheter.En mycket detaljeradstudie om funktionen och de olika operationella tillstånden hos resonansomvandlare utförs.Avhandlingen förklarar vidare hur förmågan till högfrekvent switchning hos SiC-enheterförblir ofullständigt utnyttjad på grund av förekomsten av ströinduktanser i switch-snubberlayouten.En jämförelse av alla kommersiellt tillgängliga SiC-enheter genomförs för att hittaden mest lämpliga switchen för resonansomvandlaren. Avhandlingen utförs också en mycketdetaljerad steg-för-steg-utformning av resonansomvandlaren kretsschema och kretskortlayout.Två olika layouter föreslås och jämförs därefter utifrån deras ströinduktanser ocheffektförluster. Slutligen, baserat på experimentella resultat bekräftar avhandlingen.Lämpligheten att använda diskreta SiC-effekttransistorer istället för effektmoduler medintegrerade drivarsteg för styrelektroderna.