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Using a kinetic-energy-density functional with a modified ``first-gradient'' correction, Dirac exchange functional, and a parametrized Wigner-type local correlation functional, a simple quadratic equation is solved for the ground-state electronic densities and properties of atoms and ions, including alkaline-earth-metal singly charged negative ions. The results for various expectation values and the electrostatic potential compare quite favorably with near-Hartree-Fock and relativistic density-functional results, respectively.
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Deb et al. (1992) studied this question.
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