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The Hellmann pseudopotential method is used to calculate the energies of the ground states of the atoms Mg, Ca, Sr, Ba, Ra, Zn, Cd, and Hg. Two different types of wavefunctions were employed for the valence electrons: wavefunctions of Hylleraas type explicitly containing r12, and a superposition of the configurations (1s)2 1S and (2p)2 1S. The agreement between the calculated and empirical energies is very good. The results are better with the superposition of configurations than with the wavefunction containing r12.
Szász et al. (1965) studied this question.