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Doctoral Thesis
DOI
https://doi.org/10.11606/T.54.1987.tde-07042015-150251
Document
Author
Full name
Jose Rachid Mohallem
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 1987
Supervisor
Committee
Alves, José Luiz Aarestrup
Canuto, Sylvio R a
Costa, Rogerio Cantarino Trajano da
Piza, Antonio Fernando Ribeiro de Toledo
Trsic, Milan
Title in Portuguese
Solução por discretização integral de equações de Griffin-Hill-Wheeler monoeletrônicas
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Propõe-se e discute-se em detalhes a técnica de discretização integral para o Método da Coordenada Geradora, através de argumentação formal e exemplos práticos. Nos exemplos, esta técnica é aplicada aos problemas modelo do Oscilador Harmônico e átomo de Hidrogênio usando como funções geradoras respectivamente Gaussianas transladadas e orbitais Gaussianos. Usa-se o último caso para fornecer um exemplo de integração analítica da equação de Griffin-Hill-Wheeler, discutir a qualidade da função de onda gerada e também os efeitos de uma perturbação. Na seqüência desenvolve-se um método para sistemas multi-eletrônicos com base no modelo de partículas independentes: o método Griffin-Hill-Wheeler-Hartree-Fock. As equações mono-eletrônicas de autovalores são deduzidas e resolvidas por discretização integral para os átomos de Hélio e Berílio. Com esses fundamentos, constrói-se uma rotina para átomos maiores, a qual permite a obtenção de uma base universal de Gaussianas para os átomos da primeira fila da tabela periódica
Title in English
Not available
Keywords in English
Not available
Abstract in English
On the basis of formal argumentation and practical examples, the integral discretization technique for the Generator Coordinate Method is proposed and discussed in detail. In the examples this technique is applied to the model problems of the Harmonic Oscillator and the Hydrogen atom using translated Gaussians and Gaussian orbitals as generator functions, respectively. The last case is used to provide an example of analytical integration of the Griffin-Hill-Wheeler equation, to discuss the quality of the generated wave function and also the effects of a perturbation. Pursuing further, a method for multi-electronic systems based on the independent particle model is developed: the Griffin-Hill-Wheeler-Hartree-Fock method. The mono-electronic eigenvalue equations are derived and solved by integral discretization for the Helium and Berilium atoms. Based on these foundations, a routine for larger atoms is built, allowing the obtention of a universal Gaussian basis set for the first row atoms of the periodic table
 
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Publishing Date
2015-04-08
 
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