Whether there is a hardness equalization principle analogous to the electronegativity equalization principle—A quest

Abstract

ABSTRACT: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 À 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.

Spectroscopic Evaluation of the Atomic Size

“…In the exploration of the relationship between the radius and the ionization energy of the atoms, we have relied upon our new definition of the global hardness of the atoms [38][39][40][41].…”

Comment on Ruling out Any Electrophilicity Equalization Principle? and Hardness Equalization Principle

“…In difference to Szentpaly [2,3], we [4][5][6][7][8][9] believe that the equalization process does exit and work in the formation of hetero nuclear molecule. But in deference to him, we agree to the idea that the geometric as well as other mean principles are not that successful in studying the chemical interactions and hence to study the equalization of the structural descriptors like electronegativity, hardness and electrophilicity.…”

“…The electrophilicity equalization principle is also implicit in the work of Chaquin [12] and Noorizadeh and Shakerzadeh [13][14]. Therefore, it is quite probable that there should be, similar to the physical process of electronegativity equalization [19,20] and the hardness equalization [4][5][6][7][8][9][16][17][21][22][23], an analogous process of equalization of electrophilicity during the event of molecule formation. Looking at the ansatz of Parr et al, for the definition of electrophilicity, it is given that electrophilicity is the result of conjoint action of two global quantities of CDFT, the electronegativity and the chemical hardness.…”

“…Looking at the ansatz of Parr et al, for the definition of electrophilicity, it is given that electrophilicity is the result of conjoint action of two global quantities of CDFT, the electronegativity and the chemical hardness. Thus the strongest argument in favour of the electrophilicity equalization follows from the fact that, since the electronegativity equalization is unequivocal and widely accepted and the hardness equalization is also now established [4][5][6][7][8][9], and since if electronegativity and hardness are both equalized, then electrophilicity (being their ratio) must be also inevitably equalized. Thus, the present analysis logistically establishes that it is unequivocal that electrophilicity equalization exits and is manifest during the chemical events of molecule formation.…”

“…Regarding his comment on hardness equalization we are to state that we suggested formulae for hardness equalization for some hetero nuclear di atomic systems [4] and poly atomic systems [9] which is assumed to be a cluster of atoms. We have applied our suggested scheme of hardness equalization in the study of acid-base double exchange reactions [5,9], computation of hetero nuclear bond lengths [7], computation of dipole charges and dipole moments of hetero nuclear molecules [6].…”