Lineshape theory of pigment-protein complexes: How the finite relaxation time of nuclei influences the exciton relaxation-induced lifetime broadening

Quantum chemical elucidation of a sevenfold symmetric bacterial antenna complex

The light-harvesting complex 2 (LH2) of purple bacteria is one of the most studied photosynthetic antenna complexes. Its symmetric structure and ring-like bacteriochlorophyll arrangement make it an ideal system for theoreticians and spectroscopists. LH2 complexes from most bacterial species are thought to have eightfold or ninefold symmetry, but recently a sevenfold symmetric LH2 structure from the bacterium Mch. purpuratum was solved by Cryo-Electron microscopy. This LH2 also possesses unique near-infrared absorption and circular dichroism (CD) spectral properties. Here we use an atomistic strategy to elucidate the spectral properties of Mch. purpuratum LH2 and understand the differences with the most commonly studied LH2 from Rbl. acidophilus. Our strategy exploits a combination of molecular dynamics simulations, multiscale polarizable quantum mechanics/molecular mechanics calculations, and lineshape simulations. Our calculations reveal that the spectral properties of LH2 complexes are tuned by site energies and exciton couplings, which in turn depend on the structural fluctuations of the bacteriochlorophylls. Our strategy proves effective in reproducing the absorption and CD spectra of the two LH2 complexes, and in uncovering the origin of their differences. This work proves that it is possible to obtain insight into the spectral tuning strategies of purple bacteria by quantitatively simulating the spectral properties of their antenna complexes.

Signatures of intramolecular vibrational and vibronic Q[Formula: see text]-Q[Formula: see text] coupling effects in absorption and CD spectra of chlorophyll dimers

An electron-vibrational coupling model that includes the vibronic (non-adiabatic) coupling between the Q[Formula: see text] and Q[Formula: see text] transitions of chlorophyll (Chl), created by Reimers and coworkers (Scientific Rep. 3, 2761, 2013) is extended here to chlorophyll dimers with interchlorophyll excitonic coupling. The model is applied to a Chl a dimer of the water-soluble chlorophyll binding protein (WSCP). As for isolated chlorophyll, the vibronic coupling is found to have a strong influence on the high-frequency vibrational sideband in the absorption spectrum, giving rise to a band splitting. In contrast, in the CD spectrum the interplay of vibronic coupling and static disorder leads to a strong suppression of the vibrational sideband in excellent agreement with the experimental data. The conservative nature of the CD spectrum in the low-energy region is found to be caused by a delicate balance of the intermonomer excitonic coupling between the purely electronic Q[Formula: see text] transition and the Q[Formula: see text] transition involving intramolecular vibrational excitations on one hand and the coupling to higher-energy electronic transitions on the other hand.

Spectral densities and absorption spectra of the core antenna complex CP43 from photosystem II

Besides absorbing light, the core antenna complex CP43 of photosystem II is of great importance in transferring excitation energy from the antenna complexes to the reaction center. Excitation energies, spectral densities, and linear absorption spectra of the complex have been evaluated by a multiscale approach. In this scheme, quantum mechanics/molecular mechanics molecular dynamics simulations are performed employing the parameterized density functional tight binding (DFTB) while the time-dependent long-range-corrected DFTB scheme is applied for the excited state calculations. The obtained average spectral density of the CP43 complex shows a very good agreement with experimental results. Moreover, the excitonic Hamiltonian of the system along with the computed site-dependent spectral densities was used to determine the linear absorption. While a Redfield-like approximation has severe shortcomings in dealing with the CP43 complex due to quasi-degenerate states, the non-Markovian full second-order cumulant expansion formalism is able to overcome the drawbacks. Linear absorption spectra were obtained, which show a good agreement with the experimental counterparts at different temperatures. This study once more emphasizes that by combining diverse techniques from the areas of molecular dynamics simulations, quantum chemistry, and open quantum systems, it is possible to obtain first-principle results for photosynthetic complexes, which are in accord with experimental findings.

Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes

Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.

Normal mode analysis of spectral density of FMO trimers: Intra- and intermonomer energy transfer

The intermolecular contribution to the spectral density of the exciton-vibrational coupling of the homotrimeric Fenna-Matthews-Olson (FMO) light-harvesting protein of green sulfur bacteria P. aestuarii is analyzed by combining a normal mode analysis of the protein with the charge density coupling method for the calculation of local transition energies of the pigments. Correlations in site energy fluctuations across the whole FMO trimer are found at low vibrational frequencies. Including, additionally, the high-frequency intrapigment part of the spectral density, extracted from line-narrowing spectra, we study intra- and intermonomer exciton transfer. Whereas the intrapigment part of the spectral density is important for fast intramonomer exciton relaxation, the intermolecular contributions (due to pigment-environment coupling) determine the intermonomer exciton transfer. Neither the variations of the local Huang-Rhys factors nor the correlations in site energy fluctuations have a critical influence on energy transfer. At room temperature, the intermonomer transfer in the FMO protein occurs on a 10 ps time scale, whereas intramonomer exciton equilibration is roughly two orders of magnitude faster. At cryogenic temperatures, intermonomer transfer limits the lifetimes of the lowest exciton band. The lifetimes are found to increase between 20 ps in the center of this band up to 100 ps toward lower energies, which is in very good agreement with the estimates from hole burning data. Interestingly, exciton delocalization in the FMO monomers is found to slow down intermonomer energy transfer, at both physiological and cryogenic temperatures.

Absorption and Circular Dichroism Spectra of Molecular Aggregates With the Full Cumulant Expansion

The exciton Hamiltonian of multichromophoric aggregates can be probed by spectroscopic techniques such as linear absorption and circular dichroism. To compare calculated Hamiltonians to experiments, a lineshape theory is needed, which takes into account the coupling of the excitons with inter- and intramolecular vibrations. This coupling is normally introduced in a perturbative way through the cumulant expansion formalism and further approximated by assuming a Markovian exciton dynamics, for example with the modified Redfield theory. Here, we present the implementation of the full cumulant expansion (FCE) formalism (J. Chem. Phys.142, 2015, 09410625747060) to efficiently compute absorption and circular dichroism spectra of molecular aggregates beyond the Markov approximation, without restrictions on the form of exciton–phonon coupling. By employing the LH2 system of purple bacteria as a challenging test case, we compare the FCE lineshapes with the Markovian lineshapes obtained with the modified Redfield theory, showing that the latter presents a less satisfying agreement with experiments. The FCE approach instead accurately describes the lineshapes, especially in the vibronic sideband of the B800 peak. We envision that the FCE approach will become a valuable tool for accurately comparing model exciton Hamiltonians with optical spectroscopy experiments.

Exciton properties and optical spectra of light harvesting complex II from a fully atomistic description

We present a fully atomistic simulation of linear optical spectra (absorption, fluorescence and circular dichroism) of the Light Harvesting Complex II (LHCII) trimer using a hybrid approach, which couples a quantum chemical description of the chlorophylls with a classical model for the protein and the external environment (membrane and water). The classical model uses a polarizable Molecular Mechanics force field, thus allowing mutual polarization effects in the calculations of the excitonic properties. The investigation is performed both on the crystal structure and on structures generated by a μs long classical molecular dynamics simulation of the complex within a solvated membrane. The results show that this integrated approach not only provides a good description of the excitonic properties and optical spectra without the need for additional refinements of the excitonic parameters, but it also allows an atomistic investigation of the relative importance of electronic, structural and environment effects in determining the optical spectra.

Modeling irreversible molecular internal conversion using the time-dependent variational approach with sD2 ansatz

A model of irreversible molecular internal conversion dynamics due to molecular thermal energy dissipation to the bath is presented.

Coupling to Charge Transfer States is the Key to Modulate the Optical Bands for Efficient Light Harvesting in Purple Bacteria

The photosynthetic apparatus of purple bacteria uses exciton delocalization and static disorder to modulate the position and broadening of its absorption bands, leading to efficient light harvesting. Its main antenna complex, LH2, contains two rings of identical bacteriochlorophyll pigments, B800 and B850, absorbing at 800 and 850 nm, respectively. It has been an unsolved problem why static disorder of the strongly coupled B850 ring is several times larger than that of the B800 ring. Here we show that mixing between excitons and charge transfer states in the B850 ring is responsible for the effect. The linear absorption spectrum of the LH2 system is simulated by using a multiscale approach with an exciton Hamiltonian generalized to include the charge transfer states that involve adjacent pigment pairs, with static disorder modeled microscopically by molecular dynamics simulations. Our results show that sufficient inhomogeneous broadening of the B850 band, needed for efficient light harvesting, is only obtained by utilizing static disorder in the coupling between local excited and interpigment charge transfer states.