Since, the hardness is a conceptual hypothesis only and not observable; there is no possibility of its quantum mechanical evaluation. Any attempt of modeling this abstract semiotic representation for the purpose of developing some mathematical algorithms and to convert it into theoretical quantities of cognitive representations, it is required that the hardness should be reified in terms of the physico-chemical behavior of such conundrums goaded by the quantum mechanical principles. Some scales of measurement of hardness are introduced with the evolution of time.
TopIntroduction
The hardness is an important conceptual constructs of chemistry and physics. It has equal rank and status with other two very important conceptual constructs viz. atomic radius and the electronegativity. The importance of the hypothetical constructs is self evident from the statement that, without the concept and operational significance of radius, hardness and electronegativity, chemistry and many aspects of condensed matter physics, become chaotic and the long established unique order in chemico-physical world would be disturbed. The notion of hardness was first introduced by Mulliken (1952) when he pointed out that the ‘Hard’ and ‘Soft’ behavior of various atoms, molecules and ions can be conceived during acid-base chemical interaction. Soon after Mulliken’s classification, the terms “hardness” and “softness” were in the glossary of conceptual chemistry and implicitly signified the resistance towards the deformability of atoms, molecules and ions under small perturbation usually developed during the event of chemical reaction. Thereafter, Pearson (1963) and Klopman (1964) tried to systematize and rationalize this intrinsic property of atoms and molecules. Pearson (1963) qualitatively classified molecules, atoms and ions in three classes, hard, soft and borderline- known as the HSAB principle and Klopman (1964) had drawn a link to Hard –Soft behavior with the HOMO-LUMO gap of the frontier orbital theory.
It is unequivocal that the hardness as conceived in chemistry fundamentally signifies the resistance towards the deformation or polarization of the electron cloud of the atoms, ions or molecules under small perturbation generated during the process of the chemical reaction. Thus, the general operational significance of the hard-soft behavior of a chemical species may be understood in the following statement. If the electron cloud is strongly held by the nucleus, the chemical species is ‘hard’ but if the electron cloud is loosely held by the nucleus, the system is ‘soft’(Klopman, 1964; Pearson, 1963).
The quest for the theoretical basis of the hardness and softness of atoms and molecules has created such a surge of fundamental research in chemistry that it gave birth of a new branch of density functional based theoretical science known as ‘Conceptual Density Functional Theory, CDFT’ (Geerlings, Proft, & Langenaeker 2003).
The conceptual density functional theory has added Maximum Hardness Principle, (MHP) (Pearson 1987, 1993; Parr et al., 1991) and Minimum Polarizability Principle, (MPP) (Chattaraj et al 1996) to the list of the fundamental laws of nature. The CDFT has been successfully exploited in elucidating and correlating mechanistic aspects viz. regio-selectivity, catalysis, aromaticity, intramolecualr rotation, inversion and isomerization reactions (Zhou et al., 1989; Parr et al., 1991; Chattaraj et al. 1994; Pearson et al., 1992; Pal et al 1993, Chattaraj et al 1995, Ayers et al 2000, Ghosh et al 2000, 2002).