Numerical investigation of a lower bound to the Thomas—Fermi kinetic energy and the validity of the Lieb conjecture for H⁻, He, Li⁺, B3⁺, O6⁺, Ne⁸⁺, and Mg¹²⁺

The purpose of the present work was twofold: First, a lower bound of Gálvez and Dehesa to the Thomas-Fermi kinetic energy was investigated for the two-electron systems H⁻, He, Li⁺, B³⁺, O⁶⁺, Ne⁸⁺, and Mg¹²⁺. Second, a conjecture of Lieb, relating the kinetic energy to the Thomas-Fermi kinetic energy, was examined. For both investigations, the analytical approximations of Benesch to the radial electron densities of the two-electron systems were used. These approximations are based on the explicitly correlated (Hylleraas-type) 20 variational parameter wave functions of Hart and Herzberg. © 1996 John Wiley & Sons, Inc.