Structure of the optimized effective Kohn—Sham exchange potential and its gradient approximations

An analysis of the structure of the optimized effective Kohn-Sham exchange potential v_x and its gradient approximations is presented. The potential is decomposed into the Slater potential v_s and the response of v_s to density variations, v_resp. The latter exhibits peaks that reflect the atomic shell structure. Kohn—Sham exchange potentials derived from current gradient approaches for the exchange energy are shown to be quite reasonable for the Slater potential, but they fail to approximate the response part, which leads to poor overall potentials. Improved potentials are constructed by a direct fit of v_x with a gradient-dependent Padé approximant form. The potentials obtained possess proper asymptotic and scaling properties and reproduce the shell structure of the exact v_x. © 1996 John Wiley & Sons, Inc.