and the same calculation can show different convergence, as is shown by the curves of the C and O atoms of a CO molecule. To have the population of the system atoms converged to within $0.001$ electron a few hundred grid points per shell are required. For a molecular calculation the multi-center grid, S$_{sys}$, only requires a few tens of thousands of grid points, as is seen in Fig. \[fig:HirI\_nlebConv\]b. However, a Hirshfeld-I calculation for a bulk material such as diamond, which also has only two atoms in its unit cell, requires a multi-center grid S$_{sys}$ with several tens of millions of grid points. This difference by a factor thousand originates from the fact that the SoI for the diamond unit cell contains a few thousand atoms, which all contribute to the total number of grid points that need to be evaluated. This makes it very important to reduce the SoI to an as small as possible size without significant loss of accuracy.

![image](radialdens_art.png){width="18cm"}\

Atomic radial CDDs
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The atomic CDDs are calculated in a periodic cell under PBC, and stored on $3$D charge density grids V$_{atom}$ (*cf.* Sec. \[ssc:chargedensitygrid\]). The atomic radial CDDs are obtained from these through spherical 