Theoretical analysis of bonding in N-heterocyclic carbene-rhodium complexes

The natural orbitals for chemical valence and the Ziegler-Rauk bond energy decomposition analysis were used to describe the donor/acceptor character of the N-heterocyclic carbenes (NHC)-metal bond in two groups of square-planar rhodium(I) complexes: (NHC)RhCl(cod) (1-X; cod = 1,5-cyclooctadiene) and (NHC)RhCl(CO)(2) (2-X), with a group X = H, Cl, NO(2), or CN located on the NHC ligand. The results show that the NHC-metal bond consists of the components originating from donation (sigma symmetry) and back-donation (two contributions of the pi symmetry, out-of-plane and in-plane, accompanied by one sigma-back-bonding component). The charge-flow measures from NOCV indicate that the total back-bonding contribution is of comparable importance to donation. The out-of-plane pi component contributes to ca. 50% of the total back-bonding charge-flow. The energy measures from the Ziegler-Rauk analysis show that the total back-bonding energy corresponds to ca. 40% of the orbital interaction energy. The ligand trans to NHC (CO or cod) strongly affects the back-bonding component; for the complexes 1-X, the back-donation is substantially enhanced compared to 2-X. The back-bonding component increases with an increase in the pi-withdrawing ability of X for both, 1-X and 2-X. However, this effect is relatively small. Back-bonding components of the two bonds involving the metal are strongly coupled; an increase in NHC-Rh leads to a decrease in Rh-olefin/CO(trans). The changes in the back-bonding are too small to be followed by the trends in bond energies, which are finally determined by the electrostatic and Pauli repulsion energy.