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The exact exchange-correlation kernel is a functional derivative of the exact time-dependent exchange-correlation (XC) potential with respect to the time-dependent density, evaluated at the ground-state density. As the XC potential is not known, the exact kernel is also unavailable. Therefore, it must be modeled either using many-body perturbation theory or by satisfying the exact constraints for various prototype systems such as the paradigm uniform electron gas (UEG). The random phase approximation (RPA) neglects the kernel, therefore, fails to provide the accurate ground- and excited-state properties for various systems from a simple uniform electron gas to more complex periodic ones. There are numerous corrections to RPA available, including kernel-corrected RPA, often called the beyond-RPA (bRPA) methods. In this work, we employed various bRPA methods for a diverse set of systems together with RPA. At first, we applied RPA based methods to study the phase stability of the cesium halides. Cesium halides phase stability is one of the stringent tests for a density functional approximation to assess its accuracy for dispersion interaction. Experimentally, CsF prefers the rocksalt (B1) phase, while the other halides CsCl, CsBr, and CsI prefer the cesium chloride (B2) phase. Without dispersion interaction, PBE and PBE0 predict all halides to prefer the B1 phase. However, all RPA based methods predict the experimental observations. The bRPA methods usually improve the quantitative prediction over RPA for the ground-state equilibrium properties of cesium halides. Next, we explored binary intermetallic alloys, where we showed that RPA successfully predicts the accurate formation energies of weakly bonded alloys. However, a kernel corrected RPA is needed when dealing with strongly bonded alloys with partially filled d-band metals. We utilized the renormalized ALDA (rALDA) and rAPBE kernel as bRPA methods. Exact constraints and appropriate norms such as the uniform electron gas are very useful to construct various approximations for the exchange-correlation potentials in the ground-state, and the exchange-correlation kernel in the linear-response theory within the TDDFT. These mathematical formulations not only guide us to formulate more robust nonempirical methods, but they also have more predictive power. We showed the importance of these constraints by calculating plasmon dispersion of the uniform electron gas using the non-local, energy-optimized (NEO) kernel using only a few constraints. More predictive power comes with more constraint satisfaction. As a result, we developed a new wavevector- and frequency-dependent exchange-correlation kernel that satisfies all the constraints that it should satisfy with a real frequency. It gives accurate ground-state correlation energy and describes the charge density wave in low-density UEG. It also predicts an accurate plasmon dispersion with a finite lifetime at wavevectors less than the critical one, where the plasmon dispersion meets the electron-hole continuum. / Physics

Density functional theory is the most commonly used computational tool to study properties of solids and molecules. Self-interaction error, that arises due to improper cancellation of the self-Hartree and the self exchange correlation energy, has long been identified as a major limitation of practical density functional approximations. We develop and test the performance of different self-interaction corrected functionals in accurately predicting a wide range of properties. This work focuses on use of the Fermi-L\"{o}wdin orbital self-interaction correction (FLOSIC) method to study neutral water complexes and interaction of ions with water clusters. The strongly constrained and appropriately normed (SCAN) density functional approximation (DFA) has been found to give the correct energy ordering of low-lying isomers of water hexamers, resolves the density anomaly between water and ice, and improves the relative lattice energy of ice polymorphs and the infrared spectra of liquid water. However, SCAN is not without its drawbacks. The binding energies of water clusters and lattice energies of ice phases are overestimated by SCAN. We find that by explicitly removing the self-interaction error, the hydrogen-bond binding energy of water clusters can be significantly improved. In particular, self-interaction correction to the SCAN functional (FLOSIC-SCAN) improves binding energies without altering the correct energetic ordering of the low-lying water hexamers. So, orbital-by-orbital removal of self-interaction error applied on top of a proper DFA can lead to an improved description of water complexes. To gain further insight into the performance of different functionals on the relative stability of water clusters, we decompose the total interaction energy into many-body components. We see that the major portion of error in SCAN comes from the two-body interaction, and the FLOSIC-SCAN improves two-body interactions over SCAN and predicts higher-order many-body interactions with about the same accuracy as SCAN. The SCAN functional gives good account of monomer deformation energy (one-body energy), PBE estimated it too low and self-interaction corrected methods FLOSIC-PBE and FLOSIC-SCAN estimated too high monomer deformation energies. Improvement in the total interaction energy by FLOSIC-PBE and FLOSIC-SCAN is happening because of error cancellation by one-body interaction energy. Aqueous solutions of ions are of particular interest due to their profound applications in environmental chemistry, solvation mechanics, the desalination process, etc. This motivated us to study ion-water systems, which include hydronium ion-water clusters, hydroxyl ion-water clusters, halide ion-water clusters, and alkali ion-water clusters. The erroneous delocalization of the extra-electron in anions obtained with DFAs is basis-set dependent. DFAs like LSDA, PBE, or SCAN can bind only a fraction of the excess electron in the complete basis set limit, implying that a moderate-sized localized basis would be a good choice for them. But, accurate description of hydrogen bonds often requires a large basis with some extra diffuse functions. So, in negatively charged hydrogen-bonded systems like deprotonated water clusters, the suitable choice of basis-set is both difficult and ambiguous. We explore this issue systematically in this work. Further, we have found that the better performance by application of FLOSIC is seen in all systems that are connected at least with one hydrogen bond and the error in the binding energy decreases with increase in the size of an ion or equivalently decreases with the length of the hydrogen bond. Moreover, within the same ion-water system, error in the binding energy decreases with increase in the size of the cluster. Non-hydrogen-bonded water-alkali clusters are not affected by the self-interaction errors. / Physics

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

This thesis presents a means of enhancing the iterative calculation techniques used in electronic structure calculations, particularly Kohn-Sham DFT. Based on the subspace iteration method of the FEAST eigenvalue solving algorithm, this nonlinear FEAST algorithm (NLFEAST) improves the convergence rate of traditional iterative methods and dramatically improves their robustness. A description of the algorithm is given, along with the results of numerical experiments that demonstrate its effectiveness and offer insight into the factors that determine how well it performs.

<p> </p> <ol> <li>This dissertation investigates the thermodynamics and transport of vacancies and interstitials of oxygen (O) and thorium (Th) in thorium dioxide (ThO₂) with varying charge states from neutral to maximum, with respect to temperature and oxygen pressure. The study also explores the impact of varying fractions of uranium (U) as a cation (<em>y</em>) on the defect disorder in mixed oxide fuels (Th_1-<em>y</em>U_<em>y</em>O₂). Understanding the properties of point defects in these oxides lays a strong foundation, as defects influence the properties of bulk materials, such as thermal transport. To accomplish the stated objectives of this dissertation, the research is structured into three sections that employ first principles density functional theory (DFT) and phonon calculations. The first section focuses on the structure, internal energy of formation, and vibrational entropy of point defects in ThO₂. The results demonstrate that defect energetics increase with an increase in defect charge for O interstitials and Th vacancies, while the opposite is true for O vacancies and Th interstitials. The lowest internal energy of formation shifts from O vacancies of charge 2+ to O interstitials and Th vacancies at various temperature ranges of 0 to 600 K, 600 to 1300 K, and 1300 to 2000 K. The second section develops a model to calculate the defect disorder and off-stoichiometry in ThO_{2±<em>x</em>} and Th_1-<em>y</em>U_<em>y</em>O_{2±<em>x</em>}. The model shows that ThO₂ exists mainly as a hypo-stoichiometric oxide between 1200 K to 2900 K for oxygen pressures ranging from 10^-30 to 10 atm, with O defects dominating this off-stoichiometric regime. The addition of U increases the thermodynamic window over which Th_1-<em>y</em>U_<em>y</em>O2 is hyper-stoichiometric, with O vacancies dominating in the hypo-stoichiometric regime, and cation vacancies and O interstitials dominating at low and high temperatures, respectively. Specifically, at low U content and low temperatures, U vacancies dominate hyper-stoichiometry, while at high U content and low temperatures, Th vacancies are dominant. This research facilitates the comprehension of the intricate changes in structural and defect equilibria that take place during nuclear fuel irradiation, where the fuel is not in a stoichiometric condition. The third section of the dissertation investigates migration barriers and diffusivities of defects and of O and Th in ThO₂. Results indicate that the migration energy of a point defect is dependent on its charge state. The average diffusivity of O vacancies exceeds that of O interstitials, while the similar is true for Th vacancies and Th interstitials above 1650 K. The self-diffusion coefficient of O and Th increases with temperature and is influenced by oxygen pressure, showing a close agreement with experimental and molecular-dynamics-based computational data. At 1500 K, the self-diffusivity of O and Th in ThO2 is 7.47 x 10^-16 m²s^-1 and 4.48 x 10^-23 m²s^-1 , respectively, while at 2500 K, the values increase to 1.06 x 10^-12 m²s^-1  and 2.28 x 10^-17 m²s^-1 , respectively. The chemical diffusion coefficients of defects decrease initially and then plateau as the hypo-stoichiometry in the oxide increases. These findings serve as a fundamental framework for understanding the diffusion-controlled processes of defects, which affect the radiation tolerance and microstructural evolution of ThO₂ as a nuclear fuel.  </li> </ol>

Increasing energy demand draws attention to new materials for improving current energy storage technologies. Particular interest is directed at solid state batteries and glass Na3ClO electrolyte is a promising candidate. In this report we explore some of the properties of this new glass and its capabilities as a potential electrolyte for a solid-state battery. The two aims of the study were to model the amorphous structure of the glass using the stochastic quenching method based on density functional theory as well as assessing the electrochemical stability of it against a metallic sodium electrode. Using VASP, a computational code based on density functional theory, we performed calculations of two 150 atom supercells, where the atoms were moved around until the systems were relaxed to obtain two glass models and the resulting structures were analyzed and characterized. The characterization of the structures was made by means of partial radial distribution functions, angle distribution functions, coordination numbers and bond lengths, which showed that the two models are statistically equivalent and either one can be used for the stability assessment of the glass. The electrochemical stability was assessed by inserting an extra sodium atom in possible holes in the glass model and calculating the energetics of Na insertion in each of these holes. This was made for 30 different hole positions. The reduction potential indicates the stability of each hole and the results was plotted as an energy distribution. Two peaks in the energy distribution, located at positive and negative energies, indicating stable and unstable holes, respectively. This indicates that the amorphous structure of the glass allows Na ions to travel (unstable holes). The stable peak has a greater probability density, which indicates a stable electrolyte against sodium metal electrode, though a larger sampling of holes is required for better statistics. / Ökande krav på energiefterfrågan uppmärksammar nya material för att förbättra nuvarande energilagringsteknik, med fokus på solida batterier och glaset Na3ClO som en lovande kandidat för elektrolyt. I denna rapport undersöks några av egenskaperna för glaset samt möjligheten för denna att fungera som elektrolyt i ett solid-state batteri. Målen med projektet var att modellera den amorfa strukturen av glaset genom att använda stochastic quenching method som baseras på density functional theory samt undersöka den elektrokemiska stabiliteten mot en metallisk natrium elektrod. Genom användning av VASP, beräkningskoder baserade på density functional theroy, beräknades två superceller med 150 atomer vardera där atomerna flyttas runt tills dess att systemet var relaxerat och två modeller av glaset erhölls. Dessa var sedan visualiserades och karakteriserade. Karakterisering av strukturerna gjordes genom en partiella radiella fördelningsfunktioner, vinkel distrubitionsfunktioner, koordinationsnummer och bindningslängder. Detta visade på statistisk ekvivalens, vilket innebär att båda modellerna kan användas för vidare stabilitetsundersökning. Den elektrokemiska stabiliteten undersöktes genom att sätta in en extra natrium atom i möjliga hål i glas modellen samt beräkna dess energier av Na insättning i respektive hål. Detta gjordes för 30 olika positioner för hålen. Reduktionspotentialen indikerar stabiliteten för respektive hål, och resultatet plottades som en energidistribution. Två toppar i energidistributionen, lokaliserade vid positiva och negativa energier, indikerar stabila respeltive instabila hål. Detta indikerar på att den amorfa strukturen för glaset tillåter Na joner att färdas (instabila hål). Den stabila toppen har en större sannolikhetstäthet vilket indikerar på en stabil elektrolyt mot en metallisk natrium elektrod, men en större samling hål krävs för en bättre statistisk säkerhet.

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Organic π-conjugated solids are promising candidates for new optoelectronic materials. The large body of evidence points at their advantageous properties such as high charge-carrier mobility, large nonlinear polarizability, mechanical flexibility, simple and low cost fabrication and superior luminescence. They can be used as nonlinear optical (NLO) materials with large two-photon absorption (2PA) and as electronic components capable of generating nonlinear neutral (excitonic) and charged (polaronic) excitations. In this work, we investigate the appropriate theoretical methods used for the (a) prediction of 2PA properties for rational design of organic materials with improved NLO properties, and (b) understanding of the essential electronic excitations controlling the energy-transfer and charge-transport properties in organic optoelectronics. Accurate prediction of these electro-optical properties is helpful for structureactivity relationships useful for technological innovations. In Chapter 1 we emphasize on the potential use of the organic materials for these two applications. The 2PA process is advantageous over one-photon absorption for deep-tissue fluorescence microscopy, photodynamic therapy, microfabrication and optical data storage owing to the three-dimensional spatial selectivity and improved penetration depth in the absorbing or scattering media. The design of the NLO materials with large 2PA cross-sections may reduce the optical damage due to the use of the high intensity laser beams for excitation. The organic molecules also possess self-localized excited states which can decay radiatively or nonradiatively to form excitonic states. This suggests the use of these materials in the electroluminescent devices such as light-emitting diodes and photovoltaic cells through the processes of exciton formation or dissociation, respectively. It is therefore necessary to understand ultrafast relaxation processes required in understanding the interplay between the iv efficient radiative transfer between the excited states and exciton dissociation into polarons for improving the efficiency of these devices. In Chapter 2, we provide the detailed description of the various theoretical methods applied for the prediction as well as the interpretation of the optical properties of a special class of substituted PPV [poly (p-phenylene vinylene)] oligomers. In Chapter 3, we report the accuracy of different second and third order time dependent density functional theory (TD-DFT) formalisms in prediction of the 2PA spectra compared to the experimental measurements for donor-acceptor PPV derivatives. We recommend a posteriori Tamm-Dancoff approximation method for both qualitative and quantitative analysis of 2PA properties. Whereas, Agren's quadratic response methods lack the double excitations and are not suitable for the qualitative analysis of the state-specific contributions distorting the overall quality of the 2PA predictions. We trace the reasons to the artifactual excited states above the ionization threshold. We also study the effect of the basis set, geometrical constraints and the orbital exchange fraction on the 2PA excitation energies and cross-sections. Higher exchange (BMK and M05-2X) and range-separated (CAM-B3LYP) hybrid functionals are found to yield inaccurate predictions both quantitatively and qualitatively. The failure of the exchangecorrelation (XC) functionals with correct asymptotic is traced to the inaccurate transition dipoles between the valence states, where functionals with low HF exchange succeed. In Chapter 4, we test the performance of different semiempirical wavefunction theory methods for the prediction of 2PA properties compared to the DFT results for the same set of molecules. The spectroscopic parameterized (ZINDO/S) method is relatively better than the general purpose parameterized (PM6) method but the accuracy is trailing behind the DFT methods. The poor performances of PM6 and ZINDO/S methods are attributed to the incorrect description of excited-to-excited state transition and 2PA energies, respectively. The different v semiempirical parameterizations can at best be used for quantitative analysis of the 2PA properties. The ZINDO/S method combined with different orders of multi-reference configuration interactions provide an improved description of 2PA properties. However, the results are observed to be highly dependent on the specific choice for the active space, order of excitation and reference configurations. In Chapter 5, we present a linear response TD-DFT study to benchmark the ability of existing functional models to describe the extent of self-trapped neutral and charged excitations in PPV and its derivative MEH-PPV considered in their trans-isomeric forms. The electronic excitations in question include the lowest singlet (S1) and triplet (T1 † ) excitons, positive (P+ ) and negative (P- ) polarons and the lowest triplet (T1) states. Use of the long-range-corrected DFT functional, such as LC-wPBE, is found to be crucial in order to predict the physically correct spatial localization of all the electronic excitations in agreement with experiment. The inclusion of polarizable dielectric environment play an important role for the charged states. The particlehole symmetry is preserved for both the polymers in trans geometries. These studies indicate two distinct origins leading to self-localization of electronic excitations. Firstly, distortion of molecular geometry may create a spatially localized potential energy well where the state wavefunction self-traps. Secondly, even in the absence of geometric and vibrational dynamics, the excitation may become spatially confined due to energy stabilization caused by polarization effects from surrounding dielectric medium. In Chapter 6, we aim to separate these two fundamental sources of spatial localization. We observe the electronic localization of P + and Pis determined by the polarization effects of the surrounding media and the character of the DFT functional. In contrast, the self-trapping of the electronic wavefunctions of S1 and T1(T1 † ) mostly follows their lattice distortions. Geometry vi relaxation plays an important role in the localization of the S1 and T1 † excitons owing to the nonvariational construction of the excited state wavefunction. While, mean-field calculated P + , Pand T1 states are always spatially localized even in ground state S0 geometry. Polaron P+ and Pformation is signified by the presence of the localized states for the hole or the electron deep inside the HOMO-LUMO gap of the oligomer as a result of the orbital stabilization at the LCwPBE level. The broadening of the HOMO-LUMO band gap for the T1 exciton compared to the charged states is associated with the inverted bond length alternation observed at this level. The molecular orbital energetics are investigated to identify the relationships between state localization and the corresponding orbital structure. In Chapter 7, we investigate the effect of various conformational defects of trans and cis nature on the energetics and localization of the charged P + and Pexcitations in PPV and MEHPPV. We observe that the extent of self-trapping for P+ and Ppolarons is highly sensitive on molecular and structural conformations, and distribution of atomic charges within the polymers. The particle-hole symmetry is broken with the introduction of trans defects and inclusion of the polarizable environment in consistent with experiment. The differences in the behavior of PPV and MEH-PPV is rationalized based on their orbital energetics and atomic charge distributions. We show these isomeric defects influence the behavior and drift mobilities of the charge carriers in substituted PPVs.