A valence-shell atomic orbital whose derivation involves diagonalising the localized block of the full density matrix of a given molecule associated with basis functions χ i A on that atom. A distinguishing feature of NAOs is that they meet the simultaneous requirement of orthonormality and maximum occupancy. For isolated atoms, NAOs coincide with natural orbitals. In a polyatomic molecule the NAOs (in contrast to natural orbitals that become delocalised over all nuclear centres) mostly retain one-centre character, and thus are optimal for describing the molecular electron density around each atomic centre.