Most Probable Distance between the Nucleus and HOMO Electron: The Latent Meaning of Atomic Radius from the Product of Chemical Hardness and Polarizability

The simple relationship between size of an atom, the Pearson hardness, and electronic polarizability is described. The estimated atomic radius correlates well with experimental as well as theoretical covalent radii reported in the literature. Furthermore, the direct connection of atomic radius to HOMO electron density and important notions of conceptual DFT (such as frontier molecular orbitals and Fukui function) has been shown and interpreted. The radial maximum of HOMO density distribution at (alpha eta)(1/2) minimizes the system energy. Eventually, the knowledge of the Fukui function of an atom is sufficient to estimate its electronic polarizability, chemical potential, and hardness.