contribution. Note that for these distributions, the curves are limited to a distance of $10$Å from the core, i.e. the same maximum radius as is available from the $20\times 20\times 20$Å$^3$ periodic cells. Because the excess tail electrons are not included anymore, the spherically integrated populations of the negative ions are slightly smaller than they are for the R1 set.\
For the third set, R3, the same procedure as for R2 is used, but this time the curves are normalized for the negative ions such that the correct population is given on spherical integration of these radial CDDs.\
To test the accuracy of the results obtained in our periodic implementation using these three different atomic radial density distribution sets, we compare the results for a large benchmark set of molecules with those obtained by a Hirshfeld-I implementation based on a molecular program (*cf.* Sec. \[ssc:Hir\_Methods\_solstatecodes\]).\

![Correlation plots of the charges obtained using the periodic Hirshfeld-I implementation and the standard molecular implementation. (a) using the atomic radial density distributions of set R2 with the corrected tails, and (b) those of set R3 with the corrected tails and correctly normalized distributions (see text). In both cases the VASP optimized geometry was used 