Relativistic Hartree-Fock-Roothaan theory for open-shell atoms

Kagawa, T.

doi:10.1103/physreva.12.2245

Cited by 136 publications

(23 citation statements)

References 35 publications

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“…The value of A can also used to find out a spurious solution. In our experience of the RHFR calculations for atomic systems [7], it occasionally happens that a deformed orbital for positive K symmetries is obtained. In this case, the total energy and the value of the virial theorem is not always bad.…”

Section: Resultsmentioning

confidence: 94%

“…Schwarz et al [5] have extensively studied on the problems of variational collapse and the basis set in stability of energies obtained by a relativistic calculation with the expansion method. In the relativistic Hartree-Fock-Roothaan (RHFR) calculations for atomic systems [6,7], the relativistic virial theorem has been used as a criterion in selecting a good basis set. However, the relativistic virial theorem is not a necessary and sufficient condition for an exact energy so that an energy obtained so as to satisfy the virial theorem is not guaranteed to be an exact one.…”

Section: Introductionmentioning

confidence: 99%

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General variation method for the relativistic calculations of atoms and molecules

Kagawa

1983

Int J of Quantum Chemistry

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Use of the general variation method of Weinstein and MacDonald for the relativistic calculation of atoms and molecules is proposed. It is shown from the numerical calculations for hydrogenlike atomic systems that this method is useful in judging an accuracy of energies and wave functions obtained with a relativistic Hamiltonian whose spectra are not bounded. It is also shown that this method can be used to find spurious solutions such as Ipllz or 2d3/2 appearing in atomic systems. Problems in extending the method to manyelectron atoms and molecules are discussed.

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Section: Resultsmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

General variation method for the relativistic calculations of atoms and molecules

Kagawa

1983

Int J of Quantum Chemistry

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“…Thus, the diagonalization can be performed on each V I independently. An explicit solution for the diagonalization in case of k = 2 is well known in terms of the Clebsch-Gordan coefficients, which can be iteratively extended to higher k. We obtain (12) such that for all ϕ ∈ V I,ℓ s m ℓ ms ,…”

Section: B Ls Diagonalizationmentioning

confidence: 99%

“…Our results, detailed in Section VII below, provide an ab initio explanation of the anomalous magnetic moment of Chromium (experimentally, the ground state has six instead of the expected four aligned spins) and the underlying anomaly in the filling order of 3d versus 4s orbitals in the semi-empirical orbital picture of transition metal atoms (Chromium, unlike its four predecessors Ca, Sc, Ti, V, possesses only one instead of two 4s electrons). It is well known [11][12][13][14] that singledeterminant Hartree-Fock, relativistic Hartree-Fock, and density functional theory calculations (even with the best exchange-correlation functionals such as B3LYP) render the correct filling orders and ground state symmetries only for some but not all transition metal elements (see Section VII).…”

Section: Introductionmentioning

confidence: 99%

Efficient algorithm for asymptotics-based configuration-interaction methods and electronic structure of transition metal atoms

Mendl

Friesecke

2010

The Journal of Chemical Physics

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Asymptotics-based configuration-interaction (CI) methods B. D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods for atoms which reproduce, at fixed finite subspace dimension, the exact Schrödinger eigenstates in the limit of fixed electron number and large nuclear charge. Here we develop, implement, and apply to 3d transition metal atoms an efficient and accurate algorithm for asymptotics-based CI.Efficiency gains come from exact (symbolic) decomposition of the CI space into irreducible symmetry subspaces at essentially linear computational cost in the number of radial subshells with fixed angular momentum, use of reduced density matrices in order to avoid having to store wavefunctions, and use of Slater-type orbitals (STO's). The required Coulomb integrals for STO's are evaluated in closed form, with the help of Hankel matrices, Fourier analysis, and residue calculus.Applications to 3d transition metal atoms are in good agreement with experimental data. In particular we reproduce the anomalous magnetic moment and orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.

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“…Kagawa (18) extended Kim's method to open-shell atoms and results were reported for a large number of transition elements (18) and Rn (19). In these studies, the same STF basis set was used for the large and small radial components, and often the problem of so-called variational failure was encountered.…”

Section: Gaussian Basis Set For Relativistic Calculationsmentioning

confidence: 99%

Universal Gaussian basis functions in relativistic quantum chemistry: atomic Dirac–Fock–Coulomb and Dirac–Fock–Breit calculations

Malli¹,

Silva²,

Ishikawa³

1992

Can. J. Chem.

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Matrix Dirac-Fock-Coulomb and Dirac-Fock-Breit self-consistent field calculations are performed for a number of neutral atoms, He (Z = 2) through Xe (Z = 54), using the universal Gaussian basis set ( l 8 s , 12p, 1 l d ) reported recently by Da Silva et al. The total Dirac-Fock-Coulomb, the Dirac-Fock-Breit, and the Breit interaction energies calculated with this universal Gaussian basis set are in good agreement with the corresponding values obtained by using an extensive well-tempered Gaussian basis set for the He through Ca (Z = 20) atoms. Although this universal Gaussian basis set is inadequate for the calculation of total Dirac-Fock-Coulomb and Dirac-Fock-Breit energies for the Kr, Sr, and Xe atoms, the Breit interaction energies calculated with this basis for these three atoms are in very good agreement with the corresponding Breit interaction energies obtained by using the extensive well-tempered Gaussian basis sets. Work is in progress to generate a more extensive and energetically better universal Gaussian basis set for He through Xe for its use in non-relativistic Hartree-Fock as well as Dirac-Fock self-consistent field calculations on polyatomics involving heavy atoms. [Traduit par la rCdaction]

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Relativistic Hartree-Fock-Roothaan theory for open-shell atoms

Cited by 136 publications

References 35 publications

General variation method for the relativistic calculations of atoms and molecules

General variation method for the relativistic calculations of atoms and molecules

Efficient algorithm for asymptotics-based configuration-interaction methods and electronic structure of transition metal atoms

Universal Gaussian basis functions in relativistic quantum chemistry: atomic Dirac–Fock–Coulomb and Dirac–Fock–Breit calculations

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