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.

The Electron Localization Function (ELF) measures electron localization within matter and provides insights into the nature of bonds in materials and molecules. This thesis examines the relationship between ELF and binding energy in bimolecular systems, focusing on van der Waals interactions—specifically Keesom forces, Debye forces, and London dispersion forces—which play significant roles in molecular and crystalline materials. This research addresses the challenge of accurately calculating binding energies in crystalline materials by exploring their correlation with ELF. Using Density Functional Theory (DFT) with two exchange-correlation functionals, rev-vdW-DF2 and PBE-D3(BJ), this study proposes a method for calculating binding energies in crystalline materials with promising accuracy. By analysing the ELF and its correlation with binding energies in 75 bimolecular systems, the research demonstrates a strong linear correlation, with a coefficient of determination (R2) reaching up to 0.956. The findings suggest that ELF can effectively differentiate between weak and strong van der Waals interactions, providing a reliable metric for evaluating interaction strengths. The results indicate that ELF is a valuable tool for understanding the strength of molecular interactions, with potential applications in materials science and electronic structure theory. The study highlights the importance of refining the accuracy of the ELF-based method and expanding its scope to include other types of non-covalent interactions, such as halogen bonds. The main contribution of this thesis is the exploration of methodologies for analysing and predicting molecular interaction strengths within crystalline materials, which may improve computational approaches in the field. Deriving binding energies within the unit cell directly from the ELF has the potential to simplify practical calculations.

Das „Strongly Constrained and Appropriately Normed“ (SCAN) Austausch-Korrelations-Funktional gehört zur Familie der meta-GGA (generalized gradient approximation) Funktionale. Es gibt aber auch Nachteile Zum einen leiden SCAN Rechnungen oft unter numerischen Instabilitäten, wodurch sehr viele Iteration zum Erreichen von Selbst-Konsistenz benötigt werden. Zum anderen leidet SCAN unter dem von GGA Methoden bekannten Selbstwechselwirkung-Fehler. Im ersten Teil der Arbeit habe ich die numerischen Stabilitätsprobleme in SCAN Rechnungen im Rahmen der numerischen Realraum-Integrationsroutinen im Code FHI-aims untersucht. Diese Analyse zeigt, dass die genannte Probleme durch Anwendung von standardisierten Dichte-Mischalgorithmen für die kinetische Energiedichte abgemildert werden können. Dadurch wird auch in SCAN-Rechnungen eine schnelle und stabile Konvergenz zur selbstkonsistenten Lösung ermöglicht. Im zweiten Teil der Arbeit habe ich untersucht, in welchem Rahmen sich der Selbstwechselwirkung-Fehler in SCAN mittels des von Perdew und Zunger vorgeschlagenen Selbstinteraktionskorrekturalgorithmus (PZ-SIC) verringern lässt. Es wurden aber auch Optimierungen für die PZ-SIC Methode entwickelt. Inspiriert von den ursprünglichen Argumenten in der PZ-SIC-Methode und anderen lokalisierten Methoden, wird in dieser Arbeit eine neuartige Randbedingung (orbital density constraint) vorgeschlagen, die sicherstellt, dass die PZ-SIC Orbitale während des Selbstkonsistenzzyklus lokalisiert bleiben. Dies mildert die Anfangswertabhängigkeit deutlich ab und hilft dabei, in die korrekte selbst-konsistente Lösung mit minimaler Energie zu konvergieren, unabhängig davon ob reelle oder komplexe SIC Orbitale verwendet werden. Die in dieser Arbeit getägtigen Entwicklungen und Untersuchungen sind Wegbereiter dafür, in Zukunft mit SIC-SCAN Rechnungen deutlich genauere ab initio Rechnungen mit nur gering höherem Rechenaufwand durchführen zu können. / The state-of-the-art “Strongly Constrained and Appropriately Normed” (SCAN) functional pertains to the family of meta-generalized-gradient approximation (meta-GGA) exchange-correlation functionals. Nonetheless, SCAN suffers from some well-documented deficiencies. In the first part of this thesis, I revisited the known numerical instability problems of the SCAN functional in the context of the numerical, real-space integration framework used in the FHI-aims code. This analysis revealed that applying standard density-mixing algorithms to the kinetic energy density attenuates and largely cures these numerical issues. By this means, SCAN calculations converge towards the self-consistent solution as fast and as efficiently as lower-order GGA calculations. In the second part of the thesis, I investigated strategies to alleviate the self-interaction error in SCAN calculations by using the self-interaction correction algorithm proposed by Perdew and Zunger (PZ-SIC). Inspired by the original arguments in PZ-SIC and other localized methods, I introduced a mathematical constraint, i.e., the orbital density constraint, that forces the orbitals to retain their localization throughout the self-consistency cycle. In turn, this alleviates the multiple-solutions problem and facilitates the convergence towards the correct, lowest-energy solution both for complex and real SIC orbitals. The developments and investigations performed in this thesis pave the road towards a more wide-spread use of SIC-SCAN calculations in the future, allowing more accurate predictions within only moderate increases of computational cost.

Submitted by Angela Maria de Oliveira (amolivei@uepg.br) on 2019-03-14T19:25:14Z No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Renan Augusto Pontes Ribeiro.pdf: 9570923 bytes, checksum: a291ba63c045a11cb0a642a480367e27 (MD5) / Made available in DSpace on 2019-03-14T19:25:14Z (GMT). No. of bitstreams: 2 license_rdf: 811 bytes, checksum: e39d27027a6cc9cb039ad269a5db8e34 (MD5) Renan Augusto Pontes Ribeiro.pdf: 9570923 bytes, checksum: a291ba63c045a11cb0a642a480367e27 (MD5) Previous issue date: 2019-02-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / O desenvolvimento da spintrônica tem motivado a busca por novos materiais multiferróicos devido à multifuncionalidade desses compostos associada ao acoplamento entre diferentes ordens ferróicas em uma estrutura cristalina. No presente estudo, propomos a investigação teórica, baseada na Teoria do Funcional de Densidade, dos materiais ATiO3 (A = Mn, Fe, Ni) na estrutura R3c com objetivo de esclarecer o efeito da substituição do cátion A sobre as propriedades estruturais, magnéticas e eletrônicas, bem como descrever diferentes mecanismos de controle das propriedades multiferróicas baseados em arquiteturas de filmes-finos, morfologia e controle de defeitos intrínsecos. Para uma maior compreensão dos efeitos envolvidos nos materiais ATiO3, diferentes funcionais de troca e correlação foram investigados e o funcional PBE0 apresentou os menores desvios, consequentemente, a melhor representação comparado aos resultados experimentais. Com objetivo de investigar as propriedades conectadas a filmes-finos dos materiais ATiO3, propomos uma metodologia inovadora que permite descrever as deformações uni- e biaxial que se originam na região de interface entre o filme e o substrato. Nesse caso, os resultados obtidos indicam que as distorções estruturais induzem uma transição magnética para o NiTiO3, originando ordenamento ferromagnético a partir de um critério magneto-estrutural associado a deformação dos clusters [MO6] que reproduz satisfatoriamente os resultados experimentais reportados na literatura. De modo análogo, para elucidar a relação entre o magnetismo e a morfologia dos materiais ATiO3, combinamos cálculos de Energia de Superfície, Construção de Wulff e um formalismo avançado para descrever o magnetismo superficial considerando a existência de spins não compensados ao longo dos planos polares (100), (001), (101), (012), (111) e apolares (110). Os resultados indicam que a redução do número de coordenação dos metais A e Ti para os planos (001) e (111) resulta na transferência de carga entre os cátions A2+ e Ti4+, originando espécies Ti3+ magnéticas que aumentam o magnetismo superficial ao longo desses planos. Além disso, esse efeito é capaz de induzir uma alteração do caráter eletrônico para esses materiais, permitindo indicar que a clivagem das superfícies contribui para o controle das propriedades eletrônicas, reduzindo o valor de band-gap ou gerando comportamento meio-metálico. Os mapas morfológicos obtidos indicam que o controle da exposição majoritária do plano (001) para obtenção de discos hexagonais induz um aumento do magnetismo superficial para os materiais ATiO3 em acordo com resultados experimentais, além de predizer diferentes morfologias acessíveis com interessantes propriedades magnéticas. Ademais, o efeito de defeitos intrínsecos como vacâncias de oxigênio no bulk e superfície apolar (110) dos materiais ATiO3 foi investigado indicando que a redução do número de coordenação na região do defeito induz que os elétrons remanescentes sejam localizados, principalmente, nos orbitais 3d vazios dos cátions Ti vizinhos, gerando espécies [TiO5]ꞌ e [TiO4]ꞌ (3d1 ) que possibilitam uma interação ferromagnética nos materiais MnTiO3 e FeTiO3. A combinação entre os diferentes mecanismos investigados permitiu estabelecer um guia científico para o estudo teórico de materiais multiferróicos, contribuindo para descrever as potencialidades dos diferentes materiais bem como predizer novos candidatos. / The development of spintronic has motivated the search for new multiferroic materials due to the multifunctionality of these materials that are associated with the coupling of different ferroic orders into a single crystalline structure. In the present study, we propose a theoretical investigation, based on Density Functional Theory, of ATiO3 (A = Mn, Fe, Ni) materials in the R3c structure in order to clarify the effect of A-site cation replacement on the structural, magnetic and electronic properties, as well as to describe a different mechanism to control the multiferroic properties based on thin-film architectures, morphology and point defects. For a more comprehensive overview of the main effects involved on the ATiO3 materials several exchange-correlation functionals were investigated, being the PBE0 the functional with smallest deviations and, consequently, the best representation in comparison to the experimental results. Aiming to describe the main fingerprints related with the creation of ATiO3 thin-films, we propose an innovative methodology that allows to describe the uniaxial and biaxial deformations originated in the interface region between the film and the substrate. In this case, the results indicate that structural distortions induce a magnetic transition for the NiTiO3, originating ferromagnetic ordering from magneto-structural criteria, which is associated to the deformation of the [MO6] clusters that reproduces satisfactorily the experimental results reported in the literature. Similarly, in order to elucidate the relationship between the magnetism and the morphology of the ATiO3 materials, we combined Surface Energy, Wulff Construction, and an advanced formalism to describe surface magnetism by considering the existence of uncompensated spins along the polar planes (100), (001), (101), (012), (111) and non-polar (110). The results indicate that the reduction of the coordination for both A and Ti metals along the (001) and (111) planes induces a charge transfer between the A 2+ and Ti4+ cations, resulting in magnetic Ti3+ species that increase the superficial magnetism along such planes. Moreover, this effect allowed a change in the electronic structure for these materials, allowing to point out that the cleavage of the surfaces contribute to the control of the electronic properties reducing the band-gap value or generating half-metallic behavior. The morphological maps indicated that the control of the major exposure for the (001) surface to obtain hexagonal discsinduces an increase of the superficial magnetism for the ATiO3 materials according to experimental results, besides predicting different accessible morphologies with interesting magnetic properties. In addition, the effect of intrinsic defects such as oxygen vacancies on the bulk and non-polar (110) surface of the ATiO3 materials were investigated, indicating that the reduction of coordination in the defect region induces the localization of the remaining electrons in the empty 3d orbitals of neighboring Ti cations, generating [TiO5]'and [TiO4]' (3d1 ) species that allow a ferromagnetic interaction for MnTiO3 and FeTiO3 materials. The combination of the different mechanisms investigated has allowed to stablish a scientific guide for the theoretical study of multiferroic materials, contributing to describe the potentialities of the different materials as well as to predict new candidates.