The well known Thomas-Fermi theory with its subsequent development, provides a local density functional in terms of powers of the free electron gas parameter p1/3. For spherically symmetric charge densities, additional terms including 1/r, 1/r2, ∂/∂r and ∂2/∂r2 should be studied. The way they arise from the study of charge densities and the results that could be expected with their use, are analyzed in the present paper.