University, Diss., 2004--Würzburg.

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 research over-viewed in this dissertation concerns very accurate variational calculations of the molecular systems with more than two electrons under the assumption of the Born-Oppenheimer (BO) approximation. The centerpiece of this research is the use of explicitly correlated Gaussian (ECG) basis functions with floating centers to generate the potential energy curve (PEC) and potential energy surface (PES) of the considered molecular systems. One challenge of such calculations is the occurrence of the linear dependency between basis functions in the process of basis set optimization. The BO PECs generated with ECG basis sets were limited to two-electron molecular systems for a few decades prior to the implementation of the author's approaches to this issue. These approaches include methods for a partial remedy to linear dependence, better guessing of initial basis functions, permanently removing the restriction of memory usage in parallel computer systems, and efficiently paralleling the calculations. The approach effectively utilizing the super computer systems yields benefits not only to the ECG calculations but could also be useful in the fields that require the significant amount of the computational resources. These procedures were implemented in computer codes that were run quite extensively on several parallel computer systems during the period of the author's Ph.D study. The calculated adiabatic PECs and the rovibrational energy levels are proven to be the most accurate ones to date. The dissertation is primarily based on the content of the papers that were published in co-authorship with my scientific advisor and other collaborators in several scientific journals. It also includes some details that were not considered in the publications but are essential for the completeness and good understanding of the presented work. In order to provide readers an insight into the development of the ECG based BO molecular calculation, the published results of many calculations are classified and presented in a comprehensive way.

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

No description available.

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

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