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Overcoming the Problem of Crown Ethers in Generating

Due to an overly-optimistic algorithm, AMG was not generating crown ethers properly. In fact it was missing out on a whole bunch of structures, but these particular ones are a good example:

The familiar structure is on the left, but the one on the right is the key to the problem that AMG had. Carbons are connected only to oxygens, and oxygens to carbons - in other words the molecule graph is elementally bipartite. Well, ok that's not really a phrase anyone uses - but it should be clear from the image.

The flaw in AMG's algorithm was (again) in failing to try disconnected structures. It is not obviously not possible to reach a (CO)n structure from a C-C bond, only from C.C - that is, from two disconnected carbons. Surprisingly, after a fruitless attempt to use partition refinement on the connected parts and then 'add back' the disconnected atoms it turned out that refinement works just great on disconnected structures.

So (for now) results for C3H6O3 and similar spaces appear to be working...


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[1] Common vertex matrix: A novel characterization of molecular graphs by counting
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