Deciphering Atomic Polarizability: The Absolute Radii and Orbital Contributions Visited

Polarizability is a fundamental property in molecular sciences. It depends on the atom and molecule size and characterizes the ease of deforming the electron cloud by an electric field. Previous studies suggested that the electronic distribution of the outermost orbital can be used to determine the ground-state properties of the atom like hardness, polarizability, and electronegativity. Additionally, the "absolute radius"─the most probable radius of the outermost orbital─has been used to derive atomic properties. In our study, we present a new set of absolute radii for various atoms and ions across the periodic table, obtained based on high-level quantum mechanical calculations. These radii exhibit greater accuracy compared to those previously derived using Slater shielding constants and could offer enhanced utility for diverse scientific applications. We also calculated atomic polarizabilities for a range of atoms and ions using three different approaches. One method assumes a spherical electron distribution based on the absolute radii, while the other two rely on the radial distribution function(s) of the outermost orbital(s). Comparisons with reference polarizabilities obtained from density functional theory (DFT) indicate that while these strategies provide qualitative insights, they do not yield quantitative agreement. To better understand the factors influencing atomic polarizability, we evaluated the contributions of different orbitals. Interestingly, our results reveal that inner orbitals contribute significantly to the atomic polarizability, which are comparable to the outermost orbital. This finding challenges the conventional view of polarizability as solely a volume-dependent property linked to the valence orbital. Moreover, our analysis of three molecules─CO₂, CH₄, and SF₆─indicates that molecular polarizability is primarily governed by the outermost orbitals, likely because chemical bonds constrain the electron clouds of the inner orbitals, a limitation absent in isolated atoms. These findings imply that polarizability is best understood as a property influenced by both atomic volume and the energetic contributions of various orbitals.