Hyperhardness for atoms and ions has been calculated by eq. 6a. The comparison of hardness (positive values) and hyperhardness (negative values) has been presented as two functions of the atomic number in joint diagrams for 36 neutral atoms (Fig. ) and for their cations (Fig. ) and anions (Fig. ). The range on the ordinate axis have been adjusted to expose the details of the diagrams. Several common di-cations and di-anions have also been included in Fig. and Fig. , respectively. They provide an additional quick test for the rational character of the results: hardness increasing with further ionization for cations, decreasing for anions. The common di-cations and di-anions have also been marked by the green diamonds.