Applications to crystals of naphthalene type

Consider, as an example, crystals of naphthalene type, C%h being the factor group and C the site group. Their characters are collected in Tables 2.1 and 2.2. 

Consider, for example, what happens with the state transforming according to the irreducible representation / = Asu9 of site group in the crystal. Using the formula (2.68) we obtain 

This means that each state which is transformed according to the irreducible representation Au of the site group is split in the crystal into two exciton states of symmetry corresponding to the factor group irreducible representations Au and Bu, respectively. Sometimes such splitting is named a factor group splitting. 

It follows also from the data of Table 2.1 that transitions to these exciton states are allowed transition to the state Afus for the polarization along the b-axis of the crystal, and transition to the state Blus for the in-plane polarization, where the plane is determined by vectors a and c. 

Now it is important to establish the relation between states in a site group and states in an isolated molecule. An isolated naphthalene molecule has the symmetry properties of group D211, which contains the group Ci as its subgroup. 

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