![]() The proposed explanation was that the antenna protein holding the pigments somehow preserves electronic coherence. 12 The first 2D study reporting these oscillations 11 raised the puzzle that they had an amplitude too strong for the Franck-Condon excitation of vibrations in the isolated pigments but a decay time significantly longer than usual for electronic coherence in the condensed phase. 10 Over the last several years, experiments on photosynthetic antennas 11–15 and reaction centers 16,17 using femtosecond two-dimensional (2D) electronic spectroscopy 18 have revealed that energy transfer in these systems is associated with oscillations in 2D peak amplitude, shape, and phase which last for picoseconds. 8,9 In this regime, a pioneering paper by Womick and Moran showed that vibrational-excitonic resonance can allow energetic disorder to assist energy transfer and increase the energy transfer rate by an order of magnitude. Much of photosynthetic energy transfer takes place in Förster’s “intermediate coupling” regime, 7 which has presented a modeling challenge. A partial trace analysis shows that vibronic decoherence for a vibrational-excitonic resonance between two excitons is slower than their purely excitonic decoherence. Diabatic criteria for vibrational-excitonic resonance demonstrate that anti-correlated vibrations increase the range and speed of vibronically resonant energy transfer (the Golden Rule rate is a factor of 2 faster). With exchange symmetry, the correlation and tuning vectors become delocalized intramolecular vibrations that are symmetric and antisymmetric under pigment exchange. For equal pigment vibrational frequencies, the nonadiabatic tuning vector becomes an anti-correlated delocalized linear combination of intramolecular vibrations of the two pigments, and the nonadiabatic energy transfer dynamics become separable. The correlation and tuning vectors are not always orthogonal, and both can be asymmetric under pigment exchange, which affects energy transfer. ![]() Excitonic coupling modifies the tuning vector. Optical decoherence between the ground and singly excited states involves linear combinations of the correlation and tuning vectors. ![]() A correlation vector is connected to decoherence between the ground state and the doubly excited state. For this generalized dimer model, the vibrational tuning vector that drives energy transfer is derived and connected to decoherence between singly excited states. Here, a generalized dimer model incorporates asymmetries between pigments, coupling to the environment, and the doubly excited state relevant for nonlinear spectroscopy. Non-adiabatic vibrational-electronic resonance in the excited electronic states of natural photosynthetic antennas drastically alters the adiabatic framework, in which electronic energy transfer has been conventionally studied, and suggests the possibility of exploiting non-adiabatic dynamics for directed energy transfer.
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