NBOs

NBOs, or Natural Bond Orbitals, are a way to describe the electronic structure of molecules by representing the molecular wavefunction with localized orbitals that resemble intuitive Lewis structures. The analysis partitions electron density into natural atomic orbitals and organizes them into bonding, antibonding, and lone-pair orbitals (BD, BD*, LP) that best describe the Lewis-like picture. The approach is based on Natural Bond Orbital theory developed by Frank Weinhold and collaborators and is widely used in computational chemistry.

NBO analysis provides quantitative measures of bonding and delocalization through donor-acceptor interactions. In this framework, electrons in occupied donor orbitals (such as LP or BD) can donate into empty acceptor orbitals (LP*, BD*, etc.), with a stabilization energy referred to as E(2) for each interaction. This yields insight into hyperconjugation, pi-delocalization, and n→σ* or other resonance effects. NBO calculations also report natural charges (NPA), bond indices, and occupancy values that reflect orbital participation and charge transfer.

Applications include interpreting bonding patterns in organic and inorganic compounds, characterizing resonance and hyperconjugation, and aiding in the interpretation of reactivity and reaction mechanisms. In practice, NBO analysis is typically performed as a post-processing step on quantum-chemical wavefunctions produced by programs such as Gaussian, ORCA, or Q-Chem, using the dedicated NBO software. Results are most informative when complemented by other analyses, and they depend on the chosen level of theory and basis set, so interpretations should be made cautiously for highly delocalized systems.