| The method proposed by Krieger, Li and Iafrate (KLI) for the construction of the optimized effective potential (OEP) is examined to determine whether it can be significantly simplified while still retaining its high accuracy. The need for simplification arises because the KLI method may be difficult to employ in multi-atom calculations.; We construct a simplified KLI (SKLI) potential by approximating the V{dollar}sb{lcub}rm isigma{rcub}{dollar} corresponding to the core electrons by the corresponding expression in the local spin density (LSD) approximation or the LSD with self interaction correction (SIC) while employing the HF V{dollar}sb{lcub}rm isigma{rcub}{dollar} only for the occupied valance electron states. We show analytically that such an approximation continues to maintain the important analytic properties of both the OEP and KLI. The SKLI makes only a modest improvement over the LSD (or LSDSIC) in the calculation of the total energy. However, calculations of {dollar}epsilonsb{lcub}rm msigma{rcub}{dollar}, the energy eigenvalue of the highest occupied single particle state, and of {dollar}langle {lcub}rm r{rcub}sp2rangle{dollar}, are nearly identical to the OEP and KLI results demonstrating that the behavior of the valence electrons, which are important in molecular binding calculations, can be accurately predicted by this approximation. These conclusions are substantiated by performing similar calculations on negative ions.; We investigate correlation energy by extending the exactly soluble Laufer-Krieger model to the case of two electrons with parallel spin. We find the exact value of the total energy, the exchange-correlation energy, the exchange-correlation potential as well as the separate exchange and correlation contributions to these quantities and compare these results to various approximations. In exchange only case, the LSD, LSDSIC and the KLI method which constructs the OEP single potential from the effective single particle HF exchange potentials are examined. Also we test exchange-correlation functionals. We use the LSD, LSDSIC and HF to calculate the exchange energy and add the correlation energy by invoking the LSD, LSDSIC, GGA and GGA with SIC. The KLI method (with correlation) is employed to construct the OEP potential as the sum of the effective HF exchange potential and the LSD, LSDSIC, GGA, GGASIC correlation potential respectively. |
