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

Abstract

The vibrational spectral density is an important physical parameter needed to describe both linear and non-linear spectra of multi-chromophore systems such as photosynthetic complexes. Low-temperature techniques such as hole burning (HB) and fluorescence line narrowing are commonly used to extract the spectral density for a given electronic transition from experimental data. We report here that the lineshape function formula reported by Hayes et al. [J. Phys. Chem. 98, 7337 (1994)] in the mean-phonon approximation and frequently applied to analyzing HB data contains inconsistencies in notation, leading to essentially incorrect expressions in cases of moderate and strong electron-phonon (el-ph) coupling strengths. A corrected lineshape function L(ω) is given that retains the computational and intuitive advantages of the expression of Hayes et al. [J. Phys. Chem. 98, 7337 (1994)]. Although the corrected lineshape function could be used in modeling studies of various optical spectra, we suggest that it is better to calculate the lineshape function numerically, without introducing the mean-phonon approximation. New theoretical fits of the P870 and P960 absorption bands and frequency-dependent resonant HB spectra of Rb. sphaeroides and Rps. viridis reaction centers are provided as examples to demonstrate the importance of correct lineshape expressions. Comparison with the previously determined el-ph coupling parameters [Johnson et al., J. Phys. Chem. 94, 5849 (1990); Lyle et al., ibid. 97, 6924 (1993); Reddy et al., ibid. 97, 6934 (1993)] is also provided. The new fits lead to modified el-ph coupling strengths and different frequencies of the special pair marker mode, ωsp, for Rb. sphaeroides that could be used in the future for more advanced calculations of absorption and HB spectra obtained for various bacterial reaction centers.

Exact simulation of pigment-protein complexes unveils vibronic renormalization of electronic parameters in ultrafast spectroscopy

“…Every underdamped intra-pigment mode contributes a Lorentzian of width γ k ~ 1 ps −1 , resulting in J ( ω ) = J l ( ω ) + J h ( ω ) where and the reorganization energy of the high-frequency modes is given by . The reorganization energy of the 55 intra-pigment modes of WSCP 13 (SP 15 ) is 660 cm −1 (379 cm −1 ), which is several times larger than that of quasi-continuous protein spectrum 58 , 61 and quasi-resonant intra-pigment modes with ω k ≈ Δ (see Supplementary Note 5) . The presence of underdamped vibrational modes can lead to long-lived correlations between electronic and vibrational degrees of freedom that make the rigorous numerical treatment of the ensuing vibronic dynamics very costly.…”

Exact Simulation of Pigment-Protein Complexes Unveils Vibronic Renormalization of Electronic Parameters in Ultrafast Spectroscopy

“…For SP heterodimers, it has been estimated that the difference in mean site energies is ε 1 − ε 2 = 315 cm −1 , electronic coupling is V = 625 cm −1 , and the angle between transition dipole moments of monomers [57] is 143 • . Experimentally estimated spectral density consists of a log-normal distribution function [68]…”

“…with S l = 1.7, σ l = 0.47, Ω l = 35 cm −1 , the special pair marker mode [68], modelled by vibrational frequency ω sp = 125 cm −1 , Huang-Rhys factor s sp = 1.5 and damping rate γ sp = 15 cm −1 , and 55 intra-pigment vibrational modes of BChla pigments [15] with vibrational frequencies and Huang-Rhys factors [13] summarised in Table II.…”

“…). We introduce an effective mode b = on experiments on excitonic systems [68], we multiply the renormalisation factor ∼ 1.9 to S l and s sp . Since the parameters in Table II were estimated based on experiments on BChla monomers [15], we do not renormalise the Huang-Rhys factors s k of the intra-pigment modes.…”

“…and the reorganisation energy of the high-frequency modes is given by λ h = ∞ 0 dωJ h (ω)/ω = 55 k=1 ω k s k . The values of the environmental parameters of WSCP [13,65] and SP [15,68] are summarised in section IV of the SI. The presence of underdamped vibrational modes can lead to long-lived correlations between electronic and vibrational degrees of freedom that make the rigorous numerical treatment of the ensuing vibronic dynamics very costly.…”