A NEW DEFINITION FOR CHEMICAL HARDNESS

The molecular or atomic hardness, defined as the second derivative of the electronic energy of the molecule (or atom) with respect to the electron charge, exhibits two different values according to whether the reaction involves a gain or a loss of electrons. Within the framework of the standard SCF method, these hardness values are equal to the Coulomb integral J corresponding respectively to the lowest unoccupied molecular (or atomic) orbital and to the highest occupied one. For conjugated molecules, these two hardnesses are practically equal. On the contrary, for atoms and molecules which carry electron lone pairs (e.g. H2CO), the two hardnesses are very different. An empirical relationship is proposed for the hardness of linear conjugated hydrocarbons as a function of the number of carbon atoms.