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We overview experimental and theoretical studies of energy transfer in the photosynthetic light-harvesting complexes LH1, LH2, and LHCII performed during the past decade since the discovery of high-resolution structure of these complexes. Experimental findings obtained with various spectroscopic techniques makes possible a modelling of the excitation dynamics at a quantitative level. The modified Redfield theory allows a precise assignment of the energy transfer pathways together with a direct visualization of the whole excitation dynamics where various regimes from a coherent motion of delocalized exciton to a hopping of localized excitations are superimposed. In a single complex it is possible to observe the switching between these regimes driven by slow conformational motion (as we demonstrate for LH2). Excitation dynamics under quenched conditions in higher-plant complexes is discussed.

Two-dimensional photon echo in the photosystem II reaction center reveals the exciton-vibrational coherences that promote directed energy/electron transfers.

Structure-based calculations are combined with quantitative modeling of spectra and energy transfer dynamics to detemine the energy transfer scheme of the PE545 principal light-harvesting antenna of the cryptomonad Rhodomonas CS24. We use a recently developed quantum-mechanics/molecular mechanics (QM/MM) method that allows us to account for pigment-protein interactions at atomic detail in site energies, transition dipole moments, and electronic couplings. In addition, conformational flexibility of the pigment-protein complex is accounted for through molecular dynamics (MD) simulations. We find that conformational disorder largely smoothes the large energetic differences predicted from the crystal structure between the pseudosymmetric pairs PEB50/61C-PEB50/61D and PEB82C-PEB82D. Moreover, we find that, in contrast to chlorophyll-based photosynthetic complexes, pigment composition and conformation play a major role in defining the energy ladder in the PE545 complex, rather than specific pigment-protein interactions. This is explained by the remarkable conformational flexibility of the eight bilin pigments in PE545, characterized by a quasi-linear arrangement of four pyrrole units. The MD-QM/MM site energies allow us to reproduce the main features of the spectra, and minor adjustments of the energies of the three red-most pigments DBV19A, DBV19B, and PEB82D allow us to model the spectra of PE545 with a similar quality compared to our original model (model E from Novoderezhkin et al. Biophys. J.2010, 99, 344), which was extracted from the spectral and kinetic fit. Moreover, the fit of the transient absorption kinetics is even better in the new structure-based model. The largest difference between our previous and present results is that the MD-QM/MM calculations predict a much smaller gap between the PEB50/61C and PEB50/61D sites, in better accord with chemical intuition. We conclude that the current adjusted MD-QM/MM energies are more reliable in order to explore the spectral properties and energy transfer dynamics in the PE545 complex.

We perform a quantitative comparison of different energy transfer theories, i.e. modified Redfield, standard and generalized Förster theories, as well as combined Redfield-Förster approach. Physical limitations of these approaches are illustrated and critical values of the key parameters indicating their validity are found. We model at a quantitative level the spectra and dynamics in two photosynthetic antenna complexes: in phycoerythrin 545 from cryptophyte algae and in trimeric LHCII complex from higher plants. These two examples show how the structural organization determines a directed energy transfer and how equilibration within antenna subunits and migration between subunits are superimposed.

We model the spectra (absorption and circular dichroism) and excitation dynamics in the B800 ring of the LH2 antenna complex from Rs. molischianum using different theoretical approaches, i.e., Förster theory, standard and modified versions of the Redfield theory, and the more versatile nonperturbative approach based on hierarchically coupled equations for the reduced density operator. We demonstrate that, although excitations in the B800 ring are localized due to disorder, thermal effects, and phonons, there are still sizable excitonic effects producing shift, narrowing, and asymmetry of the spectra. Moreover, the excitation dynamics reveals the presence of long-lived (up to 1 ps) non-oscillatory coherences between the exciton states maintained due to nonsecular population-to-coherence transfers. The sub-ps decay of the coherences is followed by slow motion of the excitation around the ring, producing equilibration of the site populations with a time constant of about 3-4 ps, which is slower than the B800 → B850 transfer. The exact solution obtained with the hierarchical equations is compared with other approaches, thus illustrating limitations of the Förster and Redfield pictures.

AbstractNuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two‐level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer‐lived mixed coherences.

We have studied the relationship between the realizations of static disorder and the emission spectra observed for a single LH2 complex. We show that the experimentally observed spectral fluctuations reflect realizations of the disorder in the B850 ring associated with different degrees of exciton delocalization and different effective coupling of the excitons to phonon modes. The main spectral features cannot be explained using models with correlated disorder associated with elliptical deformations of the ring. A quantitative explanation of the measured single-molecule spectra is obtained using the modified Redfield theory and a model of the B850 ring with uncorrelated disorder of the site energies. The positions and spectral shapes of the main exciton components in this model are determined by the disorder-induced shift of exciton eigenvalues in combination with phonon-induced effects (i.e., reorganization shift and broadening, that increase in proportion to the inverse delocalization length of the exciton state). Being dependent on the realization of the disorder, these factors produce different forms of the emission profile. In addition, the different degree of delocalization and effective couplings to phonons determines a different type of excitation dynamics for each of these realizations. We demonstrate that experimentally observed quasistable conformational states are characterized by excitation energy transfer regimes varying from a coherent wavelike motion of a delocalized exciton (with a 100-fs pass over half of the ring) to a hopping-type motion of the wavepacket (with a 350-fs jump between separated groups of 3-4 molecules) and self-trapped excitations that do not move from their localization site.

We compare various theoretical approaches that are frequently used for modeling the excitation dynamics in photosynthetic light-harvesting complexes. As an example, we calculate the dynamics in the major light-harvesting complex from higher plants using the standard Redfield theory, the coherent modified Redfield theory combined with the generalized Forster theory, and the scaled hierarchical equation of motion (HEOM). The modified Redfield and coherent modified Redfield theories predict unrealistically fast transfers between weakly coupled and isoenergetic sites due to the secular character of these approaches. This shortcoming can be excluded by the artificial breaking of exciton mixing between these sites and invoking a generalized Forster theory to calculate the transfers between them. A critical cutoff indicating which exciton couplings should be broken is dependent on the energy gap between the corresponding sites (and therefore can be different for different parts of the complex). An adequate determination of the strongly coupled compartments of the whole complex allows us to obtain a quantitatively correct description with the combined Redfield-Forster approach, resulting in kinetics not much different from the exact HEOM solution.