Structure, Group Theory and Spectroscopic

Let us consider as example PHTh in the anti-coplanar-centrosym-metric structure with the alkyl side chains in the all transplanar conformation and lying in the plane of the Th rinqs. In such a model the translational repeat unit in the 1-d crystal contains two Th rings as in fig. 13 Similar considerations can be made for POTh. 

With such a structure the factor group of the 1-d crystal is isomorphous to the 02 point group. Since N = 50 are the masses in the repeating unit, 3N-4 =146 are the optical q=0 phonons expected in the IR/Raman spectra and 150 are the phonon dispersion branches V(q). The structure of the irreducible representation for q=0 phonons is the following  

From the above group theory treatment we would expect to observe an extremely complicated spectrum, but in reality the observed spectra are extremely simple. The following theoretical consid- 

V) The normal modes of the side chains in the all-trans structure can be better identified when the band progressions of the q O phonons are considered [5-7]. We expect, in principle, to find the well known and characteristic band progressions for the CH2 wagging-twisting (very weak) (1400-1200 cm ) and CH2 rocking modes (1100-700 cm ) [35]. The band progression of the C-C stretching modes should 

If the anti-coplanar -non centrosymmetric structure of PHTh is considered the point group is and the structure of the irreducible representation is the following  

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