Charged Frenkel biexcitons in organic molecular crystals

It is known that the energy of the lowest electronic transition in neutral molecules of anthracene, tetracene and other polyacenes is blue shifted in comparison with the corresponding transition energy in mono-valent molecular ions. This effect in molecular crystal may be responsible for the attraction between molecular (Frenkel) exciton and charge carrier. Due to this attraction the bound state of Frenkel exciton and free charge (charged Frenkel exciton) may be formed. As we demonstrate below, the same mechanism can be responsible for formation of charged biexciton (bound state of two Frenkel excitons and a charge carrier). One-dimensional lattice model is used which corresponds to $J$-aggregates and is also a good approximation for quasi-one-dimensional crystals. Calculations are performed for molecular crystals like tetracene where at low temperature the exciton band is much narrower than that of the charge carrier.