This has two small but interesting side effects on the calculated radial charge distributions. Firstly, the integrated charge equals the number of valence electrons only, since the core electrons are not explicitly treated. Secondly, the resulting radial profile is not necessarily monotonically decreasing, showing a minimum or even negative values at the core of the atom (*e.g.* Fig. \[fig:radialdens\]). The origin of this behavior lies in the practical implementation of the PAW pseudo-potentials.[@Blochl:prb94; @Kresse:prb99] By using the same pseudo-potentials for generating the atomic charge distributions and the charge distribution of the system under study, however, no errors are introduced since both systems contain the same frozen core contribution.

Results and Discussion {#sc:Hir_Res_and_Dis}
======================

To this date we are aware of few implementations for periodic systems of the Hirshfeld and approach, but their number is steadily rising. Pendás *et al.*[@PendasAM:2002JChemPhys] investigated Hirshfeld surfaces as approximations for interatomic surfaces for LiF and CS$_2$ crystals. The Cut3D plugin of the <span style="font-variant:small-caps;">ABINIT</span> code can be used to calculate Hirshfeld charges,[@ABINIT_REFERENCE:ComputerPhysCommun2009; @SmithMD:CrystGrowthDes2011; @GlorEC:JSolStateChem2011; @SchierJ:2011ApplMaterInter] and recently Leenaerts *et al.* implemented a “subsystem” based Hirshfeld-I method to study graphane, graphene fluoride and paramagnetic adsorbates on graphene.[@LeenaertsOPeetersF:2010PhysRevB; @LeenaertsO:AplPhysLett2008; @LeenaertsO:PRB2009] In a recent publication Watanabe *et al.*[@WatanabeManzSholl:JPhysChemC2011] 