Origin of the derivative discontinuity in density functional theory

Abstract

The local electron-interaction potential of Kohn-Sham density functional theory is representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects which are a consequence of the correlation contribution to the kinetic energy. This potential exhibits a discontinuity as the electron number passes through an integer value. We show, via quantal density functional theory, that the physical origin of the discontinuity is the correlation-kinetic effect. The magnitude of the discontinuity is derived to be the work done to move an electron in a conservative field representative of this effect. An explanation is given as to how these correlation-kinetic effects give rise to such a discontinuity. Further, how this understanding relates to that within traditional Kohn-Sham theory and other previous explanations of the discontinuity is also discussed.