A new algorithm for the evaluation of the global hardness of polyatomic molecules

Abstract

Relying upon the commonality of the basic philosophy of the origin and development of electronegativity and hardness, we have attempted to explore whether a hardness equalization principle can be conceived for polyatomic molecules analogous to the electronegativity equalization principle. Starting from the new radial-dependent electrostatic definition of hardness of atoms suggested by the present authors and assuming that the hardness equalization principle is operative and valid, we have derived a formula for evaluating the hardness of polyatomic molecule, , where n is the number of ligands, r_i is the atomic radius of the ith atom and C is a constant. The formula has been used to calculate the hardness values of 380 polyatomic molecules with widely divergent physico-chemical properties. The computed hardness data of a set of representative molecules are in good agreement with the corresponding hardness data evaluated quantum mechanically. The hardness data of the present work are found to be quite efficacious in explaining the known reaction surfaces of some well-known hard–soft acid–base exchange reactions in the real world. However, the hardness data evaluated through the ansatz and operational and approximate formula of Parr and Pearson poorly correlate the same reaction surface. This study reveals that the new definition of hardness and the assumed model of hardness equalization are scientifically acceptable valid propositions.

Keywords:

• electronegativity
• hardness
• commonality of electronegativity and hardness
• equalization principles
• electrostatic theorems for computing hardness
• charge transfer