Correlation of electron density and bond length to band gap for binary oxides and halides

Abstract

The best quantity correlated to the electronic energy band gap is found for alkali and alkaline‐earth metal oxides and halides with face centered cubic (fcc) structure based on density functional theory and Bader's atom‐in‐molecule theory. Previous studies show the correlation of the band gap to the ground state electron density at the bond critical point (BCP). Whereas, in quantum mechanics, the gap between the energy levels of one dimensional square well potential is inversely proportional to the square of the width of the well which is the metal–nonmetal chemical bond length in our case. These motivate the proposition of a new quantity Q, the ratio of the density at the BCP to the square of the bond length. Our study reveals that, for the aforementioned materials, the band gap has a strong correlation to Q when they are multiplied by the density at the BCP.