The variational quantum eigensolver (VQE) approach is currently one of the most promising strategies for simulating chemical systems on quantum hardware. In this work, I will describe a new quantum algorithm and a new set of classical algorithms based on VQE. The quantum algorithm, ADAPT-VQE, shows promise in mitigating many of the known limitations of VQEs: Ansatz ambiguity, local minima, and barren plateaus are all addressed to varying degrees by ADAPT-VQE. The classical algorithm family, O2DX-UCCSD, draws inspiration from VQEs, but is classically solvable in polynomial time. This group of algorithms yields equations similar to those of the linearized coupled cluster theory (LCCSD) but is more systematically improvable and, for X = 3 or X = ∞, can break single bonds, which LCCSD cannot do. The overall aim of this work is to showcase the richness of the VQE algorithm and the breadth of its derivative applications. / Doctor of Philosophy / A core goal of quantum chemistry is to compute accurate ground-state energies for molecules. Quantum computers promise to simulate quantum systems in ways that classical computers cannot. It is believed that quantum computers may be able to characterize molecules that are too large for classical computers to treat accurately. One approach to this is the variational quantum eigensolver, or VQE. The idea of a VQE is to use a quantum computer to measure the molecular energy associated with a quantum state which is parametrized by some classical set of parameters. A classical computer will use a classical optimization scheme to update those parameters before the quantum computer measures the energy again. This loop is expected to minimize the quantum resources needed for a quantum computer to be useful, since much of the work is outsourced to classical computers. In this work, I describe two novel algorithms based on the VQE which solve some of its problems.

The efficient computation of dynamic (time-dependent) molecular properties is a broad field with numerous applications in aiding molecular synthesis and design, with a particular preva- lence in spectroscopic predictions. Typical methods for computing the response of a molecu- lar system to an electromagnetic field (EMF) considers a quantum mechanical description of the molecule and a classical approximation for the EMF. Methods for describing light-matter interactions with high-accuracy electronic structure methods, such as coupled cluster (CC), are discussed, with a focus on improving the efficiency of such methods. The CC method suffers from high-degree polynomial scaling. In addition to the ground-state calculation, computing dynamic properties requires the description of sensitive excited-state effects. The cost of such methods often prohibits the accurate calculation of response prop- erties for systems of significant importance, such as large-molecule drug candidates or chiral species present in biological systems. While the literature is ripe with reduced-scaling meth- ods for CC ground-state calculations, considerably fewer approaches have been applied to excited-state properties, with even fewer still providing adequate results for realistic systems. This work presents three studies on the reduction of the cost of molecular property evalu- ations, in the hopes of closing this gap in the literature and widening the scope of current theoretical methods. There are two main ways of simulating time-dependent light-matter interactions: one may consider these effects in the frequency domain, where the response of the system to an EMF is computed directly; or, the response may be considered explicitly in the time domain, where wave function (or density) parameters can be propagated in time and examined in detail. Each methodology has unique advantages and computational bottlenecks. The first two studies focus on frequency-domain calculations, and employ fragmentation and machine- learning techniques to reduce the cost of single-molecule calculations or sets of calculations across a series of geometric conformations. The third study presents a novel application of the local correlation technique to real-time CC calculations, and highlights deficiencies and possible solutions to the approach. / Doctor of Philosophy / Theoretical chemistry plays a key role in connecting experimental results with physical inter- pretation. Paramount to the success of theoretical methods is the ability to predict molecular properties without the need for costly high-throughput synthesis, aiding in the determina- tion of molecular structure and the design of new materials. Light-matter interactions, which govern spectroscopic techniques, are particularly complicated, and sensitive to the theoreti- cal tools employed in their prediction. Compounding the issue of accuracy is one of efficiency — accurate theoretical methods typically incur steep scaling of computational cost (memory and processor time) with respect to the size of the system. An important aspect in improving the efficiency of these methods is understanding the nature of light-matter interactions at a quantum level. Many unanswered questions still remain, such as, "Can light-matter interactions be thought of as a sum of interactions be- tween smaller fragments of the system?" and "Can conventional methods of accelerating ground-state calculations be expected to perform well for spectroscopic properties?" The present work seeks to answer these questions through three studies, focusing on improving the efficiency of these techniques, while simultaneously addressing their fundamental flaws and providing reasonable alternatives.

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.

Diese Dissertation beschreibt einen Fortschritt in der Vorhersage elektronischer Materialeigenschaften durch quantenchemische Methoden höherer Ordnung, mit Fokus auf der Berechnung elektronischer Bandlücken innerhalb des FHI-aims-Softwarepakets. Im Rahmen dieser Arbeit werden Coupled-Cluster-Methoden durch eine neue Schnittstelle zwischen FHI-aims und dem Coupled cluster for solids (Cc4s) Code implementiert. Dabei werden zwei zentrale Herausforderungen in Equation-of-Motion-Coupled-Cluster-Rechnungen mit Einfach- und Zweifachanregungen diskutiert: Konvergenz im Bezug auf den Basissatz und auf die Systemgröße. Für die Untersuchung der Basissatzunvollständigkeit werden numerische atomzentrierte Funktionen verwendet und Extrapolationstechniken unter Verwendung von valenz-korrelationskonsistenter Basissätze untersucht. Für Effekte endlicher Systemgröße wird der Equation-of-Motion-Coupled-Cluster-Strukturfaktor hergeleitet, um die Konvergenz der elektronischen Korrelation im langreichweitigen Limes zu analysieren, wobei Konvergenzraten für Ionisationspotentiale und Elektronenaffinitäten in verschiedenen Dimensionen hergeleitet werden. Die Arbeit identifiziert einen Zusammenhang zwischen der Konvergenz der Bandlücke der Equation-of-Motion-Coupled-Cluster- und der G0W0-Methode, was eine GW-gestützte Abschätzung verbleibender systemgrößenbedingter Fehler ermöglicht. Diese Methodik wird durch Bandlückenberechnungen für Materialien wie Diamant, Borphosphid, Lithiumhydrid und Magnesiumoxid validiert, wobei für einige Materialien eine verbesserte Genauigkeit nachgewiesen wird, während verbleibende Herausforderungen für Isolatoren mit großer Bandlücke identifiziert werden. / This thesis advances the prediction of electronic properties in materials through high-level quantum chemistry methods, focusing on electronic band gap calculations within the FHI-aims software package. The work implements coupled-cluster methods through a new interface between FHI-aims and the Coupled cluster for solids (Cc4s) code. The research addresses two primary challenges in equation-of-motion coupled-cluster calculations with single and double excitations: basis set convergence and system size convergence. For basis set incompleteness, the study evaluates numeric atom-centered functions and explores extrapolation techniques using valence-correlation consistent basis sets. For finite-size effects, the equation-of-motion coupled-cluster structure factor is derived to analyze electronic correlation convergence in the long-range limit, establishing convergence rates for ionization potentials and electron affinities across different dimensions. The work identifies a correlation between finite-size convergence in equation-of-motion coupled-cluster and G0W0 methods, enabling GW-aided estimation of remaining finite-size errors. The methodology is validated through band gap calculations for materials including diamond, boron phosphide, lithium hydride, and magnesium oxide, demonstrating improved accuracy for some materials while identifying persistent challenges for wide-gap insulators.