Statistical atomic models with piecewise exponentially decaying electron densities

If it is assumed that the electron density of an atom in its ground state is piecewise exponentially decreasing as a function of the distance from the nucleus, then it is shown that much improved values for the energy, and electron densities exhibiting shell structure, are obtained from optimization of the density functionals of Thomas-Fermi, Thomas-Fermi-Dirac, and Thomas-Fermi-Dirac with inhomogeneity correction. An inhomogeneity correction which is one-ninth of the original Weizsacker correction is favored. Numerical results are presented for all first-row atoms and selected second-row atoms, and comparisons are made with results of other methods.