The Calculation of Atomic Structure

Hartree, D. R.; Blatt, F. J.

doi:10.1119/1.1996102

Cited by 94 publications

(81 citation statements)

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“…In [3,9] convergence difficulties are demonstrated for elementary two-dimensional models; in [24,25], a stability condition of the Roothaan algorithm in the neighbourhood of a minimum of the Hartree-Fock energy is given for the so-called closed-shell systems. More sophisticated SCF algorithms for solving the Hartree-Fock equations have also been proposed to improve the convergence using various techniques like for instance relaxation (or damping [6,26]) or level-shifting [21]. Relaxation cures some convergence problems but many other remain.…”

Section: Introductionmentioning

confidence: 99%

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On the convergence of SCF algorithms for the Hartree-Fock equations

Cancès¹,

Bris²

2000

ESAIM: M2AN

119

139

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Abstract. The present work is a mathematical analysis of two algorithms, namely the Roothaan and the level-shifting algorithms, commonly used in practice to solve the Hartree-Fock equations. The level-shifting algorithm is proved to be well-posed and to converge provided the shift parameter is large enough. On the contrary, cases when the Roothaan algorithm is not well defined or fails in converging are exhibited. These mathematical results are confronted to numerical experiments performed by chemists.Mathematics Subject Classification.

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Section: Introductionmentioning

confidence: 99%

“…The solution to the Hartree-Fock problem can be obtained either by directly minimizing the Hartree-Fock energy functional [5,8,14,23] or by solving the associated Euler-Lagrange equations, the so-called Hartree-Fock equations [6,17,20,21]. In any case, an iterative procedure has to be resorted to.…”

Section: Introductionmentioning

confidence: 99%

On the convergence of SCF algorithms for the Hartree-Fock equations

Cancès¹,

Bris²

2000

ESAIM: M2AN

119

139

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“…However, the existing A values (Wiese et al 1966(Wiese et al , 1969Lide 1994), for number of emitters, are given with high uncertainties. These values are calculated on the basis of the Coulomb approximation (Allen 1973) or by using the Self-Consistent Field (SCF) method (Hartree 1956). In the case of ionized emitters (doubly or triply ionized argon, as example) the expected uncertainties are 50% or larger (Wiese et al 1969).…”

Section: Introductionmentioning

confidence: 99%

Transition probabilities of several transitions in the Ar III and Ar IV spectra

Djeniže

Bukvić

2001

A&A

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Abstract. Using the relative line intensity ratios method between transitions that belong to the same multiplet in the Ar III (4s − 4p, 4s − 4p and 4p − 4d transitions) and Ar IV (4s − 4p and 4s − 4p transitions) spectra, some of the existing transition probability values (A) have been controlled. On the basis of the confirmed A values in Ar III (328.585 nm, 330.188 nm, 331.125 nm, 333.613 nm and 334.472 nm) and in Ar IV (280.944 nm and 278.896 nm) spectra two A values in Ar III and seven A values in Ar IV spectra have been determined, for the first time, relatively to the confirmed A values. Beside, some of the existing theoretical A data have been corrected, according to our experimentally observed relative line intensity ratio values. Measurements have been performed by using the linear low pressure pulsed arc, as an optically thin plasma source, operated in argon-helium mixture.

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“…Within the singleactive electron approximation, the TDSE (in atomic units, a.u.) is i @ @t c ðr; tÞ ¼ À 1 2 r 2 þ VðrÞ þ H I ðtÞ c ðr; tÞ; (1) where VðrÞ is a model potential [21] that reproduces the He ionization potential to an accuracy of 10 À3 . We solve Eq.…”

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confidence: 99%