In dieser Arbeit werden verschiedene Ansätze untersucht, um Tensorzerlegungsmethoden auf die Full-Configuration-Interaction-Methode (FCI) anzuwenden. Das Ziel dieser Ansätze ist es, zuverlässig konvergierende Algorithmen zu erstellen, welche es erlauben, die Wellenfunktion effizient im Canonical-Product-Tensorformat (CP) zu approximieren. Hierzu werden drei Ansätze vorgestellt, um die FCI-Wellenfunktion zu repräsentieren und darauf basierend die benötigten Koeffizienten zu bestimmen. Der erste Ansatz beruht auf einer Entwicklung der Wellenfunktion als Linearkombination von Slaterdeterminanten, bei welcher in einer Hierarchie ausgehend von der Hartree-Fock-Slaterdeterminante sukzessive besetzte Orbitale durch virtuelle Orbitale ersetzt werden. Unter Nutzung von Tensorrepräsentationen im CP wird ein lineares Gleichungssystem gelöst, um die FCI-Koeffizienten zu bestimmen. Im darauf folgenden Ansatz, welcher an Direct-CI angelehnt ist, werden Tensorrepräsentationen der Hamiltonmatrix und des Koeffizientenvektors aufgestellt, welche zur Lösung des FCI-Eigenwertproblems erforderlich sind. Hier wird ein Algorithmus vorgestellt, mit welchem das Eigenwertproblem im CP gelöst wird. In einem weiteren Ansatz wird die Repräsentation der Hamiltonmatrix und des Koeffizientenvektors im Fockraum formuliert. Dieser Ansatz erlaubt die Lösung des FCI-Eigenwertproblems mit Hilfe verschiedener Algorithmen. Diese orientieren sich an den Rayleighquotienteniterationen oder dem Davidsonalgorithmus, wobei für den ersten Algorithmus eine zweite Version entwickelt wurde, wo die Rangreduktion teilweise durch Projektionen ersetzt wurde. Für den Davidsonalgorithmus ist ein breiteres Spektrum von Molekülen behandelbar und somit können erste Untersuchungen zur Skalierung und zu den zu erwartenden Fehlern vorgestellt werden. Schließlich wird ein Ausblick auf mögliche Weiterentwicklungen gegeben, welche eine effizientere Berechnung ermöglichen und somit FCI im CP auch für größere Moleküle zugänglich macht. / In this thesis, various approaches are investigated to apply tensor decomposition methods to the Full Configuration Interaction method (FCI). The aim of these approaches is the development of algorithms, which converge reliably and which permit to approximate the wave function efficiently in the Canonical Product format (CP). Three approaches are introduced to represent the FCI wave function and to obtain the corresponding coefficients. The first approach ist based on an expansion of the wave function as a linear combination of slater determinants. In this hierarchical expansion, starting from the Hartree Fock slater determinant, the occupied orbitals are substituted by virtual orbitals. Using tensor representations in the CP, a linear system of equations is solved to obtain the FCI coefficients. In a further approach, tensor representations of the Hamiltonian matrix and the coefficient vectors are set up, which are required to solve the FCI eigenvalue problem. The tensor contractions and an algorithm to solve the eigenvalue problem in the CP are explained her in detail. In the next approach, tensor representations of the Hamiltonian matrix and the coefficient vector are constructed in the Fock space. This approach allows the application of various algorithms. They are based on the Rayleight Quotient Algorithm and the Davidson algorithm and for the first one, there exists a second version, where the rank reduction algorithm is replaced by projections. The Davidson algorithm allows to treat a broader spectrum of molecules. First investigations regarding the scaling behaviour and the expectable errors can be shown for this approach. Finally, an outlook on the further development is given, that allows for more efficient calculations and makes FCI in the CP accessible for larger molecules.

Esta tese tem como objetivo central a descrição teórica rigorosa da estrutura, de propriedades e da espectroscopia de alguns sistemas diatômicos. Como abordagem de cálculo ela se serve da metodologia interação de configurações na sua forma conhecida como excitações simples e duplas a partir de um conjunto de múltiplas referências (MRSD-CI), além de conjuntos base relativamente extensos de funções Gaussianas Cartesianas contraídas. Ela propõe a existência de duas novas espécies moleculares, BeC e BeC+, para as quais um total de 20 estados eletrônicos (13 para o BeC e 7 para o BeC+) foram caracterizados através de suas curvas de potencial e de seus respectivos estados vibro-rotacionais. Constantes espectroscópicas para cada estado foram calculadas e os momentos elétricos das transições eletrônicas mais relevantes foram também estudados. Essas transições foram analisadas tanto em termos de probabilidades de transição calculadas via momento de transição como por meio de fatores de Franck-Condon. Transições vibro-rotacionais dentro de um mesmo estado eletrônico foram ainda examinadas. Para esses vários estados, tempos de vida radiativa foram também calculados. Complementando essa descrição espectroscópica, uma discussão sobre a natureza da ligação química nesses sistemas foi ainda apresentada. Conjugando os resultados obtidos para essas duas espécies, o espectro fotoeletrônico da molécula BeC foi simulado servindo-se da aproximação de Franck-Condon para estimar as intensidades das linhas de cada banda. Além de propriedades eletrônicas como o momento de dipolo, cálculos de gradiente de campo elétrico no átomo de berílio em função da distância internuclear foram também realizados com o propósito de fornecer dados teóricos confiáveis que permitam a determinação experimental do momento quadrupolar do núcleo de 9Be sobre o qual existe certa controvérsia na literatura. Tais cálculos, realizados para os sitemas BeH+ e BeC, além de incluirem o efeito da vibração molecular no gradiente de campo elétrico na forma de uma média vibracional, mostraram que a aproximação de Buckingham usada por alguns grupos não é apropriada para descrever tal efeito. / The aim of this thesis is to describe theoretically the structure, properties, and the spectroscopy of some diatomic species using the multirefence single and double excitations configuration interaction approach, and an extensive atomic basis set of contracted Cartesian Gaussian orbitals. Two new diatomic species are proposed, BeC and BeC+, for which twenty electronic states have been characterized (13 for BeC, and 7 for BeC+) by means of their potential energy curves and vibro-rotational states. Spectroscopic constants for both of them have been computed, as well as electric moments of the most relevant electronic transitions. The transitions have been described by using either transitions probabilities computed with the aid of the theoretical transition moment functions, or by Franck-Condon factors. Vibro-rotational transitions within the same electronic state have also been described. Radiative lifetimes have been computed for several states. Complementing the spectroscopic description, a descussion on the nature of the chemical bonding has also been presented. A combination of the results for the neutral and ionic species allowed the calculation of the vertical and adiabatic ionization potentials and the Franck-Condon distribution spectrum for transitions from the ground state of BeC to selected bound states of BeC+. Besides the electronic properties, as dipole moment, the electric field gradient at the 9Be nucleus has also been computed as a function of the internuclear distance with the purpose of providing reliable theoretical results to help in the spectroscopic determination of the nuclear quadrupole moment of 9Be, since the data reported to date do not seem to be so conclusive. This kind of analysis has been carried out for the species BeH+ and BeC. By taking into account the nuclear motion effects on the electric field gradient as an average over the vibrational wavefunction, it was possible to show that the commom practice of using the Buckingham\'s expression to compute such correction is not recornrnended.

Dans une première partie, la structure électronique de deux membres de la famille des Analogues de Bleu de Prusse (ABP) a été inspectée à l'aide de méthodes basées sur la fonction d'onde. Dans l'ABP NiFe, un changement du couplage magnétique a été mis en évidence lors d'une déformation structurale locale. Basé sur les résultats obtenus pour l'ABP CoFe, un rôle clé dans le processus photomagnétique observé dans ce matériau est attribué aux lacunes cristallines. Dans une deuxième partie, un développement méthodologique a été mené jusqu'à l'implémentation de la méthode FRACCIS (FRAgmented Contracted Configuration Interaction of Single excitations). Elle permet de concentrer l'effort numérique sur un petit nombre de déterminants physiquement importants. De plus, elle constitue un outil d'analyse pour mesurer l'importance de certaines excitations dans le système inspecté. L'application à (H2)2 et C4H6 montre qu'une réduction majeure de l'espace d'IC est possible en gardant une bonne précision par rapport aux valeurs de référence. Ce travail contribue aux efforts vers l'analyse rationnelle de la corrélation électronique. / In the first part, the electronic structure of two members of the family of Prussian Blue Analogues (PBA) has been inspected using wave function-based methods. The NiFe PBA exhibits a change of the magnetic coupling under a local structural deformation. Based on the results obtained for the CoFe PBA, a key role in the photomagnetic process observed in this material is attributed to the crystal vacancies. In a second part, a methodological development has been carried out and has lead to the implementation of the FRACCIS method (FRAgmented Contracted Configuration Interaction of Single excitations). It allows to concentrate the numerical effort on a small number of physically relevant determinants. Furthermore, it constitutes an analysis tool to measure the importance of certain excitations in the inspected system. The application to (H2)2 et C4H6 shows that a major reduction of the CI space is possible while keeping good accuracy with respect to reference values. This work contributes to the efforts towards a rational analysis of electronic correlation.

The nature of the ground state and the first (lowest) singlet excited state geometrical conformations and electronic transitions in the aromatic five-membered heterocyclic oligomers &ndash / oligothiophenes (nT), oligofurans (nF), and oligopyrroles (nP)- containing up to six monomer units (total of 18 molecules) were explored using several computational methodologies. Geometry optimizations were carried out at Austin Model 1 (AM1), Restricted Hartree-Fock (RHF/6-31G*), and Density Functional Theory (DFT, B3LYP/6-31G*) levels for the ground-state conformations of these structurally well-defined heterocyclic oligomers. The Configuration Interaction Singles (CIS) method with the 6-31G* basis set was chosen in computation of the optimal geometry of the lowest singlet excited state. Lowest singlet excitation S1&szlig / S0 energies were calculated using the Zerner&rsquo / s Intermediate Neglect of Differential Overlap for Spectroscopy (ZINDO/S), CIS (CIS/6-31G*), and Time-Dependent DFT (TDDFT/6-31G* and TDDFT/6-31+G*) methods. In computation of the emission S1&agrave / S0 energies, we have employed all methods above except ZINDO/S. In investigation of geometries of the ground and lowest singlet excited state, we compared the bond length alternation (BLA) parameters, Dri in the conjugated backbone of the oligomers. Saturation of the geometrical parameters at the center of oligomers was observed after a certain chain length. Among all methodologies used in computation of excitation (S1&szlig / S0) and emission (S1&agrave / S0) energies, TDDFT results showed the best agreement with experimental data. Fits of computed and experimental excitation energies to an exponential function using the least squares method enabled us to predict Effective Conjugation Length (ECL) values. We obtained the ECLs of 17 (17), 16 (15), and 14 (13) monomer units for polythiophene (PTh), polyfuran (PFu), and polypyrrole (PPr), which have very good agreement with the results obtained from the fits of experimental data (the values in parentheses).

Esta tese tem como objetivo central a descrição teórica rigorosa da estrutura, de propriedades e da espectroscopia de alguns sistemas diatômicos. Como abordagem de cálculo ela se serve da metodologia interação de configurações na sua forma conhecida como excitações simples e duplas a partir de um conjunto de múltiplas referências (MRSD-CI), além de conjuntos base relativamente extensos de funções Gaussianas Cartesianas contraídas. Ela propõe a existência de duas novas espécies moleculares, BeC e BeC+, para as quais um total de 20 estados eletrônicos (13 para o BeC e 7 para o BeC+) foram caracterizados através de suas curvas de potencial e de seus respectivos estados vibro-rotacionais. Constantes espectroscópicas para cada estado foram calculadas e os momentos elétricos das transições eletrônicas mais relevantes foram também estudados. Essas transições foram analisadas tanto em termos de probabilidades de transição calculadas via momento de transição como por meio de fatores de Franck-Condon. Transições vibro-rotacionais dentro de um mesmo estado eletrônico foram ainda examinadas. Para esses vários estados, tempos de vida radiativa foram também calculados. Complementando essa descrição espectroscópica, uma discussão sobre a natureza da ligação química nesses sistemas foi ainda apresentada. Conjugando os resultados obtidos para essas duas espécies, o espectro fotoeletrônico da molécula BeC foi simulado servindo-se da aproximação de Franck-Condon para estimar as intensidades das linhas de cada banda. Além de propriedades eletrônicas como o momento de dipolo, cálculos de gradiente de campo elétrico no átomo de berílio em função da distância internuclear foram também realizados com o propósito de fornecer dados teóricos confiáveis que permitam a determinação experimental do momento quadrupolar do núcleo de 9Be sobre o qual existe certa controvérsia na literatura. Tais cálculos, realizados para os sitemas BeH+ e BeC, além de incluirem o efeito da vibração molecular no gradiente de campo elétrico na forma de uma média vibracional, mostraram que a aproximação de Buckingham usada por alguns grupos não é apropriada para descrever tal efeito. / The aim of this thesis is to describe theoretically the structure, properties, and the spectroscopy of some diatomic species using the multirefence single and double excitations configuration interaction approach, and an extensive atomic basis set of contracted Cartesian Gaussian orbitals. Two new diatomic species are proposed, BeC and BeC+, for which twenty electronic states have been characterized (13 for BeC, and 7 for BeC+) by means of their potential energy curves and vibro-rotational states. Spectroscopic constants for both of them have been computed, as well as electric moments of the most relevant electronic transitions. The transitions have been described by using either transitions probabilities computed with the aid of the theoretical transition moment functions, or by Franck-Condon factors. Vibro-rotational transitions within the same electronic state have also been described. Radiative lifetimes have been computed for several states. Complementing the spectroscopic description, a descussion on the nature of the chemical bonding has also been presented. A combination of the results for the neutral and ionic species allowed the calculation of the vertical and adiabatic ionization potentials and the Franck-Condon distribution spectrum for transitions from the ground state of BeC to selected bound states of BeC+. Besides the electronic properties, as dipole moment, the electric field gradient at the 9Be nucleus has also been computed as a function of the internuclear distance with the purpose of providing reliable theoretical results to help in the spectroscopic determination of the nuclear quadrupole moment of 9Be, since the data reported to date do not seem to be so conclusive. This kind of analysis has been carried out for the species BeH+ and BeC. By taking into account the nuclear motion effects on the electric field gradient as an average over the vibrational wavefunction, it was possible to show that the commom practice of using the Buckingham\'s expression to compute such correction is not recornrnended.

The binary neutron star merger of 2017 and its corresponding electromagnetic signature resembling that of a kilonova has been one of the most groundbreaking astrophysical occurrences in the last decade. Indications of r-process nucleosynthesis in this event presents new opportunities for learning about the astrophysical origin of heavy elements. This has been a long-standing mystery in our understanding of the chemical evolution of the universe. This leads to the requirement of developing more accurate calculations of the corresponding atomic properties. In this work, I have studied the potential of utilizing a combined configuration-interaction and many-body perturbation theory approach.The goal is to study if a generalized and computationally efficient method is possible with this approach, so that it can be used to develop accurate and complete atomic structures applicable to any ion of any element in the periodic table. Focusing on the lanthanide group of elements, and in Ce in particular, the method in this work builds on including the bulk of strong correlation contributions in the configuration-interaction model, complemented with perturbation theory corrections in subsequent many-body perturbation theory calculations. For all Ce ions, this was however not possible without having to compromise the completeness condition. In conclusion, in the scope of this project, we find that it is challenging to generalize a procedure for near-neutral systems due to the amount of correlation needed to be treated with configuration-interaction. / <p>Project made as part of the course: "Project in physics and astronomy - 1FA195, 15 ECTS" at Uppsala University</p>

Strongly correlated systems have been a major challenge for a long time in the field of theoretical chemistry. For such systems, the relevant portion of the Hilbert space scales exponentially, preventing efficient simulation on large systems. However, in many cases, the Hilbert space can be partitioned into clusters on the basis of strong and weak interactions. In this work, we mainly focus on an approach where we partition the system into smaller orbital clusters in which we can define many-particle cluster states and use traditional many-body methods to capture the rest of the inter-cluster correlations. This dissertation can be mainly divided into two parts. In the first part of this dissertation, the clustered ansatz, termed as tensor product states (TPS), is used to study large strongly correlated systems. In the second part, we study a particular type of strongly correlated system, correlated triplet pair states that arise in singlet fission. The many-body expansion (MBE) is an efficient tool that has a long history of use for calculating interaction energies, binding energies, lattice energies, and so on. We extend the incremental full configuration interaction originally proposed for a Slater determinant to a tensor product state (TPS) based wavefunction. By partitioning the active space into smaller orbital clusters, our approach starts from a cluster mean-field reference TPS configuration and includes the correlation contribution of the excited TPSs using a many-body expansion. This method, named cluster many-body expansion (cMBE), improves the convergence of MBE at lower orders compared to directly doing a block-based MBE from an RHF reference. The performance of the cMBE method is also tested on a graphene nano-sheet with a very large active space of 114 electrons in 114 orbitals, which would require 1066 determinants for the exact FCI solution. Selected CI (SCI) using determinants becomes intractable for large systems with strong correlation. We introduce a method for SCI algorithms using tensor product states which exploits local molecular structure to significantly reduce the number of SCI variables. We demonstrate the potential of this method, called tensor product selected configuration interaction (TPSCI), using a few model Hamiltonians and molecular examples. These numerical results show that TPSCI can be used to significantly reduce the number of SCI variables in the variational space, and thus paving a path for extending these deterministic and variational SCI approaches to a wider range of physical systems. The extension of the TPSCI algorithm for excited states is also investigated. TPSCI with perturbative corrections provides accurate excitation energies for low-lying triplet states with respect to extrapolated results. In the case of traditional SCI methods, accurate excitation energies are obtained only after extrapolating calculations with large variational dimensions compared to TPSCI. We provide an intuitive connection between lower triplet energy mani- folds with Hückel molecular orbital theory, providing a many-body version of Hückel theory for excited triplet states. The n-body Tucker ansatz (which is a truncated TPS wavefunction) developed in our group provides a good approximation to the low-lying states of a clusterable spin system. In this approach, a Tucker decomposition is used to obtain local cluster states which can be truncated to prune the full Hilbert space of the system. As a truncated variational approach, it has been observed that the self-consistently optimized n-body Tucker method is not size- extensive, a property important for many-body methods. We explore the use of perturbation theory and linearized coupled-cluster methods to obtain a robust yet efficient approximation. Perturbative corrections to the n-body Tucker method have been implemented for the Heisenberg Hamiltonian and numerical data for various lattices and molecular systems has been presented to show the applicability of the method. In the second part of this dissertation, we focus on studying a particular type of strongly correlated states that occurs in singlet fission material. The correlated triplet pair state 1(TT) is a key intermediate in the singlet fission process, and understanding the mechanism by which it separates into two independent triplet states is critical for leveraging singlet fission for improving solar cell efficiency. This separation mechanism is dominated by two key interactions: (i) the exchange interaction (K) between the triplets which leads to the spin splitting of the biexciton state into 1(TT),3(TT) and 5(TT) states, and (ii) the triplet-triplet energy transfer integral (t) which enables the formation of the spatially separated (but still spin entangled) state 1(T...T). We develop a simple ab initio technique to compute both the triplet-triplet exchange (K) and triplet-triplet energy transfer coupling (t). Our key findings reveal new conditions for successful correlated triplet pair state dissociation. The biexciton exchange interaction needs to be ferromagnetic or negligible compared to the triplet energy transfer for favorable dissociation. We also explore the effect of chromophore packing to reveal geometries where these conditions are achieved for tetracene. We also provide a simple connectivity rule to predict whether the through-bond coupling will be stabilizing or destabilizing for the (TT) state in covalently linked singlet fission chromophores. By drawing an analogy between the chemical system and a simple spin-lattice, one is able to determine the ordering of the multi-exciton spin state via a generalized usage of Ovchinnikov's rule. In the case of meta connectivity, we predict 5(TT) to be formed and this is later confirmed by experimental techniques like time-resolved electron spin resonance (TR-ESR). / Doctor of Philosophy / The study of the correlated motion of electrons in molecules and materials allows scientists to gain useful insights into many physical processes like photosynthesis, enzyme catalysis, superconductivity, chemical reactions and so on. Theoretical quantum chemistry tries to study the electronic properties of chemical species. The exact solution of the electron correlation problem is exponentially complex and can only be computed for small systems. Therefore, approximations are introduced for practical calculations that provide good results for ground state properties like energy, dipole moment, etc. Sometimes, more accurate calculations are required to study the properties of a system, because the system may not adhere to the as- sumptions that are made in the methods used. One such case arises in the study of strongly correlated molecules. In this dissertation, we present methods which can handle strongly correlated cases. We partition the system into smaller parts, then solve the problem in the basis of these smaller parts. We refer to this block-based wavefunction as tensor product states and they provide accurate results while avoiding the exponential scaling of the full solution. We present accurate energies for a wide variety of challenging cases, including bond breaking, excited states and π conjugated molecules. Additionally, we also investigate molecular systems that can be used to increase the efficiency of solar cells. We predict improved solar efficiency for a chromophore dimer, a result which is later experimentally verified.

In this thesis, a method to calculate eigenpairs is implemented for the Multipsi library. While the standard implemtentations use the Davidson method with Rayleigh-Ritz extraction to calculate the eigenpairs with the lowest eigenvalues, the new method uses the harmonic Davidson method with the harmonic Rayleigh-Ritz extraction to calculate eigenpairs with eigenvalues near a chosen target. This is done for Configuration Interaction calculations and for Multiconfigurational methods. From calculations, it seems the new addition to the Multipsi library is worth investigating further as convergence for difficult systems with a lot of near-degeneracy was improved. / I denna avhandling implementeras en metod för att beräkna egenpar för Multipsi-biblioteket. Medan standardimplementeringarna använder Davidson-metoden med Rayleigh-Ritz-extraktion för att beräkna egenparen med de lägsta egenvärdena, använder den nya metoden den harmoniska Davidson-metoden med den harmoniska Rayleigh-Ritz-extraktionen för att beräkna egenparen med egenvärden nära ett valt mål. Detta görs för konfigurationsinteraktionsberäkningar och för multikonfigurationsmetoder. Utifrån beräkningarna verkar det nya tillskottet till Multipsi-biblioteket vara värt att undersöka vidare eftersom konvergensen för svåra system med mycket nära degenerering förbättrades.

Extensive theoretical studies on the ground and excited state properties of systems containing heavy atoms have shown that accurate prediction of transition energies and related properties requires the incorporation of both relativistic and higher order correlation and relaxation effects as these effects are strongly inter- wined. The relativistic and dynamical electron correlation effects can be incor- porated in many-electron systems through a variety of many-body methods like configuration interaction (CI), coupled cluster method (CCM) etc. which are very powerful and effective tool for high precision description of electron correlation in many-electron systems. In this thesis, we investigate the relativistic and correlation effects in heavy atomic and molecular systems using these two highly correlated many-body methods. It is well recognized that, heavy polar diatomic molecules such as BaF, YbF, TlF, PbO, etc. are the leading experimental candidates for the search of violation of Parity (P ) and Time-reversal (T ) symmetry. The experimental detection of such P,T-odd effects in atoms and molecules has important consequences for the theory of fundamental interactions or for physics beyond the standard model (SM). For instance, a series of experiments on TlF have already been reported which provide the tightest limit available on the tensor coupling constant C , proton electric dipole moment (EDM) dp , etc. Experiments on YbF and BaF molecules are also of fundamental significance to the study of symmetry violation in nature, as these experiments have the potential to detect effects due to the electron EDMde. It is therefore imperative that high precession calculations are necessary to interpret these ongoing (and perhaps forthcoming) experimental outcome. For example, the knowledge of the effective electric field E(characterized by Wd) at the unpaired electron is required to link the experimentally determined P,T-odd frequency shift with the electron EDM de. We begin with a brief review of P,T-odd effects in heavy atoms and polar diatomics and the possible mechanisms which can give rise to such effects, in particular, the one arises due to the intrinsic electron EDM de. The P,T-odd interaction constant Wd is computed for the ground (2∑ ) state of YbF and BaF molecules using all-electron DF orbitals at the restricted active space (RAS) CI level. The RASCI space used for both systems in this calculation is sufficiently large to incorporate important core-core, core-valence, and valence-valence electron correlation effects. In addition to Wd, we also report the dipole moment (µe ) for these systems to assess the reliability of the method. The basis set dependency of Wd is also analyzed. The single reference coupled cluster (SRCC) method, developed by the cluster expansion of a single determinant reference function, is one of the most sophisticated method for treating dynamical correlation effects in a size-extensive manner. The non-uniqueness of the exponential nature of the wave operator diversifies the methods in multi-reference context. The multi-reference coupled cluster (MRCC) strategies fall within two broad classes: (a) State-Universal (SU), a Hilbert-space approach and (b) Valence-Universal (VU), a Fock-space approach. In this thesis, we shall be mainly concerned with the VU-MRCC which unlike SU-MRCC uses a single wave operator that not only correlates the reference functions, but also all the lower valence (or the so called subdued) sectors, obtained by deleting the occupancies systematically. The linear response theory (LRT) or equation of motion (EOM) method is another possible alternative which is nowadays extensively used to compute the atomic and molecular properties. Although, the CCLRT or EOM-CC method is not fully extensive in nature, this method has some distinct advantages over the traditional VU-MRCC theory. Further, for one-valence problem like ionization processes, the CCLRT/EOM-CC is formally equivalent to VU-MRCC, and hence, size-extensive. In this thesis, the core-extensive CCLRT and core-valence extensive (all electron) VU-MRCC methods are applied to compute the ground and excited state properties of various atomic and molecular systems (HCl, CuH, Ag, Sr, Yb and Hg) using nonrelativistic and relativistic (for heavy atoms) spinors. The similarities and differences in the structure of these two formalisms are also addressed. We also investigate the ground and excited state properties of HCN which is a system of astrophysical importance. This system has raised interest among the astrophysicists due to its detection in the atmosphere of Titan and Carbon stars. HCN has also been identified via radio-techniques in both comets and interstellar atmosphere. In the ash-photolysis of oxazole, iso-oxazole, and thiozole a transient band system was observed in the region 2500-3050 Å. This band system was attributed to a meta-stable form of HCN, i.e, either HNC or triplet HCN. We carry out detailed theoretical investigations using CCLRT and complete active space self-consistent field (CASSCF) method to characterize this unidentified band and other experimentally observed transitions.

The goal of this Thesis is to study the electronic and optical properties of semiconductor nanostructures by employing different theories. The work present in this Thesis is divided into three parts. Part I is devoted to the effective-mass theory and its several applications. A general description of the effective mass theory and several ways of solving the effective-mass Schrodinger equation with an emphasis on the potential morphing method are given in the first chapter. In the following few chapters, we apply these theories in many realistic systems for the study of many properties. They include: i) the binding energy of hydrogentic donor impurity in semiconductor quantum dots under the influence of static electric field and/or magnetic field, ii) the linear and nonlinear optical properties associated with intraband transitions in semiconductor quantum dots, core shell quantum dots and quantum-dot-quantum-ring systems. Part II is devoted to the pseudopotential theory and its several applications. The background theories primarily regarding to the empirical pseudopotential method and configuration interaction approach are described in the first chapter. In the following few chapters, we employ these theories for the study of the electronic and optical properties of many nanostructures of group II-VI materials. The optical properties studied herein include the band gap, Stokes shift, exciton fine structure, optical polarization and absorption spectra. Part III is devoted to the appendix, where twelve published papers are presented. / Στόχος της παρούσας διατριβής είναι η μελέτη των ηλεκτρονικών και οπτικών ιδιοτήτων νανοδομών ημιαγωγών κάνοντας χρήση κατάλληλων υπολογιστικών μεθόδων και τεχνικών. Η διατριβή χωρίζεται σε τρία μέρη. Το πρώτο μέρος εστιάζει στην θεωρία της ενεργούς μάζας (Effective-mass Theory) και τις εφαρμογές της. Στο πρώτο κεφάλαιο παρουσιάζεται το απαραίτητο θεωρητικό υπόβαθρο και δίνεται μία συνοπτική περιγραφή των συνηθέστερων μεθόδων επίλυσης της μονοηλεκτρονιακής εξίσωσης του Schrodinger,δίνοντας ιδιαίτερη έμφαση στην μέθοδο μορφοποίησης δυναμικού (Potential Morphing Method). Στα επόμενα κεφάλαια του πρώτου μέρους οι τεχνικές και μέθοδοι που περιγράφηκαν χρησιμοποιούνται για την μελέτη κρίσιμων ιδιοτήτων και παραμέτρων σε νανοσυστήματα ημιαγωγών. Μεταξύ αυτών είναι: i) η ενέργεια δέσμευσης υδρογονοειδών προσμίξεων τύπου δότη υπό την επίδραση στατικού ηλεκτρικού ή/και μαγνητικού πεδίου, ii) γραμμικές και μη γραμμικές οπτικές ιδιότητες που συνδέονται με intraband μεταβάσεις εντός ζώνης σε κβαντικές τελείες ημιαγωγών, κβαντικές τελείες με δομή πυρήνα-φλοιού και σε μεικτά συστήματα κβαντικής τελείας – κβαντικού δακτυλίου. Το δεύτερο μέρος εστιάζει στην θεωρία των ψευδοδυνάμικών και τις εφαρμογές της. Αρχικά παρουσιάζεται το απαραίτητο θεωρητικό υπόβαθρο της μεθόδου εμπειρικών ψευδοδυναμικών (Empirical Pseudopotential Method) καθώς επίσης και της μεθόδου αλληλεπίδρασης διαμορφώσεων (Configuration Interaction). Στην συνέχεια, οι προαναφερθείσες τεχνικές εφαρμόζονται στην μελέτη των ηλεκτρονικών και οπτικών ιδιοτήτων σε μία πληθώρα νανοδομών ημιαγωγών II-VI. Μεταξύ των ιδιοτήτων αυτών είναι: το ενεργειακό χάσμα, η μετατόπιση Stokes, η λεπτή δομή των εξιτονίων, η οπτική πόλωση και τα φάσματα απορρόφησης. Το τρίτο μέρος της διατριβής περιλαμβάνει το παράρτημα, στο οποίο παρατίθενται οι δώδεκα δημοσιευμένες εργασίες.