Semiclassical Modified Redfield and Generalized Förster Theories of Exciton Relaxation/Transfer in Light-Harvesting Complexes: The Quest for the Principle of Detailed Balance

Abstract

A conceptual problem of transfer theories that use a semiclassical description of the electron-vibrational coupling is the neglect of the correlation between momenta and coordinates of nuclei. In the Redfield theory of exciton relaxation, this neglect leads to a violation of the principle of detailed balance; equal “uphill” and “downhill” transfer rate constants are obtained. Here, we investigate how this result depends on nuclear reorganization effects, neglected in Redfield but taken into account in the modified Redfield theory. These reorganization effects, resulting from a partial localization of excited states, are found to promote a preferential “downhill” relaxation of excitation energy. However, for realistic spectral densities of light-harvesting antennae in photosynthesis, the reorganization effects are too small to compensate for the missing coordinate–momentum uncertainty. For weaker excitonic couplings as they occur between domains of strongly coupled pigments, we find the principle of detailed balance to be fulfilled in a semiclassical variant of the generalized Förster theory. A qualitatively correct description of the transfer is obtained with this theory at a significantly lower computational cost as with the quantum generalized Förster theory. Larger deviations between the two theories are expected for large energy gaps as they occur in complexes with chemically different pigments.

Explaining the Efficiency of Photosynthesis: Quantum Uncertainty or Classical Vibrations?

“…First, we discuss Redfield theory, whose classical limit according to previous studies does not correctly describe the energy funnel. 9,14,15 Second, we consider a mixed quantum−classical trajectory approach, which (as we demonstrate) is able to capture the energy funnel even though classical vibrational motion is treated explicitly with Newtonian equations of motion. We then compare the approximations behind the two strategies and discuss how to define a more appropriate classical limit of Redfield theory that is free from the previous problems.…”

“… 10 − 13 Here, we focus on the specific claim that quantum uncertainty between the nuclear positions and momenta is necessary to ensure the directed flow of energy after photoexcitation. 9 , 14 , 15 This conclusion is based on an interpretation of secular Redfield theory, 16 which is a commonly used theoretical tool for describing excitonic systems such as FMO. In this interpretation, certain contributions to the rate of excitonic population transfer are associated with quantum uncertainty between the nuclear coordinates and momenta, and it is argued that in the absence of these contributions, the energy funnel that is essential to light-harvesting systems breaks down.…”

“…The vibrational motion is responsible for site-energy fluctuations of the same order of magnitude as the energy gaps and is therefore clearly a crucial part of the energy-transfer mechanism irrespective of the importance of quantum-mechanical effects. The quantum nature of these vibrations and their relevance for efficient exciton energy transfer have been extensively discussed in the literature. − Here, we focus on the specific claim that quantum uncertainty between the nuclear positions and momenta is necessary to ensure the directed flow of energy after photoexcitation. ,, This conclusion is based on an interpretation of secular Redfield theory, which is a commonly used theoretical tool for describing excitonic systems such as FMO. In this interpretation, certain contributions to the rate of excitonic population transfer are associated with quantum uncertainty between the nuclear coordinates and momenta, and it is argued that in the absence of these contributions, the energy funnel that is essential to light-harvesting systems breaks down.…”

Robust Strategy for Photoprotection in the Light-Harvesting Antenna of Diatoms: A Molecular Dynamics Study

“…Depending on the pigment compositions and the coloring of the phenotype, photosynthetic organisms have been divided into the green and red lineages . There are a plethora of studies in the literature focused on the light-harvesting complexes of plants and bacteria; − however, computational studies on algae, or diatoms, and therefore significant insight into the physical chemistry are lacking.…”

The Relationship between the Spatial Arrangement of Pigments and Exciton Transition Moments in Photosynthetic Light-Harvesting Complexes

“…The core antenna of LH1-RC was characterized by the same as in the B850 location of the strongest in the center of the complex, which actually coincides with the RC. Further application of the generalized Förster theory [ 60 ] will make it possible to estimate the energy transfer rates between the peripheral antenna, core antenna, and the reaction centers.…”