�ber den Grundterm der Zweielektronenprobleme von H?, He, Li+, Be++ usw.

Hylleraas, Egil A.

doi:10.1007/bf01397032

Cited by 807 publications

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“…78 In order to make contact with physical reality, all orbitalconfiguration-based wavefunctions and/or energies must be extrapolated to the "complete basis set ͑CBS͒ limit." [79][80][81][82][83][84][85][86][87][88] Hylleraas 89 was the first to show that this problem can be greatly alleviated by the explicit inclusion of the interelectronic distance in the wavefunctions for He and H 2 . More recently, a number of authors have succeeded in adapting this approach to the general case of many-electron systems, [90][91][92][93][94][95][96][97] notwithstanding nontrivial algorithmic complexities.…”

Section: Introductionmentioning

confidence: 99%

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

Bytautas

Nagata

Gordon

et al. 2007

The Journal of Chemical Physics

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The recently introduced method of correlationenergy extrapolation by intrinsic scaling (CEEIS) is used to calculate the nonrelativistic electron correlations in the valence shell of the F2 molecule at 13 internuclear distances along the ground state potential energy curve from 1.14Åto8Å, the equilibrium distance being 1.412Å. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlationenergies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail. The recently introduced method of correlation energy extrapolation by intrinsic scaling ͑CEEIS͒ is used to calculate the nonrelativistic electron correlations in the valence shell of the F 2 molecule at 13 internuclear distances along the ground state potential energy curve from 1.14 Å to 8 Å, the equilibrium distance being 1.412 Å. Using Dunning's correlation-consistent double-, triple-, and quadruple-zeta basis sets, the full configuration interaction energies are determined, with an accuracy of about 0.3 mhartree, by successively generating up to octuple excitations with respect to multiconfigurational reference functions that strongly change along the reaction path. The energies of the reference functions and those of the correlation energies with respect to these reference functions are then extrapolated to their complete basis set limits. The applicability of the CEEIS method to strongly multiconfigurational reference functions is documented in detail.

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Section: Introductionmentioning

confidence: 99%

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

Bytautas

Nagata

Gordon

et al. 2007

The Journal of Chemical Physics

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“…For improving the solutions, one can use more accurate wave functions that include electron correlation by means of Hylleraas correlated wave function (Hy) and configuration interaction (CI) approaches. [1][2][3][4][5][6] We notice that the CI expansions converge much more slowly than Hy-method expansions. The Hy method first developed by James and Collidge 7 has been used for determination of the ground state energy of H2 molecule 8,9 and is still valid for two-and threeelectron atomic and molecular systems (see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 88%

Evaluation of Multicenter Multielectron Integrals Using One-range Addition Theorems in Terms of STOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials with Integer and Noninteger Indices

Guseinov¹

2009

Bulletin of the Korean Chemical Society

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Using one-range addition theorems for Slater type orbitals (STOs) and Coulomb-Yukawa like correlated interaction potentials (CIPs) introduced by the author, the series expansion formulae are derived for the multicenter multielectron integrals. The expansion coefficients occurring in these relations are presented through the overlap integrals of two STOs. The convergence of series expansion relations is tested by calculating concrete cases. The accuracy of the results is quite high for quantum number, screening constants and location of orbitals. The final results are especially useful in the calculation of multielectron properties for atoms and molecules when Hartree-Fock-Roothaan (HFR) and explicitly correlated methods are employed.

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“…Para se estabelecer os elementos de matriz do hamiltoniano na base desenvolve-se a expressão, ∫ f i Ĥf j dv + ∫ f j Ĥf i dv. Ao se usar a condição de contorno da função de onda juntamente com a propriedade hermitiana do operador, retira-se 13 (3) Para uso posterior, define-se (4) (5) (6) observando que os elementos de matriz da energia cinética são dados por M ij , da energia potencial por -L ij , enquanto os elementos de matriz da integral de superposição equivalem a N ij . Os elementos de matriz do hamiltoniano total serão, por conseguinte, equivalentes a H ij = M ij -L ij .…”

Section: Coordenadas De Hylleraas E Elementos De Matrizunclassified

“…Egil A. Hylleraas publicou, entre 1928 e 1930, uma serie de três artigos [1][2][3] em que trata da mecânica quântica de átomos de dois elé-trons. Resultados extremamente precisos, com um desenvolvimento relativamente simples, podem ser obtidos por essa abordagem.…”

Section: Introductionunclassified

The Hylleraas Method for Two Electrons Atoms

Carvalho¹,

Braga²

2017

Quim. Nova

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THE HYLLERAAS METHOD FOR TWO ELECTRONS ATOMS. The quantum mechanics of two electrons atoms, as suggested by E. A. Hylleraas in the period between [1928][1929][1930], is discussed in the present work. Hylleraas introduced explicit correlations in the wavefunction by treating the coordinates between the electrons as an independent variable of the problem, an approach that gives very precise energy values. Solution of the problem is given for one, two, three and six basis functions, as in the original work. The solution is also carried out with 140 basis functions, showing that the energy for two electron atoms can be calculated with seven significant figures. Numerical methods presented here are accessible to undergraduated level students.Keywords: Hylleraas method; two-electrons atom; electronic correlation. INTRODUÇÃOEgil A. Hylleraas publicou, entre 1928 e 1930, uma serie de três artigos 1-3 em que trata da mecânica quântica de átomos de dois elé-trons. Resultados extremamente precisos, com um desenvolvimento relativamente simples, podem ser obtidos por essa abordagem. A correlação entre os elétrons é introduzida de forma explícita na função de onda, considerando não somente as coordenadas elétron-núcleo, mas também a coordenada relativa entre os elétrons. Ao escalonar a função de onda, Hylleraas simplifica consideravelmente o cálculo variacional, pois o parâmetro variacional aparece na forma quadrática e linear, ao contrario da forma exponencial. A versão em inglês do trabalho de E.A. Hylleraas pode ser encontrada nas referências. 4,5 A história da mecânica quântica de átomos de dois elétrons é contada pelo próprio Hylleraas no excelente artigo autobiográfico, Reminiscences form the Early Quantum Mechanics of Two-Electron Atoms.6 O cálculo da energia de átomos de dois elétrons foi um teste crucial para dar credibilidade à mecânica quântica, pois resultados corretos já haviam sido obtidos para o átomo de hidrogênio por E. Schrödinger no seu trabalho original da mecânica ondulatória 7,8 e por W. Pauli usando a mecânica matricial.9,10 Era natural que se perguntasse como seriam os resultados para átomos de dois elétrons e essa era a pergunta que E.A. Hylleraas tentava responder.O presente texto é baseado nos trabalhos originais de Hylleraas, com a intenção de tornar esses trabalhos mais acessíveis para estudantes de graduação. Após uma introdução teórica do hamiltoniano nas coordenadas de Hylleraas, o cálculo da energia do átomo de hélio é realizado com uma, duas, três e seis funções de base, como tratado originalmente. O cálculo das integrais nessas coordenadas é feito, com exemplos em uma dimensão, para ilustrar integrais mais elaboradas, resumidas nas equações de Chandrasekhar-Herzberg. 11As energias calculadas serão comparadas com os resultados estabelecidos em 1966 por Frankowski e Pekeris 12 que obteve o resultado, E = -2,903724377 au, com todos algarismos significativos.Para efeito de comparação com o trabalho original, toma-se a energia de referência em E = -2,9037 au, pois os cálculos em 1929 foram feitos...

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�ber den Grundterm der Zweielektronenprobleme von H?, He, Li+, Be++ usw.

Cited by 807 publications

References 0 publications

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

Accurate ab initio potential energy curve of F2. I. Nonrelativistic full valence configuration interaction energies using the correlation energy extrapolation by intrinsic scaling method

Evaluation of Multicenter Multielectron Integrals Using One-range Addition Theorems in Terms of STOs for STOs and Coulomb-Yukawa Like Correlated Interaction Potentials with Integer and Noninteger Indices

The Hylleraas Method for Two Electrons Atoms

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