Both electronic and vibrational coherences are involved in primary electron transfer in bacterial reaction center

Understanding the mechanism behind the near-unity efficiency of primary electron transfer in reaction centers is essential for designing performance-enhanced artificial solar conversion systems to fulfill mankind’s growing demands for energy. One of the most important challenges is distinguishing electronic and vibrational coherence and establishing their respective roles during charge separation. In this work we apply two-dimensional electronic spectroscopy to three structurally-modified reaction centers from the purple bacterium Rhodobacter sphaeroides with different primary electron transfer rates. By comparing dynamics and quantum beats, we reveal that an electronic coherence with dephasing lifetime of ~190 fs connects the initial excited state, P*, and the charge-transfer intermediate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}PA+PB-; this \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ \ast \to {\mathrm{P}}_{\mathrm{A}}^ + {\mathrm{P}}_{\mathrm{B}}^ -$$\end{document}P*→PA+PB- step is associated with a long-lived quasi-resonant vibrational coherence; and another vibrational coherence is associated with stabilizing the primary photoproduct, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{P}}^ + {\mathrm{B}}_{\mathrm{A}}^ -$$\end{document}P+BA-. The results show that both electronic and vibrational coherences are involved in primary electron transfer process and they correlate with the super-high efficiency.


Supplementary Note 3
In order to prove that the charge recombination, the backward electron transfer of is responsible for the (B, P) cross peak, we employed kinetic modeling with a reversible reaction. This model did not include a real physical process, but focused on population dynamics and gave a direct view of the dependence of the cross peak amplitude on the reaction rate.
The kinetic model is , with C and D corresponded to P*/P A + P B − (because P*→P + B A − is much faster than the succedent process, P A + P B −  P + B A − , we treated P* and P A + P B − as the same component) and P + B A − , respectively. The rate equations were:

Supplementary Note 5
At room temperature, the QBs at the (P*, P A + P B − ) cross peak exhibited similar feature as that at 77 K (Supplementary Figure 7): short-lived high-amplitude oscillation followed by long-lived lower-amplitude oscillation. The short-lived high-amplitude ones reflect electronic coherence 2 , so formation of the initial CT state, P A + P B − , from P* is a coherent charge separation process, independent on the temperature. However, it is notable that the oscillation periods were different for the two cases. It was ~190 fs/193 cm −1 for 77 K while ~285 fs/129 cm −1 for room temperature. We speculated that the difference arose from the temperature dependence of the energy level of It is notable that there was an explicit below-diagonal cross peak in the -115 cm −1 frequency map around (860, 910) nm. It was near the (P*, P A + P B − ) cross-peak location determined via global analysis, (880, 910) nm (the cross in Supplementary Figure 8).
The 20-nm shift along the λ τ coordinate may reflect the involvement of higher exciton state of P. The appearance of this cross peak indicated that the excited-state vibrational mode with 115 cm −1 frequency was associated with the formation of For M2, the 151 cm −1 frequency maps consisted of a main component of diagonal P S11 peak, a minor component of diagonal B peak and a cross peak around (B, P) position.
The 30 cm −1 frequency maps contained the same components, but the proportion of B was much higher. The B-related vibrational modes may originate from direct excitation of B or from the backward reaction of electron transfer from P* to B A .
They were assigned to vibrational coherences, however, due to the complexity, it is difficult to distinguish between ground and excited states.
For M3, the -115 and -151 cm −1 frequency maps were dominated by diagonal P peak, while the +115 and +151 cm −1 ones consisted of diagonal P and a cross peak around (B, P) position. They were also assigned to vibrational coherences.
The vibrational coherences of B, although cannot be distinguished between ground and excited states, are more possibly on the ground state. Because they appeared in M2 and M3 where the primary ET rates are slower (260 and 25 ps, respectively).
During the period of population time (0-2 ps) used to calculate these frequency maps, most B remained on the ground state.