we used spherical integration grids of $1202$ grid points per shell.[]{data-label="fig:HIR_GridConv"}](atdensmodifications3.png "fig:"){width="8cm"}\

[c|ccc]{} &\
& $10$ & $20$ & $30$\
\
$\Delta^{10}_{20}$ & 0.00738 & 0.00743 & 0.00744\
$\Delta^{20}_{30}$ & 0.00126 & 0.00128 & 0.00128\
$\Delta^{30}_{40}$ & 0.00049 & 0.00048 & 0.00049\
&\
& $\Delta^{10}_{20}$ & $\Delta^{20}_{30}$ &\
\
$10$ & -0.00617 & -0.00112 &\
$20$ & -0.00612 & -0.00111 &\
$30$ & -0.00610 & -0.00111 &\
$40$ & -0.00611 & -0.00110 &\

Charge density grids V$_{sys}$ and V$_{atom}$ {#ssc:chargedensitygrid}
---------------------------------------------

As was mentioned in the previous section, the use of stored grid-based CDDs introduces small inaccuracies due to the need for interpolation between the existing grid points. The charge of the C atom in a CO molecule is shown in Fig. \[fig:HIR\_GridConv\] as a function of the grid spacing used in the V$_{sys}$ grid. The different curves are for different grid spacings used in the V$_{atom}$ grids, from which the atomic radial CDD $\rho_{C}^{i}(n_{C}^{i},\mathbf{r})$ and $\rho_{O}^{i}(n_{O}^{i},\mathbf{r})$ are generated. It clearly shows the influence of both grids to be independent, since all curves have the same shape. Looking in detail at the exact numbers reveals that for both grids the same accuracy is obtained (*cf.* Table \[table:gridConv\]). This means that 