There is a new module and package for the CDK that is currently under review. This is a short guide to how to use it - to help both reviewers and users.
The basic idea is that molecules can be considered as a kind of graph, and that one useful thing to calculate about such graphs is the automorphism group that preserves element labels and/or bond labels. To put it another way, calculating the symmetries of the molecule - although I should point out that it's not quite the same as the crystallographic symmetry groups.
As a simple example, consider these two molecules (1,4-cylohexadiene and 4h-pyran) :
They are numbered from 0-5 for programming convenience; on the right each molecule has a table of automorphisms written as permutations in cycle notation. It should be fairly obvious that - for example - the H-Flip sends atom 0 to atom 4, 1 to 3, and fixes 2 and 5. Only the H-Flip is an automorphism for 4h-pyran, due to the oxygen atom.
The code to do this is fairly short and really just involves creating an AtomDiscretePartitionRefiner and then calling the getAutomorphismGroup(IAtomContainer) method. This returns a PermutationGroup which stores the automorphisms. What you do with them then is up to you...
There is a corresponding class to find automorphisms of the bonds of an atom container. This may be less useful, but here is napthalene as an example:
Note that the bonds are numbered, not the atoms; also the two different double-bond arrangements are called a and b for reference. The a form has only the V-Flip automorphism that swaps bonds (1, 2), (3, 10) and so on.
Finally, what are the actual uses in chemistry for this? Well, one possibility is external symmetry numbers (interesting reference, actually) - as also mentioned in this post. Another is molecule generation; it's used heavily in AMG. A future possibility might also be using it in CIP or other chirality code.
The basic idea is that molecules can be considered as a kind of graph, and that one useful thing to calculate about such graphs is the automorphism group that preserves element labels and/or bond labels. To put it another way, calculating the symmetries of the molecule - although I should point out that it's not quite the same as the crystallographic symmetry groups.
As a simple example, consider these two molecules (1,4-cylohexadiene and 4h-pyran) :
They are numbered from 0-5 for programming convenience; on the right each molecule has a table of automorphisms written as permutations in cycle notation. It should be fairly obvious that - for example - the H-Flip sends atom 0 to atom 4, 1 to 3, and fixes 2 and 5. Only the H-Flip is an automorphism for 4h-pyran, due to the oxygen atom.
The code to do this is fairly short and really just involves creating an AtomDiscretePartitionRefiner and then calling the getAutomorphismGroup(IAtomContainer) method. This returns a PermutationGroup which stores the automorphisms. What you do with them then is up to you...
There is a corresponding class to find automorphisms of the bonds of an atom container. This may be less useful, but here is napthalene as an example:
Finally, what are the actual uses in chemistry for this? Well, one possibility is external symmetry numbers (interesting reference, actually) - as also mentioned in this post. Another is molecule generation; it's used heavily in AMG. A future possibility might also be using it in CIP or other chirality code.
Comments
Anyway, it was :
"Good point, Patrik - one of the strengths of the CDK is that it has multiple solutions. It's also one of the weaknesses!
There was also an ancient branch that had a class to find the symmetries from the 3D structure, that could be integrated somehow. It's a little difficult to make packages written by different authors to work neatly together without making large changes. Some sort of interface, perhaps... "