Hapticity uncovered: real-space bonding indicators for zincocene chemistry

The connectivities (hapticities) of asymmetric cyclopentadienyl zinc compounds are determined by theoretically obtained real-space bonding descriptors. The methods employed herein include the determination of the number of virial paths and electron localizability indicator (ELI-D) basins exhibited between the central Zn atom and the atoms of the ring system. Metal-ring interactions are characterized by flat electron densities and small density gradients, which are related to the high fluxionality of the rings. Due to this, the structures are topologically unstable and the conventional bond-path analysis within the atoms in molecules (AIM) scheme, which in principle can also be applied for experimental electron densities reconstructed from high-resolution X-ray diffraction data, is not a reliable tool for the determination of the hapticity. As a consequence, the theoretical investigation of other real-space bonding descriptors is the necessary primary step for discovering bonding modes that can be applied to molecular geometries obtained by subsequent experiments. By this procedure the common geometrical interpretation of connectivities, which is based on rather arbitrary decisions, is complemented by a self-consistent method using electronic descriptors. Moreover, the two-center σ contributions of all possible bonding scenarios (η(1)-η(5)) were quantified by analyzing the electron populations of the Zn-C σ-bonding basins from the ELI-D analysis inside the AIM Zn atom in relation to the corresponding populations of the C-C π basins of the unsaturated rings. The investigation of the Zn-ring interactions is extended to the delocalization index, the source function, and a new type of electron-density-based surfaces, which we introduce here (ASF = aspherical stockholder fragments). They can be used for visualization of single atoms, fragments (e.g., functional groups), and whole molecules and are based on Hirshfeld's idea of stockholder partitioning, but apply aspherical electron densities. With these surfaces the charge accumulation between the chosen fragments and the steric accessibility of the central Zn atoms become visible, which is a useful tool for explaining and predicting chemical reactivity.