Exchange narrowing in circular and cylindrical molecular aggregates: degenerate versus nondegenerate states

We study the optical absorption line shape of circular and cylindrical molecular aggregates with static Gaussian diagonal and off-diagonal disorder. We focus on the weak-disorder situation and analyze the effect of exchange narrowing of the disorder due to exciton delocalization. In particular, we show that the absorption lines originating from pairs of states that are degenerate in the ordered aggregate (e.g., the k = +/-1 pair in rings) is always broader than the one originating from a nondegenerate state. If we only account for diagonal disorder, this difference amounts to a factor of root2. Moreover, in contrast to the nondegenerate case, the degenerate states give rise to a nonGaussian absorption profile that may even reflect its origin in two states through the emergence of a double-peak structure. The latter occurs if the off-diagonal disorder dominates and if the circumference of the ring or the cylinder is small enough (<8 molecules). (C) 2002 Elsevier Science B.V. All rights reserved.