The pioneering results for hyperhardness by Fuentealba and Parr 𝛾 𝐹 = 1 6 ⁄ [ 3 𝐸/𝑁 3 ] 𝑣 have been obtained by the sophisticated interpolation based on three experimental parameters: electron affinity A1. and ionization energies I1 and I2. The hyperhardness F was found to be negative, except for the atoms in their S electronic state (e.g. noble gases), where exceedingly small, positive 𝛾 𝐹 > 0 was found. While no correlation between the present results () and 6𝛾 𝐹 was observed (Fig. ), both values span over similar numerical data with neatly equivalent average values: < 6F > =-1.86 eV, <> =-1.77 eV. This observation is meaningful, given the much different origin of the two sets of data. The notable advantage of the method applied hereby is rather regular change in (Z) function equally for neutral atoms (Fig. ) and their ions (Fig. ) whereas the dispersed 6𝛾 𝐹 (𝑍) data could not be fitted with any feasible rational interpolation (Fig. ). The applied method of calculation of the global energy derivatives (, ) from the properties of the stationary electron density alone represents an explicit example that these reactivity indices as density functionals and that electron density is the basic variable in cDFT. The wellknown problems with the degeneracy of the electronic states, that invalidates the usual reactivity indicators associated with the cDFT has been circumvented. Although this approach leads merely to a lower bound to the response parameters, the simple availability of the profound DFT descriptor may be valuable for the chemical practice, once the phenomenological method of their use is available in calculation of the variations of the state functions Δ𝐸 𝑁 , Δ𝜇 𝑁 , Δ𝑁 𝜇 . Recent efforts by Miranda-Quintana et. al. may bring a fresh interest in this matter, the problem of indexing the chemical properties by the density-based derivatives has also been focused upon in other recent papers. The hyperhardness calculated in the framework of the local approximation for atoms increases along the rows of the Periodic Table, but it tends to be rather smooth flat function of the atomic numbers for Z>10 within their periods. The hardness data from the same method