Electronic energy transfer through non-adiabatic vibrational-electronic resonance. II. 1D spectra for a dimer.

Vibrational-electronic resonance in photosynthetic pigment-protein complexes invalidates Förster's adiabatic framework for interpreting spectra and energy transfer, thus complicating determination of how the surrounding protein affects pigment properties. This paper considers the combined effects of vibrational-electronic resonance and inhomogeneous variations in the electronic excitation energies of pigments at different sites on absorption, emission, circular dichroism, and hole-burning spectra for a non-degenerate homodimer. The non-degenerate homodimer has identical pigments in different sites that generate differences in electronic energies, with parameters loosely based on bacteriochlorophyll a pigments in the Fenna-Matthews-Olson antenna protein. To explain the intensity borrowing, the excited state vibrational-electronic eigenvectors are discussed in terms of the vibrational basis localized on the individual pigments, as well as the correlated/anti-correlated vibrational basis delocalized over both pigments. Compared to those in the isolated pigment, vibrational satellites for the correlated vibration have the same frequency and precisely a factor of 2 intensity reduction through vibrational delocalization in both absorption and emission. Vibrational satellites for anti-correlated vibrations have their relaxed emission intensity reduced by over a factor 2 through vibrational and excitonic delocalization. In absorption, anti-correlated vibrational satellites borrow excitonic intensity but can be broadened away by the combination of vibronic resonance and site inhomogeneity; in parallel, their vibronically resonant excitonic partners are also broadened away. These considerations are consistent with photosynthetic antenna hole-burning spectra, where sharp vibrational and excitonic satellites are absent. Vibrational-excitonic resonance barely alters the inhomogeneously broadened linear absorption, emission, and circular dichroism spectra from those for a purely electronic excitonic coupling model. Energy transfer can leave excess energy behind as vibration on the electronic ground state of the donor, allowing vibrational relaxation on the donor's ground electronic state to make energy transfer permanent by removing excess energy from the excited electronic state of the dimer.