Thesis (Ph. D.)--University of California, San Diego, 2001. / Vita. Includes bibliographical references (leaves 673-700).

The research overviewed in this dissertation concerns highly accurate variational calculations of small molecular systems without assuming the Born--Oppenheimer approximation. The centerpiece of the research is the use of different forms of explicitly correlated Gaussian basis functions. These basis functions allow analytical evaluation of all necessary matrix elements and provide a very powerful tool for solving quantum mechanical problems encountered in various areas of physics. Most of the derivations presented in the dissertation are done within the formalism of matrix differential calculus that has proven to be a very handy and effective way of dealing with explicitly correlated Gaussians. As this fomalism is not widely used in physics or chemistry, some mathematical background is provided. The expressions obtained theoretically were implemented in a computer code that was run quite extensively on several parallel computer systems during the period of the author's Ph.D. study. The results of many such calculations are presented and discussed. The dissertation is primarily based on the content of the papers that were published in coathorship with my scientific advisor and other collaborators in several scientific journals. It also includes some topics that were not considered in the publications but are essential for the completeness and good understanding of the presented work.

Freiburg i. Br., Univ., Diss., 2007.

In this dissertation recent advances in modeling various atomic and molecular systems with quantum mechanical calculations employing explicitly correlated Gaussian functions are presented. The author has utilized multiple approaches and considered a number of approximations to develop optimal calculation frameworks. Electronic and muonic molecules and atoms have been considered. A number of unique calculations have been performed and some novel and interesting results, including high accuracy description of the charge asymmetry in the heteronuclear systems and lifetimes of rotationless vibrational levels of diatomic molecules, have been generated.

The ground state electron wavefunction of some molecules has a non-zero angular momentum about the internuclear axis. Molecular rotational momentum can couple with this angular momentum, splitting the energy degeneracy of the two directions of motion about the internuclear axis. Performing a Born-Oppenheimer approximation of such a system will break the relevant energy degeneracy at eighth order. This degeneracy breaking is known as L-doubling. / Master of Science

Im Rahmen dieser Arbeit werden unterschiedliche Aspekte der korrelierten Elektronen-Kerndynamik, anhand verschiedener Modellsysteme untersucht. Dabei wird vor allem auf den Vergleich numerisch exakter und approximativer Methoden zur Beschreibung der Wellenpaketdynamik eingegangen, wobei bei letzterem das Augenmerk auf der Born-Oppenheimer (BO) Näherung liegt. Die verwendeten Modellsysteme erlauben es, die gekoppelte Elektronen-Kern-Dynamik exakt zu beschreiben. Die daraus gewonnenen Ergebnisse dienen als Referenz für den Vergleich mit den Näherungsmethoden. Im ersten Teil der Arbeit wird die Dynamik eines Wellenpakets in der Umgebung einer Konischen-Durchschneidung (CI) untersucht, wobei die Beschreibung des Wellenpakets quantenmechanisch und durch die klassische Mechanik im Phasenraum erfolgt. Im zweiten Teil wird die Wahrscheinlichkeitsflussdichte untersucht. Zuerst wird ein Fall konstruiert, in welchem die Bewegung im elektronischen Grundzustand stattfindet, sodass die Bedingungen der BO Näherung erfüllt sind. Dabei wird vor allem auf das Verschwinden der elektronischen Wahrscheinlichkeitsflussdichte innerhalb der BO Näherung eingegangen. Im weiteren Verlauf werden die Flussdichten in der Umgebung einer CI untersucht, wobei unterschiedliche Situationen modelliert werden. Im dritten Teil wird die Berechnung des elektronischen Impulserwartungswerts innerhalb der BO Näherung untersucht. Dieser verschwindet innerhalb der BO Näherung, wenn man diesen direkt berechnet (Geschwindigkeitsform), während man über das Ehrenfest Theorem (Längenform) sehr gute Werte erhält. Im vierten Teil wird eine neue Flussdichte, die Translationsflussdichte, vorgestellt. Diese ergibt sich aus der Überlegung, dass die Geschwindigkeitsform des Impulserwartungswerts durch die Wahrscheinlichkeitsflussdichte ausgedrückt werden kann. Demnach muss auch die Längenform einer Flussdichte entsprechen und man erhält die Translationsflussdichte. / In the present work different aspects of the correlated electron nuclear dynamics are investigated based on different model systems. The focus is set on the comparison of numerically exact and approximate methods, especially on the Born-Oppenheimer (BO) approximation, for the description of wave packet dynamics. The employed model systems allows a numerically exact solution for the coupled dynamics which serves as a reference for the comparison with the approximate description. In the first part of this thesis, wave packet dynamics are studied in the vicinity of a conical intersection (CI). The wave packet motion is treated quantum mechanically and also using classical mechanics. In the second part of this work the probability flux density is examined. A case is constructed where nearly the complete dynamics take place in the electronic ground state, so that the BO approximation is valid and the disappearance of the electronic probability flux density within the BO approximation is discussed. After that flux densities are studied in the vicinity of a CI whereby different situations are constructed In the third part of this thesis, the calculation of the electronic momentum expectation value within the BO approximation is examined. The electronic momentum expectation value disappears within the BO approximation if it is directly calculated (velocity form). The Ehrenfest theorem offers the possibility to calculate the momentum expectation value via the expectation value of the position operator (length form). The length form can be used to calculated an electronic momentum expectation value within the BO approximation which is in very good agreement with the one obtained from the coupled dynamics. In the fourth part of the thesis a new flux density, the translational flux density, is presented. This flux density emerges from the property that the velocity form of the momentum expectation value can be expressed by the probability flux density. Accordingly, the length form must also result from a flux density which identifies the translation flux density.

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.

No description available.

Dans cette thèse, l'étude de la dépostion des molécules de ferrocène sur un substrat de Cu(111) par des simulations de dynamique moléculaire par premiers principes, en particulier, la dynamique moléculaire utilisant l'approche de Born-Oppenheimer (BOMD: Born-Oppenheimer Molecular Dynamics) et celle utilisant la fonctionnelle de l'énergie libre (FEMD: Free Energy Molecular Dynamics), combinées avec les études expérimentales par microscopie à effet tunnel (STM) à basse température et à courant constant ont montré que ces molécules de ferrocène peuvent être physisorbées sur un substrat de cuivre sans donner lieu à une dissociation moléculaire. Ce qui constitue un système idéal pour étudier la dynamique des états d'interfaces et leur réactivité par rapport à la déposition d’atomes métalliques. En particulier, la déposition d'un atome de Cuivre au dessus d'une molécule de ferrocène équilibrée sur le substrat de cuivre, conduit à un transfert de charges de cet atomes vers le substrat de Cu(111). On montre aussi que ces états d'interfaces ont le comportement bidimensionnel d'un gas d'électrons libres. / First-principles simulations studies, in particular Born-Oppenheimer molecular dynamics (BOMD) and free energy molecular dynamics (FEMD), combined with low-temperature scanning tunneling microscopy (STM) and spectroscopy reveal a non dissociative physisorption of ferrocene molecules on a Cu(111) surface, giving rise to ordered molecular layers. At the interface, a 2D-like electronic band is found, which shows an identical dispersion as the Cu(111) Shockley surface-state band. Subsequent deposition of Cu atoms forms charged organometallic compounds that localize interface-state electrons.

La thèse consiste en l’étude spectrale d’opérateurs partiellement semi-classiques. Quand la géométrie du problème suggère une localisation anisotrope des fonctions propres associées aux basses énergies (bord du domaine, lieu d’annulation du champs magnétique), le développement local de l’opérateur amène naturellement à une structure à double échelle. Il s'agit, via un schéma de réduction "à la Born-Oppenheimer", utilisant le formalisme du calcul pseudodifférentiel pour des symboles à valeur opérateur, de montrer l’existence d’un opérateur effectif à symbole scalaire. On en déduit ensuite des formules de Weyl pour le comptage des basses valeurs propres. Cette stratégie est appliquée : au Laplacien de Robin sur un domaine borné, en dimension quelconque et au Laplacien magnétique dans R², dans le cas où le champ magnétique s’annule sur une courbe fermée. / The thesis consists in the spectral study of partially semiclassical operators. When the geometry of the problem suggests an anisotropic localization of the eigenfunctions associated to low energies (boundary of the domain, vanishing magnetic field), the local expansion of the operator naturally brings to a doublescale structure. Via a reduction scheme "à la Born-Oppenheimer", using the formalism of pseudodifferential calculus for operator-valued symbols, we can show the existence of an effective operator, with scalar symbol. Then, we deduce Weyl formulae for the number of low-lying eigenvalues. This strategy is applied : to the Robin Laplacian on a bounded domain, in any dimension and to the magnetic Laplacian in R², in the case where the magnetic field vanishes on a closed curve.