Frenkel excitons beyond the Heitler–London approximation

We consider Frenkel excitons in molecular crystals beyond the Heitler–London approximation (HLA). Beyond the HLA the wave function of the molecular crystal with one exciton contains states with several excited molecules. In this case the statistics of the molecular excitations becomes important. Thus, the boson approximation, frequently used to go beyond the HLA, needs to be corrected. We calculate the corrections to the HLA for Frenkel exciton energy and oscillator strength taking into account the exact statistics of molecular excitations. In these calculations we consider the crystals of general structure and beyond the two-level model, thus taking into account also the mixing of molecular configurations. For the model of a one-dimensional chain of two-level molecules and in the nearest-neighbor approximation our results coincide with the results found earlier by Bakalis and Knoester who used the Jordan–Wigner transformation from paulions to fermions. We show that for multilevel molecules the crystal Hamiltonian contains additional terms that give important contributions to the corrections for the Frenkel exciton energy.