On the Shape of the Phonon Spectral Density in Photosynthetic Complexes

Abstract

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.

Comments on the optical lineshape function: Application to transient hole-burned spectra of bacterial reaction centers

“…This approach is compared below with the mean-phonon approximation used in earlier calculations, 8,9,28 where the spectral density was split into multiple effective phonon densities and the continuous weighting factor n(ω; T) was replaced by an effective factor n(ω k ; T) evaluated at a "mean" phonon frequency ω k near the peak of the kth phonon density; and where in place of numerical convolutions, multi-phonon transitions were described simply as increasingly broadened G-L profiles. We suggest that the approach with a lognormal spectral density describes the phonon lineshape more accurately, 25 although to reveal the difference between our approach and that of Hayes et al, 19 i.e., to compare our parameters with the previously published data, 8,9,28 we also show fits and parameters obtained with the G-L J(ω). On the basis of previous work, 8,9,28 only two profiles corresponding to peak frequencies ω ph and ω sp are required to simultaneously fit the P870 and P960 absorption bands and ω B -dependent photochemical (transient) HB spectra.…”

“…Figure 4 shows fits of the experimental data 8 assuming a lognormal distribution for J(ω). 25 While both functional forms of J(ω) (i.e., G-L and lognormal) fit the experimental data reasonably well, the advantages of the lognormal distribution (see Ref. 25) allow for more physically realistic parameters, including well-defined E λ , to be elucidated from simulations.…”

“…Based on the shape of experimental J(ω) obtained for several photosynthetic complexes, we showed that many J(ω) (especially the Drude-Lorentz/constant damping Brownian oscillator) display qualitatively wrong behavior when compared to experiment. 25 Therefore, we proposed that a lognormal distribution, which exhibits desired attributes for a physically meaningful phonon J(ω), should be used to fit experimental data, in contrast to several commonly used spectral densities which exhibit low frequency behavior in qualitative disagreement with experiment. We also demonstrated that the half-Gaussianhalf-Lorentzian (G-L) J(ω) used in modeling of HB spectra should be replaced with the lognormal function, which provides a more physically realistic fit of the high-energy side of experimental spectral densities (e.g., FMO and CP29).…”

“…We also demonstrated that the half-Gaussianhalf-Lorentzian (G-L) J(ω) used in modeling of HB spectra should be replaced with the lognormal function, which provides a more physically realistic fit of the high-energy side of experimental spectral densities (e.g., FMO and CP29). 25 The absence of the long Lorentzian tail in the lognormal function (that is present in G-L J(ω)) eliminates problems associated with continuously increasing reorganization energy E λ , which is not well defined since the integral does not converge for the Lorentzian. The lognormal form also solves problems with the zero frequency behavior of the constant damping Brownian oscillator J(ω), which contradicts experiment.…”

Scalable High-Performance Algorithm for the Simulation of Exciton Dynamics. Application to the Light-Harvesting Complex II in the Presence of Resonant Vibrational Modes

“…A careful measurement of the overall form of the spectral density is essential for the accurate modelling of light-harvesting complexes. 54,55 A coarse grained description of the transfer with a coupling to a continuum of phonon modes provides a good description of the transport provided that three criteria are fulfilled:…”