Abstract
Several expressions are derived that allow one to evaluate any local property at nuclear cusps in atoms and molecules. Applications of the formulas to the Hartree-Fock density and its derivatives for first- and second-row atoms show agreement with Kato's cusp condition. Applications to the exact exchange-only and exchange-correlation energy potential for neutral atoms are given. It is shown that for an atom, the values of ${\mathit{V}}_{\mathrm{x}}$(0) and ${\mathit{V}}_{\mathrm{xc}}$(0) are both close to the negative of the charge of the nucleus.
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