Mathematical aspects of Feynman integrals

In the present dissertation we consider Feynman integrals in the framework of dimensional regularization. As all such integrals can be expressed in terms of scalar integrals, we focus on this latter kind of integrals in their Feynman parametric representation and study their mathematical properties, partially applying graph theory, algebraic geometry and number theory. The three main topics are the graph theoretic properties of the Symanzik polynomials, the termination of the sector decomposition algorithm of Binoth and Heinrich and the arithmetic nature of the Laurent coefficients of Feynman integrals.rnrnThe integrand of an arbitrary dimensionally regularised, scalar Feynman integral can be expressed in terms of the two well-known Symanzik polynomials. We give a detailed review on the graph theoretic properties of these polynomials. Due to the matrix-tree-theorem the first of these polynomials can be constructed from the determinant of a minor of the generic Laplacian matrix of a graph. By use of a generalization of this theorem, the all-minors-matrix-tree theorem, we derive a new relation which furthermore relates the second Symanzik polynomial to the Laplacian matrix of a graph.rnrnStarting from the Feynman parametric parameterization, the sector decomposition algorithm of Binoth and Heinrich serves for the numerical evaluation of the Laurent coefficients of an arbitrary Feynman integral in the Euclidean momentum region. This widely used algorithm contains an iterated step, consisting of an appropriate decomposition of the domain of integration and the deformation of the resulting pieces. This procedure leads to a disentanglement of the overlapping singularities of the integral. By giving a counter-example we exhibit the problem, that this iterative step of the algorithm does not terminate for every possible case. We solve this problem by presenting an appropriate extension of the algorithm, which is guaranteed to terminate. This is achieved by mapping the iterative step to an abstract combinatorial problem, known as Hironaka's polyhedra game. We present a publicly available implementation of the improved algorithm. Furthermore we explain the relationship of the sector decomposition method with the resolution of singularities of a variety, given by a sequence of blow-ups, in algebraic geometry.rnrnMotivated by the connection between Feynman integrals and topics of algebraic geometry we consider the set of periods as defined by Kontsevich and Zagier. This special set of numbers contains the set of multiple zeta values and certain values of polylogarithms, which in turn are known to be present in results for Laurent coefficients of certain dimensionally regularized Feynman integrals. By use of the extended sector decomposition algorithm we prove a theorem which implies, that the Laurent coefficients of an arbitrary Feynman integral are periods if the masses and kinematical invariants take values in the Euclidean momentum region. The statement is formulated for an even more general class of integrals, allowing for an arbitrary number of polynomials in the integrand.

Synthesis and characterization of polymers containing oligothiophenes

In the present work a series of thiophene oligomers of three and six thiophene units were synthesized, starting from thiophene, and characterized. Polymers containing these electroative side groups were then prepared by two strategies. The oligomers were attached to existing polymer systems and were connected to a polymerizable unit leading to monomer containing the oligothiophenes as side groups. Subsequently the properties of the monomers and the polymers were investigated. A butylcellulose derivative carrying terthienyl side chains (BCTTE, 26) was synthesized starting from cellulose acetate and 5-(2-chloroethyl)-2,2':5',2'-terthiophene (4). The polymer had a degree of substitution (DS) of the butyl and terthienyl side chains of DSbutyl = 1.9 and DSterth = 0.35, respectively. It was successfully spread on a Langmuir-Blodgett (LB) trough and then transferred to several solid substrates. X-rays reflectometry showed an ordered architecture of the cellulose backbones. However, the terthiophene side groups were found as isotropically aligned by polarized UV-Vis spectroscopy. When used as anode material in the electropolymerization of 3-pentylthiophene (28), polythiophene was grafted onto the cellulose backbone through the terthienyl side groups. The polythiophene chains showed an average anisotropic alignment of 20 % along the LB dipping direction, calculated by means of polarized UV-Vis spectroscopy. A second butylcellulose derivative carrying sexithienyl side chains (BCST) was synthesized and investigated, starting from butylcellulose and 2-[b ', b ''-dipentyl-5'''-(2-hydroxyethyl)-2,2': 5',2':5',2'':5'',2'':5'',2'''-sexithiophen-5-yl]-ethyl p-toluensulfonate (7). The polymer showed formation of stable LB monolayers at the air-water interface, but its transfer onto solid substrates was not successful. A poly(p-phenylene-ethynylene) bearing sexithienyl side chains (BzAcST, 31) was prepared by reaction of the two monomers 2-[b ', b ''-dipentyl-5'''-(2-hydroxyethyl)-2,2': 5',2':5',2'':5'',2'':5'',2'''-sexithiophen-5-yl]-ethyl 2,5-diiodobenzoate (15) and 2-[b', b ''-dipentyl-5'''-(2-hydroxyethyl)-2,2':5',2':5',2'':5'',2'':5'',2'''-sexithiophen-5-yl]-ethyl 2,5-diethynylbenzoate (18). The polymer was obtained as insoluble product. Upon oxidation with FeCl3 (doping) of the polymer suspension, BzAcST showed an electrical conductivity of ó = 2.5 . 10 -6 S/cm, a typical value for semiconductors. The IR spectrum of the doped polymer presented the diagnostic bands of oxidized sexithiophene in good agreement with literature results. Along with the monomer and polymer synthesis, an a,a '-disubstituted sexithiophene, b ', b ''-dipentyl-5,5'''-bis-(2-hydroxyethyl)-2,2':5',2':5',2'':5'',2'':5'',2'''-sexithiophene (6a),was synthesized and characterized. The UV-Vis absorption of the chromophore wasinvestigated as a function of temperature and different solvents, showing a blue-shift of the absorption maximum with increasing temperature and a red-shift changing the solvent from hexane to ethanol to toluene. Monitoring the change of the UV-Vis spectrum upon electrochemical oxidation, the oxidized chromophore showed a new broad absorption band, red shifted with respect to the p -p* transition of the neutral state. Upon reduction, the new band disappeared and the UV-Vis spectrum of the chromophore was restored. Such oxidation-reduction cycles were totally reversible. This feature, together with the absorption maximum falling in the visible region, makes this chromophore a suitable compound for the development of an electrochemical sensor.Attempts to polymerize acrylic monomers carrying sexythienyl side chains both via radical polymerization, as in the case of 2-[b ', b ''-dipentyl-5'''-(2-hydroxyethyl)-2,2': 5',2':5',2'':5'',2'':5'',2'''-sexithiophen-5-yl]-ethyl acrylate (8), and anionic polymerization, as in the case of 2-{b ', b ''-dipentyl-5'''-[2-(tertbutyldimethylsiloxy)ethyl]-2,2':5',2':5',2'':5'',2'': 5'',2''' -sexithiophen-5-yl}-ethylacrylate (29), were not successful, probably due to the steric hindrance of the oligothiophene side group. However, due to the time consuming and therefore restricted availability of the monomers, a screening of the polymerization conditions towards the formation of polymeric material was not possible.

Pseudodifferential operators on Hilbert space riggings with associated psi *-algebras and generalized Hörmander classes

The present thesis is concerned with certain aspects of differential and pseudodifferential operators on infinite dimensional spaces. We aim to generalize classical operator theoretical concepts of pseudodifferential operators on finite dimensional spaces to the infinite dimensional case. At first we summarize some facts about the canonical Gaussian measures on infinite dimensional Hilbert space riggings. Considering the naturally unitary group actions in $L^2(H_-,gamma)$ given by weighted shifts and multiplication with $e^{iSkp{t}{cdot}_0}$ we obtain an unitary equivalence $F$ between them. In this sense $F$ can be considered as an abstract Fourier transform. We show that $F$ coincides with the Fourier-Wiener transform. Using the Fourier-Wiener transform we define pseudodifferential operators in Weyl- and Kohn-Nirenberg form on our Hilbert space rigging. In the case of this Gaussian measure $gamma$ we discuss several possible Laplacians, at first the Ornstein-Uhlenbeck operator and then pseudo-differential operators with negative definite symbol. In the second case, these operators are generators of $L^2_gamma$-sub-Markovian semi-groups and $L^2_gamma$-Dirichlet-forms. In 1992 Gramsch, Ueberberg and Wagner described a construction of generalized Hörmander classes by commutator methods. Following this concept and the classical finite dimensional description of $Psi_{ro,delta}^0$ ($0leqdeltaleqroleq 1$, $delta< 1$) in the $C^*$-algebra $L(L^2)$ by Beals and Cordes we construct in both cases generalized Hörmander classes, which are $Psi^*$-algebras. These classes act on a scale of Sobolev spaces, generated by our Laplacian. In the case of the Ornstein-Uhlenbeck operator, we prove that a large class of continuous pseudodifferential operators considered by Albeverio and Dalecky in 1998 is contained in our generalized Hörmander class. Furthermore, in the case of a Laplacian with negative definite symbol, we develop a symbolic calculus for our operators. We show some Fredholm-criteria for them and prove that these Fredholm-operators are hypoelliptic. Moreover, in the finite dimensional case, using the Gaussian-measure instead of the Lebesgue-measure the index of these Fredholm operators is still given by Fedosov's formula. Considering an infinite dimensional Heisenberg group rigging we discuss the connection of some representations of the Heisenberg group to pseudo-differential operators on infinite dimensional spaces. We use this connections to calculate the spectrum of pseudodifferential operators and to construct generalized Hörmander classes given by smooth elements which are spectrally invariant in $L^2(H_-,gamma)$. Finally, given a topological space $X$ with Borel measure $mu$, a locally compact group $G$ and a representation $B$ of $G$ in the group of all homeomorphisms of $X$, we construct a Borel measure $mu_s$ on $X$ which is invariant under $B(G)$.

Towards a new test of time dilation: Laser spectroscopy on lithium ions stored at a velocity of 33.8 % of the speed of light

The subject of the presented thesis is the accurate measurement of time dilation, aiming at a quantitative test of special relativity. By means of laser spectroscopy, the relativistic Doppler shifts of a clock transition in the metastable triplet spectrum of ^7Li^+ are simultaneously measured with and against the direction of motion of the ions. By employing saturation or optical double resonance spectroscopy, the Doppler broadening as caused by the ions' velocity distribution is eliminated. From these shifts both time dilation as well as the ion velocity can be extracted with high accuracy allowing for a test of the predictions of special relativity. A diode laser and a frequency-doubled titanium sapphire laser were set up for antiparallel and parallel excitation of the ions, respectively. To achieve a robust control of the laser frequencies required for the beam times, a redundant system of frequency standards consisting of a rubidium spectrometer, an iodine spectrometer, and a frequency comb was developed. At the experimental section of the ESR, an automated laser beam guiding system for exact control of polarisation, beam profile, and overlap with the ion beam, as well as a fluorescence detection system were built up. During the first experiments, the production, acceleration and lifetime of the metastable ions at the GSI heavy ion facility were investigated for the first time. The characterisation of the ion beam allowed for the first time to measure its velocity directly via the Doppler effect, which resulted in a new improved calibration of the electron cooler. In the following step the first sub-Doppler spectroscopy signals from an ion beam at 33.8 %c could be recorded. The unprecedented accuracy in such experiments allowed to derive a new upper bound for possible higher-order deviations from special relativity. Moreover future measurements with the experimental setup developed in this thesis have the potential to improve the sensitivity to low-order deviations by at least one order of magnitude compared to previous experiments; and will thus lead to a further contribution to the test of the standard model.

Development and evaluation of a 44 Ti, 44 Sc radionuclide generator and labeling of biomolecules with 44 Sc and 68 Ga for PET imaging

Non-invasive molecular-imaging technologies are playing a key role in drug discovery, development and delivery. Positron Emission Tomography (PET) is such a molecular imaging technology and a powerful tool for the observation of various deceases in vivo. However, it is limited by the availability of vectors with high selectivity to the target and radionuclides with a physical half-life which matches the biological half-life of the observed process. The 68Ge/68Ga radionuclide generator makes the PET-nuclide anywhere available without an on-site cyclotron. Besides the perfect availability 68Ga shows well suited nuclide properties for PET, but it has to be co-ordinated by a chelator to introduce it in a radiopharmaceuticals.rnHowever, the physical half-life of 68Ga (67.7 min) might limit the spectrum of clinical applications of 68Ga-labelled radiodiagnostics. Furthermore, 68Ga-labelled analogues of endoradiotherapeuticals of longer biological half-live such as 90Y- or 177Lu-labeled peptides and proteins cannot be used to determine individual radiation dosimetry directly. rnThus, radionuclide generator systems providing positron emitting daughters of extended physical half-life are of renewed interest. In this context, generator-derived positron emitters with longer physical half-life are needed, such as 72As (T½ = 26 h) from the 72Se/72As generator, or 44Sc (T½ = 3.97 h) from the 44Ti/44Sc generator.rnIn this thesis the implementation of radioactive gallium-68 and scandium-44 for molecular imaging and nuclear medical diagnosis, beginning with chemical separation and purification of 44Ti as a radionuclide mother, investigation of pilot generators with different elution mode, building a prototype generator, development and investigation of post-processing of the generator eluate, its concentration and further purification, the labeling chemistry under different conditions, in vitro and in vivo studies of labeled compounds and, finally, in vivo imaging experiments are described.

First measurements of the aSPECT spectrometer

The aSPECT spectrometer has been constructed to measure, with high precision, the integral proton spectrum of the free neutron decay. From this spectrum the neutrino electron angular correlation coefficient a can be inferred. The coefficient a is involved in several Standard Model tests, like the unitarity test of the Cabibbo-Kobayashi-Maskawa quark mixing matrix. aSPECT has been designed to determine the coefficient a with an accuracy better than 3×10−4, that is, one order of magnitude better than the best current accuracy. First measurements with neutron beam with the aSPECT spectrometer were performed in the Forschungsneutronenquelle Heinz Maier-Leibnitz, in Munich. A study of the data taken in this period is presented in this thesis, demonstrating the proof of principle of the spectrometer. However, the observation of situation and time-dependent background instabilities impedes the report of a new value of the coefficient a. A thorough data analysis is carried out to identify sources of these background instabilities in order to improve the aSPECT experiment for future beam times. The investigation indicates that trapped particles are most likely the reason for the background problems. Furthermore, it has been observed that measurements containing less trapped particles provide a-values closer to the currently Particle Data Group value. Based on this findings, different measures are proposed to eliminate potential traps in the spectrometer. Indeed, with the proposed modifications realized for the following beam-times, the observed background instabilities were greatly reduced.

The prehistoric inhabitants of the Wadi Howar : an anthropological study of human skeletal remains from the Sudanese part of the Eastern Sahara

All currently available human skeletal remains from the Wadi Howar (Eastern Sahara, Sudan) were employed in an anthropological study. The study’s first aim was to describe this unique 5th to 2nd millennium BCE material, which comprised representatives of all three prehistoric occupation phases of the region. Detecting diachronic differences in robusticity, occupational stress levels and health within the spatially, temporally and culturally heterogeneous sample was its second objective. The study’s third goal was to reveal metric and non-metric affinities between the different parts of the series and between the Wadi Howar material and other relevant prehistoric as well as modern African populations. rnThe reconstruction and comprehensive osteological analysis of 23 as yet unpublished individuals, the bulk of the Wadi Howar series, constituted the first stage of the study. The analyses focused on each individual’s in situ position, state of preservation, sex, age at death, living height, living weight, physique, biological ancestry, epigenetic traits, robusticity, occupational stress markers, health and metric as well as morphological characteristics. Building on the results of these efforts and the re-examination of the rest of the material, the Wadi Howar series as a whole, altogether 32 individuals, could be described. rnA wide variety of robusticity, occupational stress and health variables was evaluated. The pre-Leiterband (hunter-gatherer-fisher/hunter-gatherer-fisher-herder) and the Leiterband (herder-gatherer) data of over a third of these variables differed statistically significantly or in tendency from each other. The Leiterband sub-sample was characterised by higher enamel hypoplasia frequencies, lower mean ages at death and less pronounced expressions of occupational stress traits. This pattern was interpreted as evidence that the adoption and intensification of animal husbandry did probably not constitute reactions to worsening conditions. Apart from that, the relevant observations, noteworthy tendencies and significant differences were explained as results of a broader spectrum of pre-Leiterband subsistence activities and the negative side effects of the increasingly specialised herder-gatherer economy of the Leiterband phase. rnUsing only the data which could actually be collected from it, multiple, separate, individualised discriminant function analyses were carried out for each Wadi Howar skeleton to determine which prehistoric and which modern comparative sample it was most similar to. The results of all individual analyses were then summarised and examined as a whole. Thus it became possible to draw conclusions about the affinities the Wadi Howar material shared with prehistoric as well as modern populations and to answer questions concerning the diachronic links between the Wadi Howar’s prehistoric populations. When the Wadi Howar remains were positioned in the context of the selected prehistoric (Jebel Sahaba/Tushka, A-Group, Malian Sahara) and modern comparative samples (Southern Sudan, Chad, Mandinka, Somalis, Haya) in this fashion three main findings emerged. Firstly, the series as a whole displayed very strong affinities with the prehistoric sample from the Malian Sahara (Hassi el Abiod, Kobadi, Erg Ine Sakane, etc.) and the modern material from Southern Sudan and, to a lesser extent, Chad. Secondly, the pre-Leiterband and the Leiterband sub-sample were closer to the prehistoric Malian as well as the modern Southern Sudanese material than they were to each other. Thirdly, the group of pre-Leiterband individuals approached the Late Pleistocene sample from Jebel Sahaba/Tushka under certain circumstances. A theory offering explanations for these findings was developed. According to this theory, the entire prehistoric population of the Wadi Howar belonged to a Saharo-Nilotic population complex. The Jebel Sahaba/Tushka population constituted an old Nilotic and the early population of the Malian Sahara a younger Saharan part of this complex. The pre-Leiterband groups probably colonised the Wadi Howar from the east, either during or soon after the original Saharo-Nilotic expansion. Unlike the pre-Leiterband groups, the Leiterband people originated somewhere west of the Wadi Howar. They entered the region in the context of a later, secondary Saharo-Nilotic expansion. In the process, the incoming Leiterband groups absorbed many members of the Wadi Howar’s older pre-Leiterband population. The increasing aridification of the Wadi Howar region ultimately forced its prehistoric inhabitants to abandon the wadi. Most of them migrated south and west. They, or groups closely related to them, probably were the ancestors of the majority of the Nilo-Saharan-speaking pastoralists of modern-day Southern Sudan and Eastern Chad.

Characterization of electromagnetic fields in the aSPECT spectrometer and reduction of systematic errors

Das aSPECT Spektrometer wurde entworfen, um das Spektrum der Protonen beimrnZerfall freier Neutronen mit hoher Präzision zu messen. Aus diesem Spektrum kann dann der Elektron-Antineutrino Winkelkorrelationskoeffizient "a" mit hoher Genauigkeit bestimmt werden. Das Ziel dieses Experiments ist es, diesen Koeffizienten mit einem absoluten relativen Fehler von weniger als 0.3% zu ermitteln, d.h. deutlich unter dem aktuellen Literaturwert von 5%.rnrnErste Messungen mit dem aSPECT Spektrometer wurden an der Forschungsneutronenquelle Heinz Maier-Leibnitz in München durchgeführt. Jedoch verhinderten zeitabhängige Instabilitäten des Meßhintergrunds eine neue Bestimmung von "a".rnrnDie vorliegende Arbeit basiert hingegen auf den letzten Messungen mit dem aSPECTrnSpektrometer am Institut Laue-Langevin (ILL) in Grenoble, Frankreich. Bei diesen Messungen konnten die Instabilitäten des Meßhintergrunds bereits deutlich reduziert werden. Weiterhin wurden verschiedene Veränderungen vorgenommen, um systematische Fehler zu minimieren und um einen zuverlässigeren Betrieb des Experiments sicherzustellen. Leider konnte aber wegen zu hohen Sättigungseffekten der Empfängerelektronik kein brauchbares Ergebnis gemessen werden. Trotzdem konnten diese und weitere systematische Fehler identifiziert und verringert, bzw. sogar teilweise eliminiert werden, wovon zukünftigernStrahlzeiten an aSPECT profitieren werden.rnrnDer wesentliche Teil der vorliegenden Arbeit befasst sich mit der Analyse und Verbesserung der systematischen Fehler, die durch das elektromagnetische Feld aSPECTs hervorgerufen werden. Hieraus ergaben sich vielerlei Verbesserungen, insbesondere konnten die systematischen Fehler durch das elektrische Feld verringert werden. Die durch das Magnetfeld verursachten Fehler konnten sogar soweit minimiert werden, dass nun eine Verbesserung des aktuellen Literaturwerts von "a" möglich ist. Darüber hinaus wurde in dieser Arbeit ein für den Versuch maßgeschneidertes NMR-Magnetometer entwickelt und soweit verbessert, dass nun Unsicherheiten bei der Charakterisierung des Magnetfeldes soweit reduziert wurden, dass sie für die Bestimmung von "a" mit einer Genauigkeit von mindestens 0.3% vernachlässigbar sind.

Computer simulations of colloidal fluids in confinement

Computer-Simulationen von Kolloidalen Fluiden in Beschränkten Geometrien Kolloidale Suspensionen, die einen Phasenübergang aufweisen, zeigen eine Vielfalt an interessanten Effekten, sobald sie auf eine bestimmte Geometrie beschränkt werden, wie zum Beispiel auf zylindrische Poren, sphärische Hohlräume oder auf einen Spalt mit ebenen Wänden. Der Einfluss dieser verschiedenen Geometrietypen sowohl auf das Phasenverhalten als auch auf die Dynamik von Kolloid-Polymer-Mischungen wird mit Hilfe von Computer-Simulationen unter Verwendung des Asakura-Oosawa- Modells, für welches auf Grund der “Depletion”-Kräfte ein Phasenübergang existiert, untersucht. Im Fall von zylindrischen Poren sieht man ein interessantes Phasenverhalten, welches vom eindimensionalen Charakter des Systems hervorgerufen wird. In einer kurzen Pore findet man im Bereich des Phasendiagramms, in dem das System typischerweise entmischt, entweder eine polymerreiche oder eine kolloidreiche Phase vor. Sobald aber die Länge der zylindrischen Pore die typische Korrelationslänge entlang der Zylinderachse überschreitet, bilden sich mehrere quasi-eindimensionale Bereiche der polymerreichen und der kolloidreichen Phase, welche von nun an koexistieren. Diese Untersuchungen helfen das Verhalten von Adsorptionshysteresekurven in entsprechenden Experimenten zu erklären. Wenn das Kolloid-Polymer-Modellsystem auf einen sphärischen Hohlraum eingeschränkt wird, verschiebt sich der Punkt des Phasenübergangs von der polymerreichen zur kolloidreichen Phase. Es wird gezeigt, dass diese Verschiebung direkt von den Benetzungseigenschaften des Systems abhängt, was die Beobachtung von zwei verschiedenen Morphologien bei Phasenkoexistenz ermöglicht – Schalenstrukturen und Strukturen des Janustyps. Im Rahmen der Untersuchung von heterogener Keimbildung von Kristallen innerhalb einer Flüssigkeit wird eine neue Simulationsmethode zur Berechnung von Freien Energien der Grenzfläche zwischen Kristall- bzw. Flüssigkeitsphase undWand präsentiert. Die Resultate für ein System von harten Kugeln und ein System einer Kolloid- Polymer-Mischung werden anschließend zur Bestimmung von Kontaktwinkeln von Kristallkeimen an Wänden verwendet. Die Dynamik der Phasenseparation eines quasi-zweidimensionalen Systems, welche sich nach einem Quench des Systems aus dem homogenen Zustand in den entmischten Zustand ausbildet, wird mit Hilfe von einer mesoskaligen Simulationsmethode (“Multi Particle Collision Dynamics”) untersucht, die sich für eine detaillierte Untersuchung des Einflusses der hydrodynamischen Wechselwirkung eignet. Die Exponenten universeller Potenzgesetze, die das Wachstum der mittleren Domänengröße beschreiben, welche für rein zwei- bzw. dreidimensionale Systeme bekannt sind, können für bestimmte Parameterbereiche nachgewiesen werden. Die unterschiedliche Dynamik senkrecht bzw. parallel zu den Wänden sowie der Einfluss der Randbedingungen für das Lösungsmittel werden untersucht. Es wird gezeigt, dass die daraus resultierende Abschirmung der hydrodynamischen Wechselwirkungsreichweite starke Auswirkungen auf das Wachstum der mittleren Domänengröße hat.

Complementary mass spectrometric techniques for the characterization of the organic fraction in atmospheric aerosols

Aerosol particles are strongly related to climate, air quality, visibility and human health issues. They contribute the largest uncertainty in the assessment of the Earth´s radiative budget, directly by scattering or absorbing solar radiation or indirectly by nucleating cloud droplets. The influence of aerosol particles on cloud related climatic effects essentially depends upon their number concentration, size and chemical composition. A major part of submicron aerosol consists of secondary organic aerosol (SOA) that is formed in the atmosphere by the oxidation of volatile organic compounds. SOA can comprise a highly diverse spectrum of compounds that undergo continuous chemical transformations in the atmosphere.rnThe aim of this work was to obtain insights into the complexity of ambient SOA by the application of advanced mass spectrometric techniques. Therefore, an atmospheric pressure chemical ionization ion trap mass spectrometer (APCI-IT-MS) was applied in the field, facilitating the measurement of ions of the intact molecular organic species. Furthermore, the high measurement frequency provided insights into SOA composition and chemical transformation processes on a high temporal resolution. Within different comprehensive field campaigns, online measurements of particular biogenic organic acids were achieved by combining an online aerosol concentrator with the APCI-IT-MS. A holistic picture of the ambient organic aerosol was obtained through the co-located application of other complementary MS techniques, such as aerosol mass spectrometry (AMS) or filter sampling for the analysis by liquid chromatography / ultrahigh resolution mass spectrometry (LC/UHRMS).rnIn particular, during a summertime field study at the pristine boreal forest station in Hyytiälä, Finland, the partitioning of organic acids between gas and particle phase was quantified, based on the online APCI-IT-MS and AMS measurements. It was found that low volatile compounds reside to a large extent in the gas phase. This observation can be interpreted as a consequence of large aerosol equilibration timescales, which build up due to the continuous production of low volatile compounds in the gas phase and/or a semi-solid phase state of the ambient aerosol. Furthermore, in-situ structural informations of particular compounds were achieved by using the MS/MS mode of the ion trap. The comparison to MS/MS spectra from laboratory generated SOA of specific monoterpene precursors indicated that laboratory SOA barely depicts the complexity of ambient SOA. Moreover, it was shown that the mass spectra of the laboratory SOA more closely resemble the ambient gas phase composition, indicating that the oxidation state of the ambient organic compounds in the particle phase is underestimated by the comparison to laboratory ozonolysis. These observations suggest that the micro-scale processes, such as the chemistry of aerosol aging or the gas-to-particle partitioning, need to be better understood in order to predict SOA concentrations more reliably.rnDuring a field study at the Mt. Kleiner Feldberg, Germany, a slightly different aerosol concentrator / APCI-IT-MS setup made the online analysis of new particle formation possible. During a particular nucleation event, the online mass spectra indicated that organic compounds of approximately 300 Da are main constituents of the bulk aerosol during ambient new particle formation. Co-located filter analysis by LC/UHRMS analysis supported these findings and furthermore allowed to determine the molecular formulas of the involved organic compounds. The unambiguous identification of several oxidized C 15 compounds indicated that oxidation products of sesquiterpenes can be important compounds for the initial formation and subsequent growth of atmospheric nanoparticles.rnThe LC/UHRMS analysis furthermore revealed that considerable amounts of organosulfates and nitrooxy organosulfates were detected on the filter samples. Indeed, it was found that several nitrooxy organosulfate related APCI-IT-MS mass traces were simultaneously enhanced. Concurrent particle phase ion chromatography and AMS measurements indicated a strong bias between inorganic sulfate and total sulfate concentrations, supporting the assumption that substantial amounts of sulfate was bonded to organic molecules.rnFinally, the comprehensive chemical analysis of the aerosol composition was compared to the hygroscopicity parameter kappa, which was derived from cloud condensation nuclei (CCN) measurements. Simultaneously, organic aerosol aging was observed by the evolution of a ratio between a second and a first generation biogenic oxidation product. It was found that this aging proxy positively correlates with increasing hygroscopicity. Moreover, it was observed that the bonding of sulfate to organic molecules leads to a significant reduction of kappa, compared to an internal mixture of the same mass fractions of purely inorganic sulfate and organic molecules. Concluding, it has been shown within this thesis that the application of modern mass spectrometric techniques allows for detailed insights into chemical and physico-chemical processes of atmospheric aerosols.rn

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.