Quantifying Vertical Resonance Energy in Aromatic Systems with Natural Bond Orbitals

Natural bond orbitals (NBOs) provide the familiar Lewis type (2c-2e-) localized description of a molecule. Interactions between nearly filled (2e-) orbitals and empty (π* or σ*) anti-bonding orbitals represent delocalization in the system and creates a framework to study stereoelectronic interactions. Here we show that deleting the interactions between π and π* orbitals in aromatic systems and acquiring the energy with the NBO program provides a highly intuitive and quantitative picture of π-aromaticity that correlates with the well-established nucleus-independent chemical shift (NICS) method. This natural bond orbital resonance energy (NBO-RE) measures the vertical resonance energy (VRE) of aromatic systems without the use of an external reference structure. The NBO-RE method is applicable to the study of local aromaticity in polycyclic aromatic hydrocarbons (PAHs) and other non-planar systems.