Quantifying Atomic Volume, Partial Charge, and Electronegativity in Condensed Phases

The predictive and explanatory roles of atomic properties such as size, charge, and electronegativity are closely linked to their definitions. However, establishing suitable definitions becomes increasingly challenging when examining atoms within materials. This study presents a quantum-mechanical framework for the quantitative assessment of these atomic properties in crystalline structures. Our approach utilizes Kohn-Sham density functional theory to approximate the electron energy density. We then employ a quantum chemical topological analysis of this density to derive atomic properties. The average electron energy density is conceptually powerful because it can be interpreted as a product of the electron density and the average energy of occupied molecular orbitals (MOs). Our method therefore bridges descriptive and predictive theories of electronic structure, including the quantum theory of atoms in molecules and MO theory. The applicability of our methodology is demonstrated across various materials, including metals, ionic salts, semiconductors, and a hydrogen-bonded molecular crystal. This work provides insights into electronegativity inversion during bond formation. It also highlights the complementary roles of partial charge and electronegativity in electronic structure analysis, with one indicating spatial electron accumulation or depletion and the other reflecting average electron binding. Experimental ground state electronegativities of H-, Li+, C+, N-, O-, F-, K+, and Ga+ are provided to support our discussion.