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Accuracy of mean field approximations for atoms and molecules

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Abstract

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 formO(Z 5/3−δ)+D for any δ<2/231 as the total nuclear chargeZ becomes large.D is an electrostatic energy of the difference density that measures the deviation of the mean field groud state from self-consistency.

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  1. Fachbereich Mathematik MA 7-2, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin, Germany

    Volker Bach

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  1. Volker Bach
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Communicated by B. Simon

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Bach, V. Accuracy of mean field approximations for atoms and molecules. Commun.Math. Phys. 155, 295–310 (1993). https://doi.org/10.1007/BF02097395

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  • DOI: https://doi.org/10.1007/BF02097395

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