Theory of exciton-phonon coupling in one-dimensional molecular crystals: A variational treatment with delocalized solitary states

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Abstract
A one-dimensional model of Frenkel excitons and dispersionless phonons interacting via a linear site-diagonal coupling term is investigated. We present a variational theory which is, for explicit calculations, reduced to two variational parameters characterizing the excitonic coherence properties as well as the extent of lattice distortion. It includes previous theories (phonon-dressed excitons and adiabatic solitary solutions) as limiting cases. The theory fully accounts for the translation symmetry and is applicable in the weak-coupling and the self-trapping regions of the physical parameter space as well as in the crossover regime. Energetic and spectroscopic properties of the full (k-dependent) phonon-free exciton band are calculated. Important results are the band deformation due to the interaction with multiphonon states of the same symmetry, the exciton dispersion, and strong variations of the intensities and the degree of localization within the exciton band.