Assigning bond orders

This last week I've been working off and on changing the way xyz2mol.py assigns bond orders. xyx2mol is an implementation of this paper and works by first assigning connectivity and then increasing the bond order between atoms with unsatisfied valences. As the article points out the outcome depends on the order you do it in.

For example, if you start by adding a double bond between atoms 6 and 7 in biphenyl (1), you don't get the right result. The authors propose to start by adding double bonds between atoms with the lowest connectivity, which works fine for biphenyl.

But Mads found an example (2) where that doesn't work. According to the rules you would add double bonds between 1-7, 3-4, and 8-9, which is not correct.

I solved this by finding the longest path of atoms unsatisfied valences (7-1-2-3-4-5-8-9) and then adding double bonds between alternate pairs. If there is an uneven number of such atoms you get different results depending on where you start, but that could probably be fixed by some ad-hoc rules. However, this approach fails for benzoquinone (3), where the longest path is 7-6-1-2-3-4-5. (Finding the longest path can also become intractable for many atoms)

The approach I have settled on so far, finds the maximum number of non-consecutive double bonds. So if you have 6 or 7 atoms with unsatisfied valence you can have a maximum of 3 non-consecutive double bonds. I find this combination by generating all combinations of three bonds and determining the one with the most different atoms (e.g. [(1,2), (3,4)] is better than  [(1,2), (2,3)]. This doesn't scale all that well when you're trying to place 10 or more double bonds, so if you have a better idea I'm all ears.

3.09.2018 update. Thanks to Geoff's suggestion the code now runs considerably faster

Assigning bond orders, whether in an aromatic structure or not, is a specific case of the maximal weighted matching graph algorithm. You can certainly come up with fast heuristics for certain kinds of structures, but IIRC scaling is ~N^3 in general

— Geoff Hutchison (@ghutchis) September 2, 2018

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