Simple quantitative estimate of the derivative discontinuity of the exchange-correlation functional in atoms and polymers

The derivative discontinuity of the exchange-correlation functional of density-functional theory is cast as the difference of two types of electron affinities. We approximately evaluate this difference via ordinary Kohn-Sham calculations, obtaining estimates of the discontinuity for light atoms and for polyacetylene oligomers. The discontinuity is found to be quite large (typically several eV), and significantly and consistently improves the agreement of the calculated fundamental energy gap with the experimental gaps. For atoms, the error of the HOMO-LUMO gap is reduced in this way by more than one order of magnitude.