is maintained, but the resulting weights  increase. To investigate the effects of such a scaling and the erroneous tails shown in Fig. \[fig:radialdens\], we compare the results of three types of atomic radial density distributions. To that end, the reference set of molecules previously used in Hirshfeld-I studies by Bultinck *et al.*[@BultinckP:2007JCP_HirRef; @VanDamme_Bultinck:JCTC2009] is used. This set consists of $168$ neutral molecules containing only H, C, N, O, F, and Cl.\
The first set of atomic radial CDDs, called R1, contains the density distributions as shown in Fig. \[fig:radialdens\]a, where the radial distribution is obtained from a periodic cell of $20\times 20\times 20$Å$^3$.\
For the second set, which is referred to as R2, we have combined these results with the results from a periodic cell of $40\times 40\times 40$Å$^3$ but with a lower grid resolution. In this case, the core part of the radial distribution is taken from the $20\times 20\times 20$Å$^3$ unit cell with the high resolution grid and connected to the tail part obtained from the $40\times 40\times 40$Å$^3$ unit cell. As a result, the high accuracy for the core part of the distribution is maintained, and the tail is corrected through the removal of the delocalized electron 