Whether There Is a Hardness Equalization Principle Analogous to the Electronegativity Equalization Principle-A Quest

In this report, we have attempted to explore whether the hardness equalization principle can be conceived analogous to the well-established electronegativity equalization principle. We have relied upon the fact that the hardness, like the electronegativity, is a qualitative property, and there is commonality in the basic philosophy of the origin and the operational significance of these two fundamental descriptors-the electronegativity and the hardness of atoms in physics and chemistry. Starting from the empirical radial dependent formula of computing the hardness of atoms suggested by us, we have derived an ansatz of the molecular hardness assuming that hardness equalization principle is operative and justifiably valid. For a validity test, we have applied the suggested ansatz to compute the hardness of as many as four sets of compounds with widely divergent physical and chemical nature. As hardness is not an experimentally measurable property, there is no benchmark to perform any validity test of our computed data. We have, therefore, computed the hardness data of these four different sets of the compound invoking the approximate and operational formula of Parr and Pearson, (I - A)/2, to evaluate hardness values and to compute I and A, we have invoked Koopmans' theorem and an ab initio quantum chemical method. We have observed that there is a close correlation between the four sets of hardness data computed through the semi-empirical ansatz of this work and the quantum mechanical method. Thus, it appears that the ansatz of computing molecular hardness derived on the basis of the hardness equalization principle is efficacious in computing molecular hardness. The detailed comparative study suggests that the paradigm of the hardness equalization principle may be another law of nature like the established electronegativity equalization principle. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 1961-1969, 2011