LOWER BOUNDS TO DENSITY-DEPENDENT QUANTITIES OF ATOMS IN TERMS OF LOGARITHMIC EXPECTATION VALUES

Bounds to different quantities of atomic systems, related in a direct way to the single-particle electron density of the system (such as the kinetic energy, T, the exchange energy in the Dirac-Slater form, E(ex ), the average radial density, [rho], and the electron density at the nucleus, rho(0)), are given in terms of two radial expectation values of the form [r(beta)] and [r(beta)ln r]. The quality of the bounds is numerically studied within the Hartree-Fock framework.