Accurate 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.
Bibliographical noteFunding Information:
We acknowledge Rex Godby for providing us with computational resources, Neepa Maitra for a fruitful discussion and constructive comments on the manuscript, and Lizzie Brookes for careful proofreading. E.K. greatly appreciates the support of the Alexander von Humboldt Foundation.
© 2017 American Chemical Society.