Influence of the self-interaction error on the structure of the DFT exchange hole

Approximate density functional theory (DFT) covers long-range non-dynamic electron correlation via the exchange functional while the correlation functional includes just the short-range dynamic electron correlation effects. We show that the self-interaction error of approximate exchange functionals (local density approximation, LDA and others) mimics the long-range correlation effects. For this purpose the exchange hole is investigated at the Hartree–Fock, the LDA, and the self-interaction corrected (SIC)-LDA levels of theory.