NONRIGID SYMMETRY GROUPS OF MOLECULAR TRIMERS AND 3-ROTOR MOLECULES

A simple geometrical model is used to derive symmetry operators and symmetry groups for molecules with three internal rotors and for homomolecular and heteromolecular trimers. Operators are defined in terms of isometric substitutions and permutation-inversion operations. The non-rigid molecular symmetry groups were derived explicitly for molecules in which any of three internal rotors has one-, two-, or threefold periodicity. These groups are applicable also to molecular trimers in which none of the monomer units has molecular symmetry other than C-n, C-s, or C-nv (n less than or equal to 3). The symmetry groups are characterized as semidirect products and, where possible, by factorization into direct products. Among those which cannot be factored are two whose character tables are given, two which are already known, and a few for which no simple examples exist. Symmetry groups of molecules in which internal motions are restricted to concerted gearing or antigearing motions are derived for some examples but not investigated systematically.