In this work, the third derivative of the energy with respect to the number of electrons, the so-called hyper-hardness, is investigated to assess whether this quantity has a chemical meaning. To achieve this goal a new working expression for hyper-hardness is developed and analyzed. It transpired from this analysis that hyper-hardness, just like hardness, can measure the reactivity or the stability of electron systems. Interestingly, positive values of hyper-hardness point to quite stable species such as noble gases and molecules. On the other hand, radicals almost always display large negative values of hyper-hardness.
Conceptual DFT Dual descriptor Hardness derivatives Principle of maximum hardness
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All the authors thank the joint program between “Evaluation-orientation de la Coopération Scientifique” and “Comisión Nacional de Investigación Científica y Tecnológica” (ECOS-CONICYT (through action project n°C11E03. C.M. and A.G. thank “le Commissariat à l’Energie Atomtique” (CEA-Grenoble) and “Grand Equipement National de Calcul Intensif” (GENCI) through projects gen6836 and gen6834 for computational support. A.T.L. acknowledges support from “Fondo Nacional de Desarrollo Científico y Tecnológico” (FONDECYT) through project n° 1090460. H.C gratefully acknowledges the “Grand Equipement National de Calcul Intensif./Centre Informatique National de l’Enseignemenet Supérieur” (GENCI/CINES) for HPC resources/computer time (Project cpt2130). Finally the authors specially thank the reviewer for pointing out the discrepancy in electronegativity values.