Bounds for Coulomb energies

Abstract

It is shown by comparison calculations on many neutral atoms that excellent representations of the Coulomb energy J and the exchange energy K are AN^2/3Fρ ^4/3 d_T and BFρ^4/3dT, respectively (A=0.8994, B=-0.7969). It is also proved that J?1.0918N^2/3Fρ^4/3dT for all atoms and molecules, and that J (N^2/3F_ρ^4/3dT)^-1→ 0.856 as N→ ∞ . Lower bound representations for J are also given. Implications of these results for local density functional theory are discussed.