The natural orbital functionaltheory admits two unique representations in the orbital space. On the one hand, we have the natural orbitals themselves that minimize the energy functional, and which afford for a diagonal one-particle reduced density matrix but not for a diagonal Lagrangian orbital energy multipliers matrix. On the other hand, since it is possible to reverse the situation but only once the energy minimization has been achieved, we have the so-called canonical representation, where the Lagrangian orbital energy multipliers matrix is diagonal but the one-particle reduced density matrix is not. Here it is shown that the former representation, the natural orbital representation, accounts nicely for the quadrupolebond character of the ground states of C2, BN, CB−, and CN+, and for the double bond order character of the isovalent state of Si2. Similarly, the canonical orbital representation accounts correctly for the ionization spectra of all these species.
Received 13 March 2013Accepted 08 April 2013Published online 19 April 2013
Financial support comes from Basque Government (IT588-13) and the Spanish Office for Scientific Research (Grant No. CTQ2011-27374). The SGI/IZO-SGIker UPV/EHU (supported by the National Program for the Promotion of Human Resources within the National Plan of Scientific Research, Development and Innovation—Fondo Social Europeo and MCyT) is gratefully acknowledged for generous allocation of computational resources. J.M.M. would like to thank the Spanish Ministry of Science and Innovation for funding through a Ramón y Cajal fellow position (Grant No. RYC 2008-03216). Financial support from REA-FP7-IRSES TEMM1P (GA 295172) is also acknowledged.