Relativistic virial theorem for atoms

Matsuoka, Osamu; Koga, Toshikatsu

doi:10.1007/s002140000257

Cited by 4 publications

(2 citation statements)

References 4 publications

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“…In the case of a finite nucleus, Matsuoka and Koga [21] took a slightly different point of view. Their interest was primarily in the effect of a finite nucleus on the virial theorem for the total energy of many-electron systems as a correction to energy.…”

Section: Finite Volume Nucleusmentioning

confidence: 99%

Variational Methods for Atoms and the Virial Theorem

Fischer

Godefroid

2022

Atoms

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In the case of the one-electron Dirac equation with a point nucleus, the virial theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly −1, a ratio that can be an independent test of the accuracy of a computed solution. This paper studies the virial theorem for subshells of equivalent electrons and their interactions in many-electron atoms. This shows that the linear scaling of the dilation is achieved through the balancing of the contributions to the potential of an electron from inner and outer regions that some Slater integrals impose conditions on a single subshell, but others impose conditions between subshells. The latter slows the rate of convergence of the self-consistent field process in which radial functions are updated one at a time. Several cases are considered. Results are also extended to the nonrelativistic case.

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Section: Finite Volume Nucleusmentioning

confidence: 99%

Variational Methods for Atoms and the Virial Theorem

Fischer

Godefroid

2022

Atoms

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show abstract

“…In the case of a finite nucleus, Matsuoka and Koga [13] took a slightly different point of view. Their interest was primarily in the effect of a finite nucleus on the virial theorem for the total energy of many-electron systems.…”

Section: Finite Volume Nucleusmentioning

confidence: 99%

Relativistic variational methods and the Virial Theorem

Fischer¹,

Godefroid²

2021

Preprint

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In the case of the one-electron Dirac equation with a point nucleus the Virial Theorem (VT) states that the ratio of the kinetic energy to potential energy is exactly −1, a ratio that can be an independent test of the accuracy of a computed solution. This paper studies the virial theorem for subshells of equivalent electrons and their interactions in many-electron atoms. It shows that some Slater integrals impose conditions on a single subshell but others impose conditions between subshells. The latter slow the rate of convergence of the self-consistent field process in which radial functions are updated one at a time. Several cases are considered.

show abstract