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.

Na +-coupled betaine symporters involved in osmotic stress response in prokaryotes and eukaryotes

The betaine/GABA transporter BGT1 is one of the most important osmolyte transporters in the kidney. BGT1 is a member of the neurotransmitter sodium symporter (NSS) family, facilitates Na+/Cl--coupled betaine uptake to cope with hyperosmotic stress. Betaine transport in kidney cells is upregulated under hypertonic conditions by a yet unknown mechanism when increasing amounts of intracellular BGT1 are inserted into the plasma membrane. Re-establishing isotonicity results in ensuing depletion of BGT1 from the membrane. BGT1 phosphorylation on serines and threonines might be a regulation mechanism. In the present study, four potential PKC phosphorylation sites were mutated to alanines and the responses to PKC activators, phorbol 12-myristate acetate (PMA) and dioctanoyl-sn-glycerol (DOG) were determined. GABA-sensitive currents were diminished after 30 min preincubation with these PKC activators. Staurosporine blocked the response to DOG. Three mutants evoked normal GABA-sensitive currents but currents in oocytes expressing the mutant T40A were greatly diminished. [3H]GABA uptake was also determined in HEK-293 cells expressing EGFP-tagged BGT1 with the same mutations. Three mutants showed normal upregulation of GABA uptake after hypertonic stress, and downregulation by PMA was normal compared to EGFP-BGT1. In contrast, GABA uptake by the T40A mutant showed no response to hypertonicity or PMA. Confocal microscopy of the EGFP-BGT1 mutants expressed in MDCK cells, grown on glass or filters, revealed that T40A was present in the cytoplasm after 24 h hypertonic stress while the other mutants and EGFP-BGT1 were predominantely present in the plasma membrane. All four mutants co-migrated with EGFP-BGT1 on Western blots suggesting they are full-length proteins. In conclusion, T235, S428, and S564 are not involved in downregulation of BGT1 due to phosphorylation by PKC. However, T40 near the N-terminus may be part of a hot spot important for normal trafficking or insertion of BGT1 into the plasma membrane. Additionally, a link between substrate transport regulation, insertion of BGT1 into the plasma membrane and N-glycosylation in the extracellular loop 2 (EL2) could be revealed. The functional importance of two predicted N-glycosylation sites, which are conserved in EL2 within the NSS family were investigated for trafficking, transport and regulated plasma membrane insertion by immunogold-labelling, electron microscopy, mutagenesis, two-electrode voltage clamp measurements in Xenopus laevis oocytes and uptake of radioactive-labelled substrate into MDCK cells. Trafficking and plasma membrane insertion of BGT1 was clearly promoted by proper N-glycosylation in both, oocytes and MDCK cells. De-glycosylation with PNGase F or tunicamycin led to a decrease in substrate affinity and transport rate. Mutagenesis studies revealed that in BGT1 N183 is the major N-glycosylation site responsible for full protein activity. Replacement of N183 with aspartate resulted in a mutant, which was not able to bind N-glycans suggesting that N171 is a non-glycosylated site in BGT1. N183D exhibited close to WT transport properties in oocytes. Surprisingly, in MDCK cells plasma membrane insertion of the N183D mutant was no longer regulated by osmotic stress indicating unambiguously that association with N-glycans at this position is linked to osmotic stress-induced transport regulation in BGT1. The molecular transport mechanism of BGT1 remains largely unknown in the absence of a crystal structure. Therefore investigating the structure-function relationship of BGT1 by a combination of structural biology (2D and 3D crystallization) and membrane protein biochemistry (cell culture, substrate transport by radioactive labeled GABA uptake into cells and proteoliposomes) was the aim of this work. While the functional assays are well established, structure determination of eukaryotic membrane transporters is still a challenge. Therefore, a suitable heterologous expression system could be defined, starting with cloning and overexpression of an optimized gene. The achieved expression levels in P. pastoris were high enough to proceed with isolation of BGT1. Furthermore, purification protocols could be established and resulted in pure protein, which could even be reconstituted in an active form. The quality and homogeneity of the protein allowed already 2D and 3D crystallization, in which initial crystals could be obtained. Interestingly, the striking structural similarity of BGT1 to the bacterial betaine transporter BetP, which became a paradigm for osmoregulated betaine transport, provided information on substrate coordination in BGT1. The structure of a BetP mutant that showed activity for GABA was solved to 3.2Å in complex with GABA in an inward facing open state. This structure shed some light into the molecular transport mechanisms in BGT1 and might help in future to design conformationally locked BGT1 to enforce the on-going structure determination.

Analytische Ableitungen der Energie für den "Equation-of-Motion-Coupled-Cluster"-Ansatz zur Berechnung von Ionisationspotentialen

In der vorliegenden Arbeit wird die Theorie der analytischen zweiten Ableitungen für die EOMIP-CCSD-Methode formuliert sowie die durchgeführte Implementierung im Quantenchemieprogramm CFOUR beschrieben. Diese Ableitungen sind von Bedeutung bei der Bestimmung statischer Polarisierbarkeiten und harmonischer Schwingungsfrequenzen und in dieser Arbeit wird die Genauigkeit des EOMIP-CCSD-Ansatzes bei der Berechnung dieser Eigenschaften für verschiedene radikalische Systeme untersucht. Des Weiteren können mit Hilfe der ersten und zweiten Ableitungen vibronische Kopplungsparameter berechnet werden, welche zur Simulation von Molekülspektren in Kombination mit dem Köppel-Domcke-Cederbaum (KDC)-Modell - in der Arbeit am Beispiel des Formyloxyl (HCO2)-Radikals demonstriert - benötigt werden.rnrnDer konzeptionell einfache EOMIP-CC-Ansatz wurde gewählt, da hier die Wellenfunktion eines Radikalsystems ausgehend von einem stabilen geschlossenschaligen Zustand durch die Entfernung eines Elektrons gebildet wird und somit die Problematik der Symmetriebrechung umgangen werden kann. Im Rahmen der Implementierung wurden neue Programmteile zur Lösung der erforderlichen Gleichungen für die gestörten EOMIP-CC-Amplituden und die gestörten Lagrange-Multiplikatoren zeta zum Quantenchemieprogramm CFOUR hinzugefügt. Die unter Verwendung des Programms bestimmten Eigenschaften werden hinsichtlich ihrer Leistungsfähigkeit im Vergleich zu etablierten Methoden wie z.B. CCSD(T) untersucht. Bei der Berechnung von Polarisierbarkeiten und harmonischen Schwingungsfrequenzen liefert die EOMIP-CCSD-Theorie meist gute Resultate, welche nur wenig von den CCSD(T)-Ergebnissen abweichen. Einzig bei der Betrachtung von Radikalen, für die die entsprechenden Anionen nicht stabil sind (z.B. NH2⁻ und CH3⁻), liefert der EOMIP-CCSD-Ansatz aufgrund methodischer Nachteile keine aussagekräftige Beschreibung. rnrnDie Ableitungen der EOMIP-CCSD-Energie lassen sich auch zur Simulation vibronischer Kopplungen innerhalb des KDC-Modells einsetzen.rnZur Kopplung verschiedener radikalischer Zustände in einem solchen Modellpotential spielen vor allem die Ableitungen von Übergangsmatrixelementen eine wichtige Rolle. Diese sogenannten Kopplungskonstanten können in der EOMIP-CC-Theorie besonders leicht definiert und berechnet werden. Bei der Betrachtung des Photoelektronenspektrums von HCO2⁻ werden zwei Alternativen untersucht: Die vertikale Bestimmung an der Gleichgewichtsgeometrie des HCO2⁻-Anions und die Ermittlung adiabatischer Kraftkonstanten an den Gleichgewichtsgeometrien des Radikals. Lediglich das adiabatische Modell liefert bei Beschränkung auf harmonische Kraftkonstanten eine qualitativ sinnvolle Beschreibung des Spektrums. Erweitert man beide Modelle um kubische und quartische Kraftkonstanten, so nähern sich diese einander an und ermöglichen eine vollständige Zuordnung des gemessenen Spektrums innerhalb der ersten 1500 cm⁻¹. Die adiabatische Darstellung erreicht dabei nahezu quantitative Genauigkeit.