GROUP-GEN: A PROGRAM FOR GENERATING MOLECULAR SYMMETRY GROUPS
Creators:Lehmann, K. K.
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Publisher:Ohio State University
Molecular symmetry, as formalized by group theory, is a power tool whose use in spectroscopy was pioneered by E.B. Wilson. For essentially any rigid molecule one is likely to encounter, the point group has been worked out, and the character table for the group can be found in standard references. As spectroscopy has been extended to weakly bound complexes, or to stable molecules but at energies where tunneling between equivalent equilibrium structures becomes possible, the point group provides an incomplete representation of the molecular symmetry. In these cases, the Molecular Symmetry group, first developed by Longuet-Higgins, contains the relevent dynamical symmetry. In applications of this method, one often finds that the molecular symmetry group for a particular problem has not been worked out, and one may be required to do rather laborious manipulations to work out the group, its class structure, and its character table. In this talk, I will describe a general program under development that will generate a molecular symmetry group (which is a sup-group of the full permutation-inversion group), given a list of `generators, The generators are elements of the group which define certain permutation inversion operations as `feasible'. After the smallest group that contains all the generators is found, the program finds the class structure of this group, the cycle structure, and the class multiplication table. At this point the program attempts to find as many of the irreducible representation as it can. The presently used algorithm is not certain to find all the irreducible representations, but it is hoped that this defect can be corrected before the conference. The program also generates a table with the reduced representations of all direct products.
Author Institution: Department of Chemistry, Princeton University
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