Near-atomic-resolution structure of J-aggregated helical light-harvesting nanotubes.

Cryo-electron microscopy has delivered a resolution revolution for biological self-assemblies, yet only a handful of structures have been solved for synthetic supramolecular materials. Particularly for chromophore supramolecular aggregates, high-resolution structures are necessary for understanding and modulating the long-range excitonic coupling. Here, we present a 3.3 Å structure of prototypical biomimetic light-harvesting nanotubes derived from an amphiphilic cyanine dye (C8S3-Cl). Helical 3D reconstruction directly visualizes the chromophore packing that controls the excitonic properties. Our structure clearly shows a brick layer arrangement, revising the previously hypothesized herringbone arrangement. Furthermore, we identify a new non-biological supramolecular motif-interlocking sulfonates-that may be responsible for the slip-stacked packing and J-aggregate nature of the light-harvesting nanotubes. This work shows how independently obtained native-state structures complement photophysical measurements and will enable accurate understanding of (excitonic) structure-function properties, informing materials design for light-harvesting chromophore aggregates.

Coherent Spatial Control of Wave Packet Dynamics on Quantum Lattices.

Quantum lattices are pivotal in the burgeoning fields of quantum materials and information science. Novel experimental techniques allow the preparation and monitoring of wave packet dynamics on quantum lattices with high spatiotemporal resolution. We present an analytical study of wave packet diffusivity and diffusion length on tight-binding quantum lattices subject to stochastic noise. Our analysis reveals the crucial role of spatial coherence and predicts a set of novel phenomena: (1) noise can enhance the transient diffusivity and diffusion length of spatially extended initial states; (2) standing or traveling initial states, with large momentum, spread faster than a localized initial state and exhibit a noise-induced peak in the transient diffusivity; (3) the differences in the diffusivity or diffusion length of extended and localized initial states have a universal dependence on initial width. These predictions suggest the possibility of controlling the wave packet dynamics by spatial manipulations, which will have implications for materials science and quantum technologies.

Elucidating interprotein energy transfer dynamics within the antenna network from purple bacteria.

In photosynthesis, absorbed light energy transfers through a network of antenna proteins with near-unity quantum efficiency to reach the reaction center, which initiates the downstream biochemical reactions. While the energy transfer dynamics within individual antenna proteins have been extensively studied over the past decades, the dynamics between the proteins are poorly understood due to the heterogeneous organization of the network. Previously reported timescales averaged over such heterogeneity, obscuring individual interprotein energy transfer steps. Here, we isolated and interrogated interprotein energy transfer by embedding two variants of the primary antenna protein from purple bacteria, light-harvesting complex 2 (LH2), together into a near-native membrane disc, known as a nanodisc. We integrated ultrafast transient absorption spectroscopy, quantum dynamics simulations, and cryogenic electron microscopy to determine interprotein energy transfer timescales. By varying the diameter of the nanodiscs, we replicated a range of distances between the proteins. The closest distance possible between neighboring LH2, which is the most common in native membranes, is 25 Šand resulted in a timescale of 5.7 ps. Larger distances of 28 to 31 Šresulted in timescales of 10 to 14 ps. Corresponding simulations showed that the fast energy transfer steps between closely spaced LH2 increase transport distances by ∼15%. Overall, our results introduce a framework for well-controlled studies of interprotein energy transfer dynamics and suggest that protein pairs serve as the primary pathway for the efficient transport of solar energy.

Electronic-Vibrational Resonance Does Not Significantly Alter Steady-State Transport in Natural Light-Harvesting Systems.

Oscillations in time-dependent two-dimensional electronic spectra appear as evidence of quantum coherence in light-harvesting systems related to electronic-vibrational resonant interactions. Nature, however, takes place in a non-equilibrium steady-state; therefore, the relevance of these arguments to the natural process is unclear. Here, we examine the role of intramolecular vibrations in the non-equilibrium steady-state of photosynthetic dimers in the natural scenario of incoherent light excitation. Specifically, we analyze the PEB dimer in the cryptophyte algae PE545 antenna protein. It is found that vibrations resonant with the energy difference between exciton states only marginally increase the quantum yield and the imaginary part of the intersite coherence that is relevant for transport compared to non-resonant vibrations in the natural non-equilibrium steady-state. That is, the electronic-vibrational resonance interaction does not significantly enhance energy transport under natural incoherent light excitation conditions.

Superradiance and Exciton Delocalization in Perovskite Quantum Dot Superlattices.

Achieving superradiance in solids is challenging due to fast dephasing processes from inherent disorder and thermal fluctuations. Perovskite quantum dots (QDs) are an exciting class of exciton emitters with large oscillator strength and high quantum efficiency, making them promising for solid-state superradiance. However, a thorough understanding of the competition between coherence and dephasing from phonon scattering and energetic disorder is currently unavailable. Here, we present an investigation of exciton coherence in perovskite QD solids using temperature-dependent photoluminescence line width and lifetime measurements. Our results demonstrate that excitons are coherently delocalized over 3 QDs at 11 K in superlattices leading to superradiant emission. Scattering from optical phonons leads to the loss of coherence and exciton localization to a single QD at temperatures above 100 K. At low temperatures, static disorder and defects limit exciton coherence. These results highlight the promise and challenge in achieving coherence in perovskite QD solids.

Steady State Photoisomerization Quantum Yield of Model Rhodopsin: Insights from Wavepacket Dynamics?

We simulate the nonequilibrium steady state cis-trans photoisomerization of retinal chromophore in rhodopsin on the basis of a two-state, two-mode model coupled to a thermal environment. By analyzing the systematic trends within an inhomogeneously broadened ensemble of systems, we find that the steady state reaction quantum yield (QY) correlates strongly with the excess energy above the crossing point of the system, in agreement with the prediction of the short-time dynamical wavepacket picture. However, the nontrivial dependence of the QY on the system-environment interaction indicates that a pure dynamical picture is insufficient and that environment-induced partial internal energy redistribution takes place before the reaction concludes. These results imply that a proper treatment of the photoisomerization reaction, particularly its high QY, must account for the redistribution and dissipation of energy beyond the dynamical wavepacket motion that is typically employed in the literature and that is appropriate only in the transient regime.

Multi-objective optimization for retinal photoisomerization models with respect to experimental observables.

The fitting of physical models is often done only using a single target observable. However, when multiple targets are considered, the fitting procedure becomes cumbersome, there being no easy way to quantify the robustness of the model for all different observables. Here, we illustrate that one can jointly search for the best model for each desired observable through multi-objective optimization. To do so, we construct the Pareto front to study if there exists a set of parameters of the model that can jointly describe multiple, or all, observables. To alleviate the computational cost, the predicted error for each targeted objective is approximated with a Gaussian process model as it is commonly done in the Bayesian optimization framework. We applied this methodology to improve three different models used in the simulation of stationary state cis-trans photoisomerization of retinal in rhodopsin, a significant biophysical process. Optimization was done with respect to different experimental measurements, including emission spectra, peak absorption frequencies for the cis and trans conformers, and energy storage. Advantages and disadvantages of previously proposed models are exposed.

Universal Scalings in Two-Dimensional Anisotropic Dipolar Excitonic Systems.

Low-dimensional excitonic materials have inspired much interest owing to their novel physical and technological prospects. In particular, those with strong in-plane anisotropy are among the most intriguing but short of general analyses. We establish the universal functional form of the anisotropic dispersion in the small k limit for 2D dipolar excitonic systems. While the energy is linearly dispersed in the direction parallel to the dipole in plane, the perpendicular direction is dispersionless up to linear order, which can be explained by the quantum interference effect of the interaction among the constituents of 1D subsystems. The anisotropic dispersion results in a E^{∼0.5} scaling of the system density of states and predicts unique spectroscopic signatures including: (1) disorder-induced absorption linewidth, W(σ)∼σ^{2.8}, with σ the disorder strength, (2) temperature dependent absorption linewidth, W(T)∼T^{s+1.5}, with s the exponent of the environment spectral density, and (3) the out-of-plane angular θ dependence of the peak splittings in absorption spectra, ΔE(θ)∝sin^{2}θ. These predictions are confirmed quantitatively with numerical simulations of molecular thin films and tubules.

Extreme Parametric Sensitivity in the Steady-State Photoisomerization of Two-Dimensional Model Rhodopsin.

We computationally studied the photoisomerization reaction of the retinal chromophore in rhodopsin using a two-state two-mode model coupled to thermal baths. Reaction quantum yields at the steady state (10 ps and beyond) were found to be considerably different than their transient values, suggesting a weak correlation between transient and steady-state dynamics in these systems. Significantly, the steady-state quantum yield was highly sensitive to minute changes in system parameters, while transient dynamics was nearly unaffected. Correlation of such sensitivity with standard level spacing statistics of the nonadiabatic vibronic system suggests a possible origin in quantum chaos. The significance of this observation of quantum yield parametric sensitivity in biological models of vision has profound conceptual and fundamental implications.

Stochastically Realized Observables for Excitonic Molecular Aggregates.

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

LH1-RC light-harvesting photocycle under realistic light-matter conditions.

Quantum master equations are used to simulate the photocycle of the light-harvesting complex 1 (LH1) and the associated reaction center (RC) in purple bacteria excited with natural incoherent light. The influence of the radiation and protein environments and the full photocycle of the complexes, including the charge separation and RC recovery processes, are taken into account. Particular emphasis is placed on the steady state excitation energy transfer rate between the LH1 and the RC and the steady state dependence on the light intensity. The transfer rate is shown to scale linearly with light intensity near the value in the natural habitat and at higher light intensities is found to be bounded by the rate-determining step of the photocycle, the RC recovery rate. Transient (e.g., pulsed laser induced) dynamics, however, shows rates higher than the steady state value and continues to scale linearly with the intensity. The results show a correlation between the transfer rate and the manner in which the donor state is prepared. In addition, the transition from the transient to the steady state results can be understood as a cascade of ever slower rate-determining steps and quasi-stationary states inherent in multi-scale sequential processes. This type of transition of rates is relevant in most light-induced biological machinery.

Photochemical Control of Exciton Superradiance in Light-Harvesting Nanotubes.

Photosynthetic antennae and organic electronic materials use topological, structural, and molecular control of delocalized excitons to enhance and direct energy transfer. Interactions between the transition dipoles of individual chromophore units allow for coherent delocalization across multiple molecular sites. This delocalization, for specific geometries, greatly enhances the transition dipole moment of the lowest energy excitonic state relative to the chromophore and increases its radiative rate, a phenomenon known as superradiance. In this study, we show that ordered, self-assembled light-harvesting nanotubes (LHNs) display excitation-induced photobrightening and photodarkening. These changes in quantum yield arise due to changes in energetic disorder, which in turn increases/decreases excitonic superradiance. Through a combination of experiment and modeling, we show that intense illumination induces different types of chemical change in LHNs that reproducibly alter absorption and fluorescence properties, indicating control over excitonic delocalization. We also show that changes in spectral width and shift can be sensitive measures of system dimensionality, illustrating the mixed 1-2D nature of LHN excitons. Our results demonstrate a path forward for mastery of energetic disorder in an excitonic antenna, with implications for fundamental studies of coherent energy transport.

Quantum Diffusion on Molecular Tubes: Universal Scaling of the 1D to 2D Transition.

The transport properties of disordered systems are known to depend critically on dimensionality. We study the diffusion coefficient of a quantum particle confined to a lattice on the surface of a tube, where it scales between the 1D and 2D limits. It is found that the scaling relation is universal and independent of the temperature, disorder, and noise parameters, and the essential order parameter is the ratio between the localization length in 2D and the circumference of the tube. Phenomenological and quantitative expressions for transport properties as functions of disorder and noise are obtained and applied to real systems: In the natural chlorosomes found in light-harvesting bacteria the exciton transfer dynamics is predicted to be in the 2D limit, whereas a family of synthetic molecular aggregates is found to be in the homogeneous limit and is independent of dimensionality.

Excitonic effects from geometric order and disorder explain broadband optical absorption in eumelanin.

Eumelanin is a ubiquitous biological pigment, and the origin of its broadband absorption spectrum has long been a topic of scientific debate. Here, we report a first-principles computational investigation to explain its broadband absorption feature. These computations are complemented by experimental results showing a broadening of the absorption spectra of dopamine solutions upon their oxidation. We consider a variety of eumelanin molecular structures supported by experiments or theoretical studies, and calculate the absorption spectra with proper account of the excitonic couplings based on the Frenkel exciton model. The interplay of geometric order and disorder of eumelanin aggregate structures broadens the absorption spectrum and gives rise to a relative enhancement of absorption intensity at the higher-energy end, proportional to the cube of absorption energy. These findings show that the geometric disorder model is as able as the chemical disorder model, and complements this model, to describe the optical properties of eumelanin.

Scaling relations and optimization of excitonic energy transfer rates between one-dimensional molecular aggregates.

We theoretically study the distance, chain length, and temperature dependence of the electronic couplings as well as the excitonic energy transfer rates between one-dimensional (1D) chromophore aggregates. In addition to the well-known geometry dependent factor that leads to the deviation from Förster's classic R(DA)(­6) scaling on the donor­acceptor separation, nonmonotonic dependence on aggregate size and the breakdown of far-field dipole selection rules are also investigated in detail and compared to prior calculations. Our analysis provides a simple, unifying framework to bridge the results of the ground state electronic couplings at low temperatures and those from the classical rate-summation at high temperatures. At low temperatures and in the near-field limit, the exciton transfer integral scales as R(DA)(­1), in analogy to that of electric monopoles. For the case of aligned 1D J-aggregates, we predict a maximal excitonic energy transfer rate at temperatures on the order of the intra-aggregate coupling strength.

Optimal fold symmetry of LH2 rings on a photosynthetic membrane.

An intriguing observation of photosynthetic light-harvesting systems is the N-fold symmetry of light-harvesting complex 2 (LH2) of purple bacteria. We calculate the optimal rotational configuration of N-fold rings on a hexagonal lattice and establish two related mechanisms for the promotion of maximum excitation energy transfer (EET). (i) For certain fold numbers, there exist optimal basis cells with rotational symmetry, extendable to the entire lattice for the global optimization of the EET network. (ii) The type of basis cell can reduce or remove the frustration of EET rates across the photosynthetic network. We find that the existence of a basis cell and its type are directly related to the number of matching points S between the fold symmetry and the hexagonal lattice. The two complementary mechanisms provide selection criteria for the fold number and identify groups of consecutive numbers. Remarkably, one such group consists of the naturally occurring 8-, 9-, and 10-fold rings. By considering the inter-ring distance and EET rate, we demonstrate that this group can achieve minimal rotational sensitivity in addition to an optimal packing density, achieving robust and efficient EET. This corroborates our findings i and ii and, through their direct relation to S, suggests the design principle of matching the internal symmetry with the lattice order.

Hypothetical toroidal, cylindrical, and helical analogs of C60.

Toroidal, cylindrical, and helical analogs of C(60) buckyball are theoretically constructed and analyzed. In these structures, pentagons and heptagons are separated compactly by hexagons in analogy to pentagons in C(60) and heptagons in C(168) proposed by Vanderbilt and Tersoff (1992) [2]. Specifically, all nonhexagons therein are surrounded by hexagons and hexagons are surrounded alternatively by hexagons and nonhexagons, i.e. these structures are polyhedra of Clar type with all their Clar rings nonhexagonal. Quantum chemical calculations have been carried out which show that they possess stabilities comparative to that of C(60). And their structural features are also investigated in detail. Buckled carbon nanotubes deriving from buckytori with periodically varying radii are suggested to be candidacies for the product of coalescing arrays of C(60). The helicity of the buckyhelices as a function of their characterizing shifting parameters is studied. In the limit of large shifting parameter, the buckyhelices adopt an unusual geometric form that has not been reported in the literature yet.

Systematics of high-genus fullerenes.

In this article, we present a systematic way to classify a family of high-genus fullerenes (HGFs) by decomposing them into two types of necklike structures, which are the negatively curved parts of parent toroidal carbon nanotubes. By replacing the faces of a uniform polyhedron with these necks, an HGF polyhedron corresponding to the vertex configuration of the polyhedron can be obtained. HGF polyhedra including tetrahedron, cube, octahedron, dodecahedron, icosahedron, and truncated icosahedron are proposed under the same construction scheme, which contains nonhexagons other than heptagons. Moreover, simple criteria for determining the stabilities of the proposed HGFs based on four geometric parameters are discussed.

Dual space approach to the classification of toroidal carbon nanotubes.

We apply the dual space approach to the classification of toroidal carbon nanotubes. We show that the realizations of most of the geometric manipulations described in the literature become explicit in the dual space of the original molecular graph. In particular, dual graph can be easily constructed on a rectangular strip in the parametric plane of the torus. Generalization to other forms of graphitic cages with different topologies can also be done. Manifested chirality and the criteria for the existence of highly symmetric isomers are discussed.