Detailed analysis is done for the case of a single pseudo local phonon interacting with an electronic molecular transition and a phonon bath. Both the sudden-jump model and the master equation formalism predict a complex optical line shape for a single-molecule embedded in a solid matrix. In addition to the conventional Lorentzian, the line consists of a dispersive component in the core region and a side band. The sudden jump model is applicable only if the vibration-phonon coupling is independent of the electronic wave functions. However if the line wings are neglected, the sudden jump model can fit experimental data even when the condition of its applicability is not fulfilled. An interesting property of the complex line was found at strong excitation. In this case the line behaves in a fashion intermediate to the homogeneously and inhomogeneously broadened spectra. (C) 2001 American Institute of Physics.