Light-matter interactions lead to a variety of interesting phenomena, for example photosynthesis which is a process fundamental to life on earth. There exists many different spectroscopic methods to measure light-matter interactions, for example UV/Vis spectroscopy, that can provide information about electronically excited states. However, numerical methods and theory are important to model and gain understanding of these experiments. Quantum chemistry provides that understanding, giving the possibility to numerically calculate molecular properties like excitation energies. The aim of this thesis was to implement a reduced-space algorithm in Dalton, to solve an eigenvalue equation obtained by response theory, for the calculation of excitation energies of molecular systems. There already was a similar algorithm in Dalton, that was able to perform these calculations. However, in a different module of Dalton used mainly for complex response theory, an algorithm to obtain eigenvalues was missing. The new implementation was similar to the existing one, except for the division of the reduced space into even and odd parts used in the complex response module. The thesis starts with a quick introduction of light-matter interactions and proceeds with a description of many-body theory, including numerical methods used in that field. In the end of the theoretical part, the eigenvalue equation, used to calculate excitation energies, is derived. In the following section, the reduced-space algorithm is described. In the end of the thesis, numerical results obtained with the algorithm are presented, including a small basis set and method study. The comparison with the existing implementation of the similar algorithm verified the successful implementation of the algorithm presented in this thesis.

La théorie de la fonctionnelle de la densité dépendante du temps (TDDFT) est aujourd'hui une méthode de référence pour le calcul des énergies d'excitation électroniques. Cependant, dans les approximations usuelles, elle n'est pas capable de décrire correctement les excitations de Rydberg, à transfert de charge ou présentant un caractère multiple. La séparation de portée de l'interaction électronique permet de combiner rigoureusement les méthodes fonctionnelles pour décrire la courte portée de l'interaction et les méthodes fonctions d'onde ou fonctions de Green pour la longue portée. Dans cette thèse, les effets de cette séparation de portée sur les énergies d'un système en interaction partielle sont d'abord étudiés le long de la connection adiabatique dans le cas indépendant du temps afin d'aider le développement des méthodes à séparation de portée pour les énergies d'excitation. La séparation de portée est ensuite appliquée dans le cadre de la TDDFT aux noyaux d'échange et de corrélation, où dans le cas d'une approximation monodéterminentale, la longue portée du noyau de corrélation est absente. Afin de prendre en compte l'effet des doubles excitations, un noyau de corrélation de longue portée dépendant de la fréquence est développé en s'inspirant du noyau Bethe-Salpeter. Ce noyau est alors ajouté de façon perturbative au noyau TDDFT à séparation de portée afin de prendre en compte les effets des excitations doubles. / Linear-response time-dependent density-functional theory (TDDFT) is nowadays a method of choice to compute molecular excitation energies. However, within the usual adiabatic semi-local approximations, it is not able to describe properly Rydberg, charge-transfer or multiple excitations. Range separation of the electronic interaction allows one to mix rigorously density-functional methods at short range and wave function or Green’s function methods at long range. When applied to the exchange functional, it already corrects most of these deficiencies but multiple excitations remain absent as they need a frequency-dependent kernel. In this thesis, the effects of range separation are first assessed on the excitation energies of a partially-interacting system in an analytic and numerical study in order to provide guidelines for future developments of range-separated methods for excitation energy calculations. It is then applied on the exchange and correlation TDDFT kernels in a single-determinant approximation in which the long-range part of the correlation kernel vanishes. A long-range frequency-dependent second-order correlation kernel is then derived from the Bethe-Salpeter equation and added perturbatively to the range-separated TDDFT kernel in order to take into account the effects of double excitations.

Chirality is a nuclear symmetry which is suggested to occur in nuclei when the total angular momentum of the system has an aplanar orientation [Fra97, Fra01]. It can occur for nuclei with triaxial shape, which have valence protons and neutrons with predominantly particle and hole nature. It is expected that the angular momenta of an odd particle and an odd hole (both occupying high-j orbitals) are aligned predominantly along the short and the long axes of the nucleus respectively, whereas the collective rotation occurs predominantly around the intermediate axis of a triaxially deformed nucleus in order to minimize the total energy of the system. Such symmetry is expected to be exhibited by a pair of degenerate DI = 1 rotational bands, i.e. all properties of the partner bands should be identical. The results suggested that spin independence of the energy staggering parameter S(I ) within two-quasiparticle chiral bands (previously suggested a fingerprint of chirality) is found only if the Coriolis interaction can be completely neglected. However, if the configuration is nonrestricted, the Coriolis interaction is often strong enough to create considerable energy staggering. It was also found that staggering in the intra- and inter-band B(M1) reduced transition probabilities (proposed as another fingerprint of chirality) may be a result of effects other than strongly broken chirality. Therefore, the use of the B(M1) staggering as a fingerprint of strongly broken chiral symmetry seems rather risky, in particular if the phase of the staggering is not checked.

Chirality is a nuclear symmetry which is suggested to occur in nuclei when the total angular momentum of the system has an aplanar orientation [Fra97, Fra01]. It can occur for nuclei with triaxial shape, which have valence protons and neutrons with predominantly particle and hole nature. It is expected that the angular momenta of an odd particle and an odd hole (both occupying high-j orbitals) are aligned predominantly along the short and the long axes of the nucleus respectively, whereas the collective rotation occurs predominantly around the intermediate axis of a triaxially deformed nucleus in order to minimize the total energy of the system. Such symmetry is expected to be exhibited by a pair of degenerate DI = 1 rotational bands, i.e. all properties of the partner bands should be identical. The results suggested that spin independence of the energy staggering parameter S(I ) within two-quasiparticle chiral bands (previously suggested a fingerprint of chirality) is found only if the Coriolis interaction can be completely neglected. However, if the configuration is nonrestricted, the Coriolis interaction is often strong enough to create considerable energy staggering. It was also found that staggering in the intra- and inter-band B(M1) reduced transition probabilities (proposed as another fingerprint of chirality) may be a result of effects other than strongly broken chirality. Therefore, the use of the B(M1) staggering as a fingerprint of strongly broken chiral symmetry seems rather risky, in particular if the phase of the staggering is not checked.

Philosophiae Doctor - PhD / In the first experiment high spin states in 194Tl, excited through the 181Ta (18O, 5n) heavyion fusion evaporation reaction were studied using the AFRODITE array at iThemba LABS. The γ-γ coincidences, RAD ratios and linear polarization measurements were carried out and the previously known level scheme of 194Tl was significantly extended. A total of five rotational bands four of which are new were observed. A pair of rotational bands associated with the πh9/2 ⊗ νi−1 13/2 configuration at lower spins and with the πh9/2 ⊗ νi−3 13/2 configuration at higher spins was found and interpreted as the first possible chiral bands followed above the band crossing. The two 4-quasiparticle bands show exceptionally close near-degeneracy in the excitation energies. Furthermore close similarity is also found in their alignments and B(M1)/B(E2) reduced transition probability ratios. In the second experiment lifetimes in 194Tl were measured using the DSAM technique with the excited states in this nucleus populated through the 181Ta (18O, 5n) reaction. A total of 25 lifetimes and 30 reduced transition probabilities of magnetic dipole B(M1) and electric quadrupole B(E2) have been evaluated. Furthermore B(M1) and B(E2) reduced transition probabilities in Bands 1 and 4, which have been regarded as chiral candidates, were found to be close to each other and reveals strong splitting along spin values. This further supports the proposed chiral nature of these two bands.

No description available.

Philosophiae Doctor - PhD / Chirality is a nuclear symmetry which is suggested to occur in nuclei when the total angular momentum of the system has an aplanar orientation [Fra97, Fra01]. It can occur for nuclei with triaxial shape, which have valence protons and neutrons with predominantly particle and hole nature. It is expected that the angular momenta of an odd particle and an odd hole (both occupying high-j orbitals) are aligned predominantly along the short and the long axes of the nucleus respectively, whereas the collective rotation occurs predominantly around the intermediate axis of a triaxially deformed nucleus in order to minimize the total energy of the system. Such symmetry is expected to be exhibited by a pair of degenerate DI = 1 rotational bands, i.e. all properties of the partner bands should be identical. The results suggested that spin independence of the energy staggering parameter S(I ) within two-quasiparticle chiral bands (previously suggested a fingerprint of chirality) is found only if the Coriolis interaction can be completely neglected. However, if the configuration is nonrestricted, the Coriolis interaction is often strong enough to create considerable energy staggering. It was also found that staggering in the intra- and inter-band B(M1) reduced transition probabilities (proposed as another fingerprint of chirality) may be a result of effects other than strongly broken chirality. Therefore, the use of the B(M1) staggering as a fingerprint of strongly broken chiral symmetry seems rather risky, in particular if the phase of the staggering is not checked. / South Africa

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.