between the atoms, with the highest electron density at the center of the unit cell; *i.e.* as far from the atoms as possible.\
It is interesting to note that this artifact is purely due to the use of plane waves, which try to smear out the unbound electrons over the entire (empty) space. If one uses Gaussians instead, the additional electrons are bound by definition through the basis set used, even if these electrons should not be bound to the atom anymore. From the modeling point of view one might prefer this latter type of artifact over the former, since we are interested in the CDD of the electrons for ‘free ions’, irrespective of their bound or unbound nature. Later in this section we show how this delocalization problem can be solved in a simple way.\
Figure \[fig:radialdens\]b shows that this artifact is independent of the resolution used for the V$_{atom}$ grid, as the different curves nicely overlap. Figure \[fig:radialdens\]c shows the influence of the periodic cell size on this artefact. In case of the presented hydrogen ions, it shows that using a cubic periodic cell with a side of $20$Å, the curves for H$^-$ and H$^{2-}$ coincide in the 