  Vibrational-electronic (vibronic) resonance and its role in energy and charge
transfer has 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 with reduced vibrational dimensionality -
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, 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 under reduced basis set descriptions
of vibronic resonance.
