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It is known that the asymptotic decay of the electron density $n(\br)$outside a molecule is informative about its first ionization potential $I_0$,$n(|\br|\to\infty) \sim \text{exp}(-2\sqrt{2I_0}\,r)$. This dictates theorbital energy of the highest occupied Kohn-Sham (KS) molecular orbital (HOMO)to be $\epsilon_H=-I_0$, if the KS potential goes to zero at infinity. However,when the Kohn-Sham HOMO has a nodal plane, the KS density in that plane willdecay as $\exp{(-2\sqrt{-2\epsilon_{H-1}}\,r)}$. Conflicting proposals existfor the KS potential: from exact exchange calculations it has been found thatthe KS potential approaches a {\em positive} constant in the plane, but fromthe assumption of isotropic decay of the exact (interacting) density it hasbeen concluded this constant needs to be {\em negative}. Here we show thateither 1) the exact density decays differently (according to the secondionization potential $I_1$) in the HOMO nodal plane than elsewhere, and the KSpotential has a regular asymptotic behavior (going to zero everywhere) providedthat $\epsilon_{H-1}=-I_1$; or 2) the density does decay like$\text{exp}(-2\sqrt{2I_0}\,r)$ everywhere but the KS potential exhibitsstrongly irregular if not divergent behavior around (at) the nodal plane.11pages, 5 figures

Asymptotic behavior of the electron density and the Kohn-Sham potential in case of a Kohn-Sham HOMO nodal plane