Atomic softness: The inherent empirical parameter calculated analytically for an atom-in-molecule by the conceptual DFT method

By exploring our previously published gradient theorem [P. Ordon and L. Komorowski, in Chemical Reactivity: Volume 1: Theories and Principles, edited by S. Kaya, L. von Szentpaly, G. Serdaroglu, and L. Guo (Elsevier, 2023), Chap. 9], that provides a relationship of the gradient of the electron density function and the electric field with the softness kernel as the response function, we introduce the method for analytical calculation of the local softness as the trace of the electronic softness tensor and the global softness index of a molecule is obtained by its integration. The atomic contributions to the global softness have also been calculated analytically. These softness parameters for bonded atoms have been tested as the potential indicators of site reactivity in a collection of linear molecules. The analysis has been extended to the rational hypersoftness parameter dsr/dNv, the leading factor for calculations of the local hypersoftness s2r as well as the atomic contributions thereof.