Symmetry, double point group, allowed

A partial character table of the point group D3h is given in Table 8.4. Find the missing characters of the vector and spinor representations of the double group D3h. Determine whether El transitions E-/ E3/2 and E./2 —> E5/2 are allowed in a weak crystal field of D3h symmetry. State the polarization of allowed transitions. 

The directions of transition moments in every chromophore are dictated by molecular symmetry. For the cis tautomers of porphycene ( 2 point group), only three mutually orthogonal transition moment directions are allowed. On the other hand, the trans form is of 2 symmetry and, therefore, any direction in the molecular plane is possible, as well as the direction perpendicular to the plane. The determination of transition moment directions in such low symmetry molecules is not an easy task. However, in the case of narcissistic type of reactions exemplified by trans-trans conversion in 1, one can take advantage of an additional symmetry element introduced by the tautomerization process. Double hydrogen transfer converts the molecule into its image, with the horizontal and vertical mirror symmetry planes perpendicular to the molecular plane (Fig. 8.13). Thus, tautomerization results in the rotation of each in-plane transition moment direction. The angle of rotation is twice the value of the angle formed by a particular transition moment with the horizontal (or vertical) in-plane axis. It can be shown [80] that, for a fast excited state process, which results in equal population of both trans tautomers, the measured fluorescence anisotropy r will be expressed by the formula ... 

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