Vibrational-electronic (vibronic) resonance and its possible role in energy and charge transfer have been experimentally and theoretically investigated in several photosynthetic proteins. Using a dimer modeled on a typical photosynthetic protein, we contrast the description of such excitons provided by an exact basis set description, as opposed to a basis set with reduced vibrational dimensionality. Using a reduced analytical description of the full Hamiltonian, we show that in the presence of vibrational excitation both on electronically excited as well as unexcited sites, constructive interference between such basis states causes vibronic coupling between excitons to become progressively stronger with increasing quanta of vibrational excitation. This effect leads to three distinguishing features of excitons coupled through a vibronic resonance, which are not captured in basis sets that restrict ground state vibrations: (1) the vibronic resonance criterion itself, (2) vibronically assisted perfect delocalization between sites even though purely electronic mixing between the sites is imperfect due to energetic disorder, and (3) the nuclear distortion accompanying vibronic excitons becoming increasingly larger for resonant vibronic coupling involving higher vibrational quanta. In terms of spectroscopically observable limitations of reduced basis set descriptions of vibronic resonance, several differences are seen in absorption and emission spectra but may be obscured on account of overwhelming line broadening. However, we show that several features such as vibronic exciton delocalization and vibrational distortions associated with electronic excitations, which ultimately dictate the excited state wavepacket motions and relaxation processes, are fundamentally not described by basis sets that restrict ground state vibrations.
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