Selection function

[rapodaca]

Canonicalization requires an input molecule whose double bonds will not give rise to DIME. There should be a function that selects atoms such that the resulting molecule is incapable of DIME.

A thumbnail of the approach:

1. Find the set of all atoms (A) having just one double bond.
2. From A, build a set of connected subgraphs (S).
3. For each subgraph s in S, build a matching based on single/double bond pattern.
4. Perform a symmetric difference on s, demoting double bonds to single and promoting single bonds to double. If this operation does not place an atom at the vertex of two double bonds, it passes. Otherwise it fails.
5. Select all atoms for each passing subgraph s.

This avoids gratuitous selection in that heteroatoms without double bonds are excluded.

But it also avoids the selection of atoms whose connected subgraph can't possibly undergo DIME. For example, no atom in C1=C(C=CC=C1)1 would be selected using the above approach.

[rapodaca]

The algorithm as presented will fail for biphenyl ("C1=CC=CC=C1C1=CC=CC=C1") but it should succeed. The reason is that the bond between the phenyl groups will be toggled to eventually yield hypervalent terminals.

What's needed is an efficient way to detect DIME-capable systems. The minimum requirement is an alternating cyclic path. A start may be to devise a search for those.

[rapodaca]

Here's alternative selection algorithm:

1. Find the set of atoms belonging cycles (A) via walk.
2. Pick an atom from A (a) connected via a double bond.
3. Perform directed depth-first search from a to find the longest alternating cyclic path P. It may or may not end at a (e.g., loop).
4. Select the atoms along P.
5. Pick an unsuspected atom from A, go to (3).

[rapodaca]

The paper Kekulé structure enumeration yields unique SMILES appears to offer an approach:

... Only these edges are treated differently in the SMILES generation, which results in a slightly different but aromaticity-independent SMILES encoding. The new SMILES encoding is only encoding ambiguity information where needed and results in a general, unique molecule string encoding.