Natural orbitals for chemical valence as descriptors of chemical bonding in transition metal complexes

Natural orbitals for chemical valence (NOCV) are defined as the eigenvectors of the chemical valence operator defined by Nalewajski et al.; they decompose the deformation density (differential density, Delta rho) into diagonal contributions. NOCV were used in a description of the chemical bond between the organometallic fragment and the ligand in example transition-metal complexes: heme-CO ([FeN5C20H15]-CO), [Ni-diimine hydride]-ethylene ([(NN)-N-boolean AND-Ni-H]-C2H4, (NN)-N-boolean AND=-NH-CH-CH-NH-), and [Ni(NH3)(3)]-CO. DFT calculations were performed using gradient-corrected density functional theory (DFT) in the fragments resolution, using the fragment/ligand Kohn-Sham orbitals as a basis set in calculations for the whole fragment-ligand complex. It has been found that NOCV lead to a very compact description of the fragment-ligand bond, with only a few orbitals exhibiting non-zero eigenvalues. Results of NOCV analysis, compared with Mulliken populations analysis and Zigler-Rauk interaction-energy decomposition, demonstrate that the use of the natural valence orbitals allows for a separation of the sigma-donation and pi-back-donation contributions to the ligand-fragment bond. They can be also useful in comparison of these contributions in different complexes.