Electron Localization in Non-Compact Covalent Bonds Captured by the r2SCAN+V Approach

In density functional theory, the SCAN (Strongly Constrained and Appropriately Normed) and r2SCAN functionals significantly improve over generalized gradient approximation functionals such as PBE (Perdew-Burke-Ernzerhof) in predicting electronic, magnetic, and structural properties across various materials, including transition-metal compounds. However, there remain puzzling cases where SCAN and r2SCAN underperform, such as in calculating the band structure of graphene, the magnetic moment of Fe, the potential energy curve of the Cr2 molecule, and the bond length of VO2. This research identifies a common characteristic among these challenging materials: non-compact covalent bonding through s-s, p-p, or d-d electron hybridization. While SCAN and r2SCAN excel at capturing electron localization at local atomic sites, they struggle to accurately describe electron localization in non-compact covalent bonds, resulting in a biased improvement. To address this issue, we propose the r2SCAN+V approach as a practical modification that improves accuracy across all the tested materials. The parameter V is 4 eV for metallic Fe, but substantially lower for the other cases. Our findings provide valuable insights for the future development of advanced functionals.