A quest for the algorithm for evaluating the molecular hardness

Abstract

ABSTRACT:In this work, we have basically launched a search whether the molecular hardness, an important conceptual descriptor of chemistry and physics, can be evaluated in terms of the atomic hardness values invoking various mathematical algorithms for averaging or not. Starting from the semi-empirical radial dependent formula of computing global hardness of atoms suggested by us, we have derived an ansatz of the molecular hardness assuming that the hardness equalization principle is operative and justifiably valid. In this work, we have attempted a validity test of our ansatz for computing molecular hardness by application to real world. We have also computed the hardness of considerable number of molecules through various mathematical averaging techniques. We have also computed the hardness data of such molecules by invoking ab initio quantum chemical method through the formula of Parr and Pearson, (I À A)/2. Results demonstrate that the set of hardness data evaluated through our suggested ansatz have very close agreement with the ab initio hardness data compared to the sets of data obtained through the various averaging techniques. In our next effort, by exploiting the suggestion of Gazquez, we have evaluated the reaction energy of a number of hard-soft acid-base exchange reactions. On a comparative study, it is found that (i) the arithmetic formula does not predict the reaction path at all, (ii) other methods fail to explain all the reactions efficiently, and (iii) the molecular hardness evaluated by the method suggested by us represent the reaction surface quite reasonably.

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.…”

“…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]. In our study, we have discovered the commonality of the operational significance, origin and development of electronegativity and hardness.…”

“…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.…”

Validation of the Charge Equalization Principles during the Formation of Small Molecules

“…Chemical hardness is an extremely meaningful concept in terms of understanding of chemical reactivity and stability of chemical systems [13][14][15]. Chemical principles based on chemical hardness concept such as Hard and Soft Acid-Base Principle (HSAB) [16][17][18][19] and Principle of Maximum Hardness (PMH) [20][21][22] present theoretical justification to chemists for many issue of chemistry.…”