Inquantum chemistry, anatural bond orbital orNBO is a calculatedbonding orbital with maximumelectron density. The NBOs are one of a sequence of natural localized orbital sets that include "natural atomic orbitals" (NAO), "natural hybrid orbitals" (NHO), "natural bonding orbitals" (NBO) and "natural (semi-)localized molecular orbitals" (NLMO). These natural localized sets are intermediate between basis atomic orbitals (AO) and molecular orbitals (MO):
Natural (localized) orbitals are used incomputational chemistry to calculate the distribution of electron density in atoms and in bonds between atoms. They have the "maximum-occupancy character" in localized 1-center and 2-center regions of the molecule. Natural bond orbitals (NBOs) include the highest possible percentage of the electron density, ideally close to 2.000, providing the most accurate possible “natural Lewis structure” of ψ. A high percentage of electron density (denoted %-ρL), often found to be >99% for common organic molecules, correspond with an accurate natural Lewis structure.
The concept ofnatural orbitals was first introduced byPer-Olov Löwdin in 1955, to describe the unique set oforthonormal 1-electron functions that are intrinsic to theN-electron wavefunction.[1]
Each bonding NBO σAB (the donor) can be written in terms of two directed valence hybrids (NHOs) hA, hB on atoms A and B, with corresponding polarization coefficientscA,cB:
The bonds vary smoothly from covalent (cA =cB) to ionic (cA >>cB) limit.
Each valence bonding NBO σ must be paired with a corresponding valenceantibonding NBO σ* (the acceptor) to complete the span of the valence space:
The bonding NBOs are of the "Lewis orbital"-type (occupation numbers near 2); antibonding NBOs are of the "non-Lewis orbital"-type (occupation numbers near 0). In an idealizedLewis structure, fullLewis orbitals (two electrons) are complemented by formally empty non-Lewis orbitals. Weak occupancies of the valence antibonds signal irreducible departures from an idealized localized Lewis structure, which means true "delocalization effects".[1]
With a computer program that can calculate NBOs, optimal Lewis structures can be found. An optimal Lewis structure can be defined as that one with the maximum amount of electronic charge in Lewis orbitals (Lewis charge). A low amount of electronic charge in Lewis orbitals indicates strong effects of electron delocalization.
Inresonance structures, major and minor contributing structures may exist. For amides, for example, NBO calculations show that the structure with a carbonyldouble bond is the dominant Lewis structure. However, in NBO calculations, "covalent-ionic resonance" is not needed due to the inclusion of bond-polarity effects in the resonance structures.[2] This is similar to othermodern valence bond theory methods.