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 (<i>E</i>)-{(η⁵-C₅H₄)CFCF(η⁵-C₅H₄)}(η⁵-C₅H₅)₂Fe₂

Abstract

Experimental charge densities for (C₅H₅)Mn(CO)₃ (<b>2</b>), (η⁶-C₆H₆)Cr(CO)₃ (<b>3</b>), and (<i>E</i>)-{(η⁵-C₅H₄)CFCF(η⁵-C₅H₄)}(η⁵-C₅H₅)₂Fe₂ (<b>4</b>) 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 <i>n</i>-hapto (η^<i>n</i>-C_<i>n</i>H_<i>n</i>)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.