On the properties of natural orbitals for chemical valence

Natural orbitals for chemical valence (NOCV) were recently introduced as descriptors of chemical bond. They were shown to provide a valuable bond diagnosis in transition metal complexes (Mitoraj and Michalak in J Mol Model 13:347-355, 2007). The present paper treats the mathematical basis for the proposed method. In particular, the algebraic properties of NOCV, on which this methodology relies, are rigorously proven.