  From the perspective of perturbation theory, we propose a systematic
procedure for the evaluation of the derivative discontinuity (DD) of the
exchange-correlation energy functional in Kohn-Sham density functional theory
(KS-DFT), wherein the exact DD can in principle be obtained by summing up all
the perturbation corrections to infinite order. Truncation of the perturbation
series at low order yields an efficient scheme for obtaining the approximate
DD. While the zeroth-order theory yields a vanishing DD, the first-order
correction to the DD can be expressed as an explicit universal functional of
the ground-state density and the KS lowest unoccupied molecular orbital
density, allowing the direct evaluation of the DD in the standard KS method
without extra computational cost. The fundamental gap can be predicted by
adding the estimated DD to the KS gap. This scheme is shown to be accurate in
the prediction of the fundamental gaps for a wide variety of atoms and
molecules.
