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.     

Simulation of the two-dimensional electronic spectra of the Fenna-Matthews-Olson complex using the hierarchical equations of motion method

We apply the Liouville space hierarchical equations of motion method to calculate the linear and two-dimensional (2D) electronic spectra of the Fenna-Matthews-Olson (FMO) protein complex from Chlorobium tepidum, using a widely used model Hamiltonian. The absorption and linear dichroism spectra of the FMO complex, as well as the main features of the 2D spectra are well reproduced. However, comparison with the recent experimental 2D spectra reveals several limitations of the current model: (1) The homogeneous and inhomogeneous broadening seems to be overestimated for the first exciton peak, but may be underestimated for several other exciton peaks. (2) The calculated oscillations of the diagonal and off-diagonal peaks in the 2D spectra are much weaker than the experimental observations, which indicates that an improved model is needed for the excitonic dynamics of the FMO complex.     

Thermal broadening of the J-band in disordered linear molecular aggregates: a theoretical study

We theoretically study the temperature dependence of the J-band width in disordered linear molecular aggregates, caused by dephasing of the exciton states due to scattering on vibrations of the host matrix. In particular, we consider inelastic one- and two-phonon scatterings between different exciton states (energy-relaxation-induced dephasing), as well as the elastic two-phonon scattering of the excitons (pure dephasing). The exciton states follow from numerical diagonalization of a Frenkel exciton Hamiltonian with diagonal disorder; the scattering rates between them are obtained using the Fermi golden rule. A Debye-type model for the one- and two-phonon spectral densities is used in the calculations. We find that, owing to the disorder, the dephasing rates of the individual exciton states are distributed over a wide range of values. We also demonstrate that the dominant channel of two-phonon scattering is not the elastic one, as is often tacitly assumed, but rather comes from a similar two-phonon inelastic scattering process. In order to study the temperature dependence of the J-band width, we simulate the absorption spectrum, accounting for the dephasing-induced broadening of the exciton states. We find a power-law (T(p)) temperature scaling of the effective homogeneous width, with an exponent p that depends on the shape of the spectral density of the host vibrations. In particular, for a Debye model of vibrations, we find p approximately 4, which is in good agreement with the experimental data on J aggregates of pseudoisocyanine [I. Renge and U. P. Wild, J. Phys. Chem. A, 101, 7977 (1997)].     

Nonmonotonic energy harvesting efficiency in biased exciton chains

We theoretically study the efficiency of energy harvesting in linear exciton chains with an energy bias, where the initial excitation is taking place at the high-energy end of the chain and the energy is harvested (trapped) at the other end. The efficiency is characterized by means of the average time for the exciton to be trapped after the initial excitation. The exciton transport is treated as the intraband energy relaxation over the states obtained by numerically diagonalizing the Frenkel Hamiltonian that corresponds to the biased chain. The relevant intraband scattering rates are obtained from a linear exciton-phonon interaction. Numerical solution of the Pauli master equation that describes the relaxation and trapping processes reveals a complicated interplay of factors that determine the overall harvesting efficiency. Specifically, if the trapping step is slower than or comparable to the intraband relaxation, this efficiency shows a nonmonotonic dependence on the bias: it first increases when introducing a bias, reaches a maximum at an optimal bias value, and then decreases again because of dynamic (Bloch) localization of the exciton states. Effects of on-site (diagonal) disorder, leading to Anderson localization, are addressed as well.     

2DIR spectroscopy of human amylin fibrils reflects stable β-sheet structure

The aggregation of human amylin to form amyloid contributes to islet β-cell dysfunction in type 2 diabetes. Studies of amyloid formation have been hindered by the low structural resolution or relatively modest time resolution of standard methods. Two-dimensional infrared (2DIR) spectroscopy, with its sensitivity to protein secondary structures and its intrinsic fast time resolution, is capable of capturing structural changes during the aggregation process. Moreover, isotope labeling enables the measurement of residue-specific information. The diagonal line widths of 2DIR spectra contain information about dynamics and structural heterogeneity of the system. We illustrate the power of a combined atomistic molecular dynamics simulation and theoretical and experimental 2DIR approach by analyzing the variation in diagonal line widths of individual amide I modes in a series of labeled samples of amylin amyloid fibrils. The theoretical and experimental 2DIR line widths suggest a "W" pattern, as a function of residue number. We show that large line widths result from substantial structural disorder and that this pattern is indicative of the stable secondary structure of the two β-sheet regions. This work provides a protocol for bridging MD simulation and 2DIR experiments for future aggregation studies.     

Optical spectra and localization of excitons in inhomogeneous helical cylindrical aggregates

We study the linear optical properties of helical cylindrical molecular aggregates accounting for the effects of static diagonal disorder. Absorption, linear dichroism, and circular dichroism spectra are presented, calculated using brute force numerical simulations and a modified version of the coherent potential approximation that accounts for finite size effects by using the appropriate open boundary conditions. Excellent agreement between both approaches is found. It is also shown that the inclusion of disorder results in a better agreement between calculated and measured spectra for the chlorosomes of green bacteria as compared to our previous report, where we restricted ourselves to homogeneous cylinders [Didraga, Klugkist, and Knoester, J. Phys. Chem. B 106, 11474 (2002)]. For the excitons that govern the optical response, we also investigate the disorder-induced localization properties. By analyzing an autocorrelation function of the exciton wave function, we find a strongly anisotropic localization behavior, closely following the properties of chiral wave functions which previously have been found for homogenoeus helical cylinders [Didraga and Knoester, J. Chem. Phys. 121, 946 (2004)]. It is shown that the circular dichroism spectrum may still show a strong dependence on the cylinder length, even when the exciton wave function is localized in a region small compared to the cylinder's size.     

Size-dependent exciton chirality in (R)-(+)-1,1'-bi-2-naphthol dimethyl ether nanoparticles

Organic nanoparticles from a chiral auxiliary, (R)-(+)-1,1'-bi-2-naphthol dimethyl ether (BNDE), with a range of particle sizes from 25 to 100 nm were fabricated through the reprecipitation method. It is found that BNDE nanoparticles exhibit positive exciton chirality in 200-260 nm region in circular dichroism (CD) spectra, which are completely opposite to CD spectra of the dilute solution. The exciton chirality of the particles displays size-dependent behavior; that is, the exciton chirality peaks evolve to the low-energy side with increase in particles size. CD spectra accompanied with UV, fluorescence spectra, lifetime measurements of the excited states, and quantum mechanical calculations reveal that the chirality inversion results from intermolecular exciton coupling between two adjacent BNDE molecules in the nanoparticles, and the bathochromic shift of the peaks is attributed to the increased intermolecular interaction with increasing particle size.     

Modeling of multi-exciton transient absorption spectra of protochlorophyllide aggregates in aqueous solution

Protochlorophyllide (Pchlide) is a natural porphyrin, a precursor of chlorophyll, synthesized by plants for its photosynthetic apparatus. The pigment spontaneously forms aggregates when dissolved in neat water solution. We present here calculations of the transient absorption spectra and its comprising components (ground-state bleach, stimulated emission, and excited-state absorption) for a strongly excitonically coupled linear chain of four Pchlide chromophores, using exciton theory with phenomenological Gaussian line shapes and without energetic disorder. A refined multiexciton model that includes static disorder is applied to fit the experimental power-dependent transient absorption spectra of aqueous protochlorophyllide and the kinetics for delay times up to 20 ps after photoexcitation. We show that population up to the 4-exciton manifold is sufficient to explain the pronounced saturation of the bleaching and the shape changes in the instantaneous, t = 0.2 ps transient spectra when the pulse energy is increased from 10 to 430 nJ per pulse. The decay of the multiexciton manifold is relatively slow and is preceded by a spectroscopically distinct process. We suggest that the exciton states in the Pchlide aggregates are mixed with charge-transfer states (CTS) and that the population and repopulation of the CTS coupled to the exciton states explains the relatively slow decay of the multiexciton manifold. The relevance of our results to the optical properties and dynamics of natural photosynthetic complexes and the possible physical origin of CTS formation are discussed.     

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.     

A pulse sequence for directly measuring the anharmonicities of coupled vibrations: Two-quantum two-dimensional infrared spectroscopy

We have experimentally demonstrated a pulse sequence for the acquisition of heterodyned two-dimensional infrared (2D IR) spectra that correlates the overtone and combination bands to the fundamental frequencies. The spectra are generated by Fourier transforming the time domain signal that is allowed to evolve during one- and two-quantum coherence times. In this manner, the overtone and combination bands appear along the two-quantum axis, resulting in a direct determination of the diagonal and off-diagonal anharmonicities. To demonstrate this pulse sequence, we have collected two-quantum 2D IR spectra of a ruthenium dicarbonyl complex, extracted the diagonal and off-diagonal anharmonicities, and simulated the spectra using an exciton model. Several polarization conditions are presented that suppress the diagonal or cross peaks and we have used them to improve the accuracy of the measurement.     

Excitonic effects in two-dimensional vibrational spectra of liquid formamide

The linear and two-dimensional infrared (2DIR) responses of the amide I vibrational mode in liquid formamide are investigated experimentally and theoretically using molecular dynamics simulations. The recent method based on the numerical integration of the Schr?dinger equation is employed to calculate the 2DIR spectra. Special attention is devoted to the interplay of the structural dynamics and the excitonic nature of the amide I modes in determining the optical response of the studied system. In particular, combining experimental data, simulated spectra and analysis of the simulated atomic trajectory in terms of a transition dipole coupling model, we provide a convincing explanation of the peculiar features of the 2DIR spectra, which show a substantial increase of the antidiagonal bandwidth with increasing frequency. We point out that, at variance with liquid water, the 2DIR spectral profile of formamide is determined more by the excitonic nature of the vibrational states than by the fast structural dynamics responsible for the frequency fluctuations.     

Ultrafast dynamical localization of photoexcited states in conformationally disordered poly(p-phenylenevinylene)

We consider two types of ultrafast dynamical localization of photoexcited states in conformationally disordered poly(p-phenylenevinylene). First, we discuss nonadiabatic interconversion from higher energy extended exciton states to lower energy more localized local exciton ground states. Second, we calculate the dynamics of local exciton ground states on their Born-Oppenheimer potential energy surfaces. We show that within the first C-C bond oscillation following photoexcitation (～35 fs) the exciton becomes self-trapped and localized over approximately eight monomers. This process is associated with a Calderia-Leggett type loss of phase coherence owing to the coupling of the polymer to a dissipative environment. Subsequent torsional relaxation (on a time scale of approximately picoseconds) has little effect on the localization. We conclude from this that the initial torsional disorder determines the spatial distribution and localization length of vertical excitations but that electron-phonon coupling is largely responsible for the localization length of self-trapped excitons. We next consider the effect of dynamical localization on fluorescence depolarization. We show that exciting higher energy states causes a larger fluorescence depolarization, because these states have a larger initial delocalization. Using the observation that fluorescence depolarization is a function of excitation wavelength and polymer conformation, we show how the models of exciton localization discussed here can be experimentally investigated.     

Localization and coherent dynamics of excitons in the two-dimensional optical spectrum of molecular J-aggregates

Two-dimensional optical spectra of J-aggregates at low temperature provide a large amount of information about the nature and dynamics of exciton states that is hidden in conventional broad band pump-probe spectra. By using numerical simulations, we study the two-dimensional absorption spectrum and find that it is dominated by a V-shaped negative peak and a blueshifted elliptic positive peak. We demonstrate a simple method to derive the energy dependence of the exciton localization size from the distance between these two features in the zero waiting time experiment. When the waiting time is turned on, the V peak is filled with an extra positive peak resulting from population relaxation. From the time evolution of this peak, energy dependent relaxation rates can be obtained. The oscillations of coherent contributions to the two-dimensional spectrum are not damped by inhomogeneous mechanisms and can be seen clearly.     

Low-temperature dynamics of weakly localized Frenkel excitons in disordered linear chains

We calculate the temperature dependence of the fluorescence Stokes shift and the fluorescence decay time in linear Frenkel exciton systems resulting from the thermal redistribution of exciton population over the band states. The following factors, relevant to common experimental conditions, are accounted for in our kinetic model: (weak) localization of the exciton states by static disorder, coupling of the localized excitons to vibrations in the host medium, a possible nonequilibrium of the subsystem of localized Frenkel excitons on the time scale of the emission process, and different excitation conditions (resonant or nonresonant). A Pauli master equation, with microscopically calculated transition rates, is used to describe the redistribution of the exciton population over the manifold of localized exciton states. We find a counterintuitive nonmonotonic temperature dependence of the Stokes shift. In addition, we show that depending on experimental conditions, the observed fluorescence decay time may be determined by vibration-induced intraband relaxation, rather than radiative relaxation to the ground state. The model considered has relevance to a wide variety of materials, such as linear molecular aggregates, conjugated polymers, and polysilanes.     

Discrimination between coupling networks of glucopyranosides varying at a single stereocenter using two-dimensional vibrational correlation spectroscopy

A combination of two-dimensional infrared (2DIR) correlation spectroscopy, linear absorption spectroscopy, and density functional theory quantum calculations was used to identify characteristic spectral features of two anomers of acetylated 2-azido-2-deoxy-D-glucopyranose. While the linear absorption spectra for the α and β anomers were distinctive, a substantial difference between them was observed only in the spectral region below 1200 cm(-1). The infrared correlation spectra of the two anomers differed significantly, even in regions where their linear absorption spectra were similar. Very substantial differences were found for the N≡N/C=O stretch mode region of the 2DIR correlation spectrum, indicating differences in the anharmonic coupling of the N≡N stretching mode of the equatorially oriented N(3) group with the CO modes when the C(1) ester was either in the axial (α anomer) or equatorial (β anomer) orientation. In addition, the energy transport patterns originating from the excited N≡N stretching mode were found to be different for the two anomers; up to a 1.8-fold difference in the energy transport times was observed for the probed modes of the same type in the two anomers. The results demonstrate the capability of 2DIR and relaxation-assisted 2DIR (RA 2DIR) spectroscopies to provide unique spectroscopic data specific to sugar anomers that vary at a single stereochemical center. These methods identify unique coupling networks within individual sugar stereochemical units and demonstrate the potential to identify a number of stereochemical differences among them.     

One-dimensional J-aggregates: Dependence of the properties of the exciton band on the model of the intermolecular coupling

The spectral properties of one-dimensional thiacarbocyanine dye aggregates were simulated by the combination of exciton interaction with a diagonal energetic disorder. Contrary to previous models incorporating disorder, the exciton interaction was calculated using the transition densities obtained form PPP-wave functions and interactions between all molecules were considered. The effects of the aggregate size, non-nearest neighbor interactions, diagonal disorder and to some extent exciton phonon coupling on the spectral position of the maxima, the FWHM of the spectra and the superradiance are investigated for H- and J-aggregates at 298 and 20 K. At 298 K the experimental properties of H-aggregates and J-aggregates of 3,3^′-disulfopropyl-5,5^′-dichloro-carbocyanine with 1 molecule per unit cell are compared to the simulations.     

Stochastic Liouville equation simulation of multidimensional vibrational line shapes of trialanine

The line shapes detected in coherent femtosecond vibrational spectroscopies contain direct signatures of peptide conformational fluctuations through their effect on vibrational frequencies and intermode couplings. These effects are simulated in trialanine using a Green's function solution of a stochastic Liouville equation constructed for four collective bath coordinates (two Ramachandran angles affecting the mode couplings and two diagonal energies). We find that fluctuations of the Ramachandran angles which hardly affect the linear absorption can be effectively probed by two-dimensional spectra. The signal generated at k(1)+k(2)-k(3) is particularly sensitive to such fluctuations.     

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.     

Multiple structures and dynamics of [CpRu(CO)2]2 and [CpFe(CO)2]2 in solution revealed with two-dimensional infrared spectroscopy

Two-dimensional infrared (2DIR) spectroscopy is applied to both (Cp)(2)Fe(2)(CO)(4) and its ruthenium analog (Cp)(2)Ru(2)(CO)(4) in order to study the vibrational dynamics of these two systems. Combining the results of 2DIR spectroscopy and DFT calculations, the different structural forms of both the iron and the ruthenium complexes were characterized, furthering the previous assignment of the linear IR spectrum by determining the transition frequencies associated with the different isomeric forms. Monitoring the time-dependent amplitudes of the cross peaks enabled the observation of equilibrium energy transfer dynamics between different vibrational modes of the cis-B (Cp)(2)Fe(2)(CO)(4) and the gauche-NB (Cp)(2)Ru(2)(CO)(4) complexes. Treating the energy transfer as an equilibrium process, we extracted the rate constants associated with both the uphill and the downhill transfer of vibrational energy, finding that the difference in the rate constants of the two metal complexes maps to the difference in the energy gap between the two modes involved.