Gekreuzt konjugierte Oligomere aus Benzolringen und Heterocyclen

Gekreuzt konjugierte Oligomere aus Benzolringen und Heterocyclen Oligomere aus Arylen- oder/und Hetarylen-Bausteinen stellenein aktuelles Arbeitsgebiet in der organischen Synthese undder Materialwissenschaft dar. Die Enoneinheit der Chalkonerepräsentiert ein bifunktionelles Elektrophil, das für denAufbau von unterschiedlichen Heterocyclen hervorragendgeeignet ist. Im Rahmen der vorliegenden Arbeit wurden dreineue Reihen von heterocyclischen Oligomeren hergestellt:1H-Pyrrole, 1H-Pyrazole und Pyridine, die über eine alter-nierende Sequenz von Phenylen- oder Benzoylen-Einheitenverbunden sind. Ihre Herstellung basierte auf Michael-Additionen von den kettenförmigen, gekreuzt konjugiertenOligochalkonen und den jeweiligen geeigneten N-haltigenBausteinen: Tosylmethylisocyanid, Methylhydrazin undPhenacylpyridiniumbromid in der Reihe der Pyrrole, Pyrazoleund Pyridine. Die UV/Vis-Untersuchung aller Reihen der Oligoheterocyclenzeigte als allgemeinen Trend im Vergleich mit dem UV/Vis-Verhalten der Oliogochalkone eine ausgeprägte hypsochromeVerschiebung der langwelligen Absorption. Dieser beobachtetehypsochrome Shift geht auf die veränderten Chromophore zurück und deutet außerdem darauf hin, dass die effektiveKonjugation bei wachsender Moleküllänge geringer sein sollte. In den einzelnen Reihen der Oligoheterocyclenerkennt man jeweils bei Vergrößerung der Chromophore einenkleinen bathochromen Shift der langwelligen Absorption.

Persistent currents in quantum rings

In this thesis, three different types of quantum rings arestudied. These are quantum rings with diamagnetic,paramagnetic or spontaneous persistent currents. It turns out that the main observable to characterizequantum rings is the Drude weight. Playing a key role inthis thesis, it will be used to distinguish betweendiamagnetic (positive Drude weight) and paramagnetic(negative Drude weight) ring currents. In most models, theDrude weight is positive. Especially in the thermodynamiclimit, it is positive semi-definite. In certain modelshowever, intuitivelysurprising, a negative Drude weight is found. This rareeffect occurs, e.g., in one-dimensional models with adegenerate ground state in conjunction with the possibilityof Umklapp scattering. One aim of this thesis is to examineone-dimensional quantum rings for the occurrence of anegative Drude weight. It is found, that the sign of theDrude weight can also be negative, if the band structurelacks particle-hole symmetry. The second aim of this thesis is the modeling of quantumrings intrinsically showing a spontaneous persistentcurrent. The construction of the model starts from theextended Hubbard model on a ring threaded by anAharonov-Bohm flux. A feedback term through which thecurrent in the ring can generate magnetic flux is added.Another extension of the Hamiltonian describes the energystored in the internally generated field. This model isevaluated using exact diagonalization and an iterativescheme to find the minima of the free energy. The quantumrings must satisfy two conditions to exhibit a spontaneousorbital magnetic moment: a negative Drude weight and aninductivity above the critical level. The magneticproperties of cyclic conjugated hydrocarbons likebenzene due to electron delocalization [magnetic anisotropy,magnetic susceptibility exaltation, nucleus-independent chemical shift (NICS)]---that have become important criteriafor aromaticity---can be examined using this model. Corrections to the presented calculations are discussed. Themost substantial simplification made in this thesis is theneglect of the Zeeman interaction of the electron spins withthe magnetic field. If a single flux tube threads a quantumring, the Zeeman interaction is zero, but in mostexperiments, this situation is difficult to realize. In themore realistic situation of a homogeneous field, the Zeemaninteraction has to be included, if the electrons have atotal spin component in the direction of the magnetic field,or if the magnetic field is strong.