Optical signatures of the coupling between excitons and charge transfer states in linear molecular aggregates.

Charge Transfer (CT) has enjoyed continuous interest due to increasing experimental control over molecular structures, leading to applications in, for example, photovoltaics and hydrogen production. In this paper, we investigate the effect of CT states on the absorption spectrum of linear molecular aggregates using a scattering matrix technique that allows us to deal with arbitrarily large systems. The presented theory performs well for both strong and weak mixing of exciton and CT states, bridging the gap between previously employed methods, which are applicable in only one of these limits. In experimental spectra, the homogeneous linewidth is often too large to resolve all optically allowed transitions individually, resulting in a characteristic two-peak absorption spectrum in both the weak- and strong-coupling regime. Using the scattering matrix technique, we examine the contributions of free and bound states in detail. We conclude that the skewness of the high-frequency peak may be used as a new way to identify the exciton-CT-state coupling strength.

Scaling relations of exciton diffusion in linear aggregates with static and dynamic disorder.

Exciton diffusion plays an important role in many opto-electronic processes and phenomena. Understanding the interplay of intermolecular coupling, static energetic disorder, and dephasing caused by environmental fluctuations (dynamic disorder) is crucial to optimize exciton diffusion under various physical conditions. We report on a systematic analysis of the exciton diffusion constant in linear aggregates using the Haken-Strobl-Reineker model to describe this interplay. We numerically investigate the static-disorder scaling of (i) the diffusion constant in the limit of small dephasing rate, (ii) the dephasing rate at which the diffusion is optimized, and (iii) the value of the diffusion constant at the optimal dephasing rate. Three scaling regimes are found, associated with, respectively, fully delocalized exciton states (finite-size effects), weakly localized states, and strongly localized states. The scaling powers agree well with analytically estimated ones. In particular, in the weakly localized regime, the numerical results corroborate the so-called quantum Goldilocks principle to find the optimal dephasing rate and maximum diffusion constant as a function of static disorder, while in the strong-localization regime, these quantities can be derived fully analytically.

Probing size variations of molecular aggregates inside chlorosomes using single-object spectroscopy.

We theoretically investigate the possibility to use single-object spectroscopy to probe size variations of the bacteriochlorophyll aggregates inside chlorosomes. Chlorosomes are the light-harvesting organelles of green sulfur and non-sulfur bacteria. They are known to be the most efficient light-harvesting systems in nature. Key to this efficiency is the organization of bacteriochlorophyll molecules in large self-assembled aggregates that define the secondary structure inside the chlorosomes. Many studies have been reported to elucidate the morphology of these aggregates and the molecular packing inside them. It is widely believed that tubular aggregates play an important role. Because the size (radius and length) of these aggregates affects the optical and excitation energy transport properties, it is of interest to be able to probe these quantities inside chlorosomes. We show that a combination of single-chlorosome linear polarization resolved spectroscopy and single-chlorosome circular dichroism spectroscopy may be used to access the typical size of the tubular aggregates within a chlorosome and, thus, probe possible variations between individual chlorosomes that may result, for instance, from different stages in growth or different growth conditions.

Unraveling intra-aggregate structural disorder using single-molecule spectroscopy.

Structural disorder within self-assembled molecular aggregates may have strong effects on their optical functionality. Such disorder, however, is hard to explore using standard ensemble measurements. In this paper, we report on the characterization of intra-aggregate structural disorder through a linewidth analysis of fluorescence excitation experiments on individual zinc-chlorin (ZnChl) nanotubular molecular aggregates. Recent experiments suggest an anomaly in the linewidths of the two absorption bands that dominate the spectra: the higher-energy bands on average show a smaller linewidth than the lower-energy bands. This anomaly is explored in this paper by analyzing and modeling the correlation of the two linewidths for each aggregate. We exploit a Frenkel exciton model to show that the experimentally observed correlation of linewidths and other statistical properties of the single-aggregate spectra can be explained from small variations of the molecular orientations within individual aggregates.

Signature of anomalous exciton localization in the optical response of self-assembled organic nanotubes.

We show that the disorder scaling of the low-temperature optical absorption linewidth of tubular molecular assemblies sharply contrasts with that known for one-dimensional aggregates. The difference can be explained by an anomalous localization of excitons, which arises from the combination of long-range intermolecular interactions and the tube's higher-dimensional geometry. As a result, the exciton density of states near the band bottom drops to zero, leading to a strong suppression of exciton localization. Our results explain the strong linear dichroism and weak exciton-exciton scattering in tubular J aggregates observed in experiments and suggest that for nanoscale wirelike applications a tubular shape is to be preferred over a truly one-dimensional chain.

Optical nanoantennas with tunable radiation patterns.

We address new optical nanoantenna systems with tunable highly directional radiation patterns. The antenna comprises a regular linear array of metal nanoparticles in the proximity of an interface with high dielectric contrast. We show that the radiation pattern of the system can be controlled by changing parameters of the excitation, such as the polarization and/or incidence angles. In the case of excitation under the total reflection condition, the system operates as a nanoscopic source of radiation, converting the macroscopic incident plane wavefront into a narrow beam of light with adjustable characteristics. We derive also simple analytical formulas which give an excellent description of the radiation pattern and provide a useful tool for analysis and antenna design.

Calculating two-dimensional spectra with the mixed quantum-classical Ehrenfest method.

We present a mixed quantum-classical simulation approach to calculate two-dimensional spectra of coupled two-level electronic model systems. We include the change in potential energy of the classical system due to transitions in the quantum system using the Ehrenfest method. We study how this feedback of the quantum system on the classical system influences the shape of two-dimensional spectra. We show that the feedback leads to the expected Stokes shift of the energy levels in the quantum system. This subsequently leads to changes in the population transfer between quantum sites, which in turn influence the intensities of the peaks in two-dimensional spectra. The obtained spectra are compared with spectra calculated using the Hierarchical Equations of Motion method which is exact. While the spectra match perfectly for short waiting times, clear differences are found for longer waiting times. This is attributed to a violation of detailed balance between the quantum states in the Ehrenfest method. The energy of the total quantum-classical system however does obey a Boltzmann distribution, when coupled to a stochastic heat bath.

Subdiffusive exciton motion in systems with heavy-tailed disorder.

We study the transport of collective excitations (Frenkel excitons) in systems with static disorder in the transition energies, not limiting ourselves to Gaussian transition energy distributions. Instead, we generalize this model to the wider class of Lévy stable distributions, characterized by heavy tails. Phonon-assisted scattering of excitons, localized by the disorder, leads to thermally activated exciton motion. The time evolution of the second moment of the exciton distribution is shown to be sublinear, thus indicating that the exciton dynamics in such systems is not diffusive, but rather subdiffusive instead. The heavier the tail in the transition energy distribution is, the larger are the deviations from the diffusive regime. This from fluctuations of site energies larger than the exciton band width (outliers). We show that the occurrence of subdiffusive transport for heavy-tailed disorder distributions can be understood from the scattering rate distributions, which possess a (second) peak at zero scattering rate.

Photon emission statistics and photon tracking in single-molecule spectroscopy of molecular aggregates: dimers and trimers.

Based on the generating function formalism, we investigate broadband photon statistics of emission for single dimers and trimers driven by a continuous monochromatic laser field. In particular, we study the first and second moments of the emission statistics, which are the fluorescence excitation line shape and Mandel's Q parameter. Numerical results for this line shape and the Q parameter versus laser frequency in the limit of long measurement times are obtained. We show that in the limit of small Rabi frequencies and laser frequencies close to resonance with one of the one-exciton states, the results for the line shape and Q parameter reduce to those of a two-level monomer. For laser frequencies halfway the transition frequency of a two-exciton state, the photon bunching effect associated with two-photon absorption processes is observed. This super-Poissonian peak is characterized in terms of the ratio between the two-photon absorption line shape and the underlying two-level monomer line shapes. Upon increasing the Rabi frequency, the Q parameter shows a transition from super- to sub- to super-Poissonian statistics. Results of broadband photon statistics are also discussed in the context of a transition (frequency) resolved photon detection scheme, photon tracking, which provides a greater insight in the different physical processes that occur in the multi-level systems.

Disorder-induced exciton localization and violation of optical selection rules in supramolecular nanotubes.

Using numerical simulations, we study the effect of disorder on the optical properties of cylindrical aggregates of molecules with strong excitation transfer interactions. The exciton states and the energy transport properties of such molecular nanotubes attract considerable interest for application in artificial light-harvesting systems and energy transport wires. In the absence of disorder, such nanotubes exhibit two optical absorption peaks, resulting from three super-radiant exciton states, one polarized along the axis of the cylinder, the other two (degenerate) polarized perpendicular to this axis. These selection rules, imposed by the cylindrical symmetry, break down in the presence of disorder in the molecular transition energies, due to the fact that the exciton states localize and no longer wrap completely around the tube. We show that the important parameter is the ratio of the exciton localization length and the tube's circumference. When this ratio decreases, the distribution of polarization angles of the exciton states changes from a two-peak structure (at zero and ninety degrees) to a single peak determined by the orientation of individual molecules within the tube. This is also reflected in a qualitative change of the absorption spectrum. The latter agrees with recent experimental findings.

Excitons in molecular aggregates with Lévy-type disorder: anomalous localization and exchange broadening of optical spectra.

We predict the existence of exchange broadening of optical line shapes in disordered molecular aggregates and a nonuniversal disorder scaling of the localization characteristics of the collective electronic excitations (excitons). These phenomena occur for heavy-tailed Lévy disorder distributions with divergent second moments-distributions that play a role in many branches of physics. Our results sharply contrast with aggregate models commonly analyzed, where the second moment is finite. They bear a relevance for other types of collective excitations as well.

Exciton spectra and the microscopic structure of self-assembled porphyrin nanotubes.

The optical properties of tubular aggregates formed by self-assembly of zwitterionic meso-tetra(4-sulfonatophenyl)porphyrin (TPPS4) molecules are studied through a combination of experimental and theoretical techniques. The interest in these systems, with diameters of 18 nm and lengths extending up to micrometers, derives from their strong interaction with light and their similarity to natural light-harvesting systems for photosynthesis. The absorption and linear dichroism spectra are obtained in the spectral region from 300 to 750 nm, which includes the exciton bands deriving from the molecular B (Soret) as well as the Q transitions. We demonstrate that a Frenkel exciton model which takes into account the four dominant molecular excited states (Bx, By, Qx, and Qy) provides a good global fit to the experimental spectra. From comparison between theory and experiment, we propose a detailed molecular structure within the nanotube.

Spectral and Structural Variations of Biomimetic Light-Harvesting Nanotubes.

Bioinspired, self-assembled nanotubes have been investigated by low-temperature, polarization-resolved single-tube spectroscopy. These assemblies are based on zinc chlorin monomers and are considered as model systems that resemble the secondary structural elements in the natural light-harvesting systems of green (non)sulfur bacteria. Compared to the natural systems, the spectral parameters extracted from the single-nanotube spectra feature distributions with significantly smaller widths, which is ascribed to a tremendous reduction of structural heterogeneity in the artificial systems. Employing quantum chemical molecular modeling the spectra of individual nanotubes can be explained consistently only for a molecular packing model that is fundamentally different from those considered so far for the natural systems. Subsequent theoretical simulations reveal that the remaining spectral variations between single nanotubes can be traced back to small variations of the mutual orientations of the monomer transition dipole moments that are far beyond the resolving power of high-resolution electron microscopy imaging techniques.

Excitation energy transfer between closely spaced multichromophoric systems: effects of band mixing and intraband relaxation.

We theoretically analyze the excitation energy transfer between two closely spaced linear molecular J-aggregates, whose excited states are Frenkel excitons. The aggregate with the higher (lower) exciton band edge energy is considered as the donor (acceptor). The celebrated theory of Förster resonance energy transfer (FRET), which relates the transfer rate to the overlap integral of optical spectra, fails in this situation. We point out that, in addition to the well-known fact that the point-dipole approximation breaks down (enabling energy transfer between optically forbidden states), also the perturbative treatment of the electronic interactions between donor and acceptor system, which underlies the Förster approach, in general loses its validity due to overlap of the exciton bands. We therefore propose a nonperturbative method, in which donor and acceptor bands are mixed and the energy transfer is described in terms of a phonon-assisted energy relaxation process between the two new (renormalized) bands. The validity of the conventional perturbative approach is investigated by comparing to the nonperturbative one; in general, this validity improves for lower temperature and larger distances (weaker interactions) between the aggregates. We also demonstrate that the interference between intraband relaxation and energy transfer renders the proper definition of the transfer rate and its evaluation from experiment a complicated issue that involves the initial excitation condition. Our results suggest that the best way of determining this transfer rate between two J-aggregates is to measure the fluorescence kinetics of the acceptor J-band after resonant excitation of the donor J-band.

Temperature-dependent relaxation of excitons in tubular molecular aggregates: Fluorescence decay and stokes shift.

We report temperature-dependent steady-state and time-resolved fluorescence studies to probe the exciton dynamics in double-wall tubular J-aggregates formed by self-assembly of the dye 3,3'-bis(3-sulfopropyl)-5,5',6,6'-tetrachloro-1,1'-dioctylbenzimidacarbocyanine. We focus on the lowest energy fluorescence band, originating from the inner cylindrical wall. At low temperatures, the experiments reveal a nonexponential decay of the fluorescence, with a typical time scale that depends on the emission wavelength. At these temperatures we also find a dynamic Stokes shift of the fluorescence spectrum and its nonmonotonic dependence on temperature under steady-state conditions. All these data indicate that below about 20 K the excitons in the lowest fluorescence band do not reach thermal equilibrium before emission occurs, while above about 60 K thermalization on this time scale is complete. By comparing the two lowest fluorescence bands, we also find indications for fast energy transfer from the outer to the inner wall. We show that the Frenkel exciton model with diagonal disorder, which previously has been proposed to explain the absorption and linear dichroism spectra of these aggregates, yields a quantitative explanation to the observed dynamics. To this end, we extend the model to account for weak phonon-induced scattering of the localized exciton states; the spectral dynamics are then described by solving a Pauli master equation for the exciton populations.

Atomistic modeling of two-dimensional electronic spectra and excited-state dynamics for a Light Harvesting 2 complex.

The Light Harvesting 2 (LH2) complex is a vital part of the photosystem of purple bacteria. It is responsible for the absorption of light and transport of the resulting excitations to the reaction center in a highly efficient manner. A general description of the chromophores and the interaction with their local environment is crucial to understand this highly efficient energy transport. Here we include this interaction in an atomistic way using mixed quantum-classical (molecular dynamics) simulations of spectra. In particular, we present the first atomistic simulation of nonlinear optical spectra for LH2 and use it to study the energy transport within the complex. We show that the frequency distributions of the pigments strongly depend on their positions with respect to the protein scaffold and dynamics of their local environment. Furthermore, we show that although the pigments are closely packed the transition frequencies of neighboring pigments are essentially uncorrelated. We present the simulated linear absorption spectra for the LH2 complex and provide a detailed explanation of the states responsible for the observed two-band structure. Finally, we discuss the energy transfer within the complex by analyzing population transfer calculations and 2D spectra for different waiting times. We conclude that the energy transfer from the B800 ring to the B850 ring is mediated by intermediate states that are delocalized over both rings, allowing for a stepwise downhill energy transport.

OH-stretching in synthetic hydrogen-bonded chains.

We study hydrogen bond dynamics in stereoselectively synthesized polyalcohols by combining linear and two-dimensional (2D) infrared spectroscopy experiments with simulations. We consider two variants of the polyalcohols: the all-syn and all-anti tetrol, which because of their different stereochemistry of the hydroxyl groups form a linear hydrogen-bonded chain that is stable for tens of picoseconds or a system where hydrogen bonds are formed and broken on a picosecond timescale, respectively. The differences in structure and hydrogen bond dynamics gives rise to significant differences in the linear spectra for the two compounds. Furthermore, we show that the stronger hydrogen bonding for the all-syn variant leads to faster fluctuations of the site frequencies than for the all-anti one, which is reflected in the higher degree of homogeneous broadening in the 2D spectra. Because of the different stereochemistry, the coupling in the all-syn molecule is stronger than for the all-anti one, which leads to a faster delocalization of a local excitation. This explains the previously observed pump-frequency independent vibrational lifetime for the all-syn variant, since the excitation loses the memory of the pump frequency before relaxation. For the all-anti form, the coupling is weak and the excitation remains in the initially excited state, maintaining the memory of the pump frequency.

Utilizing redox-chemistry to elucidate the nature of exciton transitions in supramolecular dye nanotubes.

Supramolecular assemblies that interact with light have recently garnered much interest as well-defined nanoscale materials for electronic excitation energy collection and transport. However, to control such complex systems it is essential to understand how their various parts interact and whether these interactions result in coherently shared excited states (excitons) or in diffusive energy transport between them. Here, we address this by studying a model system consisting of two concentric cylindrical dye aggregates in a light-harvesting nanotube. Through selective chemistry we are able to unambiguously determine the supramolecular origin of the observed excitonic transitions. These results required the development of a new theoretical model of the supramolecular structure of the assembly. Our results demonstrate that the two cylinders of the nanotube have distinct spectral responses and are best described as two separate, weakly coupled excitonic systems. Understanding such interactions is critical to the control of energy transfer on a molecular scale, a goal in various applications ranging from artificial photosynthesis to molecular electronics.