Whether electronegativity and hardness are manifest two different descriptors of the one and the same fundamental property of atoms—A quest

Abstract

ABSTRACT:In this report, we have tried to reveal that there is much conceptual commonality between the two fundamental theoretical descriptors of chemistry and physics-the electronegativity and the hardness. The physical hardness was introduced and theorized by condensed matter physicists. The chemical hardness was introduced by chemists to generalize and rationalize the HSAB principle. We have tried to establish that the physical hardness and the chemical hardness with evolution of time have converged to one and the same general principle-the hardness. We have also tried to understand the physical basis and operational significance of another very important descriptor arising out of theoretical constructs of chemistry-the electronegativity. We have relied upon the fact that, since these descriptors are not observables, there is no possibility of their quantum mechanical evaluation. These descriptors, therefore, should be and must be reified before suggesting ansatz for their evaluation. We have dwelt at length upon the effort of density functional definition and evaluation of electronegativity and hardness and discovered the inherent inner contradiction of the theory and measurement. We have also noted that a good number of scientists hold the opinion that the density functional formula of electronegativity is ϭ I and that of hardness is ϭ I, where I is the ionization potential of the chemical system. This study concludes that the two fundamental descriptors-the hardness and the electronegativity originate from the same source-the electron attracting power of the screened nucleus upon valence electrons and discovers the surprising result that if one measures hardness, the electronegativity is simultaneously measured and vice versa. We have also explored the ansatz of semiempirical evaluation of electronegativity and hardness of atomic systems involving the radius of the atoms. We have noted that the ansatz for electronegativity and hardness is the same. To justify our statement that if one measures hardness, the electronegativity is simultaneously measured and vice versa, we have used the evaluated set of hardness for 103 elements of the periodic table as a scale of electronegativity and found that such set of hardness data satisfies the sine qua non of a satisfactory scale of electronegativity. The electronegativity and the hardness are two different appearances of the one and the same fundamental property of atoms. They are different and also nondifferent. They are different in their fields of application. They are nondifferent when we discuss the basic philosophical structures of their origin and development.

Spectroscopic Evaluation of the Atomic Size

“…The evaluated inter nuclear bond distances of the molecules under reference through the formula (36) and their experimental counterparts are reported in the Table 2. A close look in to the Table 2 reveals that there is a very good correlation between the inter nuclear bond distances of the nine sets of molecules computed through ansatz (36) using the computed size data and the electronegativity values published by us [15] and their spectroscopically evaluated counter parts. It is surprising to note that the linear correlation coefficient value (R 2 ) of each set of compound is above 0.9.…”

“…We have evaluated atomic size through equation (15) without using the ionization energy determined experimentally or evaluated through Hartree-Fock SCF scheme and invoking Koopmans theorem. Rather, we have explored a new route relying upon spectral transitions and spectroscopy.…”

“…6), and the equation (Eq. 12) derived by us, we get (I-A)/2 = e 2 / 2 r ( 1 3 ) or, r = e 2 / (I-A) (14) Now in most cases of atoms, A is either negligibly small or zero [14,15,52,53], we can simplify the Eq. (14) as…”

“…(36), the computed radii data of corresponding atoms A and B, and the electronegativity values of those atoms published by us [15]. The calculated inter nuclear bond distances of the hetero nuclear diatomics vis-à-vis their experimental counterparts [71] are present in Table 2.…”

“…The screened nuclear charge increases horizontally along a period. Since the screened nuclear charge is primarily controlling the atomic and ionic sizes, the size should decrease and electronegativity and hardness should increase monotonically along the horizontal row [15]. This further suggests that electronegativity, hardness and the atomic radius are intimately connected to each other because of their commonality in the origin and development.…”