Effect of removing the no-virtual pair approximation on the correlation energy of the He isoelectronic sequence. II. Point nuclear charge model

2010 ◽  
Vol 132 (12) ◽  
pp. 124105 ◽  
Author(s):  
Yoshihiro Watanabe ◽  
Haruyuki Nakano ◽  
Hiroshi Tatewaki
Keyword(s):  
Correlation Energy ◽  
Nuclear Charge ◽  
Pair Approximation ◽  
Isoelectronic Sequence ◽  
Charge Model

An expansion method for calculating atomic properties. IX. The dipole polarizabilities of the lithium sequence*

1966 ◽  
Vol 293 (1434) ◽  
pp. 365-377 ◽  
Keyword(s):  
Nuclear Charge ◽  
Expansion Method ◽  
Zero Order ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
Atomic Properties ◽  
Dipole Polarizabilities

A theory is developed for expanding the dipole polarizabilities and shielding factors of an atom or ion in inverse powers of the nuclear charge Z in cases where the field links degenerate zero order configurations. Results for all members of the lithium isoelectronic sequence are presented both within the Hartree-Fock approximation and in a more accurate formulation, and are found to be in agreement with earlier work.

An expansion method for calculating atomic properties VII. The correlation energies of the lithium sequence

1966 ◽  
Vol 292 (1429) ◽  
pp. 264-271 ◽  
Keyword(s):  
Electron Pair ◽  
Correlation Energy ◽  
Atomic System ◽  
Nuclear Charge ◽  
Expansion Method ◽  
Weighted Sum ◽  
Atomic Properties ◽  
Variational Calculations ◽  
Leading Term

If the energy of an atomic system is expanded in inverse powers of the nuclear charge Z, the leading term of the correlation energy after degeneracies have been removed is a constant which can be expressed as a weighted sum of electron pair energies and certain non-additive terms. The pair energies may be obtained from direct two-electron variational calculations and the non-additive terms may be evaluated exactly. Calculations are carried out for the lithium 2 S sequence with the result that the non-relativistic eigenvalues are given by E(Z) = − 1.125Z 2 + 1.02280521Z−0.40814899 + O (Z -1 ).

A relationship between correlation energies and sizes: the series of beryllium- and neon-like ions

1977 ◽  
Vol 55 (12) ◽  
pp. 2417-2419 ◽  
Author(s):  
Fernando Bernardi ◽  
Paul G. Mezey ◽  
Imre G. Csizmadia
Keyword(s):  
Good Accuracy ◽  
Correlation Energy ◽  
Nuclear Charge ◽  
Pair Correlation ◽  
Empirical Relation ◽  
Effective Nuclear Charge ◽  
Isoelectronic Series

A simple empirical relation for the estimation of the correlation energy (Ecorr) is found to be valid for the isoelectronic series of Be- and Ne-like ions to a very good accuracy. Although originally such a relation was proposed for the He-like ions, the present results indicate that it is applicable for layer systems as well. Thus the interelectron pair correlation in systems such as Be or Ne does not affect adversely the accuracy of the relation:[Formula: see text]where the denominator is the size [Formula: see text] weighted by the square of the effective nuclear charge Zeff.

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