É bem conhecido que os intervalos proibidos de energia (gaps) de sólidos semicondutores e isolantes calculados resolvendo-se a equação de Kohn-Sham (KS) com alguma aproximação ao funcional de troca e correlação (XC) da teoria do funcional da densidade (density-functional theory, DFT) são geralmente muito pequenos quando comparados com os valores de gap obtidos experimentalmente. Estes erros, que podem atingir 100%, indicam uma falha nos funcionais de troca e correlação aproximados usados na DFT. Em particular, encontrou-se que o potencial XC, obtido através da derivada do funcional de energia XC, apresenta uma descontinuidade (xc ) quando um elétron extra é adicionado. Portanto, mesmo o gap KS exato não é idêntico ao gap verdadeiro, pois pode haver uma descontinuidade no funcional XC que tem de ser adicionado ao gap KS. Este trabalho propõe uma nova abordagem matemática para o cálculo da descontinuidade do funcional XC e a correção do gap. Inicialmente, as conseqüências desta nova abordagem foram estudadas para os 36 primeiros átomos da tabela periódica (do átomo de hidrogênio, H, ao átomo de criptônio, Kr), utilizando-se para isso os funcionais LDA, GGA e também funcionais híbridos, em combinação com diversos conjuntos de base. A partir da comparação entre valores da descontinuidade calculados teoricamente e resultados prévios da descontinuidade obtidos na literatura para os átomos de lítio (Li) e berílio (Be), foram escolhidos os melhores funcionais em combinação com as melhores bases. Num segundo passo, a nova metodologia para o cálculo da descontinuidade, com os melhores funcionais e bases eleitos, foi aplicada ao cálculo de fragmentos de poliacetileno. / It is well-known that the energy gaps of insulators and semiconductors calculated via the Kohn-Sham (KS) scheme with some approximation to the exchange-correlation (XC) functional of density-functional theory (DFT) are in general too small when compared to experimental gaps. These errors, which can be up to 100%, indicate a fault in the approximate exchange-correlation functionals currently available in DFT. Specifically, it was found that the XC potential, the functional derivative of the XC energy, shows a discontinuity (xc ) when an electron is added. Therefore, the exact KS gap is not identical to true gap, since there can be a discontinuity in the XC functional which should be added to KS gap. The present work proposes a new mathematical approach to the calculation of the discontinuity of the XC functional and the correction of the gap. In a first step, the consequences of this new approach were studied for the first 36 atoms of the periodic table (from Hydrogen, H, to Krypton, Kr), with the LDA and GGA functionals and also some hybrids, in combination with several kinds of basis set. From the comparison between calculated discontinuity values and previous results for the discontinuity reported in the literature for the Lithium (Li) and Beryllium (Be) atoms, the best functionals in combination with the best basis set were selected. In a second step, the new methodology with the best functionals/basis set was applied to the calculation of energy gaps of polyacetylene fragments.

É bem conhecido que os intervalos proibidos de energia (gaps) de sólidos semicondutores e isolantes calculados resolvendo-se a equação de Kohn-Sham (KS) com alguma aproximação ao funcional de troca e correlação (XC) da teoria do funcional da densidade (density-functional theory, DFT) são geralmente muito pequenos quando comparados com os valores de gap obtidos experimentalmente. Estes erros, que podem atingir 100%, indicam uma falha nos funcionais de troca e correlação aproximados usados na DFT. Em particular, encontrou-se que o potencial XC, obtido através da derivada do funcional de energia XC, apresenta uma descontinuidade (xc ) quando um elétron extra é adicionado. Portanto, mesmo o gap KS exato não é idêntico ao gap verdadeiro, pois pode haver uma descontinuidade no funcional XC que tem de ser adicionado ao gap KS. Este trabalho propõe uma nova abordagem matemática para o cálculo da descontinuidade do funcional XC e a correção do gap. Inicialmente, as conseqüências desta nova abordagem foram estudadas para os 36 primeiros átomos da tabela periódica (do átomo de hidrogênio, H, ao átomo de criptônio, Kr), utilizando-se para isso os funcionais LDA, GGA e também funcionais híbridos, em combinação com diversos conjuntos de base. A partir da comparação entre valores da descontinuidade calculados teoricamente e resultados prévios da descontinuidade obtidos na literatura para os átomos de lítio (Li) e berílio (Be), foram escolhidos os melhores funcionais em combinação com as melhores bases. Num segundo passo, a nova metodologia para o cálculo da descontinuidade, com os melhores funcionais e bases eleitos, foi aplicada ao cálculo de fragmentos de poliacetileno. / It is well-known that the energy gaps of insulators and semiconductors calculated via the Kohn-Sham (KS) scheme with some approximation to the exchange-correlation (XC) functional of density-functional theory (DFT) are in general too small when compared to experimental gaps. These errors, which can be up to 100%, indicate a fault in the approximate exchange-correlation functionals currently available in DFT. Specifically, it was found that the XC potential, the functional derivative of the XC energy, shows a discontinuity (xc ) when an electron is added. Therefore, the exact KS gap is not identical to true gap, since there can be a discontinuity in the XC functional which should be added to KS gap. The present work proposes a new mathematical approach to the calculation of the discontinuity of the XC functional and the correction of the gap. In a first step, the consequences of this new approach were studied for the first 36 atoms of the periodic table (from Hydrogen, H, to Krypton, Kr), with the LDA and GGA functionals and also some hybrids, in combination with several kinds of basis set. From the comparison between calculated discontinuity values and previous results for the discontinuity reported in the literature for the Lithium (Li) and Beryllium (Be) atoms, the best functionals in combination with the best basis set were selected. In a second step, the new methodology with the best functionals/basis set was applied to the calculation of energy gaps of polyacetylene fragments.

Simulações de propriedades de estrutura eletrônica possuem fundamental importância para a física do estado sólido e química quântica. A teoria do funcional da densidade (DFT) é atualmente o método de estrutura eletrônica mais empregado, desde escalas atômicas e nanoscópicas até aglomerados biomoleculares. A acurácia da DFT depende essencialmente de aproximações para os efeitos de troca e correlação, para as quais existem vínculos a serem satisfeitos como forma de controlar sua construção. Esse é um tópico de grande importância, pois a construção de melhores funcionais é necessária para uma descrição cada vez mais precisa dos efeitos de muitos corpos na DFT. No presente trabalho, investigamos o comportamento da energia de troca e correlação e o desenvolvimento de funcionais aproximados sob a ótica de um vínculo universal de sistemas de interação Coulombiana, o limite inferior de Lieb-Oxford. Primeiramente apresentamos evidências de que em diversas classes de sistemas a energia de troca e correlação é distante do limite de Lieb-Oxford. A redução do limite foi implementada nos funcionais Perdew-Burke-Erzenhof (PBE), porém a forma com que o vínculo é implementado apenas aumentou a energia de troca. Propusemos em seguida que o limite de Lieb-Oxford não fosse utilizado apenas para determinar o valor de um parâmetro, como em PBE, mas que fosse ponto-de-partida de uma nova forma família de funcionais, do tipo hiper-GGA. Exploramos uma construção não-empírica, com implementação pós-autoconsistente. A particular forma proposta se beneficiou da redução do limite Lieb-Oxford, obtendo resultados satisfatórios para as energias de correlação. / Electronic-structure calculations play a fundamental role in solid-state physics and quantum chemistry. Density-functional theory (DFT) is today the most-widely used electronic-structure method, from atomic and nanoscopic scales to biomolecular aggregates. The accuracy of DFT depends essentially on approximations to the exchange and correlation energy, which are controlled by exact constraints. This is a very important issue, since the improvement of functionals is the key to a better description of many-body effects. In the present work, we investigate the exchange-correlation energy and approximate functionals from the viewpoint of an universal constraint on interacting Coulomb systems: the Lieb-Oxford lower bound. Initially we present evidence that for several classes of systems (atoms, ions, molecules and solids), the actual exchange-correlation energies are far from the Lieb-Oxford lower bound. A tighter form of this bound was conjectured; implemented in the Perdew-Burke-Erzenhof (PBE) functionals, and tested for atoms, molecules and solids. Finally, we propose to use the Lieb-Oxford bound not just to fix the value of a parameter as in PBE, but as a starting point for a new family of hyper-GGA functionals. For these, we explored a non-empirical construction, investigating its performance for atoms and small molecules post-selfconsistently. The particular HGGA proposed benefited from the tightening of the Lieb-Oxford bound and exhibited satisfactory correlation energies.

Simulações de propriedades de estrutura eletrônica possuem fundamental importância para a física do estado sólido e química quântica. A teoria do funcional da densidade (DFT) é atualmente o método de estrutura eletrônica mais empregado, desde escalas atômicas e nanoscópicas até aglomerados biomoleculares. A acurácia da DFT depende essencialmente de aproximações para os efeitos de troca e correlação, para as quais existem vínculos a serem satisfeitos como forma de controlar sua construção. Esse é um tópico de grande importância, pois a construção de melhores funcionais é necessária para uma descrição cada vez mais precisa dos efeitos de muitos corpos na DFT. No presente trabalho, investigamos o comportamento da energia de troca e correlação e o desenvolvimento de funcionais aproximados sob a ótica de um vínculo universal de sistemas de interação Coulombiana, o limite inferior de Lieb-Oxford. Primeiramente apresentamos evidências de que em diversas classes de sistemas a energia de troca e correlação é distante do limite de Lieb-Oxford. A redução do limite foi implementada nos funcionais Perdew-Burke-Erzenhof (PBE), porém a forma com que o vínculo é implementado apenas aumentou a energia de troca. Propusemos em seguida que o limite de Lieb-Oxford não fosse utilizado apenas para determinar o valor de um parâmetro, como em PBE, mas que fosse ponto-de-partida de uma nova forma família de funcionais, do tipo hiper-GGA. Exploramos uma construção não-empírica, com implementação pós-autoconsistente. A particular forma proposta se beneficiou da redução do limite Lieb-Oxford, obtendo resultados satisfatórios para as energias de correlação. / Electronic-structure calculations play a fundamental role in solid-state physics and quantum chemistry. Density-functional theory (DFT) is today the most-widely used electronic-structure method, from atomic and nanoscopic scales to biomolecular aggregates. The accuracy of DFT depends essentially on approximations to the exchange and correlation energy, which are controlled by exact constraints. This is a very important issue, since the improvement of functionals is the key to a better description of many-body effects. In the present work, we investigate the exchange-correlation energy and approximate functionals from the viewpoint of an universal constraint on interacting Coulomb systems: the Lieb-Oxford lower bound. Initially we present evidence that for several classes of systems (atoms, ions, molecules and solids), the actual exchange-correlation energies are far from the Lieb-Oxford lower bound. A tighter form of this bound was conjectured; implemented in the Perdew-Burke-Erzenhof (PBE) functionals, and tested for atoms, molecules and solids. Finally, we propose to use the Lieb-Oxford bound not just to fix the value of a parameter as in PBE, but as a starting point for a new family of hyper-GGA functionals. For these, we explored a non-empirical construction, investigating its performance for atoms and small molecules post-selfconsistently. The particular HGGA proposed benefited from the tightening of the Lieb-Oxford bound and exhibited satisfactory correlation energies.

O presente trabalho é um estudo sobre a importância da informação dos orbitais atômicos no cálculo de propriedades optoeletrônicas de heteroestruturas semicondutoras de baixa dimensionalidade. O trabalho é dividido em duas partes: na primeira parte, é estudada a simetria de reversão temporal no hamiltoniano k . p, analisando a preservação da informação de spin presente nos orbitais atômicos. O hamiltoniano obtido é inserido na equação de massa efetiva expandida para superredes. São calculadas estruturas de bandas de alguns poços quânticos de semicondutores III-V e grupo-IV. Compara-se o novo método com os tradicionais, e então são analisadas algumas grandezas que apresentam alteração significativa entre os métodos usados; A segunda parte é composta por um estudo detalhado do potencial de troca-correlação em semicondutores dopados. A matriz que descreve este potencial é escrita usando a distribuição de portadores presentes nos orbitais atômicos da rede cristalina, e os coeficientes desta matriz foram calculados usando quatro modelos para a correção de muitos corpos, baseadas nas aproximações LDA (Local density approximation) e LSDA (Local spin density approximation), com o objetivo de comparar as diversas parametrizações. Usando o método k . p tradicional, expandido para superredes, foram simulados sistemas δ-doped e hMni-δ-doped de Si, através de um cálculo autoconsistente baseado na equação de Poisson. A magnetização dos portadores é descrita por um modelo de campo médio. Foram analisados os perfis de potencial, estruturas de bandas, polarização de portadores e espectros de fotoluminescência para determinar as diferenças entre as aproximações utilizadas. / This work is a study about the atomic orbitals information importance in the calculation of optoelectronics properties of low dimensionality semiconductors. The work is divided in two parts. In the first one, a study of the time reversal symmetry of the k . p Hamiltonian is realized analyzing the preservation of the spin information present in the atomic orbitals. The obtained Hamiltonian is applied in the effective mass equation expanded to superlattices. Some calculations of quantum wells band structures are made using III-V and group-IV semiconductors, comparing the new method with the conventional ones to obtain an analysis of the difference of some physics properties. The second part is a detailed study of the exchangecorrelation potential in doped semiconductors. The matrix coefficients are calculated using the charge distribution of the crystalline lattice atomic orbitals, applied in some LDA (Local density approximation) and LSDA (Local spin density approximation) parameterizations to compare them. Using the conventional k . p method expanded to superlattices, Si δ-doped and hMni-δ-doped systems were calculated through a self consistent calculation based on Poissons equation. The carriers magnetization is described by an average field model. The potential profiles, band structures, carrier polarization and photoluminescence spectra were analyzed to obtain the difference between the approaches.

La thèse présente une étude dans le cadre de la conception ab initio de nouveaux matériaux, avec des applications aux alliages intermétalliques et semi-conducteurs, aux oxydes transparents conducteurs et aux solides moléculaires. Des simulations avec la méthode Minima Hopping combinée avec la théorie de la fonctionnelle de la densité ont été utilisées pour trouver des nouveaux composés dans les diagrammes de phase des composés binaires de Lithium-Aluminium et Sodium-Or, aussi bien que des géométries de faible symétrie de CuBO2 à plus basses énergies que la structure delafossite qui était considérée comme son état fondamental. Nous avons aussi couplé la méthode Minima Hopping et la recherche de structures avec prototypes pour trouver de nouvelles perovskites de nitrure. Egalement, nous avons trouvé que la molécule H3 peut être stabilisée dans des structures à cages de CI à pressions d'environ 100 GPa. Nous avons aussi étudié les propriétés électroniques des alliages de chalcopyrite Cu(In, Ga)S2. Dans un sujet plus fondamental, nous proposons une fonctionnelle d'échange-corrélation semi-empirique optimisée pour obtenir des énergies de formation plus précises pour les solides / In this work we present an ab initio materials design study of several systems covering intermetallic and semiconducting alloys, transparent conductive oxides and molecular solids. We performed Minima Hopping calculations combined with Density Functional Theory that made possible to unveil several stable compounds in the phase diagrams of lithium-aluminium and sodium-gold binary alloys, as well as low-symmetry geometries of CuBO2, significantly lower in energy than the controversial delafossite structure reported as its ground state. We also found that the H3 molecule can be stabilized inside Cl cages at pressures of around 100 GPa. Additionally, we combined high-throughput techniques and global structure prediction methods to find nitride perovskites structures. In a different line, we studied the change in the absorption properties of the Cu(In,Ga)S2 chalcopyrite alloys as it was unexpectedly observed in experiment that with the change of the In/Ga ratio, the S K-absorption edge shifts, while the absorption edges of the other species is largely independent of the composition. In a more fundamental chapter, we propose a semi empirical exchange correlation functional optimized to yield accurate energies of formation of solids. The manuscript is organized as follows

O presente trabalho é um estudo sobre a importância da informação dos orbitais atômicos no cálculo de propriedades optoeletrônicas de heteroestruturas semicondutoras de baixa dimensionalidade. O trabalho é dividido em duas partes: na primeira parte, é estudada a simetria de reversão temporal no hamiltoniano k . p, analisando a preservação da informação de spin presente nos orbitais atômicos. O hamiltoniano obtido é inserido na equação de massa efetiva expandida para superredes. São calculadas estruturas de bandas de alguns poços quânticos de semicondutores III-V e grupo-IV. Compara-se o novo método com os tradicionais, e então são analisadas algumas grandezas que apresentam alteração significativa entre os métodos usados; A segunda parte é composta por um estudo detalhado do potencial de troca-correlação em semicondutores dopados. A matriz que descreve este potencial é escrita usando a distribuição de portadores presentes nos orbitais atômicos da rede cristalina, e os coeficientes desta matriz foram calculados usando quatro modelos para a correção de muitos corpos, baseadas nas aproximações LDA (Local density approximation) e LSDA (Local spin density approximation), com o objetivo de comparar as diversas parametrizações. Usando o método k . p tradicional, expandido para superredes, foram simulados sistemas δ-doped e hMni-δ-doped de Si, através de um cálculo autoconsistente baseado na equação de Poisson. A magnetização dos portadores é descrita por um modelo de campo médio. Foram analisados os perfis de potencial, estruturas de bandas, polarização de portadores e espectros de fotoluminescência para determinar as diferenças entre as aproximações utilizadas. / This work is a study about the atomic orbitals information importance in the calculation of optoelectronics properties of low dimensionality semiconductors. The work is divided in two parts. In the first one, a study of the time reversal symmetry of the k . p Hamiltonian is realized analyzing the preservation of the spin information present in the atomic orbitals. The obtained Hamiltonian is applied in the effective mass equation expanded to superlattices. Some calculations of quantum wells band structures are made using III-V and group-IV semiconductors, comparing the new method with the conventional ones to obtain an analysis of the difference of some physics properties. The second part is a detailed study of the exchangecorrelation potential in doped semiconductors. The matrix coefficients are calculated using the charge distribution of the crystalline lattice atomic orbitals, applied in some LDA (Local density approximation) and LSDA (Local spin density approximation) parameterizations to compare them. Using the conventional k . p method expanded to superlattices, Si δ-doped and hMni-δ-doped systems were calculated through a self consistent calculation based on Poissons equation. The carriers magnetization is described by an average field model. The potential profiles, band structures, carrier polarization and photoluminescence spectra were analyzed to obtain the difference between the approaches.

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

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

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.