Physical origin of the discontinuity of the Kohn-Sham theory effective potential

Abstract

We derive a formal line-integral expression for the discontinuity that occurs in the electron-interaction potential of the Kohn-Sham (KS) theory as the electron number passes through an integer. The discontinuity may thus be interpreted as the work done to move an electron in the force of a conservative field. This result is derived via the rigorous description of the KS theory in terms of density matrices, and as such we provide an explanation for the physical origin of the discontinuity from a distinctly different perspective. The derivation further shows that the different electron correlations represented in the KS potentials, viz. those due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, all contribute to the discontinuity, and the contribution of each to the conservative field is given explicitly. The same physics shows that the KS representation of Hartree-Fock and Hartree theories as well as other approximations must also exhibit the discontinuity, and we demonstrate this for the work formalism Hartree-Fock approximation.