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

Stabilization of Charge-Transfer Excited States in Biological Systems: A Computational Focus on the Special Pair in Photosystem II Reaction Centers

Charge-transfer (CT) excited states play an important role in many biological processes. However, many computational approaches often inadequately address the equilibration effects of nuclear and environmental degrees of freedom on these states. One prominent example of systems in which CT states are of utmost importance is reaction centers (RC) in photosystems. Here we use a multiscale approach combined with time-dependent density functional theory to explore the lowest CT excited state of the special pair PD1-PD2 in the Photosystem II-RC of a cyanobacterium. We find that the nonequilibrium CT excited state resides near the Soret band, making an exciton the lowest-energy excited state. However, accounting for nuclear and state-specific dielectric equilibration along the CT potential energy surface (PES), the CT state PD1--PD2+ stabilizes energetically below the excitonic state. This underscores the crucial role of state-specific solvation in mapping the PES of CT states, as demonstrated in a simplified dimer model.

Exciton dynamics from the mapping approach to surface hopping: comparison with Förster and Redfield theories

We compare the recently introduced multi-state mapping approach to surface hopping (MASH) with the Förster and Redfield theories of excitation energy transfer. Whereas Förster theory relies on weak coupling between chromophores, and Redfield theory assumes the electronic excitations to be weakly coupled to fast chromophore vibrations, MASH is free from any perturbative or Markovian approximations. We illustrate this with an example application to the rate of energy transfer in a Frenkel-exciton dimer, showing that MASH interpolates correctly between the opposing regimes in which the Förster and Redfield results are reliable. We then compare the three methods for a realistic model of the Fenna-Matthews-Olson complex with a structured vibrational spectral density and static disorder in the excitation energies. In this case there are no exact results for comparison so we use MASH to assess the validity of Förster and Redfield theories. We find that Förster theory is the more accurate of the two on the picosecond timescale, as has been shown previously for a simpler model of this particular light-harvesting complex. We also explore various ways to sample the initial electronic state in MASH and find that they all give very similar results for exciton dynamics.

Gaussian Decomposition vs. Semiclassical Quantum Simulation: Obtaining the High-Order Derivatives of a Spectrum in the Case of Photosynthetic Pigment Optical Properties Studying

In this paper, a procedure for obtaining undistorted high derivatives (up to the eighth order) of the optical absorption spectra of biomolecule pigments has been developed. To assess the effectiveness of the procedure, the theoretical spectra of bacteriochlorophyll a, chlorophyll a, spheroidene, and spheroidenone were simulated by fitting the experimental spectra using the differential evolution algorithm. The experimental spectra were also approximated using sets of Gaussians to calculate the model absorption spectra. Theoretical and model spectra can be differentiated without smoothing (high-frequency noise filtering) to obtain high derivatives. Superimposition of the noise track on the model spectra allows us to obtain test spectra similar to the experimental ones. Comparison of the high derivatives of the model spectra with those of the test spectra allows us to find the optimal parameters of the filter, the application of which leads to minimal differences between the high derivatives of the model and test spectra. For all four studied pigments, it was shown that smoothing the experimental spectra with optimal filters makes it possible to obtain the eighth derivatives of the experimental spectra, which were close to the eighth derivatives of their theoretical spectra.

Unravelling the Roles of Integral Polypeptides in Excitation Energy Transfer of Photosynthetic RC-LH1 Supercomplexes

Elucidating the photosynthetic processes that occur within the reaction center-light-harvesting 1 (RC-LH1) supercomplexes from purple bacteria is crucial for uncovering the assembly and functional mechanisms of natural photosynthetic systems and underpinning the development of artificial photosynthesis. Here, we examined excitation energy transfer of various RC-LH1 supercomplexes of Rhodobacter sphaeroides using transient absorption spectroscopy, coupled with lifetime density analysis, and studied the roles of the integral transmembrane polypeptides, PufX and PufY, in energy transfer within the RC-LH1 core complex. Our results show that the absence of PufX increases both the LH1 → RC excitation energy transfer lifetime and distribution due to the role of PufX in defining the interaction and orientation of the RC within the LH1 ring. While the absence of PufY leads to the conformational shift of several LH1 subunits toward the RC, it does not result in a marked change in the excitation energy transfer lifetime.

Dynamics of an excitation-transfer trimer: Interference, coherence, Berry's phase development, and vibrational control of non-adiabaticity

We detail several interesting features in the dynamics of an equilaterally shaped electronic excitation-transfer (EET) trimer with distance-dependent intermonomer excitation-transfer couplings. In the absence of electronic-vibrational coupling, symmetric and antisymmetric superpositions of two single-monomer excitations are shown to exhibit purely constructive, oscillatory, and purely destructive interference in the EET to the third monomer, respectively. In the former case, the transfer is modulated by motion in the symmetrical framework-expansion vibration induced by the Franck-Condon excitation. Distortions in the shape of the triangular framework degrade that coherent EET while activating excitation transfer in the latter case of an antisymmetric initial state. In its symmetrical configuration, two of the three single-exciton states of the trimer are degenerate. This degeneracy is broken by the Jahn-Teller-active framework distortions. The calculations illustrate closed, approximately circular pseudo-rotational wave-packet dynamics on both the lower and the upper adiabatic potential energy surfaces of the degenerate manifold, which lead to the acquisition after one cycle of physically meaningful geometric (Berry) phases of π. Another manifestation of Berry-phase development is seen in the evolution of the vibrational probability density of a wave packet on the lower Jahn-Teller adiabatic potential comprising a superposition of clockwise and counterclockwise circular motions. The circular pseudo-rotation on the upper cone is shown to stabilize the adiabatic electronic state against non-adiabatic internal conversion via the conical intersection, a dynamical process analogous to Slonczewski resonance. Strategies for initiating and monitoring these various dynamical processes experimentally using pre-resonant impulsive Raman excitation, short-pulse absorption, and multi-dimensional wave-packet interferometry are outlined in brief.

Tight inner ring architecture and quantum motion of nuclei enable efficient energy transfer in bacterial light harvesting

The efficient, directional transfer of absorbed solar energy between photosynthetic light-harvesting complexes continues to pose intriguing questions. In this work, we identify the pathways of energy flow between the B800 and B850 rings in the LH2 complex of Rhodopseudomonas molischianum using fully quantum mechanical path integral methods to simulate the excited-state dynamics of the 24 bacteriochlorophyll molecules and their coupling to 50 normal mode vibrations in each chromophore. While all pigments are identical, the tighter packing of the inner B850 ring is responsible for the thermodynamic stabilization of the inner ring. Molecular vibrations enable the 1-ps flow of energy to the B850 states, which would otherwise be kinetically inaccessible. A classical treatment of the vibrations leads to uniform equilibrium distribution of the excitation, with only 67% transferred to the inner ring. However, spontaneous fluctuations associated with the quantum motion of the nuclei increase the transfer efficiency to 90%.

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

Photosynthetic organisms are known to use a mechanism of vibrationally assisted exciton energy transfer to efficiently harvest energy from light. The importance of quantum effects in this mechanism is a long-standing topic of debate, which has traditionally focused on the role of excitonic coherences. Here, we address another recent claim: that the efficient energy transfer in the Fenna-Matthews-Olson complex relies on nuclear quantum uncertainty and would not function if the vibrations were classical. We present a counter-example to this claim, showing by trajectory-based simulations that a description in terms of quantum electrons and classical nuclei is indeed sufficient to describe the funneling of energy to the reaction center. We analyze and compare these findings to previous classical-nuclear approximations that predicted the absence of an energy funnel and conclude that the key difference and the reason for the discrepancy is the ability of the trajectories to properly account for Newton's third law.

Two-dimensional electronic spectroscopy of the Qx to Qy relaxation of chlorophylls a in photosystem II core complex

Using two-dimensional electronic spectroscopy, we measured the Qx to Qy transfer dynamics of the chlorophyll a (Chl a) manifold in the photosystem II (PSII) monomeric core complex from Arabidopsis thaliana. A PSII monomeric core consists of 35 Chls a and no Chl b, thus allowing for a clear window to study Chl a Qx dynamics in a large pigment-protein complex. Initial excitation in the Qx band results in a transfer to the Qy band in less than 60 fs. Upon the ultrafast transfer, regardless of the excitation frequency within the Qx band, the quasi-transient absorption spectra are very similar. This observation indicates that Chl a’s Qx to Qy transfer is not frequency selective. Using a simple model, we determined that this is not due to the lifetime broadening of the ultrafast transfer but predominantly due to a lack of correlation between the PSII core complex’s Chl a Qx and Qy bands. We suggest the origin to be the intrinsic loss of correlation during the Qx to Qy internal conversion as observed in previous studies of molecular Chl a dissolved in solvents.

Searching for a Unique Exciton Model of Photosynthetic Pigment–Protein Complexes: Photosystem II Reaction Center Study by Differential Evolution

Studying the optical properties of photosynthetic pigment–protein complexes (PPCs) in the visible light range, both experimentally and theoretically, is one of the ways of gaining knowledge about the function of the photosynthetic machinery of living species. To simulate the PPC optical response, it is necessary to use semiclassical theories describing the effect of external fields–matter interaction, energy migration in molecular crystals, and electron–phonon coupling. In this paper, we report the results of photosystem II reaction center (PSIIRC) linear optical response simulations. Applying the multimode Brownian oscillator model and the theory of molecular excitons, we have demonstrated that the absorption, circular and linear dichroism, and steady-state fluorescence of PSIIRC can be accurately fitted with the help of differential evolution (DE), the multiparametric evolutionary optimization algorithm. To explore the effectiveness of DE, we used the simulated experimental data as the target functions instead of those actually measured. Only 2 of 10 DE strategies have shown the best performance of the optimization algorithm. With the best tuning parameters of DE/rand-to-best/1/exp strategy determined from the strategy tests, we found the exact solution for the PSIIRC exciton model and fitted the spectra with a reasonable convergence rate.

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

Diatoms generate a large portion of the oxygen produced on earth due to their exceptional light-harvesting properties involving fucoxanthin and chlorophyll-binding proteins (FCP). At the same time, an efficient adaptation of these complexes to fluctuating light conditions is necessary to protect the diatoms against photodamage. So far, structural and dynamic data for the interaction between FCP and the photoprotective LHCX family of proteins in diatoms are lacking. In this computational study, we provide a structural basis for a remarkable pH-dependent adaptation at the molecular level. Upon binding of the LHCX1 protein to the FCP complex together with a change in pH, conformational changes within the FCP protein result in a variation of the electronic coupling in a specific chlorophyll-fucoxanthin pair, leading to a change in the exciton transfer rate by almost an order of magnitude. A common strategy for photoprotection between diatoms and higher plants is identified and discussed.

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

Considering bacteriochlorophyll molecules embedded in the protein matrix of the light-harvesting complexes of purple bacteria (known as LH2 and LH1-RC) as examples of systems of interacting pigment molecules, we investigated the relationship between the spatial arrangement of the pigments and their exciton transition moments. Based on the recently reported crystal structures of LH2 and LH1-RC and the outcomes of previous theoretical studies, as well as adopting the Frenkel exciton Hamiltonian for two-level molecules, we performed visualizations of the LH2 and LH1 exciton transition moments. To make the electron transition moments in the exciton representation invariant with respect to the position of the system in space, a system of pigments must be translated to the center of mass before starting the calculations. As a result, the visualization of the transition moments for LH2 provided the following pattern: two strong transitions were outside of LH2 and the other two were perpendicular and at the center of LH2. The antenna of LH1-RC was characterized as having the same location of the strongest moments in the center of the complex, exactly as in the B850 ring, which actually coincides with the RC. Considering LH2 and LH1 as supermolecules, each of which has excitation energies and corresponding transition moments, we propose that the outer transitions of LH2 can be important for inter-complex energy exchange, while the inner transitions keep the energy in the complex; moreover, in the case of LH1, the inner transitions increased the rate of antenna-to-RC energy transfer.