Coarse-Grained Approach to Simulate Signatures of Excitation Energy Transfer in Two-Dimensional Electronic Spectroscopy of Large Molecular Systems.

Two-dimensional electronic spectroscopy (2DES) has proven to be a highly effective technique in studying the properties of excited states and the process of excitation energy transfer in complex molecular assemblies, particularly in biological light-harvesting systems. However, the accurate simulation of 2DES for large systems still poses a challenge because of the heavy computational demands it entails. In an effort to overcome this limitation, we devised a coarse-grained 2DES method. This method encompasses the treatment of the entire system by dividing it into distinct weakly coupled segments, which are assumed to communicate predominantly through incoherent exciton transfer. We first demonstrate the efficiency of this method through simulation on a model dimer system, which demonstrates a marked improvement in calculation efficiency, with results that exhibit good concordance with reference spectra calculated with less approximate methods. Additionally, the application of this method to the light-harvesting antenna 2 (LH2) complex of purple bacteria showcases its advantages, accuracy, and limitations. Furthermore, simulating the anisotropy decay in LH2 induced by energy transfer and its comparison with experiments confirm that the method is capable of accurately describing dynamical processes in a biologically relevant system. This method presented lends itself to an extension that accounts for the effect of intrasegment relaxation processes on the 2DES spectra, which for computational efficiency are ignored in the implementation reported here. It is envisioned that the method will be employed in the future to accurately and efficiently calculate 2D spectra of more extensive systems, such as photosynthetic supercomplexes.

Inter-subunit energy transfer processes in a minimal plant photosystem II supercomplex.

Photosystem II (PSII) is an integral part of the photosynthesis machinery, in which several light-harvesting complexes rely on inter-complex excitonic energy transfer (EET) processes to channel energy to the reaction center. In this paper, we report on a direct observation of the inter-complex EET in a minimal PSII supercomplex from plants, containing the trimeric light-harvesting complex II (LHCII), the monomeric light-harvesting complex CP26, and the monomeric PSII core complex. Using two-dimensional (2D) electronic spectroscopy, we measure an inter-complex EET timescale of 50 picoseconds for excitations from the LHCII-CP26 peripheral antenna to the PSII core. The 2D electronic spectra also reveal that the transfer timescale is nearly constant over the pump spectrum of 600 to 700 nanometers. Structure-based calculations reveal the contribution of each antenna complex to the measured inter-complex EET time. These results provide a step in elucidating the full inter-complex energy transfer network of the PSII machinery.

Watching Molecular Nanotubes Self-Assemble in Real Time.

Molecular self-assembly is a fundamental process in nature that can be used to develop novel functional materials for medical and engineering applications. However, their complex mechanisms make the short-lived stages of self-assembly processes extremely hard to reveal. In this article, we track the self-assembly process of a benchmark system, double-walled molecular nanotubes, whose structure is similar to that found in biological and synthetic systems. We selectively dissolved the outer wall of the double-walled system and used the inner wall as a template for the self-reassembly of the outer wall. The reassembly kinetics were followed in real time using a combination of microfluidics, spectroscopy, cryogenic transmission electron microscopy, molecular dynamics simulations, and exciton modeling. We found that the outer wall self-assembles through a transient disordered patchwork structure: first, several patches of different orientations are formed, and only on a longer time scale will the patches interact with each other and assume their final preferred global orientation. The understanding of patch formation and patch reorientation marks a crucial step toward steering self-assembly processes and subsequent material engineering.

An efficient time-domain implementation of the multichromophoric Förster resonant energy transfer method.

The excitation energy transfer (EET) process for photosynthetic antenna complexes consisting of subunits, each comprised of multiple chromophores, remains challenging to describe. The multichromophoric Förster resonance energy transfer theory is a popular method to describe the EET process in such systems. This paper presents a new time-domain method for calculating energy transfer based on the combination of multichromophoric Förster resonance energy transfer theory and the Numerical Integration of the Schrödinger Equation method. After validating the method on simple model systems, we apply it to the Light-Harvesting antenna 2 (LH2) complex, a light harvesting antenna found in purple bacteria. We use a simple model combining the overdamped Brownian oscillators to describe the dynamic disorder originating from the environmental fluctuations and the transition charge from the electrostatic potential coupling model to determine the interactions between chromophores. We demonstrate that with this model, both the calculated spectra and the EET rates between the two rings within the LH2 complex agree well with experimental results. We further find that the transfer between the strongly coupled rings of neighboring LH2 complexes can also be well described with our method. We conclude that our new method accurately describes the EET rate for biologically relevant multichromophoric systems, which are similar to the LH2 complex. Computationally, the new method is very tractable, especially for slow processes. We foresee that the method can be applied to efficiently calculate transfer in artificial systems as well and may pave the way for calculating multidimensional spectra of extensive multichromophoric systems in the future.

Structural Disorder as the Origin of Optical Properties and Spectral Dynamics in Squaraine Nano-Aggregates.

In contrast to regular J- and H-aggregates, thin film squaraine aggregates usually have broad absorption spectra containing both J-and H-like features, which are favorable for organic photovoltaics. Despite being successfully applied in organic photovoltaics for years, a clear interpretation of these optical properties by relating them to specific excited states and an underlying aggregate structure has not been made. In this work, by static and transient absorption spectroscopy on aggregated n-butyl anilino squaraines, we provide evidence that both the red- and blue-shifted peaks can be explained by assuming an ensemble of aggregates with intermolecular dipole-dipole resonance interactions and structural disorder deriving from the four different nearest neighbor alignments─in sharp contrast to previous association of the peaks with intermolecular charge-transfer interactions. In our model, the next-nearest neighbor dipole-dipole interactions may be negative or positive, which leads to the occurrence of J- and H-like features in the absorption spectrum. Upon femtosecond pulse excitation of the aggregated sample, a transient absorption spectrum deviating from the absorbance spectrum emerges. The deviation finds its origin in the excitation of two-exciton states by the probe pulse. The lifetime of the exciton is confirmed by the band integral dynamics, featuring a single-exponential decay with a lifetime of 205 ps. Our results disclose the aggregated structure and the origin of red- and blue-shifted peaks and explain the absence of photoluminescence in squaraine thin films. Our findings underline the important role of structural disorder of molecular aggregates for photovoltaic applications.

Ultrafast Excitation Energy Transfer Dynamics in the LHCII-CP29-CP24 Subdomain of Plant Photosystem II.

We measure the two-dimensional electronic spectra of the LHCII(M)-CP29-CP24 complex in photosystem II (PSII) and provide the first study of the ultrafast excitation energy transfer (EET) processes of an asymmetric and native light-harvesting assembly of the antenna of PSII. With comparisons to LHCII, we observe faster energy equilibrations in the intermediate levels of the LHCII(M)-CP29-CP24 complex at 662 and 670 nm. Notably, the putative "bottleneck" states in LHCII exhibit faster effective dynamics in the LHCII(M)-CP24-CP29 complex, with the average lifetime shortening from 2.5 ps in LHCII to 1.2 ps in the bigger assembly. The observations are supported by high-level structure-based calculations, and the accelerated dynamics can be attributed to the structural change of LHCII(M) in the bigger complex. This study shows that the biological functioning structures of the complexes are important to understand the overall EET dynamics of the PSII supercomplex.

Limitations of Linear Dichroism Spectroscopy for Elucidating Structural Issues of Light-Harvesting Aggregates in Chlorosomes.

Linear dichroism (LD) spectroscopy is a widely used technique for studying the mutual orientation of the transition-dipole moments of the electronically excited states of molecular aggregates. Often the method is applied to aggregates where detailed information about the geometrical arrangement of the monomers is lacking. However, for complex molecular assemblies where the monomers are assembled hierarchically in tiers of supramolecular structural elements, the method cannot extract well-founded information about the monomer arrangement. Here we discuss this difficulty on the example of chlorosomes, which are the light-harvesting aggregates of photosynthetic green-(non) sulfur bacteria. Chlorosomes consist of hundreds of thousands of bacteriochlorophyll molecules that self-assemble into secondary structural elements of curved lamellar or cylindrical morphology. We exploit data from polarization-resolved fluorescence-excitation spectroscopy performed on single chlorosomes for reconstructing the corresponding LD spectra. This reveals that LD spectroscopy is not suited for benchmarking structural models in particular for complex hierarchically organized molecular supramolecular assemblies.

An Exciton Dynamics Model of Bryopsis corticulans Light-Harvesting Complex II.

Bryopsis corticulans is a marine green macroalga adapted to the intertidal environment. It possesses siphonaxanthin-binding light-harvesting complexes of photosystem II (LHCII) with spectroscopic properties markedly different from the LHCII in plants. By applying a phenomenological fitting procedure to the two-dimensional electronic spectra of the LHCII from B. corticulans measured at 77 K, we can extract information about the excitonic states and energy-transfer processes. The fitting method results in well-converged parameters, including excitonic energy levels with their respective transition dipole moments, spectral widths, energy-transfer rates, and coupling properties. The 2D spectra simulated from the fitted parameters concur very well with the experimental data, showing the robustness of the fitting method. An excitonic energy-transfer scheme can be constructed from the fitting parameters. It shows the rapid energy transfer from chlorophylls (Chls) b to a at subpicosecond time scales and a long-lived state in the Chl b region at around 659 nm. Three weakly connected terminal states are resolved at 671, 675, and 677 nm. The lowest state is higher in energy than that in plant LHCII, which is probably because of the fewer number of Chls a in a B. corticulans LHCII monomer. Modeling based on existing Hamiltonians for the plant LHCII structure with two Chls a switched to Chls b suggests several possible Chl a-b replacements in comparison with those of plant LHCII. The adaptive changes result in a slower energy equilibration in the complex, revealed by the longer relaxation times of several exciton states compared to those of plant LHCII. The strength of our phenomenological fitting method for obtaining excitonic energy levels and energy-transfer network is put to the test in systems such as B. corticulans LHCII, where prior knowledge on exact assignment and spatial locations of pigments are lacking.

Molecular versus Excitonic Disorder in Individual Artificial Light-Harvesting Systems.

Natural light-harvesting antennae employ a dense array of chromophores to optimize energy transport via the formation of delocalized excited states (excitons), which are critically sensitive to spatio-energetic variations of the molecular structure. Identifying the origin and impact of such variations is highly desirable for understanding and predicting functional properties yet hard to achieve due to averaging of many overlapping responses from individual systems. Here, we overcome this problem by measuring the heterogeneity of synthetic analogues of natural antennae-self-assembled molecular nanotubes-by two complementary approaches: single-nanotube photoluminescence spectroscopy and ultrafast 2D correlation. We demonstrate remarkable homogeneity of the nanotube ensemble and reveal that ultrafast (∼50 fs) modulation of the exciton frequencies governs spectral broadening. Using multiscale exciton modeling, we show that the dominance of homogeneous broadening at the exciton level results from exchange narrowing of strong static disorder found for individual molecules within the nanotube. The detailed characterization of static and dynamic disorder at the exciton as well as the molecular level presented here opens new avenues in analyzing and predicting dynamic exciton properties, such as excitation energy transport.

Multiscale modeling of molecular structure and optical properties of complex supramolecular aggregates.

Supramolecular aggregates of synthetic dye molecules offer great perspectives to prepare biomimetic functional materials for light-harvesting and energy transport. The design is complicated by the fact that structure-property relationships are hard to establish, because the molecular packing results from a delicate balance of interactions and the excitonic properties that dictate the optics and excited state dynamics, in turn sensitively depend on this packing. Here we show how an iterative multiscale approach combining molecular dynamics and quantum mechanical exciton modeling can be used to obtain accurate insight into the packing of thousands of cyanine dye molecules in a complex double-walled tubular aggregate in close interaction with its solvent environment. Our approach allows us to answer open questions not only on the structure of these prototypical aggregates, but also about their molecular-scale structural and energetic heterogeneity, as well as on the microscopic origin of their photophysical properties. This opens the route to accurate predictions of energy transport and other functional properties.

Exciton localization in tubular molecular aggregates: Size effects and optical response.

We study the exciton localization and resulting optical response for disordered tubular aggregates of optically active molecules. It has previously been shown that such tubular structures allow for excitons delocalized over more than a thousand molecules, owing to the combined effects of long-range dipole-dipole interactions and the higher-dimensional (not truly one-dimensional) nature of the aggregate. Such large delocalization sizes prompt the question to what extent in experimental systems the delocalization may still be determined by the aggregate size (diameter and length) and how this affects the aggregate's optical response and dynamics. We perform a systematic study of the size effects on the localization properties using numerical simulations of the exciton states in a cylindrical model structure inspired by the previously derived geometry of a cylindrical aggregate of cyanine dye molecules (C8S3). To characterize the exciton localization, we calculate the participation ratio and the autocorrelation function of the exciton wave function. We also calculate the density of states and absorption spectrum. We find strong effects of the tube's radius on the localization and optical properties in the range of parameters relevant to the experiment. In addition, surprisingly, we find that even for tubes as long as 750 nm, the localization size is limited by the tube's length for disorder values that are relevant to experimental circumstances, while observable effects of the tube's length in the absorption spectrum still occur for tube lengths up to about 150 nm. The latter may explain the changes in the optical spectra observed during the aging process of bromine-substituted C8S3 aggregates. For weak disorder, the exciton wave functions exhibit a scattered, fractal-like nature, similar to the quasi-particles in two-dimensional disordered systems.

Interplay between structural hierarchy and exciton diffusion in artificial light harvesting.

Unraveling the nature of energy transport in multi-chromophoric photosynthetic complexes is essential to extract valuable design blueprints for light-harvesting applications. Long-range exciton transport in such systems is facilitated by a combination of delocalized excitation wavefunctions (excitons) and exciton diffusion. The unambiguous identification of the exciton transport is intrinsically challenging due to the system's sheer complexity. Here we address this challenge by employing a spectroscopic lab-on-a-chip approach: ultrafast coherent two-dimensional spectroscopy and microfluidics working in tandem with theoretical modeling. We show that at low excitation fluences, the outer layer acts as an exciton antenna supplying excitons to the inner tube, while under high excitation fluences the former converts its functionality into an exciton annihilator which depletes the exciton population prior to any exciton transfer. Our findings shed light on the excitonic trajectories across different sub-units of a multi-layered artificial light-harvesting complex and underpin their great potential for directional excitation energy transport.

Structural Variations in Chlorosomes from Wild-Type and a bchQR Mutant of Chlorobaculum tepidum Revealed by Single-Molecule Spectroscopy.

Green sulfur bacteria can grow photosynthetically by absorbing only a few photons per bacteriochlorophyll molecule per day. They contain chlorosomes, perhaps the most efficient light-harvesting antenna system found in photosynthetic organisms. Chlorosomes contain supramolecular structures comprising hundreds of thousands of bacteriochlorophyll molecules, which are properly positioned with respect to one another solely by self-assembly and not by using a protein scaffold as a template for directing the mutual arrangement of the monomers. These two features-high efficiency and self-assembly-have attracted considerable attention for developing light-harvesting systems for artificial photosynthesis. However, reflecting the heterogeneity of the natural system, detailed structural information at atomic resolution of the molecular aggregates is not yet available. Here, we compare the results for chlorosomes from the wild type and two mutants of Chlorobaculum tepidum obtained by polarization-resolved, single-particle fluorescence-excitation spectroscopy and theoretical modeling with results previously obtained from nuclear-magnetic resonance spectroscopy and cryo-electron microscopy. Only the combination of information obtained from all of these techniques allows for an unambiguous description of the molecular packing of bacteriochlorophylls within chlorosomes. In contrast to some suggestions in the literature, we find that, for the chlorosomes from the wild type as well as for those from mutants, the dominant secondary structural element features tubular symmetry following a very similar construction principle. Moreover, the results suggest that the various options for methylation of the bacteriochlorophyll molecules, which are a primary source of the structural (and spectral) heterogeneity of wild-type chlorosome samples, are exploited by nature to achieve improved spectral coverage at the level of individual chlorosomes.

Identification and characterization of diverse coherences in the Fenna-Matthews-Olson complex.

The idea that excitonic (electronic) coherences are of fundamental importance to natural photosynthesis gained popularity when slowly dephasing quantum beats (QBs) were observed in the two-dimensional electronic spectra of the Fenna-Matthews-Olson (FMO) complex at 77 K. These were assigned to superpositions of excitonic states, a controversial interpretation, as the strong chromophore-environment interactions in the complex suggest fast dephasing. Although it has been pointed out that vibrational motion produces similar spectral signatures, a concrete assignment of these oscillatory signals to distinct physical processes is still lacking. Here we revisit the coherence dynamics of the FMO complex using polarization-controlled two-dimensional electronic spectroscopy, supported by theoretical modelling. We show that the long-lived QBs are exclusively vibrational in origin, whereas the dephasing of the electronic coherences is completed within 240 fs even at 77 K. We further find that specific vibrational coherences are produced via vibronically coupled excited states. The presence of such states suggests that vibronic coupling is relevant for photosynthetic energy transfer.

The origin of absorptive features in the two-dimensional electronic spectra of rhodopsin.

In rhodopsin, the absorption of a photon causes the isomerization of the 11-cis isomer of the retinal chromophore to its all-trans isomer. This isomerization is known to occur through a conical intersection (CI) and the internal conversion through the CI is known to be vibrationally coherent. Recently measured two-dimensional electronic spectra (2DES) showed dramatic absorptive spectral features at early waiting times associated with the transition through the CI. The common two-state two-mode model Hamiltonian was unable to elucidate the origin of these features. To rationalize the source of these features, we employ a three-state three-mode model Hamiltonian where the hydrogen out-of plane (HOOP) mode and a higher-lying electronic state are included. The 2DES of the retinal chromophore in rhodopsin are calculated and compared with the experiment. Our analysis shows that the source of the observed features in the measured 2DES is the excited state absorption to a higher-lying electronic state and not the HOOP mode.

Exciton-Exciton Annihilation Is Coherently Suppressed in H-Aggregates, but Not in J-Aggregates.

We theoretically demonstrate a strong dependence of the annihilation rate between (singlet) excitons on the sign of dipole-dipole couplings between molecules. For molecular H-aggregates, where this sign is positive, the phase relation of the delocalized two-exciton wave functions causes a destructive interference in the annihilation probability. For J-aggregates, where this sign is negative, the interference is constructive instead; as a result, no such coherent suppression of the annihilation rate occurs. As a consequence, room temperature annihilation rates of typical H- and J-aggregates differ by a factor of ∼3, while an order of magnitude difference is found for low-temperature aggregates with a low degree of disorder. These findings, which explain experimental observations, reveal a fundamental principle underlying exciton-exciton annihilation, with major implications for technological devices and experimental studies involving high excitation densities.

Spectral line shapes in linear absorption and two-dimensional spectroscopy with skewed frequency distributions.

The effect of Gaussian dynamics on the line shapes in linear absorption and two-dimensional correlation spectroscopy is well understood as the second-order cumulant expansion provides exact spectra. Gaussian solvent dynamics can be well analyzed using slope line analysis of two-dimensional correlation spectra as a function of the waiting time between pump and probe fields. Non-Gaussian effects are not as well understood, even though these effects are common in nature. The interpretation of the spectra, thus far, relies on complex case to case analysis. We investigate spectra resulting from two physical mechanisms for non-Gaussian dynamics, one relying on the anharmonicity of the bath and the other on non-linear couplings between bath coordinates. These results are compared with outcomes from a simpler log-normal dynamics model. We find that the skewed spectral line shapes in all cases can be analyzed in terms of the log-normal model, with a minimal number of free parameters. The effect of log-normal dynamics on the spectral line shapes is analyzed in terms of frequency correlation functions, maxline slope analysis, and anti-diagonal linewidths. A triangular line shape is a telltale signature of the skewness induced by log-normal dynamics. We find that maxline slope analysis, as for Gaussian dynamics, is a good measure of the solvent dynamics for log-normal dynamics.

Steering Self-Assembly of Amphiphilic Molecular Nanostructures via Halogen Exchange.

In the field of self-assembly, the quest for gaining control over the supramolecular architecture without affecting the functionality of the individual molecular building blocks is intrinsically challenging. By using a combination of synthetic chemistry, cryogenic transmission electron microscopy, optical absorption measurements, and exciton theory, we demonstrate that halogen exchange in carbocyanine dye molecules allows for fine-tuning the diameter of the self-assembled nanotubes formed by these molecules, while hardly affecting the molecular packing determined by hydrophobic/hydrophilic interactions. Our findings open a unique way to study size effects on the optical properties and exciton dynamics of self-assembled systems under well-controlled conditions.

Direct Imaging of Exciton Transport in Tubular Porphyrin Aggregates by Ultrafast Microscopy.

Long-range exciton transport is a key challenge in achieving efficient solar energy harvesting in both organic solar cells and photosynthetic systems. Self-assembled molecular aggregates provide the potential for attaining long-range exciton transport through strong intermolecular coupling. However, there currently lacks an experimental tool to directly characterize exciton transport in space and in time to elucidate mechanisms. Here we report a direct visualization of exciton diffusion in tubular molecular aggregates by transient absorption microscopy with ∼200 fs time resolution and ∼50 nm spatial precision. These direct measurements provide exciton diffusion constants of 3-6 cm2 s-1 for the tubular molecular aggregates, which are 3-5 times higher than a theoretical lower bound obtained by assuming incoherent hopping. These results suggest that coherent effects play a role, despite the fact that exciton states near the band bottom crucial for transport are only weakly delocalized (over <10 molecules). The methods presented here establish a direct approach for unraveling the mechanisms and main parameters underlying exciton transport in large molecular assemblies.