Universal Method to Calculate the Stability, Electronegativity, and Hardness of Dianions

Abstract

The electronic stability of gas-phase dianions of arbitrary size, X(2-), is determined by the first universal method to calculate second electron affinities, A(2). The model expresses A(2,calc) = A(1) - (7/6)η(0) by the first electron affinity, A(1), and chemical hardness, η(0), of the neutral "grandparent" species. A comparison with 37 reference data of atoms, molecules, superatoms, and clusters yields A(2,ref) = 1.004A(2,calc) - 0.023 eV, with a mean unsigned deviation of MUD = 0.095 eV and a correlation coefficient of R = 0.9987. Predictions of second electron affinities are given for a further 24 species. The universality of the model is apparent from the broad variety of compounds formed by 30 diverse elements. The electronegativity and hardness of dianions are determined for the first time as χ(X(2-)) = A(2) and η(X(2-)) = (7/12)η(0), respectively. Pearson and Parr's operational assumption regarding the hardness of anionic bases for the hard-soft acid-base (HSAB) principle is rationalized, and predictions for hard and soft dianionic bases are presented. For trianions, first criteria and predictions for electronic stability are given and require A(1) > (7/4)η(0).