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I am engaged in the field of quantum-chemical calculations using programs written by myself. I have found out that I have a problem in finding the point group symmetry of the molecule. The first idea that came up was to determine the possible symmetry elements by transforming the object in space by symmetry operations and testing if system coincides with itself. This way is time consuming, because finding the axes and planes of symmetry requires a very large number of comparisons. And if the system is large, it takes a long time. The second way is to use the Z-matrix. But I don’t have any idea what to start with in this direction. I don’t want to reinvent everything, if it has already been invented and checked. I'm from Ukraine, so I apologize for my English. If something is incomprehensible: please ask to repeat.

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I think you'll find better answers on math.stackexchange.com instead of here. –  Steve B Jul 10 '12 at 3:15
    
Are you trying to write a computer program to find the symmetry automatically? Or are the comparisons being done by a person? And just how big are these molecules? –  Carl Brannen Jul 10 '12 at 9:43
    
It seems to me that the right way of doing this as a computer program is to check for the big global symmetries first, i.e. does the molecule have a center of symmetry. Then work towards the lesser symmetries. –  Carl Brannen Jul 10 '12 at 9:46
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No way is this appropriate for Programmers. Since the question is asking for an algorithm, it may be appropriate on Computational Science, but I'm thinking it's perhaps off topic here. –  David Z Jul 10 '12 at 20:52
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MuKeP, please don't use edits to respond to comments. You are able to comment on your own question. –  David Z Jul 10 '12 at 20:53
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1 Answer

Work out the matrix of distances of the atoms, and then apply a graph isomorphism algorithm for the complete undirected graph whose vertices are lavbelled with atom types and whose edges are labelled with the distances.

An entry point to the graph isomorphism problem is http://www.cs.sunysb.edu/~algorith/implement/nauty/implement.shtml

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