**NBO: Natural Bond Orbitals** A natural bond orbital or NBO is a calculated bonding orbital with maximum electron density. The NBOs are one of a sequence of natural localized orbital sets.

Atomic orbital → NAO → NHO → NBO → NLMO → Molecular orbital

An NBO can be considered as the Chemist's basis set. They block diagonalise the one-particle density matrix. From NBO's Natural Localised MO's are formed.

__NBO analysis:__ Natural Bond Order analysis comprises a sequence of transformations of the input basis, the AO's, to various localised basis sets:

NAO's: Natural Atomic Orbitals

NHO's: Natural Hybrid Orbitals

NBO's: Natural Bond Orbitals

NLMO's: Natural Localised Molecular Orbitals

These localised basis sets may subsequently be transformed to delocalised natural orbitals (NO's) or canonical molecular orbitals (MO's)

__Source:__ http://en.wikipedia.org/wiki/Natural_bond_orbital http://pubs.acs.org/doi/abs/10.1021/cr00088a005