- 03-485 Paul Mancas, A. M. Klaus M"uller, Heinz Siedentop
- The Optimal Size of the Exchange Hole and Reduction to One-Particle Hamiltonians
Nov 7, 03
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Abstract. 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 Oxford.