A new proposal for the discretization of the Griffin—Wheeler—Hartree—Fock equations

Barbosa, R. C.; Silva, A. B. F. Da

doi:10.1080/0026897021000044007

Cited by 19 publications

(25 citation statements)

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“…However, the p-GCDF method does not use equally spaced discretization points and the ID is implemented through a relabeling of the generator coordinate space with the use of a polynomial expansion for each atomic orbital symmetry (w ϭ s, p, d, f, etc.) [6],…”

Section: P-gcdf Methodsmentioning

confidence: 97%

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Relativistic Gaussian basis sets obtained with a polynomial version of the generator coordinate Dirac–Fock method: Ionization energies of some closed‐shell atomic systems

Haiduke

Macedo

Barbosa

et al. 2005

Int J of Quantum Chemistry

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ABSTRACT:The purpose of this work is to analyze the relativistic Gaussian basis sets obtained with a recently developed polynomial version of the generator coordinate Dirac-Fock method. The atomic systems chosen to evaluate the basis sets are some alkaline earth and noble gas atoms: He, Be, Ne, Mg, Ar, and Ca. Hartree-Fock, relativistic, and electronic correlation contributions to the atomic total energy of the neutral and ionized atomic species were estimated using these relativistic Gaussian basis sets. The basis sets developed were able to attain energies that deviate at most by 0.47 and 0.65 mHartree, respectively, from numerical Hartree-Fock and Dirac-FockCoulomb results and are also competitive with fully optimized relativistic Gaussian basis sets of similar sizes. The electronic correlation energy contributions were obtained after two nonrelativistic calculations: a Hartree-Fock and a full quadratic configuration interaction, including single and double substitutions. The uncontracted basis sets obtained here along with polarization functions chosen to have equal exponents to selected functions already present in the original set were adequate in describing not only the neutral but also the highly ionized atomic species. The comparison of some calculated shell ionization energies with experimental results presented a maximum deviation of 3% (for a total of 15 ionization values ranging from 18 to 10,599 eV), reinforcing the quality of the basis sets developed in this work.

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Section: P-gcdf Methodsmentioning

confidence: 97%

“…The total wave function is an antisymmetrized combination of one-electron orbitals defined as (6) where P n (r) and Q n (r) are, respectively, the radial large and small components.…”

Section: P-gcdf Methodsmentioning

confidence: 99%

Relativistic Gaussian basis sets obtained with a polynomial version of the generator coordinate Dirac–Fock method: Ionization energies of some closed‐shell atomic systems

Haiduke

Macedo

Barbosa

et al. 2005

Int J of Quantum Chemistry

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“…Moreover, energy values from universal sets deteriorate rapidly as small numbers of primitive functions are chosen. Hence, as an alternative to overcome these restrictions presented by universal basis sets, Barbosa and da Silva [16] introduced in 2003 a new proposal to design adapted basis sets of GTFs through a polynomial discretization of the GWHF equations. As a preliminary study, they applied this new technique to a very few atoms of the first, second, and third row of the periodic table.…”

Section: Introductionmentioning

confidence: 99%

Accurate Gaussian basis sets for atomic and molecular calculations obtained from the generator coordinate method with polynomial discretization

et al. 2015

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Accurate Gaussian basis sets for atoms from H to Ba were obtained by means of the generator coordinate Hartree-Fock (GCHF) method based on a polynomial expansion to discretize the Griffin-Wheeler-Hartree-Fock equations (GWHF). The discretization of the GWHF equations in this procedure is based on a mesh of points not equally distributed in contrast with the original GCHF method. The results of atomic Hartree-Fock energies demonstrate the capability of these polynomial expansions in designing compact and accurate basis sets to be used in molecular calculations and the maximum error found when compared to numerical values is only 0.788 mHartree for indium. Some test calculations with the B3LYP exchange-correlation functional for N2, F2, CO, NO, HF, and HCN show that total energies within 1.0 to 2.4 mHartree compared to the cc-pV5Z basis sets are attained with our contracted bases with a much smaller number of polarization functions (2p1d and 2d1f for hydrogen and heavier atoms, respectively). Other molecular calculations performed here are also in very good accordance with experimental and cc-pV5Z results. The most important point to be mentioned here is that our generator coordinate basis sets required only a tiny fraction of the computational time when compared to B3LYP/cc-pV5Z calculations.

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“…Recentemente, Barbosa e da Silva [12] propuseram uma modificação na metodologia da discretização com o intuito de melhorar a obtenção de conjuntos de funções Gaussianas (GTF) por meio do MCG-HF, tornando possível a geração de GTF tão boas ou melhores quanto as até agora obtidas na literatura, porém mais compactas e precisas (acuradas). …”

Section: Os Resultados De Bohr Concordam Muito Bem Com a Expressão Emunclassified

“…O operador energia cinética dos núcleos não atua sobre a função de onda eletrônica, assim a energia cinética nuclear e desprezada no calculo eletrônico, o mesmo acontece com o operador energia cinética dos elétrons que não atua sobre a função de onda dos núcleos, assim reorganizando os termos de (12) temos…”

Section: Postulados Básicos Do Método Hartree-fockunclassified

Aplicação de uma nova proposta de discretização das equações Griffin-Wheeler-Hartree-Fock na geração de bases Gaussianas para cálculos de átomos e moléculas

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AgradecimentosAo Prof. Dr. Albérico Borges da Silva pela orientação segura, respeito e condições dignas de trabalho.A minha Falecida esposa Karina Nascimento que sempre foi minha companheira e esteve ao meu lado nos momentos mais importantes de minha vida.Ao Prof. Dr. Roberto Haiduke pela co-orientação, paciência, prestividade e respeito.Aos técnicos do centro de informática, pelo auxílio com a rede da USP. As secretárias Silvia e Andréia, pelo respeito, paciência, dedicação e por acompanhar a prova de ingresso ao mestrado e a prova de proficiência.À funcionária responsável pela limpeza dos laboratórios. À Wilneide, pela ajuda com os artigos na biblioteca.À todos aqueles que me fizeram ir para frente apesar de toda a tempestade que se abateu no meu caminho.À USP e ao IQSC, representadas respectivamente pelo seu reitor Prof. Dr. e pelo seu diretor pelas condições dignas de trabalho.

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A new proposal for the discretization of the Griffin—Wheeler—Hartree—Fock equations

Cited by 19 publications

References 19 publications

Relativistic Gaussian basis sets obtained with a polynomial version of the generator coordinate Dirac–Fock method: Ionization energies of some closed‐shell atomic systems

Relativistic Gaussian basis sets obtained with a polynomial version of the generator coordinate Dirac–Fock method: Ionization energies of some closed‐shell atomic systems

Accurate Gaussian basis sets for atomic and molecular calculations obtained from the generator coordinate method with polynomial discretization

Aplicação de uma nova proposta de discretização das equações Griffin-Wheeler-Hartree-Fock na geração de bases Gaussianas para cálculos de átomos e moléculas

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