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.

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.

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.

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.

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.

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.

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.

Robust excitons inhabit soft supramolecular nanotubes.

Nature's highly efficient light-harvesting antennae, such as those found in green sulfur bacteria, consist of supramolecular building blocks that self-assemble into a hierarchy of close-packed structures. In an effort to mimic the fundamental processes that govern nature's efficient systems, it is important to elucidate the role of each level of hierarchy: from molecule, to supramolecular building block, to close-packed building blocks. Here, we study the impact of hierarchical structure. We present a model system that mirrors nature's complexity: cylinders self-assembled from cyanine-dye molecules. Our work reveals that even though close-packing may alter the cylinders' soft mesoscopic structure, robust delocalized excitons are retained: Internal order and strong excitation-transfer interactions--prerequisites for efficient energy transport--are both maintained. Our results suggest that the cylindrical geometry strongly favors robust excitons; it presents a rational design that is potentially key to nature's high efficiency, allowing construction of efficient light-harvesting devices even from soft, supramolecular materials.

Elliptically polarized modes for the unidirectional excitation of surface plasmon polaritons.

We propose a new method for the directional excitation of surface plasmon polaritons by a metal nanoparticle antenna, based on the elliptical polarization of the normal modes of the antenna when it is in close proximity to a metallic substrate. The proposed theoretical model allows for the full characterization of the modes, giving the dipole configuration, frequency and lifetime. As a proof of principle, we have performed calculations for a dimer antenna and we report that surface plasmon polaritons can be excited in a given direction with an intensity of more than two orders of magnitude larger than in the opposite direction. Furthermore, using the fact that the response to any excitation can be written as a superposition of the normal modes, we show that this directionality can easily be accessed by exciting the system with a local source or a plane wave. Lastly, exploiting the interference between the normal modes, the directionality can be switched for a specific excitation. We envision the proposed mechanism to be a very useful tool for the design of antennas in layered media.

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.

Laser-Limited Signatures of Quantum Coherence.

Quantum coherence is proclaimed to promote efficient energy collection by light-harvesting complexes and prototype organic photovoltaics. However, supporting spectroscopic studies are hindered by the problem of distinguishing between the excited state and ground state origin of coherent spectral transients. Coherence amplitude maps, which systematically represent quantum beats observable in two-dimensional (2D) spectroscopy, are currently the prevalent tool for making this distinction. In this article, we present coherence amplitude maps of a molecular dimer, which have become significantly distorted as a result of the finite laser bandwidth used to record the 2D spectra. We argue that under standard spectroscopic conditions similar distortions are to be expected for compounds absorbing over a spectral range similar to, or exceeding, that of the dimer. These include virtually all photovoltaic polymers and certain photosynthetic complexes. With the distortion of coherence amplitude maps, alternative ways to identify quantum coherence are called for. Here, we use numerical simulations that reproduce the essential photophysics of the dimer to unambiguously determine the excited state origin of prominent quantum beats observed in the 2D spectral measurements. This approach is proposed as a dependable method for coherence identification.

How two-dimensional brick layer J-aggregates differ from linear ones: Excitonic properties and line broadening mechanisms.

We study the excitonic coupling and homogeneous spectral line width of brick layer J-aggregate films. We begin by analysing the structural information revealed by the two-exciton states probed in two-dimensional spectra. Our first main result is that the relation between the excitonic couplings and the spectral shift in a two-dimensional structure is different (larger shift for the same nearest neighbour coupling) from that in a one-dimensional structure, which leads to an estimation of dipolar coupling in two-dimensional lattices. We next investigate the mechanisms of homogeneous broadening--population relaxation and pure dephasing--and evaluate their relative importance in linear and two-dimensional aggregates. Our second main result is that pure dephasing dominates the line width in two-dimensional systems up to a crossover temperature, which explains the linear temperature dependence of the homogeneous line width. This is directly related to the decreased density of states at the band edge when compared with linear aggregates, thus reducing the contribution of population relaxation to dephasing. Pump-probe experiments are suggested to directly measure the lifetime of the bright state and can therefore support the proposed model.

Engineering plasmon dispersion relations: hybrid nanoparticle chain-substrate plasmon polaritons.

We consider the dispersion relations of the optical excitations in a chain of silver nanoparticles situated above a metal substrate and show that they are hybrid plasmon polaritons, composed of localized surface plasmons and surface plasmon polaritons. We demonstrate a strong dependence of the system's optical properties on the plasma frequency of the substrate and that choosing the appropriate plasma frequency allows one to engineer the modes to have a very high, very low or even negative group velocity. For the latter, Poynting vector calculations reveal opposite phase and energy propagation. We expect that our results will contribute to the design of nano-optical devices with specific transport properties.

First-principles calculation of the optical properties of an amphiphilic cyanine dye aggregate.

Using a first-principles approach, we calculate electronic and optical properties of molecular aggregates of the dye amphi-pseudoisocyanine, whose structures we obtained from molecular dynamics (MD) simulations of the self-aggregation process. Using quantum chemistry methods, we translate the structural information into an effective time-dependent Frenkel exciton Hamiltonian for the dominant optical transitions in the aggregate. This Hamiltonian is used to calculate the absorption spectrum. Detailed analysis of the dynamic fluctuations in the molecular transition energies and intermolecular excitation transfer interactions in this Hamiltonian allows us to elucidate the origin of the relevant time scales; short time scales, on the order of up to a few hundreds of femtoseconds, result from internal motions of the dye molecules, while the longer (a few picosecond) time scales we ascribe to environmental motions. The absorption spectra of the aggregate structures obtained from MD feature a blue-shifted peak compared to that of the monomer; thus, our aggregates can be classified as H-aggregates, although considerable oscillator strength is carried by states along the entire exciton band. Comparison to the experimental absorption spectrum of amphi-PIC aggregates shows that the simulated line shape is too wide, pointing to too much disorder in the internal structure of the simulated aggregates.

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.

Bistable optical response of a nanoparticle heterodimer: mechanism, phase diagram, and switching time.

We conduct a theoretical study of the bistable optical response of a nanoparticle heterodimer comprised of a closely spaced semiconductor quantum dot and a metal nanoparticle. The bistable nature of the response results from the interplay between the quantum dot's optical nonlinearity and its self-action (feedback) originating from the presence of the metal nanoparticle. The feedback is governed by a complex valued coupling parameter G = G(R) + iG(I). We calculate the bistability phase diagram within the system's parameter space: spanned by G(R), G(I), and Δ, the latter being the detuning between the driving frequency and the transition frequency of the quantum dot. Additionally, switching times from the lower stable branch to the upper one (and vice versa) are calculated as a function of the intensity of the driving field. The conditions for bistability to occur can be realized, for example, for a heterodimer comprised of a closely spaced CdSe (or CdSe/ZnSe) quantum dot and a gold nanosphere.

Surface hopping modeling of two-dimensional spectra.

Recently, two-dimensional (2D) electronic spectroscopy has become an important tool to unravel the excited state properties of complex molecular assemblies, such as biological light harvesting systems. In this work, we propose a method for simulating 2D electronic spectra based on a surface hopping approach. This approach self-consistently describes the interaction between photoactive chromophores and the environment, which allows us to reproduce a spectrally observable dynamic Stokes shift. Through an application to a dimer, the method is shown to also account for correct thermal equilibration of quantum populations, something that is of great importance for processes in the electronic domain. The resulting 2D spectra are found to nicely agree with hierarchy of equations of motion calculations. Contrary to the latter, our method is unrestricted in describing the interaction between the chromophores and the environment, and we expect it to be applicable to a wide variety of molecular systems.