Assessment of the Localization Quality:Orthogonal Versus Non-Orthogonal Localized Molecular Orbitals

Formulas of canonical molecular orbitals (CMO), orthogonal localized molecular orbital (OLMO), and non-orthogonal localized molecular orbital (NOLMO) to generate molecular orbitals are given. We have compared the orbital spread functions of some testing systems and their reduced percentage compared to the canonical molecular orbitals to assess the localization quality of each method. It is found that for the occupied orbitals, NOLMO is much more localized than CMOs and any OLMOs generated by Boys, Edmiston-Ruedenberg (ER), and Pipek-Mezey (PM) method, up to about 10-28% if the same cutoff threshold is applied.