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 later improved by Lieb and Oxford.
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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.
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The author A.M. Klaus Müller is deceased
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Mancas, P., Müller, A. & Siedentop, H. The optimal size of the exchange hole and reduction to one-particle Hamiltonians. Theor Chem Acc 111, 49–53 (2004). https://doi.org/10.1007/s00214-003-0553-0
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DOI: https://doi.org/10.1007/s00214-003-0553-0