Electronegativities and hardnesses of open shell atoms

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Abstract
A Taylor series expansion of the energy of an atomic system around the neutral atom value, which introduces the first and second derivatives of the energy with respect to the number of electrons (electronegativity χ, and hardness η, respectively) is proposed. The relaxed first derivative and the unrelaxed second derivative of the Xα and hyper‐Hartree–Fock methods are used to relate χ and η with the Lagrange multiplier εi, and the self‐repulsion integral J(i) of the highest occupied atomic orbital for the case of an open shell. A simple model, based on screening effects, is developed to get a better representation of a relaxed second derivative. This model replaces J(i) by 1/2 〈r−1〉i and leads to η= 1/4 〈r−1〉i. The use of this relation, together with the Xα expression for electronegativity, χ=−εi, and a simple charge transfer model for electronegativity equalization leads to values of molecular electronegativities which are in very good agreement with the values obtained through the use of atomic or molecular experimental information. The relations here derived only need information obtained from a neutral atom calculation.

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