Symmetry analysis of an impossible symmetry - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T18:27:59Z http://mathoverflow.net/feeds/question/118634 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/118634/symmetry-analysis-of-an-impossible-symmetry Symmetry analysis of an impossible symmetry Hauke Reddmann 2013-01-11T15:01:21Z 2013-01-11T15:01:21Z <p>I have a practical problem in chemistry. Consider a molecule MCp3 (Cp=C5H5) with the centroids of the Cp ring lying on an 60-60-60 triangle. The maximal symmetry you can get is C3h, because of the fivefold-axis Cp rings. (Orient one CH group into the centroid plane.) In praxis, though, the Cp rings rotate freely and the effective symmetry is D3h.</p> <p>Now there are the usual tools of vibrational analysis, giving for C3h that the normal vibrations are 16A'+14A''+16E'+12E'' (modulo my usual typos :-). I want to know how the 16A'+14A'' split into A1'+A2'+A1''+A2'', the irreps of the fictive D3h symmetry. This is impossible by normal means - e.g. the first step of a standard tool is to apply a symmetry operation on the atom set and count the trace of the operation matrix. But the symmetry operations aren't...</p> <p>I am quite sure that it is possible to work with half-integer characters and other abominations and in the end everything crosscancels and gives an answer that makes sense within the experimental data (which IS compatible with D3h).</p> <p>So my question: can you do representation analysis for objects with pseudo symmetry? (In this special case, it might be even doable this way: Compute the result for 4- and 6-rings, where D3h is a valid symmetry, and do the mean. :-)</p>