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 X. 1 s 2 1 S -1 snp 1 P transitions of the helium sequence

1967 ◽  
Vol 301 (1466) ◽  
pp. 253-260 ◽  
Keyword(s):  
Cross Sections ◽  
Nuclear Charge ◽  
Expansion Method ◽  
Probable Error ◽  
Oscillator Strengths ◽  
Matrix Elements ◽  
Isoelectronic Sequence ◽  
First Order ◽  
Hartree Fock ◽  
Atomic Properties

The electric dipole matrix elements connecting the 1 s 2 1 S and 1 snp 1 P states of the helium isoelectronic sequence are calculated exactly to first order in inverse powers of the nuclear charge Z and the differences from the Hartree-Fock approximation are shown to correspond to virtual transitions of the 1 s electrons. Comparison of the oscillator strengths predicted by a screening approximation with more accurate values reveals a regular variation in the error contained in the screening approximation, the correction of which allows the prediction of oscillator strengths and probabilities of 1 s 2 1 S – 1 snp 1 P transitions for all values of n and all values of Z within a probable error of 2% (table 5). Values of the photoionization cross-sections at the spectral heads are also presented.

An expansion method for calculating atomic properties

1961 ◽  
Vol 261 (1307) ◽  
pp. 565-576 ◽  
Keyword(s):  
Nuclear Charge ◽  
Quantitative Description ◽  
Exchange Interactions ◽  
Expansion Method ◽  
Expectation Values ◽  
Hartree Fock ◽  
Atomic Properties ◽  
Electron Shells

An expansion method is described which provides a simple and rapid means of calculating for any atom the expectation values of sums of one-electron operators. All the equations which arise can be solved analytically and the results are obtained as functions of the nuclear charge. For inner shells the accuracy is comparable with that of the Hartree—Fock approxi­mation. The method gives a quantitative description of the effects of direct and exchange interactions between electron shells. Results are given for all members of the helium and beryllium iso-electronic sequences.

An expansion method for calculating atomic properties IV. Transition probabilities

1964 ◽  
Vol 280 (1381) ◽  
pp. 258-270 ◽  
Keyword(s):  
Wave Function ◽  
Matrix Element ◽  
Transition Probabilities ◽  
Expansion Method ◽  
The State ◽  
Diagonal Matrix Element ◽  
Expectation Value ◽  
First Order ◽  
Hartree Fock ◽  
Atomic Properties

An earlier expression for the expectation value of a single-electron operator which isstationary with respect to first-order variations of the state wave function has been generalized to the case of an off-diagonal matrix element connecting two different states. Explicit calculations are carried out of the probabilities of dipole transitions between configurations 1 s a 2 s b 2 p c and 1 s a 2 s b–1 2 p c+1 for all members of the isoelectronic sequences from helium to neon and the importance of taking into account the mixing of degenerate configurations is demonstrated. The accuracy is at least comparable to that of the Hartree-Fock approximation and in cases where degeneracy is important it is much superior.

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 ).

An expansion method for calculating atomic properties. VI. The extended Hartree-Fock approximation

1966 ◽  
Vol 292 (1429) ◽  
pp. 193-202 ◽  
Keyword(s):  
Expansion Method ◽  
Expectation Values ◽  
Hartree Fock ◽  
Atomic Properties

An expansion method is used to calculate the expectation values of various operators for all states 1s 2 2s a 2p b SL of all members of the isoelectronic sequences from beryllium to neon. Explicit account is taken of the interaction between the configuration 1s 2 2s 2 2p b SL and 1s 2 2p b +2 SL and is found to be entirely negligible for these systems.

scholarly journals Hartree–Fock implementation using a Laguerre-based wave function for the ground state and correlation energies of two-electron atoms

2018 ◽  
Vol 376 (2115) ◽  
pp. 20170153 ◽  
Author(s):  
Andrew W. King ◽  
Adam L. Baskerville ◽  
Hazel Cox
Keyword(s):  
Wave Function ◽  
Ground State ◽  
Nuclear Charge ◽  
Analytical Form ◽  
Theoretical Chemistry ◽  
Variational Parameter ◽  
Isoelectronic Sequence ◽  
Hartree Fock ◽  
The One ◽  
Accurate Wave

An implementation of the Hartree–Fock (HF) method using a Laguerre-based wave function is described and used to accurately study the ground state of two-electron atoms in the fixed nucleus approximation, and by comparison with fully correlated (FC) energies, used to determine accurate electron correlation energies. A variational parameter A is included in the wave function and is shown to rapidly increase the convergence of the energy. The one-electron integrals are solved by series solution and an analytical form is found for the two-electron integrals. This methodology is used to produce accurate wave functions, energies and expectation values for the helium isoelectronic sequence, including at low nuclear charge just prior to electron detachment. Additionally, the critical nuclear charge for binding two electrons within the HF approach is calculated and determined to be Z HF C =1.031 177 528. This article is part of the theme issue ‘Modern theoretical chemistry’.

An expansion method for calculating atomic properties. II

1962 ◽  
Vol 269 (1339) ◽  
pp. 550-559 ◽  
Keyword(s):  
Configuration Interaction ◽  
Nuclear Charge ◽  
Expansion Method ◽  
Expectation Values ◽  
Atomic Systems ◽  
Atomic Properties ◽  
Self Consistent ◽  
Nuclear Shielding ◽  
Consistent Method

The accuracy of the methods of calculating the expectation values of perturbed atomic systems is analyzed by means of an expansion in inverse powers of the nuclear charge. Results are presented for the quadrupole polarizabilities and nuclear-shielding factors of all members of the helium and beryllium isoelectronic sequences and it is shown that the loss of accuracy entailed in replacing the full self-consistent method by a simpler one is small. Anestim ate is made of the importance of configuration interaction between the (1s 2 2s 2 ) 1 S and (1s 2 2p 2 ) 1 S states of the beryllium sequence.

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