The QTAIM approach to chemical bonding between transition metals and carbocyclic rings: a combined experimental and theoretical study of (η⁵-C₅H₅)Mn(CO)₃, (η⁶-C₆H₆)Cr(CO)₃, and (E)-{(η⁵-C₅H₄)CF=CF(η⁵- C₅H₄)}(η⁵-C₅H₅)₂Fe₂

Experimental charge densities for (C₅H₅)Mn(CO) ₃ (2), (η⁶-C₆H₆)Cr(CO) ₃ (3), and (E)-{(η⁵-C₅H₄)- CF=CF(η⁵-C₅H₄)}(η⁵-C₅H₅)₂Fe₂ (4) have been obtained by multipole refinement of high-resolution X-ray diffraction data at 100 K. The resultant densities were analyzed using the quantum theory of atoms in molecules (QTAIM). The electronic structures of these and related π-hydrocarbyl complexes have also been studied by ab initio density functional theory calculations, and a generally good agreement between theory and experiment with respect to the topological parameters was observed. The topological parameters indicate significant metal-ring covalency. A consistent area of disagreement concerns the topology of the metal-ring interactions. It is shown that because of the shared-shell bonding between the metal and the ring carbons, an annulus of very flat density ρ and very small ρ is formed, which leads to topologically unstable structures close to catastrophe points. This in turn leads to unpredictable numbers of metal-C bond paths for ring sizes greater than four and fewer M-C bond paths than expected on the basis of the formal hapticity. This topological instability is a general feature of metal-π-hydrocarbyl interactions and means that a localized approach based on individual M-C_ring bond paths does not provide a definitive picture of the chemical bonding in these systems. However, other QTAIM indicators, such as the virial paths, the delocalization indices, and the source function, clearly demonstrate that for the n-hapto (ηⁿ- C_nH _n)M unit, there is generally a very similar level of chemical bonding for all M-C_ring; interactions, as expected on the basis of chemical experience.