Symmetry decomposition of quantum chemical bond orders

Two schemes based on atomic orbital symmetry for the decomposition of Mayer, BAB, and Wiberg, WAB, bond order indices into the σ-, π-, and δ-components (AOSB-A) or into the “in-plane” and “out-of-plane”-components (AOSB-P) are proposed. The AOSB-A approach is based on the sorting of the A and B atoms atomic orbitals according to their symmetry relative to the line of A-B bonding, the AOSB-P scheme uses AO sorting relative to the plane of molecule or fragment. The AOSB technique was applied to a wide range of species including organic molecules, inorganic molecules of main group elements, transition metal complexes and complexes with multiple metal-metal bond.