Frenkel excitons interacting with phonons

Energy eigenvalues of excitons interacting with optical phonons are calculated variationally both for the ground state and for the higher excited states. A perturbation expansion is employed by assuming the (renormalized) exciton transfer energy to be small compared to the energies of optical phonons. It is shown that the ’’unsymmetric narrowing’’ of the exciton bands due to interaction with phonons appears also in higher excited states in the exciton momentum representation. However, in the total (exciton plus phonon) momentum representation, each higher excited state energy band forms a scattering continuum which makes explicit ’’unsymmetricity’’ of the band narrowing indistinguishable. When exciton–phonon coupling is strong enough, exciton band energies lie outside the band of free exciton plus free phonon states. The criterion for this is J/ω<g2/[1+exp(−g2)], with J, ω, and g representing, respectively, half of the free exciton bandwidth, phonon frequency, and exciton–phonon coupling constant parameter.