The ground state of atomic two‐electron systems in the independent particle model

Scaled variational functions of the form \documentclass{article}\pagestyle{empty}$ \phi _{\alpha k} = e^{ - (Z - 1 + e^{ - \alpha kr})kr} $ , where Z is the nuclear charge and α is a parameter, and \documentclass{article}\pagestyle{empty}$ \phi _{\beta \alpha k} = e^{ - (\beta + e^{ - \alpha kr})kr} $ , 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_αk yields already a good approximation to the Hartree–Fock solution whereas with the function ϕ_βαk the Hartree–Fock results are practically reproduced.