Journal of Molecular Modeling

, Volume 13, Issue 2, pp 347–355 | Cite as

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

  • Mariusz Mitoraj
  • Artur MichalakEmail author
Original paper


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, Δρ) 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 ([N^N–Ni–H]–C2H4, N^N = –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 σ-donation and π-back-donation contributions to the ligand–fragment bond. They can be also useful in comparison of these contributions in different complexes.


The countours of the deformation density (Δρ) and the donation/back-donation contributions from the pairs of complementary natural orbitals for the heme/CO system


Natural orbitals for chemical valence Chemical bond—bonding in transition Metal complexes σ-donation/π-back-donation Dewar–Chatt–Duncanson model 



This work was supported by a research grant from the Ministry of Education and Science in Poland (1130-T09-2005-28).


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Theoretical Chemistry, Faculty of ChemistryJagiellonian UniversityCracowPoland

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