Eliminating Fragment Group Orbital (eFGO) Analysis for Deciphering Chemical Bonding in Complex Systems

The delocalized nature of canonical molecular orbitals in quantum chemistry calculations is always in conflict with the localized nature of orbital interactions and derived chemical concepts. Localization of molecular orbitals has been achieved in many approaches, but sometimes they could be over-localized for complex systems, especially those with multicenter bonding. A fragment-based approach is thus proposed to eliminate the electron density contribution from substituents, ligands and other peripheral moieties such that the skeletal bonding is clearly revealed. To be specific, fragment group orbitals, as in analogy with ligand group orbitals in coordination chemistry, are eliminated from the space spanned by occupied molecular orbitals. Via this approach, the skeletal bonding orbitals of complex systems including but not limited to pi-delocalized systems and cluster compounds are recovered with a minimal contribution from surrounding moieties, making this method the ideal choice to analyze the electronic structure of complex systems and separate skeletal bonding contribution against peripheral moieties from various sum-over-orbital properties.