Molecular symmetry

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Abstract
Molecular symmetry of Completely Non-Rigid (CNR) molecular models is investigated using the concept of the isometric group. The CNR model is based on a systematic labelling of nuclei in a molecular graph and uses 3K — 6 finite internal coordinates to describe internal motions, that is it contains neither infinitesimal nor frozen internal degrees of freedom. An alternative method of deriving isometric substitutions allows straightforward application of the isometric group concept to CNR models. A relationship between the symmetry groups of CNR models and those of models with restricted internal coordinates is derived. These new methods are demonstrated for various coordinate sets of X 2 Y 4 molecules. It follows from these examples that internal symmetry (for example, internal coordinates or cartesian coordinates in a molecule-fixed axis system) is to some extent dependent on the actual choice of internal coordinates whereas the external symmetry (for example, the permutation-inversion group) is determined by the symmetry of the molecular graph.