Influence of exciton–exciton interaction on one-to-two exciton transitions in molecular aggregates with linear and circular geometries

One- to two-exciton transitions have been examined in molecular aggregates with linear and circular geometries at various strengths of the exciton–exciton interaction. For the interaction parameter a sufficiently different from its critical value acrit=1, the exciton–exciton interaction has been shown to have little influence on the transition dipole moments, as well as on the corresponding transition energies between the one-exciton states and the dissociated two-exciton states. The interaction between the excitons then may be represented in an effective manner by the replacement of the actual number N of molecules per aggregate by a nearby effective number Neff, the latter being a-dependent. Hence, inclusion of the exciton–exciton coupling does not affect substantially the previous analysis of one- to two-exciton transitions based on the model of noninteracting one-dimensional excitons. That is, effects such as the blue shift of the excited-state absorption and the enhancement of nonlinear susceptibilities are not sensitive to the exciton–exciton interaction. These findings are relevant, inter alia, to J-aggregates in which there is no evidence for the coupling parameter a to be in the critical region or beyond. On the other hand, for the critical value of the exciton–exciton interaction (a=acrit), the blue shift is either totally absent in the excited-state absorption, or extremely small compared with the ordinary case. The above is in full agreement with earlier calculation of the pump–probe spectrum showing a weak dependence on the exciton–exciton interaction for a<1, as well as a strong bleaching of the exciton band in the critical region.