We perform a rigorous mathematical analysis of the bending modes of a linear triatomic molecule that exhibits the Renner-Teller effect. Assuming the potentials are smooth, we prove that the wave functions and energy levels have asymptotic expansions in powers of ε, where ε4 is the ratio of an electron mass to the mass of a nucleus. To prove the validity of the expansion, we must prove various properties of the leading order equations and their solutions. The leading order eigenvalue problem is analyzed in terms of a parameter bË , which is equivalent to the parameter originally used by Renner. For 0 &lt bË &lt 1, we prove self-adjointness of the leading order Hamiltonian, that it has purely discrete spectrum, and that its eigenfunctions and their derivatives decay exponentially. Perturbation theory and finite difference calculations suggest that the ground bending vibrational state is involved in a level crossing near bË = 0.925. We also discuss the degeneracy of the eigenvalues. Because of the crossing, the ground state is degenerate for 0 &lt bË &lt 0.925 and non-degenerate for 0.925 &lt bË &lt 1. / Ph. D.

Transient molecules are of great importance due to their critical role as intermediates in the semiconductor industry, in upper atmosphere reactions, and in astrochemistry. In the present work, reactive intermediates were produced in the laboratory by applying an electric discharge through a suitable precursor gas mixture and studied by means of their laser-induced fluorescence and emission spectra. The band systems of and have been studied in detail. The energy levels of both isotopologues were fitted with a Renner-Teller model, and the isotope relations have been used to test the validity of the derived parameters. The A2Πu - X 2Πg electronic transition of jet-cooled has been detected and shown to originate from the Ω=3/2 spin-orbit component of v=0 of the ground state. For the first time, the 0-0 band has been identified and vibrational assignments have been made. Our ab initio studies show that the extensive observed perturbations are due to spin-orbit interaction between A2Πu(3/2) and B2Δu(3/2) states. The experimental data were fitted to an effective Hamiltonian and yielded the spin-orbit coupling term =240 cm-1. LIF and emission spectra of the transition of N2O+ have been recorded. Both spin-orbit components of the band were studied at high resolution and rotationally analyzed, providing precise molecular constants. Emission spectra provided extensive data on the ground state vibrational levels which were fitted to a Renner-Teller model including spin-orbit and Fermi resonance terms. The previously unknown electronic spectrum of the H2PO radical has been identified. Ab initio predictions were used to aid in the analysis of the data. The band system is assigned as the electronic transition. The excited state molecular structure was determined by rotational analysis of high resolution LIF spectra. The band systems of the HBCl and DBCl free radicals have been studied in detail. This electron promotion involves a linear-bent transition between the two Renner-Teller components of what would be a 2Π electronic state at linearity. Ab initio potential energy surface calculations were used to help in assigning the LIF spectra which involve transitions from the ground state zero-point level to high vibrational levels of the excited state.

Anhand von theoretischen Untersuchungen wird eine umfassende Beschreibung von kleinen Metalloxidclustern gegeben. Bei den untersuchten Systemen handelt es sich um Aluminium- und Eisenoxid-Ionen sowie entsprechende Oxid-Cluster, die beide Metalle enthalten. Neben der Bestimmung der geometrischen Struktur der Cluster werden auch die allgemeinen elektronischen Eigenschaften der eisenhaltigen Verbindungen untersucht. Alle Vorhersagen werden durch Vergleich mit verfügbaren experimentellen Ergebnissen -- hauptsächlich aus der Infrarot-Photodissoziations- und der Photoelektronenspektroskopie -- überprüft und bewertet. Soweit möglich werden die Bewegungen von Atomen oder kleinen Gruppen innerhalb der Cluster einzelnen experimentellen Signalen zugeordnet. Besondere Aufmerksamkeit wird dem Eisendioxidmolekül und seinem Anion gewidmet. Es wird mit spezialisierten Wellenfunktionsmethoden untersucht, mit denen ab initio Franck-Condon-Simulationen einschließlich nicht-adiabatischer und Spin-Orbit-Kopplungen für die Photoionisation des Anions erstellt werden. Sie liefern Erklärungen für die komplizierte Schwingungsstruktur des experimentellen hochauflösenden Photoelektronenspektrums. / By means of theoretical investigations, a comprehensive description of small metal oxide clusters is given. The studied systems are aluminum and iron oxide ions as well as respective bi-metallic oxide clusters. Besides the determination of the geometrical structure of the clusters, the general electronic properties of the iron-containing compounds are investigated. All predictions are checked and assessed by comparison with available experimental results, mainly infrared photodissociation and photoelectron spectroscopy measurements. As far as possible, motions of atoms or small groups within the clusters are assigned to distinct experimental vibrational features. Particular attention is paid to the iron dioxide molecule and its anion. It is studied with sophisticated wave function methods based on which ab initio Franck-Condon simulations for the photodetachment from the anion, including non-adiabatic and spin-orbit couplings, are generated. They provide explanations for the complicated vibrational structure of the experimental high-resolution photoelectron spectrum.