Normal vibrations and Jahn-Teller effect for polymers and quasi-one-dimensional systems

Normal vibrational modes of all possible quasi-one-dimensional systems and polymers are classified according to the line-group symmetry. The results are used to discuss the vibronic instabilities for such systems and to establish the Jahn-Teller theorem. A general, but simple method, involving only one monomer, is developed to construct the normal displacements for the concrete polymers. As an illustration, it is verified that the symmetry arguments confirm the Jahn-Teller effect in trans-polyacetylene, resulting in dimerization with alternating bond lengths.