Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 22

Accuracy of Mean Field Approximations for Atoms and Molecules

V. Bach

We estimate the accuracy of the mean field approximation induced by the Thomas-Fermi potential for the ground state energy of atoms and molecules. Taking the Dirac exchange correction into account, we show the error to be of the form $O(Z^{5/3 - delta}) +D$ for any $delta < 2/231$ as the total nuclear charge $Z$ becomes large. $D$ is an electrostatic energy of the difference density that measures the deviation of the mean field ground state from self-consistency.

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