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The ground state of atomic two‐electron systems in the independent particle model
Author(s) -
Hoor Marten J. Ten
Publication year - 1968
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560020112
Subject(s) - virial theorem , ground state , electron , physics , effective nuclear charge , atomic physics , function (biology) , charge (physics) , hartree–fock method , variational method , quantum mechanics , mathematical physics , chemistry , evolutionary biology , galaxy , biology
Abstract Scaled variational functions of the form \documentclass{article}\pagestyle{empty}\begin{document}$ \phi _{\alpha k} = e^{ - (Z - 1 + e^{ - \alpha kr})kr} $\end{document} , where Z is the nuclear charge and α is a parameter, and \documentclass{article}\pagestyle{empty}\begin{document}$ \phi _{\beta \alpha k} = e^{ - (\beta + e^{ - \alpha kr})kr} $\end{document} , where both α and β are parameters, are used for the description of the ground state of atomic two‐electron systems in the independent particle model. The scale factor k has been introduced in order to satisfy the virial theorem. Apart from the energy, a number of one‐electron expectation values have been calculated and the results are compared with those obtained from other variational functions. The function ϕ α k yields already a good approximation to the Hartree–Fock solution whereas with the function ϕ βα k the Hartree–Fock results are practically reproduced.