Electronegativity, Hardness and Atomic number: Mutual relationships explored via novel isoelectronic series methodology

Abstract

The novel isoelectronic methodology proposed recently, reveals electronic configuration dependent relationship between the hardness and atomic number, and electronegativity and hardness.  In eight out of the first ten isoelectronic series, the hardness measure (I-A)/2 is an excellent linear function of atomic number (Z), and the electronegativity measure, (I+A)/2 is a quadratic function of the hardness measure; Hence, it is inferred that hardness (η) is proportional to atomic number (η α Z) and electronegativity (χ) is proportional to square of hardness (χ α η²). In both the cases, the two inert gas series species are the exceptions where η α Z² and χ α η, respectively. These relationships are slightly in discord with the previously reported mutual connections. Previous reports do not indicate electronic configuration dependency as well. The linear (I-A)/2 versus Z plots arises as a result of cancellation of Z² terms, and the slopes of these plots are sensitive indicator of the electron spin pairing and orbital change. A potential use of (I-A)/2 versus Z, and (I+A)/2 versus (I-A)/2 plots in pointing the incorrect ionization potentials and their evaluation has been elaborated by the striking example of the sixth ionization potential of phosphorous. The (I-A)/2 versus Z relations also provides us a new way to obtain hardness values of cationic and anionic atomic species.