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.

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.

<p>Dissociation dynamics of the ionized molecules HCl and the deuterated system DCl has been studied in gas-phase using synchrotron based photoelectron spectroscopy (PES).</p><p>The inner-valence "(4σ)^-1" photoionization band for DCl and HCl was recorded using maximum resolution in order to probe an interference pattern between a dissociative and a bound electronic state. For HCl⁺, we clearly observed distorted Fano-type peaks even for modest resolution, whereas for DCl⁺, the pattern was hardly discernible. The observation in HCl⁺ has been explained by a coupling between two adiabatic electronic states, where the bound state was populated through non-adiabatic curve-crossing. The nuclear motion of HCl⁺ is too fast for the Born-Oppenheimer approximation to be fully valid in this case. Whereas for DCl⁺, with larger reduced mass and therefore slower nuclear motion, the non-adiabatic coupling is less pronounced, and the vibrational progression vanishes.</p><p>A comparative study between PES and threshold photoelectron spectra (TPES) of the inner-valence bands of HCl and DCl has been performed, showing differences in intensities and shapes of the vibrational bands. These differences were attributed to the fact that the sudden approximation, which can be assumed to be valid for PES, is violated in the case of TPES.</p><p>A resonant Auger electron spectroscopy study of HCl and DCl has been performed, which shows an interference pattern between atomic and molecular Auger- and photoelectron channels. The atomic features are associated with ultra-fast dissociation of the molecules, on the same time scale as the Auger decay. The observation shows that the excited molecular system has to be regarded as a superposition of fragmented and molecular states.</p><p>A study of the <i>X</i>-state of HCl⁺, populated via a core-excited state, shows a selective population of the final state. The explanation was shown to be that the magnetic orientation of the core-hole is transferred to the final state of the molecule.</p><p>A setup for data acquisition of Photo-Electron Photo-Ion Photo-Ion COincidence (PEPIPICO) measurements using a Time-Of-Flight (TOF) spectrometer has been developed. A Time-to-Digital Converter (TDC) card has been linked together with the data treatment program Igor as a user interface. Furthermore, the PEPIPICO spectrometer has been characterized to provide a solid basis for the analysis of experimental data.</p>

Dissociation dynamics of the ionized molecules HCl and the deuterated system DCl has been studied in gas-phase using synchrotron based photoelectron spectroscopy (PES). The inner-valence "(4σ)-1" photoionization band for DCl and HCl was recorded using maximum resolution in order to probe an interference pattern between a dissociative and a bound electronic state. For HCl+, we clearly observed distorted Fano-type peaks even for modest resolution, whereas for DCl+, the pattern was hardly discernible. The observation in HCl+ has been explained by a coupling between two adiabatic electronic states, where the bound state was populated through non-adiabatic curve-crossing. The nuclear motion of HCl+ is too fast for the Born-Oppenheimer approximation to be fully valid in this case. Whereas for DCl+, with larger reduced mass and therefore slower nuclear motion, the non-adiabatic coupling is less pronounced, and the vibrational progression vanishes. A comparative study between PES and threshold photoelectron spectra (TPES) of the inner-valence bands of HCl and DCl has been performed, showing differences in intensities and shapes of the vibrational bands. These differences were attributed to the fact that the sudden approximation, which can be assumed to be valid for PES, is violated in the case of TPES. A resonant Auger electron spectroscopy study of HCl and DCl has been performed, which shows an interference pattern between atomic and molecular Auger- and photoelectron channels. The atomic features are associated with ultra-fast dissociation of the molecules, on the same time scale as the Auger decay. The observation shows that the excited molecular system has to be regarded as a superposition of fragmented and molecular states. A study of the X-state of HCl+, populated via a core-excited state, shows a selective population of the final state. The explanation was shown to be that the magnetic orientation of the core-hole is transferred to the final state of the molecule. A setup for data acquisition of Photo-Electron Photo-Ion Photo-Ion COincidence (PEPIPICO) measurements using a Time-Of-Flight (TOF) spectrometer has been developed. A Time-to-Digital Converter (TDC) card has been linked together with the data treatment program Igor as a user interface. Furthermore, the PEPIPICO spectrometer has been characterized to provide a solid basis for the analysis of experimental data.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20880号 / 理博第4332号 / 新制||理||1622(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 堤 誉志雄, 教授 上 正明, 教授 宍倉 光広 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

We discuss the physical problem of a molecule interacting with an electromagnetic field pulse and model the problem using a time-dependent perturbation of the Born-Oppenheimer approximation to the Schrodinger equation. Using previous results that develop asymptotic series solutions in the Born-Oppenheimer parameter ε, we derive a formal Dyson series expansion in the perturbation parameter μ, which is proportional to the electromagnetic field strength. We then prove that this series is asymptotically accurate in both parameters, provided that the Hamiltonian for the electrons has purely discrete spectrum. Under more general hypotheses, we show that the series is accurate to first order in μ, and that it is accurate to one higher order if we place conditions on the abruptness of the EM pulse. We also show how this series development provides a justification for the Franck-Condon factors in the case of a diatomic molecule. / Ph. D.

Ce travail est destiné au développement de méthodes approchées de chimie quantique capables de traiter des systèmes biologiques de grande taille. En particulier, nous réalisons des simulations de dynamique moléculaire dans l'approximation de Born-Oppenheimer, permettant une description quantique de l'Hamiltonien électronique du système dans son entier : SEBOMD (SemiEmpirical Born-Oppenheimer Molecular Dynamics). Notre approche se base sur un Hamiltonien électronique semiempirique (SE). L'une des principales difficultés rencontrées lors d'une simulation SEBOMD de la phase condensée est représentée par le choix de la méthode SE. La plupart des méthodes courantes ne permettant pas une bonne description de certaines interactions fondamentales, nous avons développé une nouvelle approche. Cette méthode, dénommée PM3-PIF3, a été appliquée à l'étude par dynamique moléculaire de molécules organiques dans l'eau. Les résultats obtenus montrent que notre méthode est appropriée pour le traitement de molécules comportant des groupements hydrophobes et/ou hydrophiles en milieu aqueux. L'analyse des propriétés électroniques et vibrationnelles de ces molécules en présence du solvant valide également nos résultats vis-À-Vis d'autres études expérimentales et théoriques présentes dans la littérature. Finalement, nous nous sommes intéressés au processus d'autoprotolyse de l'eau en milieux confinés. Après avoir discuté du choix de l'Hamiltonien SE à utiliser pour cette étude, nous avons caractérisé le transfert de proton dans un agrégat d'eau. Nous avons établi une corrélation entre l'énergie libre associée à la première étape de ce transfert et certaines propriétés physiques collectives / The present work is devoted to the development of approximate quantum chemistry methods that are suitable to treat biological systems of large size. In particular, we run molecular dynamics under the Born-Oppenheimer approximation, allowing a quantum mechanical description of the electronic Hamiltonian of the full system: SEBOMD (SemiEmpirical Born-Oppenheimer Molecular Dynamics). Our method is based on a semiempirical (SE) electronic Hamiltonian. One of the key issues arising in a condensed phase SEBOMD simulation is represented by the choice of the SE method. Since most of the currently available approaches fail in describing some relevant intermolecular interactions, we developed a new correction of SE Hamiltonians. This method, which we named PM3-PIF3, was applied to study the molecular dynamics of organic molecules in water. The results that we obtained showed that our technique is suitable to treat molecules having hydrophobic and/or hydrophilic groups in an aqueous medium. The analysis of the electronic and vibrational properties of these molecules in the presence of the solvent validates our results with respect to experimental and theoretical studies in the literature. Finally, we investigated the water self-Dissociation process in confined environments. After discussing the choice of the SE Hamiltonian to be used for this purpose, we characterized the proton transfer in a water cluster. We established a correlation between the free energy of the first step of this process and some collective physical properties

Cette thèse est consacrée à l'étude du spectre de l'opérateur de Laplace avec conditions de Dirichlet dans différents domaines du plan ou de l'espace. Dans un premier temps on s'intéresse à des triangles asymptotiquement plats et des cônes de petite ouverture. Ces problèmes admettent une reformulation semi-classique et nous donnons des développements asymptotiques à tout ordre des premières valeurs et fonctions propres. Ce type de résultat est déjà connu pour des domaines minces à profil régulier. Pour les triangles et les cônes, on prouve que le problème admet maintenant deux échelles. Dans un second temps, on étudie une famille de couches coniques indexées par leur ouverture. Là encore, on s'intéresse à la limite semi-classique quand l'ouverture tend vers zéro: on donne un développement asymptotique à deux termes des premières valeurs propres et on démontre un résultat de localisation des fonctions propres associées. Nous donnons également, à ouverture fixée, un équivalent du nombre de valeurs propres sous le seuil du spectre essentiel. / This thesis deals with the spectrum of the Dirichlet Laplacian in various two or three dimensional domains. First, we consider asymptotically flat triangles and cones with small aperture. These problems admit a semi-classical formulation and we provide asymptotic expansions at any order for the first eigenvalues and the associated eigenfunctions. These type of results is already known for thin domains with smooth profiles. For triangles and cones, we show that the problem admits now two different scales. Second, we study a family of conical layers parametrized by their aperture. Again, we consider the semi-classical limit when the aperture tends to zero: We provide a two-term asymptotics of the first eigenvalues and we prove a localization result about the associated eigenfunctions. We also estimate, for each chosen aperture, the number of eigenvalues below the threshold of the essential spectrum.