Figure - available from: Photosynthesis Research
This content is subject to copyright. Terms and conditions apply.
An example of average site energies with the respective fluctuations as error bars for the FMO complex showing excitation energies based on the TD-LC-DFTB method along MD and DFTB/MM MD trajectories of different lengths as published in Maity et al. (2020)
Source publication
In this mini review, we focus on recent advances in the atomistic modeling of biological light-harvesting (LH) complexes. Because of their size and sophisticated electronic structures, multiscale methods are required to investigate the dynamical and spectroscopic properties of such complexes. The excitation energies, in this context also known as s...
Similar publications
In response to varying light conditions, light-harvesting complexes (LHCs) switch from a light-harvesting to a quenched state to protect the photosynthetic organism from excessive light irradiation, in a strategy known as nonphotochemical quenching (NPQ). NPQ is activated by an acidification of the thylakoid lumen which is sensed directly or indire...
Citations
... These structures consist of pigments bound by protein chains [2]. LH2 complex of Rhodoblastus acidophilus, also known as purple nonsulfur bacteria, is a well-known model object for study of LH absorption spectra [3][4][5][6][7][8][9] due to its rather simple structure: 9 rhodopin β-D-glucoside and 27 bacteriochlorophyll a (BChl a) molecules put together by 18 altering protein chains [10]. BChl a molecules are presented as two discrete structures: a closely packed ring of eighteen BChl a with their CH-planes lined up along the C 9 symmetry axis and a loosely packed ring of nine BChl a with CH-planes oriented perpendicular to the C 9 axis. ...
We use time-dependent density functional theory-based approaches, TD-DFT and TD-DFTB, to investigate the optical absorption of B800 part of Rhodoblastus acidophilus light-harvesting complex 2 (LH2). Both methods are shown to give qualitative agreement with experimental spectra for a single BChl a molecule and for the optimized structure of B800 complex containing nine of such molecules. We proved the absence of any sizable effects originating from the interaction between adjacent molecules, thus optical features of B800 LH2 part should not be attributed to the structural organization of pigments. In addition, time-dependent procedure itself was found to be crucial for the correct description of BChl a absorption spectrum.
... [30][31][32] All the above-referenced approaches are in general computationally intensive. Their applications to realistic EET models, which feature a larger number of chromophores and/or structured spectral densities (SDs) of the exciton-environment interaction extracted from experiments or atomistic simulations, [33][34][35][36][37][38] can thus be impractical. A need for computationally less demanding and reliable, although approximate, approaches to study EET dynamics in realistic multichromophoric models cannot be overemphasized. ...
... The derivation of Eq. (44), in which only g r appears, crucially relies on our assumption that individual-chromophore environments are identical. While the exact coherence dynamics, which follows from Eqs. (38), (39), and (44), can be recovered from the timeconvolutionless second-order QME, 104 the corresponding BA and SCBA results remain only approximations to the exact solution, as both involve an explicit convolution in the time domain. Still, relevant analytical insights concerning the (SC)BA can be obtained for the pure-dephasing model in the high-temperature limit 2πT ≫ γ ph . ...
... (c) Heat map of the ratio D(BA|HEOM) D(SCBA|HEOM) between the performance metrics used in (a) and (b). All quantities are computed for different values of the resonance coupling J and the site-energy gap Δε, the remaining parameters assume their default values listed inTable II, the initial condition is specified in Eq.(38), while tmax = 2 ps.(see Sec. ...
Computationally tractable and reliable, albeit approximate, methods for studying exciton transport in molecular aggregates immersed in structured bosonic environments have been actively developed. Going beyond the lowest-order (Born) approximation for the memory kernel of the quantum master equation typically results in complicated and possibly divergent expressions. Starting from the memory kernel in the Born approximation, and recognizing the quantum master equation as the Dyson equation of Green’s functions theory, we formulate the self-consistent Born approximation to resum the memory-kernel perturbation series in powers of the exciton–environment interaction. Our formulation is in the Liouville space and frequency domain and handles arbitrary exciton–environment spectral densities. In a molecular dimer coupled to an overdamped oscillator environment, we conclude that the self-consistent cycle significantly improves the Born-approximation energy-transfer dynamics. The dynamics in the self-consistent Born approximation agree well with the solutions of hierarchical equations of motion over a wide range of parameters, including the most challenging regimes of strong exciton–environment interactions, slow environments, and low temperatures. This is rationalized by the analytical considerations of coherence-dephasing dynamics in the pure-dephasing model. We find that the self-consistent Born approximation is good (poor) at describing energy transfer modulated by an underdamped vibration resonant (off-resonant) with the exciton energy gap. Nevertheless, it reasonably describes exciton dynamics in the seven-site model of the Fenna–Matthews–Olson complex in a realistic environment comprising both an overdamped continuum and underdamped vibrations.
... Here, they are obtained starting directly from a microscopic model for the system-bath interaction. In applications to chemical physics problems, such models can be, in principle, constructed by first principles quantum chemical and/or molecular dynamics simulations [42][43][44][45][46][47] or derived by experiments. 48 The system of Eq. (11) is not closed because of the dependence on the bath density matrices via the mean fields Cγ a ,JK (t). ...
Modeling the dynamics of a quantum system coupled to a dissipative environment becomes particularly challenging when the system’s dimensionality is too high to permit the computation of its eigenstates. This problem is addressed by introducing an eigenstate-free formalism, where the open quantum system is represented as a mixture of high-dimensional, time-dependent wave packets governed by coupled Schrödinger equations, while the environment is described by a multi-component quantum master equation. An efficient computational implementation of this formalism is presented, employing a variational mixed Gaussian/multiconfigurational time-dependent Hartree (G-MCTDH) ansatz for the wave packets and propagating the environment dynamics via hierarchical equations, truncated at the first or second level of the hierarchy. The effectiveness of the proposed methodology is demonstrated on a 61-dimensional model of phonon-driven vibrational relaxation of an adsorbate. G-MCTDH calculations on 4- and 10-dimensional reduced models, combined with truncated hierarchical equations for the mean fields, nearly quantitatively replicate the full-dimensional quantum dynamical results on vibrational relaxation while significantly reducing the computational time. This approach thus offers a promising quantum dynamical method for modeling complex system–bath interactions, where a large number of degrees of freedom must be explicitly considered.
... Regarding the approach to modeling the excitation energy transfer in the porphyrin-clay system, we will largely follow a procedure that has been successfully employed to model biological light-harvesting systems. [18][19][20][21][22][23] In summary, the initial step is to conduct a molecular dynamics (MD) simulation of the entire system. The equilibrated structure is then used as the starting point for QM/MM (quantum mechanics/molecular mechanics) simulations simulating the pigment molecules. ...
Natural light-harvesting antenna complexes efficiently capture solar energy using chlorophyll, i.e., magnesium porphyrin pigments, embedded in a protein matrix. Inspired by this natural configuration, artificial clay-porphyrin antenna structures have been experimentally synthesized and have demonstrated remarkable excitation energy transfer properties. The study presents the computational design and simulation of a synthetic light-harvesting system that emulates natural mechanisms by arranging cationic free-base porphyrin molecules on an anionic clay surface. We investigated the transfer of excitation energy among the porphyrin dyes using a multiscale quantum mechanics/molecular mechanics (QM/MM) approach based on the semi-empirical density functional-based tight-binding (DFTB) theory for the ground state dynamics. To improve the accuracy of our results, we incorporated an innovative multifidelity machine learning (MFML) approach, which allows the prediction of excitation energies at the numerically demanding time-dependent density functional theory level with the Def2-SVP basis set. This approach was applied to an extensive dataset of 640K geometries for the 90-atom porphyrin structures, facilitating a thorough analysis of the excitation energy diffusion among the porphyrin molecules adsorbed to the clay surface. The insights gained from this study, inspired by natural light-harvesting complexes, demonstrate the potential of porphyrin-clay systems as effective energy transfer systems.
... In practice, however, quantum systems are never truly isolated. Phenomena such as charge and energy transfer, relaxation processes, and quantum coherences in man-made quantum devices 1,2 or biological systems such as photosynthetic complexes 3,4 can only be explained in detail within the framework of open quantum systems, where the systems are separated into a primary system and a bath. Solving such quantum dynamical problems analytically is only possible for very simple setups and usually also computationally (very) challenging for larger systems. ...
... The interactions between the system and bath are then included as fluctuating site energies in effective Hamiltonian operators. Previously, these fluctuating site energies have been obtained either from excited state calculations along molecular dynamics (MD) or quantum mechanics/molecular mechanics (QM/MM) trajectories 4,47,[55][56][57][58] or generated following simple analytic spectral densities. 43,45,46,59 Similar to the progress made for the HEOM approach, it is also of interest to enable the use of the NISE scheme for complicated spectral densities. ...
... If the site energy fluctuations (noise) are based, however, on numerically much more demanding calculations, such as excited state calculations along MD or QM/MM trajectories, the noise generation is computationally expensive, resulting in a limited amount of energy values being available. 4,57 Consequently, the present study also focuses on establishing best practices and assessing the accuracy of spectral densities obtained from noise trajectories of limited length. This assessment is performed by utilizing the known correct spectral density as a reference for the generated limited noise. ...
Although recent advances in simulating open quantum systems have led to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due to their computational efficiency, enabling simulations of larger systems over extended timescales. In this study, we present advances for one such method, namely, the numerical integration of Schrödinger equation (NISE). First, we introduce a modified ensemble-averaging procedure that improves the long-time behavior of the thermalized variant of the NISE scheme, termed thermalized NISE. Second, we demonstrate how to use the NISE in conjunction with (highly) structured spectral densities by utilizing a noise generating algorithm for arbitrary structured noise. This algorithm also serves as a tool for establishing best practices in determining spectral densities from excited state calculations along molecular dynamics or quantum mechanics/molecular mechanics trajectories. Finally, we assess the ability of the NISE approach to calculate absorption spectra and demonstrate the utility of the proposed modifications by determining population dynamics.
... In practice, however, quantum systems are never truly isolated. Phenomena such as charge and energy transfer, relaxation processes and quantum coherences in man-made quantum devices [1,2] or biological systems such as photosynthetic complexes [3,4] can only be explained in detail within the framework of open quantum systems, where the systems are separated into a primary system and a bath. Solving such quantum dynamical problems analytically is only possible for very simple setups, and usually also computationally (very) challenging for larger systems. ...
... The interactions between system and bath are then included as fluctuating site energies in effective Hamiltonian operators. Previously, these fluctuating site energies have been obtained either from excited state calculations along molecular dynamics (MD) or quantum mechanics/molecular mechanics (QM/MM) trajectories [4,47,[55][56][57][58] or generated following simple analytic spectral densities [43,45,46,59]. Similar to the progress made for the HEOM approach, it is also of interest to enable the use of the NISE scheme for complicated spectral densities. ...
... In the present study, we utilize this algorithm for an additional purpose. Spectral densities in our and several other groups are determined based on excited state calculations along MD or QM/MM trajectories [4,[55][56][57][58][60][61][62][63][64]. ...
Although recent advances in simulating open quantum systems have lead to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due to their computational efficiency, enabling simulations of larger systems over extended timescales. In this study, we present advances for one such method, namely the Numerical Integration of Schr\"odinger Equation (NISE). Firstly, we introduce a modified ensemble-averaging procedure that improves the long-time behavior of the thermalized variant of the NISE scheme, termed Thermalized NISE. Secondly, we demonstrate how to use the NISE in conjunction with (highly) structured spectral densities by utilizing a noise generating algorithm for arbitrary structured noise. This algorithm also serves as a tool for establishing best practices in determining spectral densities from excited state calculations along molecular dynamics or quantum mechanics/molecular mechanics trajectories. Finally, we assess the ability of the NISE approach to calculate absorption spectra and demonstrate the utility of the proposed modifications by determining population dynamics.
... [30][31][32] All the above-referenced approaches are in general computationally intensive. Their applications to realistic EET models, which feature a larger number of chromophores and/or structured spectral densities (SDs) of the excitonenvironment interaction extracted from experiments or atomistic simulations, [33][34][35][36][37][38] can thus be impractical. A need for computationally less demanding and reliable, although approximate, approaches to study EET dynamics in realistic multichromophoric models cannot be overemphasized. ...
... The derivation of Eq. (44), in which only g r appears, crucially relies on our assumption that individual-chromophore environments are identical. While the exact coherence dynamics, which follows from Eqs. (44), (39), and (38), can be recovered from the time-convolutionless second-order QME, 98 the corresponding BA and SCBA results remain only approximations to the exact solution, as both involve an explicit convolution in the time domain. Still, relevant analytical insights concerning the (SC)BA can be obtained for the pure-dephasing model in the high-temperature limit 2πT ≫ γ ph . ...
... The same result follows from Eq. (27) Table II, the initial condition is specified in Eq. (38), while tmax = 2 ps. temperature limit, and performing a contour integration by closing the contour in the upper half-plane. ...
Computationally tractable and reliable, albeit approximate, methods for studying exciton transport in molecular aggregates immersed in structured bosonic environments have been actively developed. Going beyond the lowest-order (Born) approximation for the memory kernel of the generalized quantum master equation typically results in complicated and possibly divergent expressions. Starting from the memory kernel in the Born approximation, and recognizing the quantum master equation as the Dyson equation of the Green's functions theory, we formulate the self-consistent Born approximation to resum the memory-kernel perturbation series in powers of the exciton-environment interaction. Our formulation is in the Liouville space and frequency domain, and handles arbitrary exciton-environment spectral densities. In a molecular dimer coupled to an overdamped oscillator environment, we conclude that the self-consistent cycle significantly improves the Born-approximation energy-transfer dynamics. The dynamics in the self-consistent Born approximation agree well with solutions of hierarchical equations of motion over a wide range of parameters, including the most challenging regimes of strong exciton-environment interactions, slow environments, and low temperatures. This is rationalized by analytical considerations of coherence-dephasing dynamics in the pure-dephasing model. We find that the self-consistent Born approximation is good (poor) at describing energy transfer modulated by an underdamped vibration resonant (off-resonant) with the exciton energy gap. Nevertheless, it reasonably describes exciton dynamics in the seven-site model of the Fenna-Matthews-Olson complex in a realistic environment comprising both an overdamped continuum and underdamped vibrations.
... Ring-shaped light-harvesting (LH) aggregates, in particular, LH1 and LH2 complexes exhibit circular arrangements of multiple pigments with certain rotational symmetries [56-58, 63, 64]. In photosynthesis, the coupled ring geometries of LH complexes essentially result in a highly efficient light capture and extremely fast excitation transfer mechanism [65][66][67][68][69][70][71][72]. A network of coupled rings facilitates a near loss-less propagation of light energy towards the reaction center [73]. ...
Subwavelength ring-shaped structures of quantum emitters exhibit outstanding radiation properties and are useful for antennas, excitation transport, and storage. Taking inspiration from the oligomeric geometry of biological light-harvesting 2 (LH2) complexes, we study here generic examples and predict highly efficient excitation transfer in a three-dimensional (3D) subwavelength concentric stacked ring structure with a diameter of 400 \textit{nm}, formed by two-level atoms. Utilizing the quantum optical open system master equation approach for the collective dipole dynamics, we demonstrate that, depending on the system parameters, our bio-mimicked 3D ring enables efficient excitation transfer between two ring layers. Our findings open prospects for engineering other biomimetic light-matter platforms and emitter arrays to achieve efficient energy transfer.
... 39,40 In computing LHC excitation energies, it is crucial to consider environmental effects as they have a significant impact on the excitonic and spectroscopic properties. 43,44 Characterizing these surroundings accurately remains a challenging task. Molecular dynamics simulations provide an atomistic representation of the system, 45 while the energetic description is obtained through quantum mechanical methods. ...
... Recently, computational techniques have been developed to provide enhanced models for explaining complex mechanisms using quantum mechanical/molecular mechanical (QM/MM) setups. 43,44,46,47 In this study, we utilize a combined approach of quantum mechanics/ molecular mechanics molecular dynamics (QM/MM MD) and the time-dependent long-range corrected density functional tight binding (TD-LC-DFTB) level of theory 48 to investigate the excitonic characteristics of the CP24 complex. The computations produce Q y excitation energies, also known as site energies, for the pigments along a trajectory. ...
... Spectral densities, which are crucial inputs for density matrix calculations, are modeled based on the fluctuations in the site energies. The method used in this study to determine the excitation energies, TD-LC-DFTB/ MM, 44,49 has been shown to be both accurate and computationally efficient when compared to previous approaches such as Zerner's Intermediate Neglect of Differential Orbital method with spectroscopic parameters (ZINDO/S-CIS) 50−54 and time-dependent density functional theory 52,55 calculations along classical MD trajectories. At the same time, the excitonic couplings are determined based on the pigment distances, mutual orientations and conformations. ...
In this study, the site energy fluctuations, energy transfer dynamics, and some spectroscopic properties of the minor light-harvesting complex CP24 in a membrane environment were determined. For this purpose, a 3 μs-long classical molecular dynamics simulation was performed for the CP24 complex. Furthermore, using the density functional tight binding/molecular mechanics molecular dynamics (DFTB/MM MD) approach, we performed excited state calculations for the chlorophyll a and chlorophyll b molecules in the complex starting from five different positions of the MD trajectory. During the extended simulations, we observed variations in the site energies of the different sets as a result of the fluctuating protein environment. In particular, a water coordination to Chl-b 608 occurred only after about 1 μs in the simulations, demonstrating dynamic changes in the environment of this pigment. From the classical and the DFTB/MM MD simulations, spectral densities and the (time-dependent) Hamiltonian of the complex were determined. Based on these results, three independent strongly coupled chlorophyll clusters were revealed within the complex. In addition, absorption and fluorescence spectra were determined together with the exciton relaxation dynamics, which reasonably well agrees with experimental time scales. ■ INTRODUCTION Photosynthesis is key to sustaining life on Earth by turning sunlight into chemical energy. The photosynthetic machinery of plants and other photosynthetic organisms orchestrates this energy conversion through a series of intricate processes aided by pigment−protein complexes (PPCs). 1 Within these PPCs, pigment molecules are anchored to a protein matrix in such a way as to form an energy funnel enabling efficient energy transfer to the reaction center where charge separation takes place. 2−5 The pigments with high excitation energies pass the excitations to those with lower excitation energies in a cascaded fashion. The differences in excitation energy of each pigment molecule in the light-harvesting complexes (LHCs) facilitating the energy ladder arise due to different pigment types and the anisotropy in the protein environment. 6,7 Understanding the energy map within PPCs is crucial to comprehend the excitation energy transfer (EET) and associated properties within these complexes. An enhanced understanding of these mechanisms can potentially accelerate the development of efficient artificial light-harvesting systems, bringing sustainable energy closer to reality. Beyond light harvesting and EET, some of the PPCs, e.g., in higher plants, engage in photoprotection activities, shielding the complexes and the pigments therein from excessively high light intensities. 8 In Photosystem II (PSII) of higher plants, the antenna complexes belonging to the Lhc family undergo conformational changes in response to external stimuli such as a high light intensity inducing the transition between the light harvesting and photoprotection states. 9,10 The entirety of the antenna complexes consist of the major light-harvesting complex, i.e., the trimeric LHCII, representing the genes Lhcb1 to Lhcb3 and the minor antenna complexes CP29, CP26, and CP24 representing the genes Lhcb4, Lhbc5, and Lhbc6, respectively. 11,12 The minor antenna complexes are located between the outer LHCII trimers and the PSII core complex. In this study, we focus on the minor antenna complex CP24 of PSII, which functions in both modes, the light-harvesting and the photoprotection mode, similar to the other complexes of the same family. A network of six chlorophyll a (Chl-a) and five chlorophyll b (Chl-b) molecules is mainly responsible for the functional properties of the CP24 complex. Sunlight initiates the excitation of the chlorophyll molecules usually to their lowest excited state, commonly referred to as the Q y state, followed by a movement of the excited state energy within the system and finally toward a reaction center. 13 In addition to the chlorophyll molecules, a β-carotenoid
... Light-harvesting antennas in phototrophs are generally composed of supramolecules of pigments with peptides. Most antenna systems in chlorophotosynthetic organisms are formed by the specific interaction of chlorophyll (Chl) or bacteriochlorophyll (BChl) molecules with oligopeptides: typically see recent reports [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In contrast to the conventional photosynthetic antennas, green sulfur bacteria (GSB), filamentous anoxygenic phototrophs (FAP), and chloracidobacteria possess unique antenna systems, called chlorosomes, which are built up by the self-aggregation of BChl pigments without any interaction with peptides [20][21][22][23]. ...
Zinc 3-hydroxymethyl-pyroprotopheophorbides- a esterified with a chiral secondary alcohol at the 17-propionate residue were prepared as bacteriochlorophyll- d analogs. The synthetic zinc 3 ¹ -hydroxy-13 ¹ -oxo-porphyrins self-aggregated in an aqueous Triton X-100 micellar solution to give red-shifted and broadened Soret and Qy absorption bands in comparison with their monomeric bands. The intense, exciton-coupled circular dichroism spectra of their self-aggregates were dependent on the chirality of the esterifying groups. The observation indicated that the self-aggregates based on the J-type stacking of the porphyrin cores were sensitive to the peripheral 17-propionate residues. The supramolecular structures of the present J-aggregates as models of bacteriochlorophyll aggregates in natural chlorosomes were remotely regulated by the esterifying groups.
Graphical abstract
