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

Abstract

It is known that the asymptotic decay of the electron density outside a molecule is informative about its first ionisation potential I0,. This dictates the orbital energy of the highest occupied Kohn-Sham (KS) molecular orbital (HOMO) to be ϵH = -I0, if the KS potential goes to zero at infinity. However, when the KS HOMO has a nodal plane, the KS density in that plane will decay as. Conflicting proposals exist for the KS potential: from exact exchange calculations it has been found that the KS potential approaches a positive constant in the plane, but from the assumption of isotropic decay of the exact (interacting) density, it has been concluded this constant needs to be negative. Here, we show that either (1) the exact density decays differently (according to the second ionisation potential I1) in the HOMO nodal plane than elsewhere, and the KS potential has a regular asymptotic behaviour (going to zero everywhere) provided that ϵH - 1 = -I1; or (2) the density does decay like everywhere but the KS potential exhibits strongly irregular if not divergent behaviour around (at) the nodal plane.