On the Shape of the Phonon Spectral Density in Photosynthetic Complexes

Abstract

We provide a critical assessment of typical phonon spectral densities, <i>J</i>(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. <i>J</i>(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 <i>J</i>(ω) obtained for several photosynthetic complexes, we argue that the shape of <i>J</i>(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 <i>J</i>(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 <i>J</i>(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 <i>J</i>(ω) function proposed in this work will be further tested in theoretical modeling of both time- and frequency-domain data