Diversas metodologias foram desenvolvidas nas últimas décadas para cálculo de propriedades que representassem quantitativamente a distribuição de carga eletrônica de forma mais simplista. A mais básica destas propriedades é chamada de carga atômica. Contudo, não havendo unanimidade quanto à utilização de um formalismo de cálculo de carga para situações abrangentes de estudo, há a necessidade de trabalhos voltados para uma análise comparativa entre as respostas destes formalismos em termos de carga atômica e parâmetros derivados. Assim, fez-se nesta dissertação uma investigação sobre valores de carga atômica e propriedades dinâmicas relacionadas, com importância em estudos sobre movimentos vibracionais em moléculas, como fluxo de carga e fluxo de dipolo, obtidos com os formalismos de cálculo de carga de Mulliken, NPA, CHELPG e QTAIM. Neste trabalho também se avaliou o efeito da escolha do método de cálculo, como Hartree-Fock e métodos que incluem correlação eletrônica (MP2, MP4(SDQ) e CCSD), e do conjunto de funções de base, através de funções como cc-pVDZ, cc-pVTZ e cc-pVQZ, sobre estas propriedades dinâmicas. Os sistemas analisados incluíram moléculas diatômicas e triatômicas lineares (HF, HCl, LiH, NaH, NaCl, LiF, NaF, LiCl, BF, AlF, BeO, MgO, CO, ClF, CO2, CS2, OCS, HCN e HNC) formadas por ligações de caráter variado, desde altamente iônicas até covalentes e incluindo ligações múltiplas. Também foram estudadas moléculas de clorofluorometanos (CH4, CH3Cl, CH3F, CH2Cl2, CH2F2, CH2ClF, CHCl3, CHF3, CHCl2F, CHClF2, CCl2F2, CClF3, CFCl3, CCl4, e CF4) para observação do efeito da troca de substituintes nas propriedades citadas. Pelos resultados obtidos, pode-se afirmar que apenas os formalismos NPA e QTAIM apresentam bom comportamento quanto à convergência em relação ao método de cálculo e/ou tamanho do conjunto de funções de base utilizados no estudo do fluxo de carga. Entretanto, apenas os valores QTAIM são consistentes com certas considerações químicas fundamentais, como fluxos de carga tendendo a zero durante o estiramento de ligações de predominante caráter iônico, em moléculas com estruturas próximas à geometria de equilíbrio. As cargas e seus fluxos obtidos com Mulliken apresentaram alta dependência e problemas de convergência com a escolha da função de base, além de valores incoerentes em alguns sistemas. Por sua vez, CHELPG não se mostrou adequado à aplicação da aproximação finita de dois pontos na obtenção dos valores numéricos de fluxos de carga. A análise da resposta destas propriedades à troca de substituintes em moléculas de clorofluorometanos seguiu destacando positivamente QTAIM em relação aos outros formalismos. Enquanto CHELPG demonstrou oscilações inconsistentes em gráficos destes valores em função do número de átomos de cloro e/ou flúor, NPA e Mulliken se mostraram sensíveis à troca de substituintes, entretanto, os valores de fluxo de carga observados em alguns casos estão em desacordo com a tendência esperada na troca de átomos de hidrogênio por átomos de cloro ou flúor. / Several methodologies were developed in the last few decades in order to obtain a property which could represent quantitatively electronic charge distributions in a simple way. The fundamental quantity in this treatment is called atomic charge. However, as long as there is not an agreement about the most indicated method to determine atomic charges for general systems or responses under study, it is necessary to analyze, comparatively, how these methods behave in given situations and how the values derived from them respond in each case. Hence, an investigation including charges and related quantities as charge flux and atomic dipole flux, which are of interest to vibrational analysis, was done by means of values resulting from four formalisms, that are, Mulliken, NPA, CHELPG and QTAIM. In this study were also evaluated the changes in such dynamic properties when the calculations are done by means of different methods, as Hartree-Fock and methods that include electron correlation (MP2, MP4(SDQ) and CCSD) and, with different basis sets as cc-pVDZ, cc-pVTZ and cc-pVQZ. The systems analyzed were diatomic and linear triatomic molecules (HF, HCl, LiH, NaH, NaCl, LiF, NaF, LiCl, BF, AlF, BeO, MgO, CO, FCl, CO2, CS2, OCS, HCN and HNC) including diverse bonding character, such as highly ionic or covalent bonds along with multiple bonds. Also, charge and charge flux parameters in chlorofluoromethane molecules (CH4, CH3Cl, CH3F, CH2Cl2, CH2F2, CH2ClF, CHCl3, CHF3, CHCl2F, CHClF2, CCl2F2, CClF3, CFCl3, CCl4 and CF4) were studied to analyze the effects in these properties during the exchange of substituent atoms. Considering the data obtained, one can infer that only NPA and QTAIM formalisms result in satisfactory convergence patterns with chosen methods and/or basis set sizes during the determination of charge and charge flux values. However, only QTAIM charge fluxes seem to follow certain chemical considerations, as low values for charge flux in a bond enlargement in systems with a predominant ionic character close to their equilibrium geometry. The Mulliken formalism shows high dependence and convergence issues in basis set size increments, as well as some inconsistent values. On other hand, CHELPG formalism is not suited to the finite approach for numerical derivatives in its two-point version. The study of substituent effects in chlorofluoromethanes reinforces the performance of QTAIM when compared to other formalisms. While CHELPG returned inconsistent oscillations in plots against the number of chlorine/fluorine atoms, NPA and Mulliken exhibited some sensibility with the change of substituent, though the flux values observed in a few cases are in disagreement with the tendencies expected when the hydrogen atoms are switched by chlorine or fluorine atoms.

Desde o início do uso de ferramentas computacionais na química, pesquisadores notaram a necessidade de um adequado tratamento da correlação eletrônica para a acurada descrição da estrutura eletrônica. Algum tempo depois, perceberam que, além da correlação, haviam ainda deficiências nos resultados obtidos, as quais estavam relacionadas com efeitos relativísticos, principalmente quando tentavam tratar moléculas com átomos pesados. Um terceiro aspecto a ser levado em consideração nestes estudos diz respeito ao uso de um conjunto acurado de funções de base. No caso específico de cálculos relativísticos, se possível, tais conjuntos ainda precisam garantir a eliminação do prolapso variacional, um problema que está relacionado com uma descrição deficiente da região mais próxima dos núcleos. Com esse propósito, o conjunto RPF-4Z foi desenvolvido recentemente. Sendo assim, este projeto foi voltado para a análise comparativa da qualidade do conjunto RPF-4Z. Desta forma, foram avaliadas propriedades fundamentais das moléculas como, por exemplo, geometrias, momentos de dipolo e constantes espectroscópicas. Simultaneamente, uma propriedade desafiadora, o gradiente de campo elétrico na posição de núcleos de xenônio, também foi considerada. Os resultados obtidos até agora reforçam a eficiência do conjunto RPF-4Z, que é capaz de fornecer valores comparáveis àqueles dados por conjuntos de base de mesma qualidade, mas com menor demanda por recursos computacionais. / Early in the application of computational framework in chemistry, researchers noticed the need for an adequate electronic correlation treatment in order to accurately describe electronic structures. Some years later they realized that, besides correlation, there were also deficiencies in the results, which were related to relativistic effects, especially when dealing with molecules containing heavy atoms. A third aspect to be taken into account is related to the use of an accurate basis set. Specifically for relativistic calculations, these basis sets must also ensure the elimination of variational prolapse if possible, which is a problem related to a poor description of the innermost region close to the nuclei. Thus, the RPF-4Z basis set was recently developed for this aim. This project is focused on a comparative analysis regarding the RPF-4Z basis set\'s quality. Thereby, fundamental properties of molecules were evaluated, such as geometries, dipole moments and spectroscopic constants. At the same time, a challenging property, the electric field gradient at the xenon nuclei, was considered as well. The results obtained so far reinforce the efficiency of the RPF-4Z basis set, which is capable of providing comparable values to those obtained by same quality basis sets but with a lower demand for computational resources.

Desde o início do uso de ferramentas computacionais na química, pesquisadores notaram a necessidade de um adequado tratamento da correlação eletrônica para a acurada descrição da estrutura eletrônica. Algum tempo depois, perceberam que, além da correlação, haviam ainda deficiências nos resultados obtidos, as quais estavam relacionadas com efeitos relativísticos, principalmente quando tentavam tratar moléculas com átomos pesados. Um terceiro aspecto a ser levado em consideração nestes estudos diz respeito ao uso de um conjunto acurado de funções de base. No caso específico de cálculos relativísticos, se possível, tais conjuntos ainda precisam garantir a eliminação do prolapso variacional, um problema que está relacionado com uma descrição deficiente da região mais próxima dos núcleos. Com esse propósito, o conjunto RPF-4Z foi desenvolvido recentemente. Sendo assim, este projeto foi voltado para a análise comparativa da qualidade do conjunto RPF-4Z. Desta forma, foram avaliadas propriedades fundamentais das moléculas como, por exemplo, geometrias, momentos de dipolo e constantes espectroscópicas. Simultaneamente, uma propriedade desafiadora, o gradiente de campo elétrico na posição de núcleos de xenônio, também foi considerada. Os resultados obtidos até agora reforçam a eficiência do conjunto RPF-4Z, que é capaz de fornecer valores comparáveis àqueles dados por conjuntos de base de mesma qualidade, mas com menor demanda por recursos computacionais. / Early in the application of computational framework in chemistry, researchers noticed the need for an adequate electronic correlation treatment in order to accurately describe electronic structures. Some years later they realized that, besides correlation, there were also deficiencies in the results, which were related to relativistic effects, especially when dealing with molecules containing heavy atoms. A third aspect to be taken into account is related to the use of an accurate basis set. Specifically for relativistic calculations, these basis sets must also ensure the elimination of variational prolapse if possible, which is a problem related to a poor description of the innermost region close to the nuclei. Thus, the RPF-4Z basis set was recently developed for this aim. This project is focused on a comparative analysis regarding the RPF-4Z basis set\'s quality. Thereby, fundamental properties of molecules were evaluated, such as geometries, dipole moments and spectroscopic constants. At the same time, a challenging property, the electric field gradient at the xenon nuclei, was considered as well. The results obtained so far reinforce the efficiency of the RPF-4Z basis set, which is capable of providing comparable values to those obtained by same quality basis sets but with a lower demand for computational resources.

Diversas metodologias foram desenvolvidas nas últimas décadas para cálculo de propriedades que representassem quantitativamente a distribuição de carga eletrônica de forma mais simplista. A mais básica destas propriedades é chamada de carga atômica. Contudo, não havendo unanimidade quanto à utilização de um formalismo de cálculo de carga para situações abrangentes de estudo, há a necessidade de trabalhos voltados para uma análise comparativa entre as respostas destes formalismos em termos de carga atômica e parâmetros derivados. Assim, fez-se nesta dissertação uma investigação sobre valores de carga atômica e propriedades dinâmicas relacionadas, com importância em estudos sobre movimentos vibracionais em moléculas, como fluxo de carga e fluxo de dipolo, obtidos com os formalismos de cálculo de carga de Mulliken, NPA, CHELPG e QTAIM. Neste trabalho também se avaliou o efeito da escolha do método de cálculo, como Hartree-Fock e métodos que incluem correlação eletrônica (MP2, MP4(SDQ) e CCSD), e do conjunto de funções de base, através de funções como cc-pVDZ, cc-pVTZ e cc-pVQZ, sobre estas propriedades dinâmicas. Os sistemas analisados incluíram moléculas diatômicas e triatômicas lineares (HF, HCl, LiH, NaH, NaCl, LiF, NaF, LiCl, BF, AlF, BeO, MgO, CO, ClF, CO2, CS2, OCS, HCN e HNC) formadas por ligações de caráter variado, desde altamente iônicas até covalentes e incluindo ligações múltiplas. Também foram estudadas moléculas de clorofluorometanos (CH4, CH3Cl, CH3F, CH2Cl2, CH2F2, CH2ClF, CHCl3, CHF3, CHCl2F, CHClF2, CCl2F2, CClF3, CFCl3, CCl4, e CF4) para observação do efeito da troca de substituintes nas propriedades citadas. Pelos resultados obtidos, pode-se afirmar que apenas os formalismos NPA e QTAIM apresentam bom comportamento quanto à convergência em relação ao método de cálculo e/ou tamanho do conjunto de funções de base utilizados no estudo do fluxo de carga. Entretanto, apenas os valores QTAIM são consistentes com certas considerações químicas fundamentais, como fluxos de carga tendendo a zero durante o estiramento de ligações de predominante caráter iônico, em moléculas com estruturas próximas à geometria de equilíbrio. As cargas e seus fluxos obtidos com Mulliken apresentaram alta dependência e problemas de convergência com a escolha da função de base, além de valores incoerentes em alguns sistemas. Por sua vez, CHELPG não se mostrou adequado à aplicação da aproximação finita de dois pontos na obtenção dos valores numéricos de fluxos de carga. A análise da resposta destas propriedades à troca de substituintes em moléculas de clorofluorometanos seguiu destacando positivamente QTAIM em relação aos outros formalismos. Enquanto CHELPG demonstrou oscilações inconsistentes em gráficos destes valores em função do número de átomos de cloro e/ou flúor, NPA e Mulliken se mostraram sensíveis à troca de substituintes, entretanto, os valores de fluxo de carga observados em alguns casos estão em desacordo com a tendência esperada na troca de átomos de hidrogênio por átomos de cloro ou flúor. / Several methodologies were developed in the last few decades in order to obtain a property which could represent quantitatively electronic charge distributions in a simple way. The fundamental quantity in this treatment is called atomic charge. However, as long as there is not an agreement about the most indicated method to determine atomic charges for general systems or responses under study, it is necessary to analyze, comparatively, how these methods behave in given situations and how the values derived from them respond in each case. Hence, an investigation including charges and related quantities as charge flux and atomic dipole flux, which are of interest to vibrational analysis, was done by means of values resulting from four formalisms, that are, Mulliken, NPA, CHELPG and QTAIM. In this study were also evaluated the changes in such dynamic properties when the calculations are done by means of different methods, as Hartree-Fock and methods that include electron correlation (MP2, MP4(SDQ) and CCSD) and, with different basis sets as cc-pVDZ, cc-pVTZ and cc-pVQZ. The systems analyzed were diatomic and linear triatomic molecules (HF, HCl, LiH, NaH, NaCl, LiF, NaF, LiCl, BF, AlF, BeO, MgO, CO, FCl, CO2, CS2, OCS, HCN and HNC) including diverse bonding character, such as highly ionic or covalent bonds along with multiple bonds. Also, charge and charge flux parameters in chlorofluoromethane molecules (CH4, CH3Cl, CH3F, CH2Cl2, CH2F2, CH2ClF, CHCl3, CHF3, CHCl2F, CHClF2, CCl2F2, CClF3, CFCl3, CCl4 and CF4) were studied to analyze the effects in these properties during the exchange of substituent atoms. Considering the data obtained, one can infer that only NPA and QTAIM formalisms result in satisfactory convergence patterns with chosen methods and/or basis set sizes during the determination of charge and charge flux values. However, only QTAIM charge fluxes seem to follow certain chemical considerations, as low values for charge flux in a bond enlargement in systems with a predominant ionic character close to their equilibrium geometry. The Mulliken formalism shows high dependence and convergence issues in basis set size increments, as well as some inconsistent values. On other hand, CHELPG formalism is not suited to the finite approach for numerical derivatives in its two-point version. The study of substituent effects in chlorofluoromethanes reinforces the performance of QTAIM when compared to other formalisms. While CHELPG returned inconsistent oscillations in plots against the number of chlorine/fluorine atoms, NPA and Mulliken exhibited some sensibility with the change of substituent, though the flux values observed in a few cases are in disagreement with the tendencies expected when the hydrogen atoms are switched by chlorine or fluorine atoms.

Submitted by isabela.moljf@hotmail.com (isabela.moljf@hotmail.com) on 2017-05-08T11:42:32Z No. of bitstreams: 1 diegofernandodasilvapaschoal.pdf: 9955630 bytes, checksum: a25cace9c9785b91c273376bf940d222 (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2017-05-17T13:42:19Z (GMT) No. of bitstreams: 1 diegofernandodasilvapaschoal.pdf: 9955630 bytes, checksum: a25cace9c9785b91c273376bf940d222 (MD5) / Made available in DSpace on 2017-05-17T13:42:19Z (GMT). No. of bitstreams: 1 diegofernandodasilvapaschoal.pdf: 9955630 bytes, checksum: a25cace9c9785b91c273376bf940d222 (MD5) Previous issue date: 2014-08-26 / CAPES - Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Um estudo sistemático a respeito da importância do nível de teoria e do conjunto de funções de base no cálculo de propriedades moleculares foi conduzido. Foram realizados estudos a respeito das propriedades ópticas lineares (OL) e não-lineares (ONL) de moléculas diatômicas, pequenas moléculas poliatômicas e moléculas orgânicas conjugadas com grupos doadores e retiradores de elétrons. Além disso, foi avaliada a estrutura e reatividade de complexos de Pt(II) e Pd(II). Por fim, um estudo a respeito do deslocamento químico de 195Pt foi conduzido, onde diversos parâmetros que influenciam em tal propriedade foram extensivamente analisados. Para cada trabalho proposto um novo conjunto de funções de base foi desenvolvido. Foram propostas as bases D10 (BH), P3 (CO), F3 (CS), J5 (N2), NLO (H,C,N,O,F,S), NLO-X (X=I,II,III,V,aV) (H,B-F,Si-Cl), mDZP (Pd,Pt), kPd-ADZP(Pd) e NMR-TZPP-DKH (H-He, Li-Ne, Na-Ar, K-Ca, Ga-Kr, Rb-Sr, In-Xe e Pt). Previsões das propriedades OL e ONL de diversas moléculas foram realizadas. Para um conjunto de moléculas com valores de primeira hiperpolarizabilidade (β) variando de 0 a 190 esu um desvio médio absoluto de 13,2 esu foi encontrado no nível cam-B3LYP/NLO-V em comparação com um desvio de 27,2 esu com a base da literatura 6-31G(2d). Além disso, foram realizados estudos de estrutura e reatividade da cisplatina e do cispaládio. Para a reação de hidrólise da cDDPt foi prevista uma barreira de energia no nível B3LYP/mDZP/6-31+G(d) de 22,8 kcal.mol-1 que está em excelente acordo com o valor experimental de 22,±0,4 kcal.mol-1. Considerando a mesma reação, porém para o análogo de Pd, um valor de 17,11 kcal.mol-1 no nível B3LYP/mDZP/6-31+G(d) e de 16,94 kcal.mol-1 no nível B3LYP/kPd-ADZP/6-31+G(d) foram previstos e estão em bom acordo com o valor esperado de 16,34 kcal.mol-1. Somado a isso, uma análise a respeito do deslocamento químico de 195Pt foi abordada, onde para uma ampla faixa de 73 complexos de Pt(II) um desvio absoluto médio de apenas 156 ppm foi encontrado no nível GIAO-B3LYP(DKHSO)/NMR-TZPP-DKH/IEFPCM-UFF. Todas as bases aqui propostas foram testadas de forma sistemática e, no geral, bons resultados foram encontrados para as propriedades analisadas e com custos computacionais altamente acessíveis. / A systematic study about the importance of the level of theory and the basis sets in the calculation of molecular properties was conducted. It performed studies on the linear and nonlinear optical properties of diatomic molecules, small polyatomic molecules and conjugated donor/acceptor organic molecules. In addition, the structure and reactivity of Pt(II) and Pd(II) complexes were evaluated. Finally, a study about the 195Pt chemical shift was conducted, where various parameters that influence such property have been extensively analyzed. For each work proposed a new basis set was developed. The following basis sets were proposed: D10 (BH), P3 (CO), F3 (CS), J5 (N2), NLO (H,C,N,O,F,S), NLO-X (X=I,II,III,V,aV) (H,B-F,Si-Cl), mDZP (Pd,Pt), kPd-ADZP(Pd) and NMR-TZPP-DKH (H-He, Li-Ne, Na-Ar, K-Ca, Ga-Kr, Rb-Sr, In-Xe e Pt). Estimates of L-NLO properties of several molecules were performed. For a set of molecules with values of first hyperpolarizability (β) ranging from 0 to 190 esu, an average absolute deviation of 13,2 esu was found at cam-B3LYP/NLO-V level compared with 27,2 esu with the standard basis set 6-31G(2d). Furthermore, studies of structure and reactivity of cisplatin and cispalladium were performed. For the aquation reaction of cisplatin an energy barrier of 22.8 kcal.mol-1 was predicted at B3LYP/mDZP/6-31+G(d) level, which it is in excellent agreement with the experimental value of 22.9±0.4 kcal.mol-1. Considering the same reaction, but for Pd analogous, a value of 17.11 kcal.mol-1 at B3LYP/mDZP/6-31+G(d) level and 16.94 kcal.mol-1 at B3LYP/kPd-ADZP/6-31+G(d) level were predicted and these values are in good agreement with the expected value of 16.34 kcal.mol-1. Added to this, an analysis about the 195Pt chemical shift was addressed, where for a wide range of 73 Pt(II) complexes and average absolute deviation of only 156 ppm was found at GIAO-B3LYP(DKHSO)/NMR-TZPP-DKH/IEFPCM-UFF level. All basis sets proposed here were systematically tested and, in general, good results were found for the properties of interest and highly affordable computational costs.

The formation and patterns of a monolayer are determined by the interplay of two fundamental interactions, adsorbate-substrate and intermolecular interactions. The binding strength between adsorbate and substrate affects the mobility of the adsorbate at the surface and the stability of the complex. The intermolecular interaction plays a significant role in the monolayer patterns on the epitaxial layer of the substrate. A monolayer can be formed either by a spontaneous self-assembly, or by fabrication via atomic-layer deposition (ALD). The physical and chemical properties of the resulting monolayer have a broad array of applications in fabricating functional materials for hydrophobic or hydrophilic surfaces, biological sensors, alternating the properties of the substrate, catalysis and forming ordered layered structures. In this dissertation, the investigation focuses primarily on the influence of the surface topology on the binding behaviour of adsorbate-surface complexes. The state of the art DFT-TS method is used to simulate the sulfur-containing amino acids at complex gold surfaces and examine the relationship between the binding strengths and the binding sites with various nearest neighbouring environments. The same method is also used to determine if a chemical reaction will take place for various catalytic silicon precursors at a silicon oxide surface. Simulating surface chemistry using the DFT-TS method requires intensive com- puting resources, including CPU use and computing time. Another focus of this dissertation is to increase the data generating speed by reducing the size of the sim- ulated systems without altering the outcome. A relatively small gold cluster is used to study the binding behaviours of small organic molecules on the cluster. The same strategy is also used to simulate the chemical reactions between various self-catalying silicon precursors and a water molecule. / Graduate / 2021-10-21

In dieser Dissertation werden ab initio Theorien zur Beschreibung der Zustände von perfekten halbleitenden und nichtleitenden Kristallen, unter Berücksichtigung elektronischer Korrelationen, abgeleitet und angewandt. Als Ausgangsbasis dient hierzu die Hartree-Fock Approximation in Verbindung mit Wannier-Orbitalen. Darauf aufbauend studiere ich zunächst in Teil I der Abhandlung den Grundzustand der wasserstoffbrückengebundenen Fluorwasserstoff und Chlorwasserstoff zick-zack Ketten und analysiere die langreichweitigen Korrelationsbeiträge. Dabei mache ich die Basissatzextrapolationstechniken, die für kleine Moleküle entwickelt wurden, zur Berechnung von hochgenauen Bindungsenergien von Kristallen nutzbar. In Teil II der Arbeit leite ich zunächst eine quantenfeldtheoretische ab initio Beschreibung von Elektroneneinfangzuständen und Lochzuständen in Kristallen her. Grundlage hierbei ist das etablierte algebraische diagrammatische Konstruktionsschema (ADC) zur Approximation der Selbstenergie für die Bestimmung der Vielteilchen-Green's-Funktion mittels der Dyson-Gleichung. Die volle Translationssymmetrie des Problems wird hierbei beachtet und die Lokalität elektronischer Korrelationen ausgenutzt. Das resultierende Schema wird Kristallorbital-ADC (CO-ADC) genannt. Ich berechne damit die Quasiteilchenbandstruktur einer Fluorwasserstoffkette und eines Lithiumfluoridkristalls. In beiden Fällen erhalte ich eine sehr gute Übereinstimmung zwischen meinen Resultaten und den Ergebnissen aus anderen Methoden. / In this dissertation, theories for the ab initio description of the states of perfect semiconducting and insulating crystals are derived and applied. Electron correlations are treated thoroughly based on the Hartree-Fock approximation formulated in terms of Wannier orbitals. In part I of the treatise, I study the ground state of hydrogen-bonded hydrogen fluoride and hydrogen chloride zig-zag chains. I analyse the long-range contributions of electron correlations. Thereby, I employ basis set extrapolation techniques, which have originally been developed for small molecules, to also obtain highly accurate binding energies of crystals. In part II of the thesis, I devise an ab initio description of the electron attachment and electron removal states of crystals using methods of quantum field theory. I harness the well-established algebraic diagrammatic construction scheme (ADC) to approximate the self-energy, used in conjunction with the Dyson equation, to determine the many-particle Green's function for crystals. Thereby, the translational symmetry of the problem and the locality of electron correlations are fully exploited. The resulting scheme is termed crystal orbital ADC (CO-ADC). It is applied to obtain the quasiparticle band structure of a hydrogen fluoride chain and a lithium fluoride crystal. In both cases, a very good agreement of my results to those determined with other methods is observed.

In dieser Dissertation werden ab initio Theorien zur Beschreibung der Zustände von perfekten halbleitenden und nichtleitenden Kristallen, unter Berücksichtigung elektronischer Korrelationen, abgeleitet und angewandt. Als Ausgangsbasis dient hierzu die Hartree-Fock Approximation in Verbindung mit Wannier-Orbitalen. Darauf aufbauend studiere ich zunächst in Teil I der Abhandlung den Grundzustand der wasserstoffbrückengebundenen Fluorwasserstoff und Chlorwasserstoff zick-zack Ketten und analysiere die langreichweitigen Korrelationsbeiträge. Dabei mache ich die Basissatzextrapolationstechniken, die für kleine Moleküle entwickelt wurden, zur Berechnung von hochgenauen Bindungsenergien von Kristallen nutzbar. In Teil II der Arbeit leite ich zunächst eine quantenfeldtheoretische ab initio Beschreibung von Elektroneneinfangzuständen und Lochzuständen in Kristallen her. Grundlage hierbei ist das etablierte algebraische diagrammatische Konstruktionsschema (ADC) zur Approximation der Selbstenergie für die Bestimmung der Vielteilchen-Green's-Funktion mittels der Dyson-Gleichung. Die volle Translationssymmetrie des Problems wird hierbei beachtet und die Lokalität elektronischer Korrelationen ausgenutzt. Das resultierende Schema wird Kristallorbital-ADC (CO-ADC) genannt. Ich berechne damit die Quasiteilchenbandstruktur einer Fluorwasserstoffkette und eines Lithiumfluoridkristalls. In beiden Fällen erhalte ich eine sehr gute Übereinstimmung zwischen meinen Resultaten und den Ergebnissen aus anderen Methoden. / In this dissertation, theories for the ab initio description of the states of perfect semiconducting and insulating crystals are derived and applied. Electron correlations are treated thoroughly based on the Hartree-Fock approximation formulated in terms of Wannier orbitals. In part I of the treatise, I study the ground state of hydrogen-bonded hydrogen fluoride and hydrogen chloride zig-zag chains. I analyse the long-range contributions of electron correlations. Thereby, I employ basis set extrapolation techniques, which have originally been developed for small molecules, to also obtain highly accurate binding energies of crystals. In part II of the thesis, I devise an ab initio description of the electron attachment and electron removal states of crystals using methods of quantum field theory. I harness the well-established algebraic diagrammatic construction scheme (ADC) to approximate the self-energy, used in conjunction with the Dyson equation, to determine the many-particle Green's function for crystals. Thereby, the translational symmetry of the problem and the locality of electron correlations are fully exploited. The resulting scheme is termed crystal orbital ADC (CO-ADC). It is applied to obtain the quasiparticle band structure of a hydrogen fluoride chain and a lithium fluoride crystal. In both cases, a very good agreement of my results to those determined with other methods is observed.

In dieser Arbeit werden Algorithmen für die Berechnung elektronischer Korrelations- und Anregungsenergien mittels der Coupled-Cluster Methode auf adaptiven Gittern entwickelt und implementiert. Die jeweiligen Funktionen und Operatoren werden adaptiv durch Multiskalenanalyse dargestellt, was eine Basissatz unabängige Beschreibung mit kontrollierter numerischer Genauigkeit ermöglicht. Gleichungen für die Coupled-Cluster Methode werden in einem verallgemeinerten Rahmen, unabhängig von virtuellen Orbitalen und globalen Basissätzen, neu formuliert. Hierzu werden die amplitudengewichteten Anregungen in virtuelle Orbitale ersetzt durch Anregungen in n-Elektronenfunktionen, welche durch Gleichungen im n-Elektronen Ortsraum bestimmt sind. Die erhaltenen Gleichungen können, analog zur Basissatz abh¨angigen Form, mit leicht angepasster Interpretation diagrammatisch dargestellt werden. Aufgrund des singulären Coulomb Potentials werden die Arbeitsgleichungen mit einem explizit korrelierten Ansatz regularisiert. Coupled-Cluster singles mit genäherten doubles (CC2) und ähnliche Modelle werden, für geschlossenschalige Systeme und in regularisierter Form, in die MADNESS Bibliothek (eine allgemeine Bibliothek zur Darstellung von Funktionen und Operatoren mittels Multiskalenanalyse) implementiert. Mit der vorgestellten Methode können elektronische CC2 Paarkorrelationsenergien und Anregungsenergien mit bestimmter numerischer Genauigkeit unabhängig von globalen Basissätzen berechnet werden, was anhand von kleinen Molekülen verifiziert wird / In this work algorithms for the computation of electronic correlation and excitation energies with the Coupled-Cluster method on adaptive grids are developed and implemented. The corresponding functions and operators are adaptively represented with multiresolution analysis allowing a basis-set independent description with controlled numerical accuracy. Equations for the coupled-cluster model are reformulated in a generalized framework independent of virtual orbitals and global basis-sets. For this, the amplitude weighted excitations into virtuals are replaced by excitations into n-electron functions which are determined by projected equations in the n-electron position space. The resulting equations can be represented diagrammatically analogous to basis-set dependent approaches with slightly adjusted rules of interpretation. Due to the singular Coulomb potential, the working equations are regularized with an explicitly correlated ansatz. Coupled-cluster singles with approximate doubles (CC2) and similar models are implemented for closed-shell systems and in regularized form into the MADNESS library (a general library for the representation of functions and operators with multiresolution analysis). With the presented approach electronic CC2 pair-correlation energies and excitation energies can be computed with definite numerical accuracy and without dependence on global basis sets, which is verified on small molecules.