Higher-order molecular properties and excitation energies in single-reference and multireference coupled-cluster theory

Coupled-cluster (CC) theory is one of the most successful approaches in high-accuracy quantum chemistry. The present thesis makes a number of contributions to the determination of molecular properties and excitation energies within the CC framework. The multireference CC (MRCC) method proposed by Mukherjee and coworkers (Mk-MRCC) has been benchmarked within the singles and doubles approximation (Mk-MRCCSD) for molecular equilibrium structures. It is demonstrated that Mk-MRCCSD yields reliable results for multireference cases where single-reference CC methods fail. At the same time, the present work also illustrates that Mk-MRCC still suffers from a number of theoretical problems and sometimes gives rise to results of unsatisfactory accuracy. To determine polarizability tensors and excitation spectra in the MRCC framework, the Mk-MRCC linear-response function has been derived together with the corresponding linear-response equations. Pilot applications show that Mk-MRCC linear-response theory suffers from a severe problem when applied to the calculation of dynamic properties and excitation energies: The Mk-MRCC sufficiency conditions give rise to a redundancy in the Mk-MRCC Jacobian matrix, which entails an artificial splitting of certain excited states. This finding has established a new paradigm in MRCC theory, namely that a convincing method should not only yield accurate energies, but ought to allow for the reliable calculation of dynamic properties as well. In the context of single-reference CC theory, an analytic expression for the dipole Hessian matrix, a third-order quantity relevant to infrared spectroscopy, has been derived and implemented within the CC singles and doubles approximation. The advantages of analytic derivatives over numerical differentiation schemes are demonstrated in some pilot applications.

Non-parametric estimation of the diffusion coefficient of a branching diffusion with immigration

Wir betrachten Systeme von endlich vielen Partikeln, wobei die Partikel sich unabhängig voneinander gemäß eindimensionaler Diffusionen [dX_t = b(X_t),dt + sigma(X_t),dW_t] bewegen. Die Partikel sterben mit positionsabhängigen Raten und hinterlassen eine zufällige Anzahl an Nachkommen, die sich gemäß eines Übergangskerns im Raum verteilen. Zudem immigrieren neue Partikel mit einer konstanten Rate. Ein Prozess mit diesen Eigenschaften wird Verzweigungsprozess mit Immigration genannt. Beobachten wir einen solchen Prozess zu diskreten Zeitpunkten, so ist zunächst nicht offensichtlich, welche diskret beobachteten Punkte zu welchem Pfad gehören. Daher entwickeln wir einen Algorithmus, um den zugrundeliegenden Pfad zu rekonstruieren. Mit Hilfe dieses Algorithmus konstruieren wir einen nichtparametrischen Schätzer für den quadrierten Diffusionskoeffizienten $sigma^2(cdot),$ wobei die Konstruktion im Wesentlichen auf dem Auffüllen eines klassischen Regressionsschemas beruht. Wir beweisen Konsistenz und einen zentralen Grenzwertsatz.

Conformational transitions of glycine induced by vibrational excitation of the O-H stretch

Vibrational energy flow and conformational transitions following excitation of the OH stretching mode of the most stable conformer of glycine are studied by classical trajectories. "On the fly" simulations with the PM3 semiempirical electronic structure method for the potential surface are used. Initial conditions are selected to correspond to the v = 1 excitation of the OH stretch. The main findings are: (1) An an equilibrium-like ratio is established between the populations of the 3 lowest-lying conformers after about 10 picoseconds. (2) There is a high probability throughout the 150 ps of the simulations for finding the molecule in geometries far from the equilibrium structures of the lowest-energy conformers. (3) Energy from the initial excited OH (v = 1) stretch flows preferentially to 5 other vibrational modes, including the bending motion of the H atom. (4) RRK theory yields conformational transition rates that deviate substantially from the classical trajectory results. Possible implication of these results for vibrational energy flow and conformational transitions in small biological molecules are discussed.

Processing-structure-property relationships in solid-state shear pulverization: Parametric study of specific energy

Solid-state shear pulverization (SSSP) is a unique processing technique for mechanochemical modification of polymers, compatibilization of polymer blends, and exfoliation and dispersion of fillers in polymer nanocomposites. A systematic parametric study of the SSSP technique is conducted to elucidate the detailed mechanism of the process and establish the basis for a range of current and future operation scenarios. Using neat, single component polypropylene (PP) as the model material, we varied machine type, screw design, and feed rate to achieve a range of shear and compression applied to the material, which can be quantified through specific energy input (Ep). As a universal processing variable, Ep reflects the level of chain scission occurring in the material, which correlates well to the extent of the physical property changes of the processed PP. Additionally, we compared the operating cost estimates of SSSP and conventional twin screw extrusion to determine the practical viability of SSSP.

Processing-Structure-Property Relationships in Solid-State Shear Pulverization: Parametric Study of specific energy

Solid-state shear pulverization (SSSP) is a unique processing technique for mechanochemical modification of polymers, compatibilization of polymer blends, and exfoliation and dispersion of fillers in polymer nanocomposites. A systematic parametric study of the SSSP technique is conducted to elucidate the detailed mechanism of the process and establish the basis for a range of current and future operation scenarios. Using neat, single component polypropylene (PP) as the model material, we varied machine type, screw design, and feed rate to achieve a range of shear and compression applied to the material, which can be quantified through specific energy input (Ep). As a universal processing variable, Ep reflects the level of chain scission occurring in the material, which correlates well to the extent of the physical property changes of the processed PP. Additionally, we compared the operating cost estimates of SSSP and conventional twin screw extrusion to determine the practical viability of SSSP.

Parametric T2 and T2* mapping techniques to visualize intervertebral disc degeneration in patients with low back pain: initial results on the clinical use of 3.0 Tesla MRI

To assess, compare and correlate quantitative T2 and T2* relaxation time measurements of intervertebral discs (IVDs) in patients suffering from low back pain, with respect to the IVD degeneration as assessed by the morphological Pfirrmann Score. Special focus was on the spatial variation of T2 and T2* between the annulus fibrosus (AF) and the nucleus pulposus (NP).

Activation of the parieto-premotor network is associated with vivid motor imagery - a parametric FMRI study

The present study examined the neural basis of vivid motor imagery with parametrical functional magnetic resonance imaging. 22 participants performed motor imagery (MI) of six different right-hand movements that differed in terms of pointing accuracy needs and object involvement, i.e., either none, two big or two small squares had to be pointed at in alternation either with or without an object grasped with the fingers. After each imagery trial, they rated the perceived vividness of motor imagery on a 7-point scale. Results showed that increased perceived imagery vividness was parametrically associated with increasing neural activation within the left putamen, the left premotor cortex (PMC), the posterior parietal cortex of the left hemisphere, the left primary motor cortex, the left somatosensory cortex, and the left cerebellum. Within the right hemisphere, activation was found within the right cerebellum, the right putamen, and the right PMC. It is concluded that the perceived vividness of MI is parametrically associated with neural activity within sensorimotor areas. The results corroborate the hypothesis that MI is an outcome of neural computations based on movement representations located within motor areas.