On the Shape of the Phonon Spectral Density in Photosynthetic Complexes

We provide a critical assessment of typical phonon spectral densities, J(ω), used to describe linear and nonlinear optical spectra in photosynthetic complexes. Evaluation is based on a more careful comparison to experiment than has been provided in the past. J(ω) describes the frequency-dependent coupling of the system to the bath and is an important component in calculations of excitation energy transfer times. On the basis of the shape of experimental J(ω) obtained for several photosynthetic complexes, we argue that the shape of J(ω) strongly depends on the pigment-protein complex. We show that many densities (especially the Drude-Lorentz/constant damping Brownian oscillator) display qualitatively wrong behavior when compared to experiment. Because of divergence of J(ω) at zero frequency, the Brownian oscillator cannot fit a single-site spectrum correctly. It is proposed that a log-normal distribution can be used to fit experimental data and exhibits desired attributes for a physically meaningful phonon J(ω), in contrast to several commonly used spectral densities which exhibit low-frequency behavior in qualitative disagreement with experiment. We anticipate that the log-normal J(ω) function proposed in this work will be further tested in theoretical modeling of both time- and frequency-domain data.