Frenkel Exciton Selection Rules for k≠0 Transitions in Molecular Crystals

Three types of dipole selection rules are proved for k≠0 in a restricted Frenkel exciton limit. They are: (1) Δk=0; (2) general selection rules based on interchange symmetry; and (3) the g↔u selection rule for centrosymmetric crystals. Even though the latter two selection rules are generally valid only for special values of k, and in particular for k=0, they can be shown to be valid for all k in crystals where restrictions are placed on the magnitude of interactions between certain translationally equivalent molecules. For benzene and naphthalene, and probably for many other organic crystals, the translationally equivalent interactions that ruin the selection rules are nonnearest neighbors. Evidence suggests these in some cases are small, in which event the selection rules are excellent approximations. It is also shown that the transition matrix element in this restricted Frenkel limit is k-independent, a fact that is important in analyzing the intensity distribution of band←band transitions in terms of the density-of-states function. Inability to detect a u←u, band←band transition in crystalline benzene is consistent with the theoretical results.