Exchange-correlation potentials for high-electron-density ions in the Be isoelectronic series

Accurate reference wave functions and their densities have been used to obtain accurate exchange-correlation potentials for the beryllium isoelectronic sequence Be, Ne(+6), Ar(+14), and Kr(+32). The exchange-correlation potentials for the four-electron cations with high Z in this sequence exhibit structure prior to the intershell peak that is not present in neutral atoms. The kinetic energy contribution to the exchange-correlation potential contributes to the early structure as well as to the intershell peak. The near degeneracy in this four-electron sequence plays a significant role in the structure prior to the intershell peak. Several of the quantities on which the Perdew-Burke-Ernzerhoff and Tao-Perdew-Staroverov-Scuseria functionals are dependent are examined. The generalized gradient approximations appear not to account for the near degeneracy in this series.