PHYSICAL ORIGIN OF THE DISCONTINUITY OF THE KOHN-SHAM THEORY EFFECTIVE POTENTIAL

We derive a formal line-integral expression for the discontinuity that occurs in the electron-interaction potential of the Kohn-Sham (KS) th eory as the electron number passes through an integer. The discontinui ty 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 rigorou s description of the KS theory in terms of density matrices, and as su ch we provide an explanation for the physical origin of the discontinu ity from a distinctly different perspective. The derivation further sh ows that the different electron correlations represented in the KS pot ential, viz. those due to the Pauli exclusion principle, Coulomb repul sion, and correlation-kinetic effects, all contribute to the discontin uity, and the contribution of each to the conservative field is given explicitly. The same physics shows that the KS representation of Hartr ee-Fock and Hartree theories as well as other approximations must also exhibit the discontinuity, and we demonstrate this for the work forma lism Hartree-Fock approximation. (C) 1998 Elsevier Science B.V.