Kinematic Frenkel gap biexciton in one-dimensional structures

We consider the role of kinematical exciton–exciton interaction in two-particle spectra of Frenkel excitons induced by their paulion nature. We demonstrate that, even if the dynamical exciton–exciton interaction is absent, in the 1D crystals with several molecules in the unit cell, the bound states of two excitons may be formed within a gap between the bands of two-particle states. Numerical analysis of dispersion relation for such gap biexcitons shows that these type of biexcitons have band’s width small compared with the band’s width of free two exciton states. We can expect that these states can give essential contribution into the resonant part of the nonlinear optical polarizability and two-photon absorption of 1D molecular aggregates.