Bounds for Coulomb energies

摘要

It is shown by comparison calculations on many neutral atoms that excellent representations of the Coulomb energyJand the exchange energyKareAN2/3Frgr;4/3dtgr;andBFrgr;4/3dtgr;, respectively (A=0.8994,B=minus;0.7969). It is also proved thatJquest;1.0918N2/3Frgr;4/3dtgr; for all atoms and molecules, and thatJ(N2/3Frgr;4/3dtgr;)minus;1rarr;0.856 asNrarr;infin;. Lower bound representations forJare also given. Implications of these results for local density functional theory are discussed.