Derivative discontinuity and gaps Weitao Yang Duke University Chemistry The derivative discontinuity in the exchange correlation energy as a functional of density, and as a functional of the density matrix will be introduced. Closely related, the physical meaning of the HOMO and LUMO Kohn-Sham orbital energies, and the HOMO and LUMO generalized Kohn-Sham orbital energies will be discussed, in connection to the fundamental gap in molecules and bulks.