jz7b02615_si_liveslides.zip (9.14 MB)
How Interatomic Steps in the Exact Kohn–Sham Potential Relate to Derivative Discontinuities of the Energy
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posted on 2018-03-27, 20:47 authored by M. J. P. Hodgson, Eli Kraisler, Axel Schild, E. K. U. GrossAccurate
density functional calculations hinge on reliable approximations
to the unknown exchange-correlation (xc) potential. The most popular
approximations usually lack features of the exact xc potential that
are important for an accurate prediction of the fundamental gap and
the distribution of charge in complex systems. Two principal features
in this regard are the spatially uniform shift in the potential, as
the number of electrons infinitesimally surpasses an integer, and
the spatial steps that form, for example, between the atoms of stretched
molecules. Although both aforementioned concepts are well known, the
exact relationship between them remained unclear. Here we establish
this relationship via an analytical derivation. We support our result
by numerically solving the many-electron Schrödinger equation
to extract the exact Kohn–Sham potential and directly observe
its features. Spatial steps in the exact xc potential of a full configuration-interaction
(FCI) calculation of a molecule are presented in three dimensions.