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In quantum chemistry, scientists aim to solve the time-independent Schrödinger equation by employing a variety of approximation techniques whose accuracy are typically inversely proportional to their computational cost. This problem is amplified when it comes to chiral molecules, whose stereochemical assignments and associated chiroptical properties can be incredibly sensitive to small changes in their three-dimensional structure, requiring highly accurate theoretical methods. On the other hand, due to the polynomial scaling with system size, it is sometimes impractical to apply such methods to chemical compounds of broad scientific interest, especially when a multitude of low-energy conformations have to be accounted for as well. As a result, the assignment of absolute configurations to chiral compounds remains a tedious task. However, the characterization of these compounds is something that many different scientists are significantly invested in. The ultimate goal, then, is twofold: to gain useful insight by utilizing the electronic structure methods at your disposal while simultaneously developing new approximation techniques that can be used to push the boundaries on what is currently capable in computational chemistry. Therefore, we start by applying widely accepted density functional theory methods to predict optical rotations and electronic circular dichroism for naturally occurring antiplasmodial and anticancer drug candidates. We find that by comparing the computational results directly with those obtained through experimental measurement, we can provide reliable absolute config- uraitonal assignments to a variety of chiral compounds with numerous stereogenic centers. We also present the first ever prediction of vibrational circular dichroism with second-order Møller-Plesset perturbation theory. This extension opens the door to systematically improvable correlated wave function methods that can be employed when density functional theory fails or when higher accuracy results are required. / Doctor of Philosophy / Theoretical chemistry aims to draw a line from a molecule's three-dimensional structure to a set of physical observables, allowing for the efficient prediction of such properties. One family of chemical compounds for which this task becomes increasingly difficult is known as chiral molecules. A chiral compound is defined as one that has a non-superimposable mirror image. The concept of chirality is most tangibly seen with a pair of human hands, which demonstrate this same mirror-like behavior. In the same way that a person has left and right hands, a three-dimensonal handedness can be used to characterize many compounds that are essential to life including enzymes, sugars, and proteins. Although procedures have been developed to consistently isolate pure samples of such compounds, the correct identification of each hand poses a much larger task and costs the global pharmaceutical industry tens to hundreds of millions of dollars every year. As such, gaining insight about these incredibly valuable compounds and their associated properties is a never ending goal for many scientists. One such way to gain insight is through the direct comparison of experimental and calculated properties, namely chiroptical properties. These unique properties define how chiral compounds interact with light. While experimental scientists are limited in the degree to which they can probe a molecule's structure, theoretical chemists have the advantage of knowing the exact three-dimensional structure for the compound they are studying. On the other hand, theoretical chemists rely on comparison to experimental results to develop new methods or apply the available techniques to predict molecular properties. This work begins by attempting to match calculated properties to experimentally measured ones in order to confirm the detailed molecular structure of natural product drug candidates. Through multiple such computational studies, it is shown that the current methods are sometimes limited in the knowledge that they can provide. As a result, it is absolutely necessary to continue to improve on the existing methods. We go on to provide a first-of-its-kind implementation that allows for theoretical chemists to compare their results to experiment in a way that was not previously possible.

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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.