New quadratic nondifferential Thomas-Fermi-Dirac-type equation for atoms

This paper reports the first quadratic, nondifferential, and self-consistent solution to a Thomas-Fermi-Dirac(TFD)-type equation for many-electron atoms. The essential feature in the Euler-Lagrange equation is the inclusion of a ``first-gradient'' correction to the TF kinetic energy, which leads to chemical binding in molecules and solids. The calculations are easier to perform than other TFD-type calculations, while the radial density and energy obtained compare very well with similar calculations.