The optimal size of the exchange hole and reduction to one-particle Hamiltonians

We use the concept of the exchange hole introduced by Slater to bound the energy of atoms, molecules, and other systems interacting by Coulomb forces from below by one-particle Hamiltonians with an effective screening potential and an exchange hole around each electron. Interestingly enough the optimal size of the exchange hole is smaller than Slater proposed: the best lower bound is obtained when the exchange hole carries charge 1/2 instead of 1. To highlight the quality of our estimate we show that the Dirac exchange energy with a slightly different constant bounds the exchange–correlation energy from below, an estimate previously derived by Lieb and later improved by Lieb and Oxford. Acknowledgements The authors thank Walter Farkas and Christian Hainzl for helpful discussions. Financial support by the European Union under its IHP network program, grant HPRN-CT-2002-00277, is gratefully acknowledged.© By the authorsThe author A.M. Klaus Müller is deceased