One of the most promising methods for surmounting the high-degree polynomial scaling wall associated with electron correlating wave function methods is the local correlation technique of Pulay and Saebø. They have proposed using a set of localized occupied and virtual orbitals free of the canonical constraint commonly employed in quantum chemistry, resulting in a method that scales linearly (in the asymptotic limit) with molecular size. Pulay and Saeb$oslash; first applied their methods to configuration interaction and later to M$oslash;ller-Plesset perturbation theory. Werner et al. have have extended the local correlation scheme of Pulay and Saeb$oslash; to coupled-cluster theory. One of the pitfalls of the local correlation methods developed by Pulay and Saeb$oslash; is the dependence of domain selection on the molecular geometry. In other words, as the geometry changes the domain structure of the local correlation calculation can change also, leading to discontinuities in the potential energy surface. We have examined the size of these discontinuities for the homolytic bond cleavage of fluoromethane and the heterolytic bond dissociation of singlet ketene and propadienone. Properties such as polarizabilities and optical rotation are realized through linear response theory, where the Hamiltonian is subject to an external perturbation and the wave function is allowed to respond to the applied perturbation. Within the context of local correlation it is necessary to understand how the domain structure alters in response to an applied perturbation. We have proposed using solutions to the CPHF equations (coupled-perturbed Hartree-Fock) in order to predict the correlation response to an applied perturbation. We have applied this technique to the calculation of polarizabilities, with very favorable results, and also to optical rotation, with mixed results. / Ph. D.

Coupled cluster (CC) and density functional theory (DFT) are highly regarded as robust quantum chemical methods for accurately predicting a wide variety of properties, such as molecular structures, thermochemical data, vibrational spectra, etc., but there has been little focus on the theoretical prediction of optical rotation. This property, also referred to as circular birefringence, is inherent to all chiral molecules and occurs because such samples exhibit different refractive indices for left- and right- circularly polarized light. This thesis focuses on the theoretical prediction of this chiroptic property using CC and DFT quantum chemical models. Several small chiral systems have been studied, including (S)-methyloxirane, (R)-epichlorohydrin, (R)-methylthiirane, and the conformationally flexible molecules, (R)-3-chloro-1-butene and (R)-2-chlorobutane. All predicted results have been compared to recently published gas-phase cavity ringdown polarimetry data. When applicable, well-converged Gibbs free energy differences among confomers were determined using complete-basis-set extrapolations of CC energies in order to obtain Boltzmann-averaged specific rotations. The overall results indicate that the theoretical rotation is highly dependent on the choice of optimized geometry and basis set (diffuse functions are shown to be extremely important), and that there is a large difference between the CC and DFT predicted values, with DFT usually predicting magnitudes that are larger than those of coupled cluster theory. / Ph. D.

Quantum mechanical methods are becoming increasingly useful and applicable tools to complement and support experiment. Nonetheless, some barriers to further applications of theoretical models still remain. A coupled cluster singles and doubles (CCSD) calculation, a reliable ab initio method, scales approximately on the order of 𝑂(𝑁⁶), where 𝑁 is a measure of the system size. This unfortunately limits the use of such high-accuracy methods to relatively small systems. Coupled cluster property calculations must be used in conjunction with reduced-scaling methods in order to broaden the range of applications to larger systems. In this work, we introduce some of the underlying theory behind such calculations and test the performance of several local correlation techniques for polarizabilities, optical rotations, and excited state properties. In general, when the computational cost is significantly reduced, the necessary accuracy is lost. Polarizabilities are less sensitive to the truncation schemes than optical rotations, and the excitation data is often only in agreement with the canonical result for the first few excited states. Additionally, we present a novel application of equation-of-motion coupled cluster singles and doubles to simulated circularly polarized luminescence spectra of eight chiral ketones. Both the absorption in the ground state and emission from the excited states were examined. Extensive geometry analyses were performed, revealing that optimized structures at the density functional theory were adequate for the calculation accurate coupled cluster excitation data. / Ph. D.

Accurate theoretical predictions of optical rotation are of substantial utility to the chemical community enabling the determination of absolute configuration without the need for poten- tially lengthy total synthesis. The requirements for robust calculation of gas-phase optical rotation are well understood, but too expensive for routine use. In an effort to reduce this cost we have examined the performance of the LPol and ORP basis sets, created for use in density functional theory calculations of optical rotation, finding that at the coupled cluster level of theory they perform the same or better than comparably sized general basis sets that are often used. We have also examined the performance of a perturbational approach to inclusion of explicit solvent molecules in an effort to extend the calculation of response properties from the gas phase to the condensed phase. This N-body approach performs admirably for interaction energies and even dipole moments but breaks down for optical rotation, exhibiting large basis set superposition errors and requiring higher-order terms in the expansion to provide reasonable accuracy. In addition, we have begun the process of implementing a gauge invariant version of coupled cluster response properties to address the fundamentally unphysical lack of gauge invariance in coupled cluster optical rotations. Correcting this problem, which arises from the non- variational nature of the coupled cluster wavefunction, involves reformulating the response amplitude and function expressions and solving for all necessary amplitudes simultaneously. / Ph. D.

Neste estudo, parâmetros estruturais, energéticos e da frequências vibracionais para os estados X 3Σ- e A 3II do radical CNN e X 2II das espécies iônicas CNN+ e CNN- foram obtidos no nível de teoria CCSD(T)/CBST-5. No estudo termoquímico, os valores para o calor de formação da espécie neutra foram, ΔHf (O K) = 138,89 kcal/mol e ΔHf (298,15 K) = 139,65 kcal/mol. Para o potencial de ionização e a afinidade eletrônica, os resultados deste trabalho são 10,969 e 1,743 eV, respectivamente. Otimizações de geometria para os estados eletrônicos X 3Σ-, A 3II, a 1Δ, b 1Σ+, c 1II, d X 1Σ- e B 3Σ- realizadas com a metodologia MRCI nos permitiram obter valores para Te. Além disso, as energias de transição vertical para 15 estados eletrônicos também foram determinadas. Utilizando o nível de teoria CCSD(T)-F12b/CBSD-Q, geometrias de equilíbrio e frequências vibracionais harmônicas e anarmônicas foram estimadas para a molécula C30 e seu ânion C30-. Uma avaliação dos efeitos que inclusão dos elétrons do caroço no cálculo de diferentes propriedades foi realizada. Descrevemos a primeira determinação do calor de formação para a molécula C3O, ΔHf (0 K) = 79,41 kcal/mol e ΔHf( (298,15 K) = 83,39 kcal/mol, além do cálculo da afinidade eletrônica (1,114 eV). No que se refere à cinética e à dinâmica química, a determinação das constantes de velocidade foi realizada para duas reações de abstração de hidrogênio. Na primeira, as constantes de velocidade para a reação S (3P) + CH4 → SH + CH3, numa ampla faixa de temperaturas (T = 200 - 3000 K), foram determinadas utilizando SS-VTST/MT combinada com cálculos DFT/M05-2X/MG3S. A 1200 K, a constante de velocidade CVT/SCT para este processo (2,85 x 10-14 cm3 molécula-1 s-1) está em excelente concordância com o resultado experimental (8,14 x 10-14 cm3 molécula-1 s-1). Na segunda, o estudo a reação de abstração de hidrogênio do butanoato de metila por hidrogênio atômico foi realizada utilizando a abordagem cinética MS-VTST/MT combidada com cálculos MPWB1K/G- 31+G(d,p). Nesta aproximação cinética, a anarmonicidade associada às torções angulares amortecidas, bem como o acoplamento entre elas foram consideradas no cálculo das constante de velocidade. Neste processo, verificamos que a inclusão da anarmonicidade torcional nas constantes de velocidade aumenta a constante de velocidade em aproximadamente 8-10% a altas temperaturas (T = 1000 -2000 K). A temperaturas mais baixas, os efeitos de tunelamento são predominantes e a constante de velocidade CVT/SCT para a reação CH3CH2CH2COOCH3 + H (2S) → CH2CH2CH2COOCH3 + H (2S) a 300 K (6,17 x 10-18 cm3 molécula-1 s-1) é 8,2 vezes maior que a obtida com CVT (5,07 x 10-17 cm3 molécula-1 s-1). / In this study, the structures, energies and vibrational frequencies for the X 3Σ- e A3II electronic states of CNN, and X 2II of the ions CNN+ and CNN- were obtained at the CCSD(T)/CBST-5 level of theory. Additionally, we also estimated the heats of formation for the neutral species ΔHf (0 K) = 138.89 kcal/mol and ΔHf(298.15 K) = 139.65 kcal/mol. For the ionization potential and electron affinities, this work predicted the values of 10.969 e 1.743 eV, respectively. Geometry optimizations for the electronic states 3Σ-, A 3II, a 1Δ, b 1Σ+, c 1II, d X 1Σ- e B 3Σ- performed with the MRCI approach allowed us to compute the excitation energies (Te). Furthermore, vertical transition energies were also calculated for 15 electronic states. Using the CCSD(T)-F12b/CBSD-Q level of theory, equilibrium geometries, and harmonic and anharmonic vibrational frequencies were estimated for the C3O molecule and the anion C3O-. An assessment of the effects of inclusion of core electrons in the calculation of some properties was also carried out. The determination of the heat of formation of the molecule C3O (ΔHf (0 K) = 79.41 kcal/mol and ΔHf (298.15 K) = 83.39 kcal/mol), and its electron affinity (1,114 eV) were the first ones reported in the literature. In the kinetics investigation, we estimated the rate constants for two hydrogen abstraction reactions. Rate constants for the reaction S(3P) + CH4 → SH + CH3 were predicted for a wide range of temperatures (T = 200 - 3000 K) using VTST/MT combined with DFT/M05-2X/MG3S calculations. At 1200 K, the calculated rate constant CVT/SCT for this process is 2.85 x 10-14 cm3 molecule-1 s-1. For the reaction of hydrogen abstraction from methyl butanoate by a hydrogen atom, the MS-VTST/MT method combined with the density functional MPWB1K/G-31+G(d,p) was employed. In this study, anharmonic torsional hindered rotations were considered in calculations of the rate constants. At high temperatures, the inclusion of torsional anharmonicity increases the rate constants by approximately 8-10%. At low temperatures, tunneling effects are predominant and the rate constant CVT/SCT (6.17 x 10-18 cm3 molécula-1 s-1) is 8.2 times higher than the CVT one (5.07 x 10-17 cm3 molécula-1 s-1 ).

Neste estudo, parâmetros estruturais, energéticos e da frequências vibracionais para os estados X 3Σ- e A 3II do radical CNN e X 2II das espécies iônicas CNN+ e CNN- foram obtidos no nível de teoria CCSD(T)/CBST-5. No estudo termoquímico, os valores para o calor de formação da espécie neutra foram, ΔHf (O K) = 138,89 kcal/mol e ΔHf (298,15 K) = 139,65 kcal/mol. Para o potencial de ionização e a afinidade eletrônica, os resultados deste trabalho são 10,969 e 1,743 eV, respectivamente. Otimizações de geometria para os estados eletrônicos X 3Σ-, A 3II, a 1Δ, b 1Σ+, c 1II, d X 1Σ- e B 3Σ- realizadas com a metodologia MRCI nos permitiram obter valores para Te. Além disso, as energias de transição vertical para 15 estados eletrônicos também foram determinadas. Utilizando o nível de teoria CCSD(T)-F12b/CBSD-Q, geometrias de equilíbrio e frequências vibracionais harmônicas e anarmônicas foram estimadas para a molécula C30 e seu ânion C30-. Uma avaliação dos efeitos que inclusão dos elétrons do caroço no cálculo de diferentes propriedades foi realizada. Descrevemos a primeira determinação do calor de formação para a molécula C3O, ΔHf (0 K) = 79,41 kcal/mol e ΔHf( (298,15 K) = 83,39 kcal/mol, além do cálculo da afinidade eletrônica (1,114 eV). No que se refere à cinética e à dinâmica química, a determinação das constantes de velocidade foi realizada para duas reações de abstração de hidrogênio. Na primeira, as constantes de velocidade para a reação S (3P) + CH4 → SH + CH3, numa ampla faixa de temperaturas (T = 200 - 3000 K), foram determinadas utilizando SS-VTST/MT combinada com cálculos DFT/M05-2X/MG3S. A 1200 K, a constante de velocidade CVT/SCT para este processo (2,85 x 10-14 cm3 molécula-1 s-1) está em excelente concordância com o resultado experimental (8,14 x 10-14 cm3 molécula-1 s-1). Na segunda, o estudo a reação de abstração de hidrogênio do butanoato de metila por hidrogênio atômico foi realizada utilizando a abordagem cinética MS-VTST/MT combidada com cálculos MPWB1K/G- 31+G(d,p). Nesta aproximação cinética, a anarmonicidade associada às torções angulares amortecidas, bem como o acoplamento entre elas foram consideradas no cálculo das constante de velocidade. Neste processo, verificamos que a inclusão da anarmonicidade torcional nas constantes de velocidade aumenta a constante de velocidade em aproximadamente 8-10% a altas temperaturas (T = 1000 -2000 K). A temperaturas mais baixas, os efeitos de tunelamento são predominantes e a constante de velocidade CVT/SCT para a reação CH3CH2CH2COOCH3 + H (2S) → CH2CH2CH2COOCH3 + H (2S) a 300 K (6,17 x 10-18 cm3 molécula-1 s-1) é 8,2 vezes maior que a obtida com CVT (5,07 x 10-17 cm3 molécula-1 s-1). / In this study, the structures, energies and vibrational frequencies for the X 3Σ- e A3II electronic states of CNN, and X 2II of the ions CNN+ and CNN- were obtained at the CCSD(T)/CBST-5 level of theory. Additionally, we also estimated the heats of formation for the neutral species ΔHf (0 K) = 138.89 kcal/mol and ΔHf(298.15 K) = 139.65 kcal/mol. For the ionization potential and electron affinities, this work predicted the values of 10.969 e 1.743 eV, respectively. Geometry optimizations for the electronic states 3Σ-, A 3II, a 1Δ, b 1Σ+, c 1II, d X 1Σ- e B 3Σ- performed with the MRCI approach allowed us to compute the excitation energies (Te). Furthermore, vertical transition energies were also calculated for 15 electronic states. Using the CCSD(T)-F12b/CBSD-Q level of theory, equilibrium geometries, and harmonic and anharmonic vibrational frequencies were estimated for the C3O molecule and the anion C3O-. An assessment of the effects of inclusion of core electrons in the calculation of some properties was also carried out. The determination of the heat of formation of the molecule C3O (ΔHf (0 K) = 79.41 kcal/mol and ΔHf (298.15 K) = 83.39 kcal/mol), and its electron affinity (1,114 eV) were the first ones reported in the literature. In the kinetics investigation, we estimated the rate constants for two hydrogen abstraction reactions. Rate constants for the reaction S(3P) + CH4 → SH + CH3 were predicted for a wide range of temperatures (T = 200 - 3000 K) using VTST/MT combined with DFT/M05-2X/MG3S calculations. At 1200 K, the calculated rate constant CVT/SCT for this process is 2.85 x 10-14 cm3 molecule-1 s-1. For the reaction of hydrogen abstraction from methyl butanoate by a hydrogen atom, the MS-VTST/MT method combined with the density functional MPWB1K/G-31+G(d,p) was employed. In this study, anharmonic torsional hindered rotations were considered in calculations of the rate constants. At high temperatures, the inclusion of torsional anharmonicity increases the rate constants by approximately 8-10%. At low temperatures, tunneling effects are predominant and the rate constant CVT/SCT (6.17 x 10-18 cm3 molécula-1 s-1) is 8.2 times higher than the CVT one (5.07 x 10-17 cm3 molécula-1 s-1 ).

In this thesis the application of novel tensor decomposition and tensor representation techniques in highly accurate post Hartree-Fock methods is evaluated. These representation techniques can help to overcome the steep scaling behaviour of high level ab-initio calculations with increasing system size and therefore break the "curse of dimensionality". After a comparison of various tensor formats the application of the "canonical polyadic" format (CP) is described in detail. There, especially the casting of a normal, index based tensor into the CP format (tensor decomposition) and a method for a low rank approximation (rank reduction) of the two-electron integrals in the AO basis are investigated. The decisive quantity for the applicability of the CP format is the scaling of the rank with increasing system and basis set size. The memory requirements and the computational effort for tensor manipulations in the CP format are only linear in the number of dimensions but still depend on the expansion length (rank) of the approximation. Furthermore, the AO-MO transformation and a MP2 algorithm with decomposed tensors in the CP format is evaluated and the scaling with increasing system and basis set size is investigated. Finally, a Coupled-Cluster algorithm based only on low-rank CP representation of the MO integrals is developed. There, especially the successive tensor contraction during the iterative solution of the amplitude equations and the error propagation upon multiple application of the reduction procedure are discussed. In conclusion the overall complexity of a Coupled-Cluster procedure with tensors in CP format is evaluated and some possibilities for improvements of the rank reduction procedure tailored to the needs in electronic structure calculations are shown. / Die vorliegende Arbeit beschäftigt sich mit der Anwendung neuartiger Tensorzerlegungs- und Tensorrepesentationstechniken in hochgenauen post Hartree-Fock Methoden um das hohe Skalierungsverhalten dieser Verfahren mit steigender Systemgröße zu verringern und somit den "Fluch der Dimensionen" zu brechen. Nach einer vergleichenden Betrachtung verschiedener Representationsformate wird auf die Anwendung des "canonical polyadic" Formates (CP) detailliert eingegangen. Dabei stehen zunächst die Umwandlung eines normalen, indexbasierten Tensors in das CP Format (Tensorzerlegung) und eine Methode der Niedrigrang Approximation (Rangreduktion) für Zweielektronenintegrale in der AO Basis im Vordergrund. Die entscheidende Größe für die Anwendbarkeit ist dabei das Skalierungsverhalten das Ranges mit steigender System- und Basissatzgröße, da der Speicheraufwand und die Berechnungskosten für Tensormanipulationen im CP Format zwar nur noch linear von der Anzahl der Dimensionen des Tensors abhängen, allerdings auch mit der Expansionslänge (Rang) skalieren. Im Anschluss wird die AO-MO Transformation und der MP2 Algorithmus mit zerlegten Tensoren im CP Format diskutiert und erneut das Skalierungsverhalten mit steigender System- und Basissatzgröße untersucht. Abschließend wird ein Coupled-Cluster Algorithmus vorgestellt, welcher ausschließlich mit Tensoren in einer Niedrigrang CP Darstellung arbeitet. Dabei wird vor allem auf die sukzessive Tensorkontraktion während der iterativen Bestimmung der Amplituden eingegangen und die Fehlerfortpanzung durch Anwendung des Rangreduktions-Algorithmus analysiert. Abschließend wird die Komplexität des gesamten Verfahrens bewertet und Verbesserungsmöglichkeiten der Reduktionsprozedur aufgezeigt.

Orientador: Pedro Antonio Muniz Vazquez / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Quimica / Made available in DSpace on 2018-08-14T17:56:25Z (GMT). No. of bitstreams: 1 Vidal_LucianoNassif_D.pdf: 1273955 bytes, checksum: 79e28497883fdc3e8ebe5907183a15d9 (MD5) Previous issue date: 2009 / Resumo: O presente trabalho aborda o desenvolvimento de metodologias para o cálculo das intensidades absolutas do espalhamento Raman vibracional produzido por moléculas em fase gasosa. Com o objetivo de reduzir a demanda por recursos computacionais nestes cálculos, foram desenvolvidas duas novas famílias de funções de base compactas pela aplicação do método de polarização elétrica de Sadlej às bases para uso com potenciais efetivos de caroço SBKJC e de Stuttgart-Colônia. Utilizando estas novas funções de base, as intensidades Raman podem ser obtidas com a mesma qualidade das bases Sadlej-pVTZ, que são referência no cálculo destas propriedades, porém com um custo computacional sensivelmente menor. Além disso, como estes pseudopotenciais foram modelados para descrever os efeitos relativísticos sobre os elétrons internos, as polarizabilidades e intensidades Raman obtidas no nível Hartree-Fock com estas novas bases concordam, dentro de um erro médio de 6%, com seus respectivos valores relativísticos Dirac-Hartree-Fock/Sadlei-pVTZ com hamiltoniano de Dirac-Coulomb. Também foi desenvolvida uma metodologia para o estudo das intensidades das transições Raman fundamentais, de combinação e sobretom, que inclui as correções para a anarmonicidade cúbica do potencial, introduzidas através de uma transformação de contato. Os resultados obtidos para a molécula de acetileno e seus isotopômeros deuterados mostram que a anarmonicidade mecânica exerce grande influência sobre as intensidades Raman, particularmente das transições de segunda ordem. Excetuando as transições de combinação, em geral, as correções de anarmoniciadade melhoram a concordância dos valores teóricos com os experimentais. Uma terceira parte deste trabalho trata do efeito Raman em condições ressonantes, onde uma expressão para estas intensidades foi derivada, implementada no programa PLACZEK e aplicada no cálculo do espectro Raman da molécula de trans-butadieno nas vizinhanças de sua transição eletrônica 1Bu. Este estudo mostrou que as aproximações utilizadas com maior frequência para simplificar o cálculo desta propriedade afetam significativamente as seções de choque desta molécula, sugerindo que estas aproximações devem ser evitadas em estudos desta natureza. / Abstract: In this work new methodologies for the calculation of absolute vibrational Raman intensities of gaseous systems are presented. In order to reduce the computational requirements in these calculations two families of compact basis functions were generated from the effective core potential valence basis sets SBKJC and Stuttgart-Cologne through the Sadlej's electric polarization procedure. The Raman intensities evaluated with the new bases are close to those obtained with the well successful Sadlej-pVTZ basis but the computational requirements are significatively reduced. Furthermore, since the effective core potentials SBKJC and Stuttgart-Cologne were developed to account for the relativistic effects on the inner electrons, the polarizabilities and Raman intensities evaluated at the Hartree-Fock level with the new bases agree with the relativistic Dirac-Hartree-Fock values, obtained using the Dirac-Coulomb Hamiltonian and the Sadlej-pVTZ set, within the mean error of 6%. In the second part of this work a methodology was developed for the study of fundamental, combination and overtone Raman transitions including a treatment based on the contact transform formalism for the mechanical anharmonicity from the cubic potential energy terms. The results obtained for acetylene and its deutered isotopomers show that anharmonicity effects on the Raman intensities can be very strong, particularly in the second order transitions. With the exception of the combination transitions, in general the corrections for mechanical anharmonicity improve the agreement between ab initio and experimental values. The resonance Raman scattering is the subject of the third part of this work where an expression for the resonance cross section was derived, implemented in the PLACZEK program and applied to the calculation of the resonance Raman spectrum of the trans-butadiene molecule in the region of its. / Doutorado / Físico-Química / Doutor em Ciências

In dieser Arbeit wird eine unrestricted Coupled-Cluster CC2 Response-Methode für die Berechnung von Eigenschaften erster und zweiter Ordnung, mit dem elektronischen g-Tensor als Schwerpunkt, präsentiert. Lokale Korrelations- und Dichtefittingnäherungen wurden verwendet. Die fundamentalen Konzepte notwendig für das Verständnis von Coupled-Cluster-Theorie, Dichtefitting, lokaler Korrelation, allgemeinen Coupled-Cluster Eigenschaften und dem elektronischen g-Tensor werden diskutiert. Die berechneten g-Tensoren werden mit denen durch Coupled-Cluster Singles and Doubles, Dichtefunktionaltheorie und Experiment erhaltenen verglichen. Effizienz und Genauigkeit der Näherung wird untersucht. Ein detailierter Anhang beschreibt die diagrammatische Coupled-Cluster-Theorie sowie ihre Anwendung zur Herleitung der verwendeten Arbeitsgleichungen. Die in dieser Arbeit entwickelte Methode ermöglicht es, den elektronischen g-Tensor von ausgedehnten Systemen mit einer Methode, die nicht auf Dichtefunktionaltheorie basiert, quantitativ vorherzusagen. Damit ist sie ein wichtiger Schritt hin zur Entwicklung von niedrig skalierenden Coupled-Cluster-Methoden höherer Ordnung für diese Art von Problem. / This work presents an unrestricted coupled-cluster CC2 response method using local correlation and density fitting approximations for the calculation of first and second order properties with particular focus on the electronic g-tensor. The fundamental concepts related to coupled-cluster theory, density fitting, local correlation, general coupled-cluster properties and the electronic g-tensor are discussed. The calculated g-tensors are benchmarked against those obtained from coupled-cluster singles and doubles, density functional theory and experiment. Efficiency and accuracy of the approximations is investigated. A detailed appendix covers the fundamentals of diagrammatic coupled-cluster and its application to the derivation of the working equations. The method presented in this thesis enables the quantitative prediction of the electronic g-tensor of extended systems with a method other than density functional theory. It represents an important step towards the development of low-scaling higher order coupled-cluster methods for this type of problem.

In dieser Arbeit wird eine unrestricted Coupled-Cluster CC2 Response-Methode für die Berechnung von Eigenschaften erster und zweiter Ordnung, mit dem elektronischen g-Tensor als Schwerpunkt, präsentiert. Lokale Korrelations- und Dichtefittingnäherungen wurden verwendet. Die fundamentalen Konzepte notwendig für das Verständnis von Coupled-Cluster-Theorie, Dichtefitting, lokaler Korrelation, allgemeinen Coupled-Cluster Eigenschaften und dem elektronischen g-Tensor werden diskutiert. Die berechneten g-Tensoren werden mit denen durch Coupled-Cluster Singles and Doubles, Dichtefunktionaltheorie und Experiment erhaltenen verglichen. Effizienz und Genauigkeit der Näherung wird untersucht. Ein detailierter Anhang beschreibt die diagrammatische Coupled-Cluster-Theorie sowie ihre Anwendung zur Herleitung der verwendeten Arbeitsgleichungen. Die in dieser Arbeit entwickelte Methode ermöglicht es, den elektronischen g-Tensor von ausgedehnten Systemen mit einer Methode, die nicht auf Dichtefunktionaltheorie basiert, quantitativ vorherzusagen. Damit ist sie ein wichtiger Schritt hin zur Entwicklung von niedrig skalierenden Coupled-Cluster-Methoden höherer Ordnung für diese Art von Problem. / This work presents an unrestricted coupled-cluster CC2 response method using local correlation and density fitting approximations for the calculation of first and second order properties with particular focus on the electronic g-tensor. The fundamental concepts related to coupled-cluster theory, density fitting, local correlation, general coupled-cluster properties and the electronic g-tensor are discussed. The calculated g-tensors are benchmarked against those obtained from coupled-cluster singles and doubles, density functional theory and experiment. Efficiency and accuracy of the approximations is investigated. A detailed appendix covers the fundamentals of diagrammatic coupled-cluster and its application to the derivation of the working equations. The method presented in this thesis enables the quantitative prediction of the electronic g-tensor of extended systems with a method other than density functional theory. It represents an important step towards the development of low-scaling higher order coupled-cluster methods for this type of problem.