Step structure in the atomic Kohn-Sham potential

In this work we analyze the exchange-correlation potentialv _xc within the Kohn-Sham approach to density functional theory for the case of atomic systems. The exchange-correlation potential is written as the sum of two potentials. One of these potentialsv _xc,scr is the long-range. Coulombic potential of the coupling constant integrated exchange-correlation hole which represents the screening of the two-particle interactions due to exchange-correlation effects. The other potentialv _xc,scr ^resp contains the functional derivative with respect to the electron density of the coupling constant integrated pair-correlation function representing the sensitivity of this exchange-correlation screening to density variations. As explicit expression of the exchange-part of this functional derivative is derived using an approximation for the Greens function of the Kohn-Sham system and is shown to display a distinct atomic shell structure. The corresponding potentialv _xc,scr ^resp has a clear step structure and is constant within the atomic shells and changes rapidly at the atomic shell boundaries. Numerical examples are presented for the Be and Kr atoms using the Optimized Potential Model (OPM).