Asymptotic behavior of the electron density and the Kohn-Sham potential

Details Asymptotic behavior of the electron density and the Kohn-Sham potential Asymptotic behavior of the electron density and the Kohn-Sham potential

2011-09-10

arxiv.org/abs/1109.2204v1

Physics

Chemical Physics

Scientific paper

It is known that the asymptotic decay $(r \to \infty)$ of the electron density $n(r)$ outside a molecule is informative about its first ionization potential I_0$. Contrary to conventional wisdom, we demonstrate that this asymptotic decay may not be the same in every direction. When the highest occupied Kohn-Sham molecular orbital has a nodal plane, the decay $n(r_p \to\infty)$ on that plane is informative about a higher vertical ionization potential $I_i$. The implications for density functional theory are manifold: the Kohn-Sham potential does not need to have an asymptotic constant shift on the plane as previously believed, provided that the second highest occupied orbital energy equals $-I_i$. The effective potential for $\sqrt{n(r)}$ may diverge asymptotically on the plane.

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