How to test bond order methods for chemical consistency
Some of the bond order methods that claim to work do not give consistent results across different SZ values of a spin multiplet or different levels of theory (i.e., basis sets and exchange-correlation functionals). Consequently, there have been several published methods claimed to compute bond orders that do not work. Tests of this kind were performed in the article referenced below for the oxygen molecule in different spin states (singlet, triplet, and quintet) at different bond lengths and for different exchange-correlation approaches (e.g., DFT, CCSD, SAC-CI) and basis sets. For a fixed bond length and spin multiplet (e.g., triplet spin state at 200 pm bond length), the SZ=S and SZ=0 molecules are almost energy degenerate (except for a tiny spin-orbit coupling energy), have nearly identical electron density distributions, and therefore should have similar computed bond orders. However, many of the existing bond order methods fail this simple test for chemical consistency, because they give huge differences (1.5-2 bonds difference in some cases) between nearly chemical equivalent states.
see this article (open access): T. A. Manz, “Introducing DDEC6 atomic population analysis: part 3. Comprehensive method to compute bond orders,” RSC Advances, 7 (2017) 45552-45581 (open access) DOI: 10.1039/c7ra07400j
Additionally, one should require the bond order to work well for both molecular and periodic materials, including materials with localized bonding electrons (e.g., insulators or small molecules) as well as ones with highly delocalized bonding electrons (e.g., metallic conductors). A new bond order definition satisfying those properties was introduced in the article cited above.
As another test of bond order definitions, one could start with the smallest molecules (i.e., diatomic molecules) and ask for which bond order definitions have worked well enough to compute bond orders for a large number of diatomic bond orders. Only one quantum-mechanically computed bond order definition has ever been applied in a published systematic study of bond orders for a large number of diatomic molecules. See the article below:
T. Chen and T. A. Manz, “Bond orders of the diatomic molecules,” RSC Advances, 9 (2019) 17072-17092 (open access) DOI:10.1039/c9ra00974d