Analysis of electron interaction and atomic shell structure in terms of local potentials

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Abstract
The Kohn–Sham potential vs of an N‐electron system and the potential veff of the Euler–Lagrange equation for the square root of the electron density are expressed as the sum of the external potential plus potentials related to the electronic structure, such as the potential of the electron Coulomb repulsion, including the Hartree potential and the screening due to exchange and correlation, a potential representing the effect of Fermi–Dirac statistics and Coulomb correlation on the kinetic functional, and additional potentials representing ‘‘response’’ effects on these potentials. For atoms several of these potentials have distinct atomic shell structure: One of them has peaks between the shells, while two others are step functions. In one of those step functions the steps represent characteristic shell energies. Examples of the potentials extracted from the optimized potential model (OPM) are presented for Kr and Cd. Correlation potentials, obtained by subtracting the exchange potential of the OPM from (nearly) exact Kohn–Sham potentials, are discussed for Be and Ne.