Thèse de doctorat : Chimie. Chimie informatique et théorique : Strasbourg 1 : 2008. / Thèse soutenue sur un ensemble de travaux. Titre provenant de l'écran-titre. Bibliogr. 6 p.

Thesis (Ph. D.)--University of Chicago, Dept. of Chemistry, August 1999. / Includes bibliographical references. Also available on the Internet.

No description available.

Semiclassical and Born-Oppenheimer approximations are used to provide uniform error bounds for the energies of diatomic molecules for bounded vibrational quantum number n and large angular momentum quantum number l. Specifically, results are given when (l + 1) < κ𝛜⁻³/². Explicit formulas for the approximate energies are also given. Numerical comparisons for the H+₂ and HD+ molecules are presented. / Ph. D.

Submitted by DERICK DOS SANTOS ROSA null (derick@ift.unesp.br) on 2016-09-27T19:10:43Z No. of bitstreams: 1 dissertacao.pdf: 2019409 bytes, checksum: 0be92a2b52e4578cd4fe399bc8639856 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-09-29T16:36:56Z (GMT) No. of bitstreams: 1 rosa_ds_me_ift.pdf: 2019409 bytes, checksum: 0be92a2b52e4578cd4fe399bc8639856 (MD5) / Made available in DSpace on 2016-09-29T16:36:56Z (GMT). No. of bitstreams: 1 rosa_ds_me_ift.pdf: 2019409 bytes, checksum: 0be92a2b52e4578cd4fe399bc8639856 (MD5) Previous issue date: 2016-07-29 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Nesta dissertação vamos estudar um problema de três corpos via aproximação de Born-Oppenheimer em duas dimensões para um sistema constituído de duas partículas pesadas e uma leve. Considerando uma interação de contato entre a partícula leve e as pesadas e desconsiderando a interação entre as pesadas, estudamos o efeito do momento angular e da diferença de massa entre as partículas. Notamos que diminuindo a diferença de massa entre as partículas encontramos um número menor de estados ligados. Conforme aumentamos o momento angular observamos um número menor de estados ligados, isto porque o momento angular soma ao sistema um potencial repulsivo, tornando o sistema mais fracamente ligado. Considerando um potencial gaussiano entre as partículas pesadas calculamos a energia de três corpos e o raio quadrático médio. Observamos que a introdução deste potencial torna possível o rompimento do sistema de três corpos e o fenômeno de tunelamento. Estudando o raio quadrático médio percebemos que na região de tunelamento o tamanho do sistema varia consideravelmente, tornando esta região interessante de ser detectada experimentalmente. / In this thesis we study mass-imbalanced three-body system in two dimensions using BornOppenheimer approximation. Considering the heavy-light particle system interacting through zero-range interaction and disregarding interaction between the heavy-heavy, we study effects the angular momentum and mass ratio difference. Decreasing the mass difference between the heavy and the light particles a smaller number of bound states is found. Increasing the angular momentum we add to the system a repulsive potential, making the system weakly bounded, in this case a small number of bound states are expected. Considering a gaussian potential between the heavy-heavy particles it is possible to unbounded the system and observe tunneling phenomena. The considerable change in the tunneling region for the mean square radii indicates an increase in the system size, making this region interesting to be experimentally detected. / CNPq: 147716/2014.4

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

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.

Orientador: Marcelo Yamashita / Resumo: Nesta dissertação vamos estudar um problema de três corpos via aproximação de Born-Oppenheimer em duas dimensões para um sistema constituído de duas partículas pesadas e uma leve. Considerando uma interação de contato entre a partícula leve e as pesadas e desconsiderando a interação entre as pesadas, estudamos o efeito do momento angular e da diferença de massa entre as partículas. Notamos que diminuindo a diferença de massa entre as partículas encontramos um número menor de estados ligados. Conforme aumentamos o momento angular observamos um número menor de estados ligados, isto porque o momento angular soma ao sistema um potencial repulsivo, tornando o sistema mais fracamente ligado. Considerando um potencial gaussiano entre as partículas pesadas calculamos a energia de três corpos e o raio quadrático médio. Observamos que a introdução deste potencial torna possível o rompimento do sistema de três corpos e o fenômeno de tunelamento. Estudando o raio quadrático médio percebemos que a região de tunelamento o tamanho do sistema varia consideravelmente, tornando esta região interessante de ser detectada experimentalmente / Abstract: In this thesis we study mass-imbalanced three-body system in two dimensions using BornOppenheimer approximation. Considering the heavy-light particle system interacting through zero-range interaction and disregarding interaction between the heavy-heavy, we study effects the angular momentum and mass ratio difference. Decreasing the mass difference between the heavy and the light particles a smaller number of bound states is found. Increasing the angular momentum we add to the system a repulsive potential, making the system weakly bounded, in this case a small number of bound states are expected. Considering a gaussian potential between the heavy-heavy particles it is possible to unbounded the system and observe tunneling phenomena. The considerable change in the tunneling region for the mean square radii indicates an increase in the system size, making this region interesting to be experimentally detected. / Mestre

<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.