  In the distributed nucleus approximation we represent the singular nucleus as
smeared over a smallportion of a Cartesian grid. Delocalizing the nucleus
allows us to solve the Poisson equation for theoverall electrostatic potential
using a linear scaling multigrid algorithm.This work is done in the context of
minimizing the Kohn-Sham energy functionaldirectly in real space with a
multiscale approach. The efficacy of the approximation is illustrated
bylocating the ground state density of simple one electron atoms and
moleculesand more complicated multiorbital systems.
