Bond orders between molecular fragments

An extension of the Mayer bond order for the interaction between molecular fragments is presented. This approach allows the classical chemical concepts of bond order and valence to be utilised for fragments and the interactions between the fragments and symmetry-adapted linear combinations to be analysed. For high-symmetry systems, the approach allows the contribution from each irreducible representation to be assessed and provides a semiquantitative measure of the role of each bonding mode to interfragment interactions. The utility of this tool has been examined by a study of the bonding in symmetrical sandwich complexes. The validity of the frontier-orbital approach and the contributions from each frontier-orbital interaction can also be assessed within this model. As demonstrated by a study of a number of mixed-sandwich complexes, the model proves to be especially useful for low-symmetry systems in which separation of the sigma, pi and delta roles in bonding of the ligand is difficult to assess. The fragment bond order describes the interaction between preoptimized fragment orbitals and is independent of the charges that are placed on these fragments. Although the method allows the chemist to define fragments in any way they choose, most insight is gained by using the same frontier orbitals employed so successfully in perturbational molecular-orbital approaches. The results are free from the influence of the electron-counting method used to describe fragments, such as the rings and metals in sandwich complexes.