Application of a distributed nucleus approximation in grid based minimization of the Kohn–Sham energy functional

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Abstract
In the distributed nucleus approximation we represent the singular nucleus as smeared over a small portion of a Cartesian grid. Delocalizing the nucleus allows us to solve the Poisson equation for the overall electrostatic potential using a linear scaling multigrid algorithm. This work is done in the context of minimizing the Kohn–Sham energy functional directly in real space with a multiscale approach. The efficacy of the approximation is illustrated by locating the ground state density of simple one electron atoms and molecules and more complicated multiorbital systems.