Full Microscopic Simulations Uncover Persistent Quantum Effects in Primary Photosynthesis

TL;DR

The nonperturbative, accurate microscopic model simulations of the Fenna-Matthews-Olson photosynthetic complex are reported and the presence of long-lived excitonic coherences at [Formula: see text] and room temperature is demonstrated, similar to those of excitation energy transfer.

Abstract

The presence of quantum effects in photosynthetic excitation energy transfer has been intensely debated over the past decade. Nonlinear spectroscopy cannot unambiguously distinguish coherent electronic dynamics from underdamped vibrational motion, and rigorous numerical simulations of realistic microscopic models have been intractable. Experimental studies supported by approximate numerical treatments that severely coarse-grain the vibrational environment have claimed the absence of long-lived quantum effects. Here, we report the first non-perturbative, accurate microscopic model simulations of the Fenna-Matthews-Olson photosynthetic complex and demonstrate the presence of long-lived excitonic coherences at 77 K and room temperature, which persist on picosecond time scales, similar to those of excitation energy transfer. Furthermore, we show that full microscopic simulations of nonlinear optical spectra are essential for identifying experimental evidence of quantum effects in photosynthesis, as approximate theoretical methods can misinterpret experimental data and potentially overlook quantum phenomena.

Figures (10)

• Figure 1: The Fenna-Matthews-Olson complex. (A) Crystal structure of the trimeric FMO complex from C. TepidumBermanNucleicAcidsRes2000TronrudPhotosynthRes2009FMOstructureSehnalNucleicAcidsRes2021. (B) Seven BChl a pigments in an FMO monomer, labeled by sites 1-7. (C) Population distributions of seven exciton states $\left|{E_k}\right\rangle$ in the site basis, with $\Delta_{jk}=|E_j - E_k|$ representing the energy gap between exciton states. The exciton delocalization is approximately visualized in (B). See the SM for more details.
• Figure 2: Electron-phonon coupling spectrum. The vibrational environments of the FMO complex are described by the sum of the phonon spectral density of intra-pigment vibrational normal modes, shown in blue, and that of protein modes, shown in orange. This experimentally measured FMO phonon spectral density RatsepJL2007 differs significantly from the coarse-grained phonon spectral density from Ref. DuanPNAS2017, shown in red. The energy differences $\Delta_{ij}=|E_i - E_j|$ between exciton states $\left|{E_i}\right\rangle$ and $\left|{E_j}\right\rangle$ are indicated by black arrows, satisfying $\Delta_{ij} \lesssim 500\,{\rm cm}^{-1}$ (see Fig. 1C). See the SM for more details.
• Figure 3: Numerically exact excitonic coherence dynamics. The real and imaginary parts of excitonic coherences $\langle E_i|\rho(t)|E_j\rangle$ are shown as functions of time $t$, where $\rho(t)$ denotes the reduced electronic density matrix. The results obtained using either the microscopic FMO or the coarse-grained phonon spectral density (SD) are shown in solid and dashed lines, respectively (see Fig. 2). Simulations were performed for the following cases: (A) $(i,j)=(1,2)$ at $77\,{\rm K}$, (B) $(i,j)=(3,6)$ at $77\,{\rm K}$, (C) $(i,j)=(1,2)$ at $300\,{\rm K}$, (D) $(i,j)=(3,6)$ at $300\,{\rm K}$. (E) The frequency spectra of the long-lived excitonic coherence dynamics shown in (B) and (D) over a time window $300\,{\rm fs}\le t \le 1\,{\rm ps}$ are presented, along with the frequency spectra of the bath correlation functions (BCFs) at $77\,{\rm K}$ and $300\,{\rm K}$.
• Figure 4: Long-lived excitonic coherences and their robustness against static disorder. The lifetimes of the large-amplitude oscillations with frequencies $\Delta_{ij}$ and the amplitudes of long-lived multi-frequency oscillations in the excitonic coherence dynamics $\langle E_i|\rho(t)|E_j\rangle$ are shown at (A) $77\,{\rm K}$ and (B) $300\,{\rm K}$. (C) The excitonic coherence dynamics $\langle E_3|\rho(t)|E_6\rangle$ between $\left|{E_3}\right\rangle$ and $\left|{E_6}\right\rangle$ at $77\,{\rm K}$, computed with four randomly generated sets of electronic parameters based on a Gaussian static disorder model, are shown. The coherence dynamics exhibit essentially identical high-frequency oscillations, as shown in the inset, obtained via a high-pass filter. (D) For the initial state $\left|{E_7}\right\rangle$, the population dynamics of $\left|{E_1}\right\rangle$ are present under three different phonon spectral densities (SDs): the microscopic FMO SD, and two model SDs in which high-frequency (HF) intra-pigment modes beyond $700\,{\rm cm}^{-1}$ are either omitted or coarse-grained. See the SM for more details.
• Figure 5: Numerically exact 2D electronic spectra. (A) The rephasing spectra of a heterodimer at $t_2=0$ are shown with $\gamma$ denoting the anti-diagonal width of a diagonal peak. (B) For the three peak positions marked in (A), the peak dynamics as functions of the waiting time $t_2$ are displayed. The correlation maps of (C) ground-state bleaching (GSB), (D) stimulated emission (SE), and (E) the total 2D signals (GSB+SE) are shown, computed based on the real parts of the long-lived oscillatory signals over a finite time window of $300\,{\rm fs}\le t_2 \le 1\,{\rm ps}$. In simulations, the microscopic FMO phonon spectral density at $77\,{\rm K}$ was considered (see Fig. 2). See the SM for more details.