We all learned about single vs double vs triple bonds in high school chemistry and biology. We learned that unsaturated fats have double bonds whereas saturated fats have only single bonds, which makes unsaturated fats liquid (vs. solid) and easier to break/process by the body.
I was impressed when this Stack Exchange first went live though, to learn about the existence of about a dozen different definitions of bond order.
I wonder if/how these have led to useful insights such as the textbook example I gave in the first paragraph of this question?
I can imagine studying some large un-studied molecule in which the bond orders are not known. Once I have an approximation of the wavefunction, I can calculate one of the many types of bond orders mentioned in the aforementioned question (such as the Wiberg bond index explained here, which only needs the orbital coefficients from the LCAO model of a wavefunction); or if I have calculated the electron density, I can use one of the many techniques of "conceptual DFT" from the QTAIM framework or extensions, such as in this answer. But the existence of so many of these bond-order definitions, suggests that the very simple-to-calculate Wiberg bond index is not accurate enough for some people's liking (hence the need to formulate more complicated bond-order definitions).
- If we wish to know the length of a bond and we are using some advanced wavefunction-based or DFT software, I suppose that we would just do geometry optimization in our quantum chemistry software anyway, which would give us an even better description of the bond lengths than some "heuristic" method such as assigning a bond-order.
- If we wish to know the strength of a bond (remembering Tyberius's famous question from 3 years ago) we could just calculate the force constant for a particular bond, as MSwart said in this answer. This may add a bit to the cost of the quantum chemistry calculation, compared to just using a simple formula like the Wiberg bond-order formula, but probably not more than all of the other painful effort that goes into doing a quantum chemistry calculation (e.g. preparing a ZMAT/XYZ file, doing geometry optimization, converging an SCF, converging with respect to basis set and correlation-treatment, accounting for relativity and Born-Oppenheimer breakdown, etc.), and it seems it would be much more accurate (clearly the Wiberg formula is too simple because so many more sophisticated bond-order methods have been devised afterwards).
- I appreciate that we might want to draw the chemical structure with all its single and double bonds, but the desire to do this hinges on the bond-order actually being truly useful, which wouldn't seem to always be the case with, for example, the Wiberg bond-order which seems to have needed added levels of seemingly un-ending further sophistication in dozens of subsequent papers.
"Of course you could also compute the intrinsic force constant for that particular bond, with all kind of ifs and buts. But that would be opening up a whole new discussion."
Perhaps we can now have that discussion.