Optimal Initialization of a Quantum System for an Efficient Coherent Energy Transfer?

For an energy transfer network, the irreversible depletion of excited electron energy occurs through either an efficient flow into an outer energy sink or an inefficient decay. With a small decay rate, the energy transfer efficiency is quantitatively reflected by the average life time of excitation energy before being trapped in the sink where the decay process is omitted. In the weak dissipation regime, the trapping time is analyzed within the exciton population subspace based on the secular Redfield equation. The requirement of the noise-enhanced energy transfer is obtained, where the trapping time follows an exact or approximate 1/Γ-scaling of the dissipation strength Γ. On the opposite side, optimal initial system states are conceptually constructed to suppress the 1/Γ-scaling of the trapping time and maximize the coherent transfer efficiency. Our theory is numerically testified in four models, including a biased two-site system, a symmetric three-site branching system, a homogeneous onedimensional chain, and an 8-chromophore FMO protein complex.     

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.     

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 F?rster 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 F?rster 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.     

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.     

Electronic coherence effects in photosynthetic light harvesting

Photosynthetic light harvesting is a paradigmatic example for quantum effects in biology. In this work, we review studies on quantum coherence effects in the LH2 antenna complex from purple bacteria to demonstrate how quantum mechanical rules play important roles in the speedup of excitation energy transfer, the stabilization of electronic excitations, and the robustness of light harvesting in photosynthesis. Subsequently, we present our recent theoretical studies on exciton dynamical localization and excitonic coherence generation in photosynthetic systems. We apply a variational-polaron approach to investigate decoherence of exciton states induced by dynamical fluctuations due to system-environment interactions. The results indicate that the dynamical localization of photoexcitations in photosynthetic complexes is significant and imperative for a complete understanding of coherence and excitation dynamics in photosynthesis. Moreover, we use a simple model to investigate quantum coherence effects in intercomplex excitation energy transfer in natural photosynthesis, with a focus on the likelihoods of generating excitonic coherences during the process. Our model simulations reveal that excitonic coherence between acceptor exciton states and transient nonlocal quantum correlation between distant pairs of chromophores can be generated through intercomplex energy transfer. Finally, we discuss the implications of these theoretical works and important open questions that remain to be answered.     

Exciton dynamics of GaSe nanoparticle aggregates

Time-resolved and static spectroscopic results on GaSe nanoparticle aggregates are presented to elucidate the exciton relaxation and diffusion dynamics. These results are obtained in room-temperature TOP/TOPO solutions at various concentrations. The aggregate absorption spectra are interpreted in terms of electrostatic coupling and covalent interactions between particles. The spectra at various concentrations may then be interpreted in terms of aggregate distributions calculated from a simple equilibrium model. These distributions are used to interpret concentration-dependent emission anisotropy kinetics and time-dependent emission spectral shifts. The emission spectra are reconstructed from the static emission spectra and decay kinetics obtained at a range of wavelengths. The results indicate that the aggregate z axis persistence length is about 9 particles. The results also show that the one-dimensional exciton diffusion coefficient is excitation wavelength dependent and has a value of about 2 x 10(-5) cm(2)/s following 406 nm excitation. Although exciton diffusion results in very little energy relaxation, subsequent hopping of trapped electron/hole pairs occurs by a Forster mechanism and strongly red shifts the emission spectrum.     

Interface effects and relaxation processes in nanocomposites based on CdSe/ZnS semiconductor quantum dots and porphyrin molecules

Controllable self-assembly and properties of nanocomposites based on CdSe/ZnS semiconductor quantum dots (QDs) and tetrapyridylporphyrin molecules (H₂P) as well as the dynamics of relaxation processes in these systems were studied for solutions and single nanoobjects in the temperature range of 77–295 K. It was proved that the formation of surface states of different nature is crucial to nonradiative relaxation of exciton excitation in QDs. The efficiency of QD→Н₂Р energy transfer was shown to be at most 10–15%. Regularities of photoluminescence (PL) quenching for QDs in nanocomposites in solutions of different polarity correlate with the dependences of PL blinking for single QDs. A scheme was proposed of excited states and main relaxation channels of exciton excitation energy in semiconductor QDs and QD–Н₂Р nanocomposites.     

A model of localization,soliton propagation,and self-trapping in an electronically excited atomic lattice

The localization and propagation of electronic excitation is studied in a one-dimensional lattice of atoms, in which the interatomic potential is of Lennard-Jones (9-6) form. The dynamics are followed taking account of the full potential, bringing out aspects that do not appear in the harmonic approximation. Calculations are made first in a continuum model, and tested numerically for real systems. Electronic excitation of an atom may cause a change in its dispersive binding to neighbours, and there can be resonance coupling leading to excitation transfer and delocalization. With resonance coupling only, i.e. with no change in the dispersion interaction, the new result is found that there can be localization into states below the exciton band, arising from the changes in the strength of resonance coupling caused by variations in lattice spacing. These states become deeper when a change in dispersion energy is added; they can propagate as solitons without energy loss when the dispersion energy change is small; for larger changes the excitation is trapped.     

Modeling of photosynthetic light-harvesting: From structure to function

In order to bridge the gap between the crystal structure of photosynthetic pigment-protein complexes and the data gathered in optical experiments, two essential problems need to be solved. On one hand, theories of optical spectra and excitation energy transfer have to be developed that take into account the pigment-pigment (excitonic) and the pigment-protein (exciton-vibrational) coupling on an equal footing. On the other hand, the parameters entering these theories need to be calculated from the structural data. Good agreement between simulations and experimental data then allows to draw conclusions on structure-function relationships of these complexes and to make predictions. In the development of theory, a delicate question is how to describe the interplay between the quantum dynamics of excitons and the dephasing of coherences by the coupling of excitons to protein vibrations. Quantum mechanic coherences are utilized for efficient light harvesting. In the reaction centers of purple bacteria an energy sink is created by a coherent coupling of exciton states to intermolecular charge transfer states. The dephasing of coherences can be monitored, e.g., by the temperature dependent shift of optical lines. In the Fenna-Matthews-Olson protein, which acts as an excitation energy wire between the outer chlorosome antenna and the reaction center complex, an energy funnel for efficient light-harvesting is formed by the pigment-protein coupling. The protein shifts the local transition energies of the pigments, the so-called site energies in a specific way, such that pigments facing the reaction center are redshifted with respect to those on the chlorosome side. In the light-harvesting complex of higher plants an excitation energy funnel is created by the use of two different types of chlorophyll (Chl) pigments, Chla and Chlb and by the pigment-protein coupling that creates an energy sink at Chla 610 located in the stromal layer at the periphery of the complex. The close contact between Chla and Chlb gives rise to ultrafast subpicosecond exciton transfer, whereas dynamic localization effects are inferred to lead to long ps relaxation times between the majority of Chla pigments.     

Photoelectron energy distribution measurements from benzene in rare gas matrices

Photoelectronic energy distributions (PED's) are presented for benzene molecules embedded in solid Ar, Kr and Xe rare gas matrices obtained with monochromatized synchrotron radiation for selective excitation in the range hν = 8 eV to 15 eV. For photon energies in the transparent region of the matrices direct emission from the occupied benzene initial states in the band gap of the matrix is observed. Energy transfer from the matrix exciton states to the benzene guest molecules takes place when the host exciton states are excited. The PED's show that energy of unrelaxed excitons is transferred and that transfer to initial states just at the ionization threshold is favoured.     

Hole polarons in pure BaTiO3 studied by computer modeling

Self‐trapped hole polarons in technologically important perovskite‐type ceramic of BaTiO₃ have been modeled by means of the quantum chemical method modified for crystal calculations. The computations are carried out in the self‐consistent field (SCF) manner using the embedded molecular cluster model. The spatial configuration of a hole polaron, displacement of defect‐surrounding atoms, and wave functions of the polaron ground and excited states are obtained and analyzed. The probability of spontaneous hole self‐trapping is estimated in the perfect lattice of the BaTiO₃ crystal by calculating the value of the hole self‐trapping energy as a difference of the atomic relaxation energy and the hole localization energy. This value is found to be negative, −1.49 eV, which demonstrates the preference of the self‐trapped polaron state. The calculated polaron absorption energy, 0.5 eV, is discussed in light of the available experimental data. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 79: 358–366, 2000     

Exciton delocalization and energy transport mechanisms in R-phycoerythrin

Energy transport mechanisms in R-Phycoerythrin (RPE), a light harvesting protein located at the top of the phycobilisome antenna in red algae, are investigated using nonlinear optical spectroscopies and theoretical models. The RPE hexamer possesses a total of 30 bilin pigments, which can be subdivided into three classes based on their molecular structures and electronic resonance frequencies. Of particular interest to this study is the influence of exciton delocalization on the real-space paths traversed by photoexcitations as they concentrate on the lowest energy pigment sites. Transient grating measurements show that significant nuclear relaxation occurs at delay times less than 100 fs, whereas energy transport spans a wide range of time scales depending on the proximity of the initial and final states involved in the process. The fastest energy transport dynamics within the RPE complex are close to 1 ps; however, evidence for sub-100 fs exciton self-trapping is also obtained. In addition, photon echo experiments reveal vibronic interactions with overdamped and underdamped nuclear modes. To establish signatures of exciton delocalization, energy transport is simulated using both modified Redfield and Fo?rster theories, which respectively employ delocalized and localized basis states. We conclude that exciton delocalization occurs between six pairs of phycoerythrobilin pigments (i.e., dimers) within the protein hexamer. It is interesting that these dimers are bound in locations analogous to the well-studied phycocyanobilin dimers of cyanobacterial allophycocyanin and c-phycocyanin in which wave function delocalization is also known to take hold. Strong conclusions regarding the electronic structures of the remaining pigments cannot be drawn based on the present experiments and simulations due to overlapping resonances and broad spectroscopic line widths, which prevent the resolution of dynamics at particular pigment sites.     

Intraband relaxation in CdSe nanocrystals and the strong influence of the surface ligands

The intraband relaxation between the 1Pe and 1Se state of CdSe colloidal quantum dots is studied by pump-probe time-resolved spectroscopy. Infrared pump-probe measurements with approximately 6-ps pulses show identical relaxation whether the electron has been placed in the 1Se state by above band-gap photoexcitation or by electrochemical charging. This indicates that the intraband relaxation of the electrons is not affected by the photogenerated holes which have been trapped. However, the surface ligands are found to strongly affect the rate of relaxation in colloid solutions. Faster relaxation (<8 ps) is obtained with phosphonic acid and oleic acid ligands. Alkylamines lead to longer relaxation times of approximately 10 ps and the slowest relaxation is observed for dodecanethiol ligands with relaxation times approximately 30 ps. It is concluded that, in the absence of holes or when the holes are trapped, the intraband relaxation is dominated by the surface and faster relaxation correlates with larger interfacial polarity. Energy transfer to the ligand vibrations may be sufficiently effective to account for the intraband relaxation rate.     

Ultrafast Exciton Self‐Trapping and Delocalization in Cycloparaphenylenes: The Role of Excited‐State Symmetry in Electron‐Vibrational Coupling

Upon photon absorption, π‐conjugated organics are apt to undergo ultrafast structural reorganization via electron‐vibrational coupling during non‐adiabatic transitions. Ultrafast nuclear motions modulate local planarity and quinoid/benzenoid characters within conjugated backbones, which control primary events in the excited states, such as localization, energy transfer, and so on. Femtosecond broadband fluorescence upconversion measurements were conducted to investigate exciton self‐trapping and delocalization in cycloparaphenylenes as ultrafast structural reorganizations are achieved via excited‐state symmetry‐dependent electron‐vibrational coupling. By accessing two high‐lying excited states, one‐photon and two‐photon allowed states, a clear discrepancy in the initial time‐resolved fluorescence spectra and the temporal dynamics/spectral evolution of fluorescence spectra were monitored. Combined with quantum chemical calculations, a novel insight into the effect of the excited‐state symmetry on ultrafast structural reorganization and exciton self‐trapping in the emerging class of π‐conjugated materials is provided.     

An investigation into the excitation migration in polyfluorene solutions via temperature dependent fluorescence anisotropy

Fluorescence anisotropy of dilute polyfluorene polymer solutions has been used to show that two processes, exciton migration and conformational relaxation (twisting of part of the chain), occur within polyfluorene polymers of 20 or more repeat units. The former process is dominant and temperature independent for high excitation energy but, as the chain length is decreased, exciton migration is eliminated and the conformational relaxation becomes the only mechanism by which excited state energy relaxation to the emission site can occur. When the polymers are excited in the absorption band tails, again no migration is observed but conformational relaxation is still present.     

Calculations of the exciton coupling elements between the DNA bases using the transition density cube method

Excited states of the double-stranded DNA model (A)12.(T)12 were calculated in the framework of the Frenkel exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation associated with the lowest energy pipi* excitations of the individual nucleobases as obtained from time-dependent density functional theory calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal dipole approximation (IDA) methods were found to be significantly different for the small interchromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of structural fluctuations of the DNA chain on the magnitude of dipolar coupling were also found to be very significant. The difference between the maximum and minimum values was as large as 1000 and 300 cm(-1) for the IDA and TDC methods, respectively. To account for these effects, the properties of the excited states were averaged over a large number of conformations obtained from the molecular dynamics simulations. Our calculations using the TDC method indicate that the absorption of the UV light creates exciton states carrying the majority of the oscillator strength that are delocalized over at least six DNA bases. Upon relaxation, the excitation states localize over at least four contiguous bases.     

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.     

Efficient Light‐Harvesting Systems with Tunable Emission through Controlled Precipitation in Confined Nanospace

Light harvesting is a key step in photosynthesis but creation of synthetic light‐harvesting systems (LHSs) with high efficiencies has been challenging. When donor and acceptor dyes with aggregation‐induced emission were trapped within the interior of cross‐linked reverse vesicles, LHSs were obtained readily through spontaneous hydrophobically driven aggregation of the dyes in water. Aggregation in the confined nanospace was critical to the energy transfer and the light‐harvesting efficiency. The efficiency of the excitation energy transfer (EET) reached 95 % at a donor/acceptor ratio of 100:1 and the energy transfer was clearly visible even at a donor/acceptor ratio of 10 000:1. Multicolor emission was achieved simply by tuning the donor/acceptor feed ratio in the preparation and the quantum yield of white light emission from the system was 0.38, the highest reported for organic materials in water to date.     

Exciton states of quantum confined ZnO nanorods

Photoluminescence (PL) of zinc oxide (ZnO) nanorods with an average thickness of 5 nm and a length of 30 nm is blue-shifted compared to the bulk due to quantum confinement effects. The exciton states remain relatively stable at a high carrier density due to a smaller exciton size and an enhanced exciton binding energy in the quantum confined nanorods, whereas the electron-hole plasma states are formed in the bulk at the similar carrier density. A linear dependence of the PL intensity on the excitation intensity also corroborates the assumption that the stable exciton states are responsible for the undisturbed emission at a high carrier density.     

Energy transfer in unsymmetrical phenylene ethynylene dendrimers

We have applied the fluorescence upconversion technique to explore the electronic excitation energy transfer in unsymmetrical phenylene ethynylene dendrimers. Steady-state emission spectra show that the energy transfer from the dendrons to the core is highly efficient. Ultrafast time-resolved fluorescence measurements are performed at various excitation wavelengths to explore the possibility of assigning absorption band structures to exciton localizations. We propose a kinetic model to describe the time-resolved data. Independent of the excitation wavelength, a typical rise-time value of 500 fs is measured for the fluorescence in the dendrimer without an energy trap, indicating initial delocalized excitation. While absorption is into delocalized exciton states, emission occurs from localized states. When an energy trap such as perylene is introduced on the dendrimer, varying the excitation wavelength yields different energy-transfer rates, and the excitation energy migrates to the trap through two channels. The interaction energy between the dendrimer backbone and the trap is estimated to be 75 cm(-1). This value is small compared to the vibronic bandwidth of the dendrimer, indicating that the monodendrons and the energy trap are weakly coupled.