ANALYTICAL ASYMPTOTIC STRUCTURE OF THE PAULI, COULOMB, AND CORRELATION-KINETIC COMPONENTS OF THE KOHN-SHAM THEORY EXCHANGE-CORRELATION POTENTIAL IN ATOMS

In this article, we derive the analytical asymptotic structure in the classically forbidden region of atoms of the Kohn-Sham (KS) theory exc hange-correlation potential defined as the functional derivative nu(xc )(r) = delta E-xc(KS)[ rho]/delta rho(r), where E-xc(KS)[ rho] is the KS exchange-correlation energy functional of the density rho(r). The d erivation is via the exact description of KS theory in terms of the Sc hrodinger wave function. As such, we derive the explicit contribution to the asymptotic structure of the separate correlations due to the Pa uli exclusion principle and Coulomb repulsion, and of correlation-kine tic effects which are the source of the difference between the kinetic energy of the Schrodinger and KS systems. We first determine the asym ptotic expansion of the wave function, single-particle density matrix, density, and pair-correlation density up to terms of order involving the quadrupole moment. For atoms in which the N- and (N-1)-electron sy stems are orbitally nondegenerate, the structure of the potential is d erived to be nu(xc)(r) (r-->infinity) similar to -1/r - alpha/2r(4) 8 kappa(0) chi/5r(5), where ca is the polarizability; chi, an expectat ion value of`the (N - 1)-electron ion; and kappa(0)(2)/2, the ionizati on potential. The derivation shows the leading and second terms to ari se directly from the KS Fermi and Coulomb hole charges, respectively, and the last to be a correlation-kinetic contribution. For atoms in wh ich the N-electron system is orbitally degenerate, there are additiona l contributions of O(1/r(3)) and O(1/r(5)) due to Pauli correlations. We show further that there is no O(1/r(5)) contribution due to Coulomb correlations. (C) 1998 John Wiley & Sons, Inc.