Asymptotic Near Nucleus Structure of the Electron-Interaction Potential in Local Effective Potential Theories

In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near nucleus structure of the electron-interaction potential is $v_{ee}(r) = v_{ee}(0) + \beta r + \gamma r^{2}$. In this paper we prove via time-independent Quantal Density Functional Theory[1](Q-DFT): (i) correlations due to the Pauli exclusion principle and Coulomb repulsion do not contribute to the linear structure;(ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is \emph{solely} due to Correlation-Kinetic effects, the coefficient $\beta$ being determined analytically. By application of adiabatic coupling constant perturbation theory via QDFT we further prove: (iv) the Kohn-Sham (KS-DFT) `exchange' potential $v_{x}(r)$ approaches the nucleus linearly, this structure being due \emph{solely} to lowest- order Correlation-Kinetic effects: (v) the KS-DFT `correlation' potential $v_{c}(r)$ also approaches the nucleus linearly, being \emph{solely} due to higher-order Correlation-Kinetic contributions. The above conclusions are equally valid for system of arbitrary symmetry, provided spherical averages of the properties are employed. \\ 1 \emph{Quantal Density Functional Theory}, V. Sahni (Springer-Verlag 2004)