averaging of the density distributions. Spherical averaging is done using the S$_{atom}$ grid, with spherical shells containing Lebedev-Laikov grids of $5810$ grid points.[@LebedevVI_grid:1999DokladyMath] The resulting distributions for different C ions are shown in Fig. \[fig:radialdens\]a. The populations obtained by spherical integration over these distributions shows that the correct populations are obtained for the neutral and the positively charged ions. The negatively charged ions show a population which is too small. Moreover, the curves in Fig. \[fig:radialdens\]a increase again for longer ranges. This increase is not (only) due to overlapping tails of periodic copies in neighboring cells; extrapolating the decreasing part of the curve, and multiplying with the number of periodic nearest neighbors would give a much smaller value at a distance of $10$Å than is now the case. The origin of the increase lies in the fact that the plane wave approach used for the atom calculations can only bind a limited amount of extra electrons to a given atom. This amount varies from atom to atom. As a result, it tries to place the excess electrons as far from the atom as possible. Due to strong delocalization inherent to plane waves these electrons are spread out over the vacuum 