Use of Rescaled Eigenfunctions as Variational Wavefunctions in Calculations on Atoms and Ions

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Abstract
Electron—electron repulsion energies C̄ and electron—nuclear attraction energies L̄ are computed from the nonrelativistic total energies E for isoelectronic series of two‐, three‐, and four‐electron atoms in their lower electronic states. A limited variational approach to atomic structure is then described which uses in effect rescaled eigenfunctions (for two or more electron systems) as a basis; the ``empirical'' C̄ and L̄ obtained in the first part are employed in these calculations. Use of the eigenfunction for an atom with nucleus of charge Z+1 to predict the energy of an isoelectronic system with nucleus of charge Z yields results which are in error by about 0.3 to 0.7 eV for two‐ to four‐electron atoms, respectively. A semiempirical correction scheme of this approach gives results which are in error by 0.01 to 0.1 eV, respectively. Energies for some states of H, He, and Li negative ions are predicted.