Local conditions for the Pauli potential in order to yield self-consistent electron densities exhibiting proper atomic shell structure.

The local conditions for the Pauli potential that are necessary in order to yield self-consistent electron densities from orbital-free calculations are investigated for approximations that are expressed with the help of a local position variable. It is shown that those local conditions also apply when the Pauli potential is given in terms of the electron density. An explicit formula for the Ne atom is given, preserving the local conditions during the iterative procedure. The resulting orbital-free electron density exhibits proper shell structure behavior and is in close agreement with the Kohn-Sham electron density. This study demonstrates that it is possible to obtain self-consistent orbital-free electron densities with proper atomic shell structure from simple one-point approximations for the Pauli potential at local density level.