Techn. University, Diss., 2004--Dresden.

Full Configuration Interaction Quantum Monte–Carlo (FCIQMC) al- lows for exact results to be obtained for the ground state of a system within a finite-basis approximation of the Schrödinger equation. Work- ing within imposed symmetry constraints permits dramatic reductions in the size and internal connectivity of the Hilbert space considered, with associated reductions in the computational cost involved, as well as permitting exclusion of the natural ground state to extract a se- ries of excited states of the system. As all converged solutions are ˆ eigenfunctions of the square of the total spin operator, S 2 , as well as the Hamiltonian and the projected spin, imposing spin-purity as an additional ‘symmetry’ is a natural extension. In this thesis, the use of various spin-pure spaces is compared to the previously used determinental spaces. Variations on the FCIQMC al- gorithm which work in non-orthogonal (and non-normalised) basis sets, and with the arbitrary discretisation of imaginary time removed, are considered along with the implications of the differences to the normal FCIQMC algorithm.

In this thesis, I present a theory of electron-electron interactions in optical properties of graphene and transition metal dichalcogenides (TMDCs), two dimensional nanostructures with a hexagonal lattice. We start our discussion with electron-electron interactions in artificial rings for which the strength of interactions can be varied and exact results can be obtained. The artificial rings are described by the extended Hubbard model and solved using an exact diagonalization method in real and Fourier space of configurations. Exact and analytical results for charged rings are obtained in the limit of very strong interactions. For the quadruple quantum dot ring and the artificial benzene ring, we find that chirality leads to the appearance of a topological phase and an effective gauge field that determines the ground state character with varied interaction strength. For the charged artificial benzene ring, our numerical results show a transition from a degenerate to a non-degenerate ground state with increasing strength of Coulomb interactions. We show that the artificial gauge and the transition in the ground state can be detected as changes in the optical absorption spectrum. In the second part of the thesis, the electronic and optical properties of colloidal graphene quantum dots (CGQD) consisting of many benzene rings are determined. The CGQDs are described by the combination of tight binding, mean field Hartree Fock (HF) and Configuration Interaction methods. The single particle properties are described through the tight binding method based on the pz carbon orbitals. Screened Coulomb interactions between electrons, including direct, exchange, and scattering matrix elements, are calculated using Slater pz orbitals. HF ground states corresponding to semiconductor, Mott-insulator, and spin-polarized phases are obtained as a function of the strength of the screened interaction versus the tunnelling matrix element. The many-body ground and excited states in the semiconducting phase are constructed as a linear combination of a finite number of electron-hole pair excitations from the HF ground state (GS). The Hamiltonian is constructed in the subspace of multi-pair HF excitations to obtain the low energy, many body states by exact diagonalization using the Lanczos method. The degeneracy of the valence- and conduction-band edges of 3-fold rotationally symmetric CGQDs is shown to lead to a characteristic exciton and bi-exciton spectrum. The low-energy exciton spectrum is predicted to consist of two bright-singlet exciton states corresponding to two circular polarizations of light and a lower-energy band of dark singlets and dark triplets. The robustness of the bright degenerate singlet pair against correlations in the many-body state is demonstrated as well as the breaking of the degeneracy by the lowering of symmetry of the CGQD. Band edge biexciton energies and binding energies are predicted, and two degenerate exciton (X) states and a corresponding biexciton (XX) state are identified for the generation of an XX-X cascade. The Auger coupling of XX and excited X states is determined and our theoretical results are compared with experimental absorption and non-linear transient absorption spectra. In the third and final part of the thesis, we replace the two non-equivalent carbon atoms of the graphene hexagonal lattice with a heavy transition-metal atom M, (e.g. Mo or W) and a dimer X2 (e.g. S). The bandstructure of a monolayer MX2 is calculated using density functional theory (DFT). It is shown that a direct gap opens up at all K points of the Brillouin zone and strong spin orbit coupling leads to spin splitting of the valence and conduction bands and emergence of valley dependent optical selection rules. Finally, the magnetoluminescence experiments on a monolayer WS2 emitting circularly polarized light upon its excitation by unpolarized light are described. The emission of polarized light in zero magnetic field is explained by the possibility of formation of a valley polarized 2D electron gas in unintentionally doped WS2.

<p> This thesis examines available x-ray absorption spectroscopy (XAS) data for NiO, NaNi02 , and LiNi02 . The XAS examined is the Ni L-edge, 3d^n2p^6 →t 3d^(n+1)2p^5 . The experimental spectra are compared to spectra calculated using a configuration interaction approach. This approach reproduces the spectra accurately. The NaNi02 spectrum is shown to be sensitive to the Jahn-Teller distortion, while the LiNi02 spectrum is reproduced by a hybridized d^7-d^8 state that explains the lack of Jahn-Teller distortion in LiNi02 </p> / Thesis / Master of Science (MSc)

In dieser Arbeit werden verschiedene Ansätze untersucht, um Tensorzerlegungsmethoden auf die Full-Configuration-Interaction-Methode (FCI) anzuwenden. Das Ziel dieser Ansätze ist es, zuverlässig konvergierende Algorithmen zu erstellen, welche es erlauben, die Wellenfunktion effizient im Canonical-Product-Tensorformat (CP) zu approximieren. Hierzu werden drei Ansätze vorgestellt, um die FCI-Wellenfunktion zu repräsentieren und darauf basierend die benötigten Koeffizienten zu bestimmen. Der erste Ansatz beruht auf einer Entwicklung der Wellenfunktion als Linearkombination von Slaterdeterminanten, bei welcher in einer Hierarchie ausgehend von der Hartree-Fock-Slaterdeterminante sukzessive besetzte Orbitale durch virtuelle Orbitale ersetzt werden. Unter Nutzung von Tensorrepräsentationen im CP wird ein lineares Gleichungssystem gelöst, um die FCI-Koeffizienten zu bestimmen. Im darauf folgenden Ansatz, welcher an Direct-CI angelehnt ist, werden Tensorrepräsentationen der Hamiltonmatrix und des Koeffizientenvektors aufgestellt, welche zur Lösung des FCI-Eigenwertproblems erforderlich sind. Hier wird ein Algorithmus vorgestellt, mit welchem das Eigenwertproblem im CP gelöst wird. In einem weiteren Ansatz wird die Repräsentation der Hamiltonmatrix und des Koeffizientenvektors im Fockraum formuliert. Dieser Ansatz erlaubt die Lösung des FCI-Eigenwertproblems mit Hilfe verschiedener Algorithmen. Diese orientieren sich an den Rayleighquotienteniterationen oder dem Davidsonalgorithmus, wobei für den ersten Algorithmus eine zweite Version entwickelt wurde, wo die Rangreduktion teilweise durch Projektionen ersetzt wurde. Für den Davidsonalgorithmus ist ein breiteres Spektrum von Molekülen behandelbar und somit können erste Untersuchungen zur Skalierung und zu den zu erwartenden Fehlern vorgestellt werden. Schließlich wird ein Ausblick auf mögliche Weiterentwicklungen gegeben, welche eine effizientere Berechnung ermöglichen und somit FCI im CP auch für größere Moleküle zugänglich macht. / In this thesis, various approaches are investigated to apply tensor decomposition methods to the Full Configuration Interaction method (FCI). The aim of these approaches is the development of algorithms, which converge reliably and which permit to approximate the wave function efficiently in the Canonical Product format (CP). Three approaches are introduced to represent the FCI wave function and to obtain the corresponding coefficients. The first approach ist based on an expansion of the wave function as a linear combination of slater determinants. In this hierarchical expansion, starting from the Hartree Fock slater determinant, the occupied orbitals are substituted by virtual orbitals. Using tensor representations in the CP, a linear system of equations is solved to obtain the FCI coefficients. In a further approach, tensor representations of the Hamiltonian matrix and the coefficient vectors are set up, which are required to solve the FCI eigenvalue problem. The tensor contractions and an algorithm to solve the eigenvalue problem in the CP are explained her in detail. In the next approach, tensor representations of the Hamiltonian matrix and the coefficient vector are constructed in the Fock space. This approach allows the application of various algorithms. They are based on the Rayleight Quotient Algorithm and the Davidson algorithm and for the first one, there exists a second version, where the rank reduction algorithm is replaced by projections. The Davidson algorithm allows to treat a broader spectrum of molecules. First investigations regarding the scaling behaviour and the expectable errors can be shown for this approach. Finally, an outlook on the further development is given, that allows for more efficient calculations and makes FCI in the CP accessible for larger molecules.

In this work a systematic method for determining correlated wavefunctions of extended systems in the ground state as well as in excited states is presented. It allows to fully exploit the power of quantum-chemical programs designed for correlation calculations of finite molecules. Using localized Hartree-Fock (HF) orbitals (both occupied and virtual ones), an effective Hamiltonian which can easily be transferred from finite to infinite systems is built up. Correlation corrections to the matrix elements of the effective Hamiltonian are derived from clusters using an incremental scheme. To treat the correlation effects, multireference configuration interaction (MRCI) calculations with singly and doubly excited configurations (SD) are performed. This way one is able to generate both valence and conduction bands where all correlation effects in the excited states as well as in the ground state of the system are taken into account. An appropriate size-extensivity correction to the MRCI(SD) correlation energies is developed which takes into account the open-shell character of the excited states. This approach is applicable to a wide range of polymers and crystals. In the present work trans-polyacetylene is chosen as a test system. The corresponding band structure is obtained with the correlation of all electrons in the system being included on a very high level of sophistication. The account of correlation effects leads to substantial shifts of the &amp;quot;center-of-mass&amp;quot; positions of the bands (valence bands are shifted upwards and conduction bands downwards) and a flattening of all bands compared to the corresponding HF band structure. The method reaches the quantum-chemical level of accuracy. Further an extention of the above approach to excitons (optical excitations) in crystals is developed which allows to use standard quantum-chemical methods to describe the electron-hole pairs and to finally obtain excitonic bands.

In this work a systematic method for determining correlated wavefunctions of extended systems in the ground state as well as in excited states is presented. It allows to fully exploit the power of quantum-chemical programs designed for correlation calculations of finite molecules. Using localized Hartree-Fock (HF) orbitals (both occupied and virtual ones), an effective Hamiltonian which can easily be transferred from finite to infinite systems is built up. Correlation corrections to the matrix elements of the effective Hamiltonian are derived from clusters using an incremental scheme. To treat the correlation effects, multireference configuration interaction (MRCI) calculations with singly and doubly excited configurations (SD) are performed. This way one is able to generate both valence and conduction bands where all correlation effects in the excited states as well as in the ground state of the system are taken into account. An appropriate size-extensivity correction to the MRCI(SD) correlation energies is developed which takes into account the open-shell character of the excited states. This approach is applicable to a wide range of polymers and crystals. In the present work trans-polyacetylene is chosen as a test system. The corresponding band structure is obtained with the correlation of all electrons in the system being included on a very high level of sophistication. The account of correlation effects leads to substantial shifts of the &amp;quot;center-of-mass&amp;quot; positions of the bands (valence bands are shifted upwards and conduction bands downwards) and a flattening of all bands compared to the corresponding HF band structure. The method reaches the quantum-chemical level of accuracy. Further an extention of the above approach to excitons (optical excitations) in crystals is developed which allows to use standard quantum-chemical methods to describe the electron-hole pairs and to finally obtain excitonic bands.

Doctor of Philosophy / Department of Chemistry / Christine M. Aikens / Small silver and gold clusters (less than 2 nm) display a discrete absorption spectrum characteristic of molecular systems whereas larger particles display a strong, broad absorption band in the visible. The latter feature is due to the surface plasmon resonance, which is commonly explained by the collective dipolar motion of free electrons across the particle, creating charged surface states. The evolution between molecular properties and plasmon is investigated. Time-dependent density functional theory (TDDFT) calculations are performed to study the absorption spectrum of cluster-size silver and gold nanorods. The absorption spectrum of these silver nanorods exhibits high-intensity longitudinal and transverse modes (along the long and short axis of the nanorod respectively), similar to the plasmons observed experimentally for larger nanoparticles. These plasmon modes result from a constructive addition of the dipole moments of nearly degenerate single-particle excitations. The number of single-particle transitions involved increases with increasing system size, due to the growing density of states available. Gold nanorods exhibit a broader absorption spectrum than their silver counterpart due to enhanced relativistic effects, affecting the onset of the longitudinal plasmon mode. The high-energy, high-intensity beta-peak of acenes also results from a constructive addition of single-particle transitions and I show that it can be assigned to a plasmon. I also show that the plasmon modes of both acenes and metallic nanoparticles can be described with a simple configuration interaction (CI) interpretation. The evolution between molecular absorption spectrum and plasmon is also investigated by computing the density of states of spherical thiolate-protected gold clusters using a charge-perturbed particle-in-a-sphere model. The electronic structure obtained with this model gives good qualitative agreement with DFT calculations at a fraction of the cost. The progressive increase of the density of states with particle size observed is in accordance with the appearance of a plasmon peak. The optical properties of nanoparticles can be tuned by varying their composition. Therefore, the optical behavior of the bimetallic Au[subscript](25-n)Ag[subscript]n(SH)[subscript]18[superscript]- cluster for different values of n using TDDFT is analyzed. A large blue shift of the HOMO-LUMO absorption peak is observed with increasing silver content, in accordance with experimental results.

Stuttgart, Univ., Diss., 2008.

No description available.