Resonance energy transfer: Spectral overlap, efficiency, and direction

The efficiency and directedness of resonance energy transfer, by means of which electronic excitation passes between molecular units or subunits, fundamentally depend on the spectral features of donor and acceptor components. In particular, the flow of energy between chromophores in complex energy harvesting materials is crucially dependent on a spectral overlap integral reflecting the relative positioning and shapes of the absorption and fluorescence bands. In this paper, analytical results for this integral are derived for bands of Gaussian and log normal line shape; the methods also prove applicable to double Gaussian curves under suitable conditions. Underlying principles have been ascertained through further development of theory, with physically reasonable assumptions. Consideration of the Gaussian case, widely applicable to spectra of symmetric form, reveals that the directional efficiency of energy transfer depends equally on a frequency shift characterizing the spectroscopic gradient and the Stokes shift. On application to tryptophan residues, calculations based on a minimal parameter set give excellent agreement with experiment. Finally, an illustrative application highlights the critical role that the spectroscopic gradient and Stokes shift can exercise in extended, multichromophore energy harvesting systems.