ABSTRACT
The concept of chemical hardness was introduced in the 1960s by Pearson to explain reactivity preferences in certain acid-base reactions. He noted that, besides the principle establishing that strong acids-bases prefer binding to strong bases-acids, there should be a second tiebreaker principle explaining the reactivity preferences of acids and bases of similar strength. Pearson then postulated the hard-soft acids-bases (HSAB) principle, which states that when the strengths of acids and bases (Lewis acids and bases) involved in a reaction are similar, hard acids prefer binding to hard bases, and soft acids prefer binding to soft bases. In his original works, the hardness of a molecule was not sharply dened, but the principal characteristics of hard and soft species were outlined.1-6 It was observed that the reactive site of hard species tends to be small, highly charged, and barely polarizable, whereas the reactive site of a soft reagent tends be large, less charged, and highly polarizable. At that time, no operative (mathematical) denition or numerical scale was given for hardness. However, in the late 1970s, Parr and Yang,7 Chermette,8 Ayers et al.,9 Chattaraj
3.1 Introduction ....................................................................................................65 3.2 Difculties in Finding Suitable Denition for Local Hardness .....................66 3.3 Local Hardness in an Isomorphic Ensemble ..................................................68 3.4 Relationship with Nuclear Reactivity Descriptors in Isomorphic Ensemble .....69 3.5 Results and Discussion ................................................................................... 72 3.6 Conclusions ..................................................................................................... 75 Acknowledgments .................................................................................................... 76 References ................................................................................................................ 76
et al.,10 Gazquez,11 and Liu12 began a search for a common physical and mathematical basis for basic concepts in chemistry within the framework of density functional theory. The rst achievement in this direction was the association of the negative of electronegativity χ13 with Lagrange’s multiplier in the Euler equation of the density functional theory μ14
µ ν χ ν
=
∂ ∂
= −E NN r
[ , ( )]
r , (3.1)
where E[N,v(r)] is the energy functional, and N and v(r) stand for the number of electrons and the external potential, respectively. The chemical potential μ measures the tendency of electrons to escape from a molecule.
