Exact Test of the Adiabatic Approximation for Exciton–Phonon Interactions

The adiabatic approximation, used recently by Davydov to study the deformation of molecular crystals in the presence of electronic excitation, is examined with the aid of a numerically exactly soluble model of an exciton in a deformable dimer. This approximation, valid when the phonon energy is small compared to the exciton–phonon binding energy, gives a generally good upper bound on the ground state exciton energy for this model, but is insufficient to characterize exciton propagation. Delocalization of the exciton wavefunction in this approximation is not necessarily equivalent to free exciton motion but implies a weak exciton–phonon correlation.