Dissipation Pathways in a Photosynthetic Complex

TL;DR

The paper addresses how excitation energy dissipates in the Fenna-Matthews-Olson (FMO) complex by mapping contributions from the protein environment and intramolecular vibrations. It introduces MQME-D, a general fully quantum framework that embeds local bath degrees of freedom into chromophores and computes dissipation via second-order perturbation theory and Nakajima-Zwanzig projection, yielding mode-resolved dissipation through $\mathcal{J}_{BA}^{A}(\omega)$ and related quantities. Applying to a state-of-the-art FMO model with pigment-specific spectral densities, the results show energy dissipation is dominated by low-frequency modes $<800\ \mathrm{cm}^{-1}$, with the $\sim 200\ \mathrm{cm}^{-1}$ in-plane breathing mode of Bchls being the most important, while high-frequency modes $>800\ \mathrm{cm}^{-1}$ contribute negligibly; energy transfer is non-monotonic, with initial environmental energy absorption enabling uphill transfer. The approach enables disentangling environmental contributions with high accuracy, guiding design of artificial light-harvesting systems and offering a framework for environment engineering in chemical and quantum control tasks; code is available on GitHub.

Abstract

Determining how energy flows within and between molecules is crucial for understanding chemical reactions, material properties, and even vital processes such as photosynthesis. While the general principles of energy transfer are well established, elucidating the specific molecular pathways by which energy is funneled remains challenging as it requires tracking energy flow in complex molecular environments. Here, we demonstrate how photon excitation energy is partially dissipated in the light-harvesting Fenna-Matthews-Olson (FMO) complex, mediating the excitation energy transfer from light-harvesting chlorosomes to the photosynthetic reaction center in green sulfur bacteria. Specifically, we isolate the contribution of the protein and specific vibrational modes of the pigment molecules to the energy dynamics. For this, we introduce an efficient computational implementation of a recently proposed theory of dissipation pathways for open quantum systems. Using it and a state-of-the-art FMO model with highly structured and chromophore-specific spectral densities, we demonstrate that energy dissipation is dominated by low-frequency modes ($<$ 800 cm$^{-1}$) as their energy range is near-resonance with the energy gaps between electronic states of the pigments. We identify the most important mode for dissipation to be in-plane breathing modes ($\sim$200 cm$^{-1}$) of the bacteriochlorophylls in the complex. Conversely, far-detuned intramolecular vibrations with higher frequencies ($>$ 800 cm$^{-1}$) play no role in dissipation. Interestingly, the FMO complex first needs to borrow energy from the environment to release excess photonic energy, making the energy dissipation dynamics non-monotonic. Beyond their fundamental value, these insights can guide the development of artificial light-harvesting devices and, more broadly, engineer environments for chemical and quantum control tasks.

Figures (3)

• Figure 1: Dissipation pathways in the FMO complex. (a) Schematic illustration of the energy dynamics in the FMO complex. The Bacteriochlorophyll (Bchl) chromophores are labeled with bold numbers, and the intensity of the green (red) color indicates the amount of energy being dissipated (absorbed). (b) Scaled spectral density $J(\omega)/\omega$ for Bchl1 (light blue), Bchl2 (pink), Bchl3 (orange), and Bchl4 (purple). The baselines for Bchl3 and Bchl4 were vertically shifted for visual clarity. (c) Total dissipation as a function of the environmental frequency. (d) Site energies for Bchl1, Bchl2, Bchl3 and Bchl4. (e) Dissipation decomposition in terms of individual Bchl chromophores.
• Figure 2: Vibrational mode driving energy dissipation in the FMO complex. The figure shows the vibrational mode around 200 cm$^{-1}$ in Bchl3, crucial for energy dissipation. This mode is remarkably similar across all chromophores (see animations in the Supplementary Materials). The mode was extracted from molecular dynamics simulations as detailed in the Supplementary Information.
• Figure 3: Time-dependent energy dissipation in the FMO complex. The panels show the cumulative dissipation by environmental modes at different frequencies at selected times during the dynamics: (a) 40 fs, (b) 200 fs, (c) 600 fs, and the overall dissipation at (d) 5000 fs. The colored lines quantify the contributions of nuclear modes belonging to Bchl1 (light blue), Bchl2 (pink), Bchl3 (orange), and Bchl4 (purple). The green line quantifies the total dissipation. Note that negative values of the dissipation indicate energy absorption.