How solvent controls electronic energy transfer and light harvesting: toward a quantum-mechanical description of reaction field and screening effects

This paper presents a quantum-mechanical study of electronic energy transfer (EET) coupling on over 100 pairs of chromophores taken from photosynthetic light-harvesting antenna proteins. Solvation effects due to the protein, intrinsic waters, and surrounding medium are analyzed in terms of screening and reaction field contributions using a model developed recently that combines a linear response approach with the polarizable continuum model (PCM). We find that the screening of EET interactions is quite insensitive to the quantum-mechanical treatment adopted. In contrast, it is greatly dependent on the geometrical details (distance, shape, and orientation) of the chromophore pair considered. We demonstrate that implicit (reaction field) as well as screening effects are dictated mainly by the optical dielectric properties of the host medium, while the effect of the static properties is substantially less important. The empirical distance-dependent screening function we proposed in a recent letter (Scholes, G. D.; Curutchet, C.; Mennucci, B.; Cammi, R.; Tomasi, J. J. Phys. Chem. B 2007, 111, 6978-6982) is analyzed and compared to other commonly used screening factors. In addition, we show that implicit medium effects on the coupling, resulting from changes in the transition densities upon solvation, are strongly dependent on the particular system considered, thus preventing the possibility of defining a general empirical expression for such an effect.     

Excitation energy transfer in ion pairs of polymethine cyanine dyes: efficiency and dynamics

The present work deals with singlet excitation energy transfer (EET) occurring in contact ion pairs (CIPs) of several anionic oxonol analogues (acting as EE donors) and cationic cyanines (acting as acceptors) characterized by off resonance individual transitions. Combining conductometric and spectroscopic measurements with decreasing solvent polarity, we were able to observe a progressive ion pairing leading first to solvent-separated ion pairs (SSIPs) and then to CIPs. Analysis of the absorption spectra of three selected salts (A2,C1, A2,C2, and A1,C4) in chloroform-toluene mixtures showed that the transformation of SSIP into CIP involves the appearance of a certain exciton coupling, the extent of which decreases regularly with increasing gap between the local excitation energies. Fluorescence excitation spectra showed that EET occurs in CIP, and EET efficiencies were evaluated with a procedure expressly devised for weakly emitting donors. These were between 0.2 and 0.65 for the examined ion pairs involving anions A1 and A2. The spectroscopic study was complemented by a theoretical investigation aimed at establishing the dynamic regime of the observed EET. From classical MD simulations and local full geometry optimizations, A2,C1 and A2,C2 were found to form rather stable sandwich-type CIP structures with interchromophore distances (R) of about 0.45-0.50 nm. The donor-acceptor electronic coupling was calculated in terms of Coulombic interactions between atomic transition charges. For CIP, the electronic coupling was decidedly beyond the limit of the weak coupling required for an incoherent F?rster-type mechanism. Thus, we tried to arrange the EET dynamics within the theory developed by Kimura, Kakitani, and Yamato (J. Phys. Chem. B 2000, 104, 9276) for the intermediate coupling case, which provides analytical expressions of time-dependent occupation probability, EET rate, and coherency in terms of two basic quantities: the electronic coupling and a correlation time related to the Franck-Condon factor. The latter was shown to be primarily modulated by F?rster's spectral overlap integral (related in turn to the excitation energy gap). Calculations were carried out for the three sample systems using three values of the electronic coupling roughly corresponding to CIP, 1.0, and 2.0 nm interchromophore distances. At the CIP distance, EET in both A2,C1 and A2,C2 was predicted to occur with a partial exciton mechanism, very short transfer times (about 10 fs), and high degree of coherence. In A1,C4 (having the largest energy gap), EET was found to occur with a hot-transfer mechanism. More or less hot-transfer dynamics appeared to be retained by all three systems at R = 1.0 nm. Fully incoherent EET appeared to become operative only at distances larger than 2.0 nm.     

Effect of an underdamped vibration with both diagonal and off-diagonal exciton–phonon interactions on excitation energy transfer

A numerically exact approach, named as the hierarchical stochastic Schrödinger equation, is employed to investigate the resonant vibration-assisted excitation energy transfer in a dimer system, where an underdamped vibration with both diagonal and off-diagonal exciton–phonon interactions is incorporated. From a large parameter space over the site-energy difference, excitonic coupling, and reorganization energy, it is found that the promotion effect of the underdamped vibration is significant only when the excitonic coupling is smaller than the site-energy difference. Under the circumstance, there is an optimal strength ratio between diagonal and off-diagonal exciton–phonon interactions for the resonant vibration-assisted excitation energy transfer as the site-energy difference is greater than the reorganization energy, whereas in the opposite situation the most efficient energy transfer occurs as the exciton–phonon interaction is totally off-diagonal. © 2018 Wiley Periodicals, Inc.     

Energy transfer in molecular layer-by-layer films of water-soluble perylene diimides

Multilayer films of water-soluble anionic and cationic perylene diimide (PDI) moieties have been prepared using the molecular layer-by-layer method described in an earlier publication (Tang, T. J.; Qu, J. Q.; Müllen, K.; Webber, S. E. Langmuir 2006, 22, 26-28) and the fluorescence intensity compared with and without a base layer prepared using an anionic terrylene diimide dye (n-TDI), which serves as an energy-trapping layer for the PDI exciton. The fluorescence quenching data could be fit equally well to a modification of a model used by Kuhn to describe energy transfer from a J aggregate or a model developed by Kenkre and Wong to describe excitonic transfer. For both models, we obtain a characteristic energy-transfer distance on the order of 5.4 nm. Fluorescence quenching of the PDI via a single F?rster energy-transfer step to the n-TDI layer is ruled out on the basis of the observed power-law dependence. We also consider a model in which the excitation is trapped at the outermost surface. This model provides a reasonable fit to the data only if the Kuhn relationship is used.     

Bacterial photosynthesis begins with quantum-mechanical coherence

In the antenna system of photosynthetic bacteria, pigments form circular aggregates whose excitations are excitons with quantum-mechanical coherence extending over many pigments. These excitons play crucial roles in light harvesting, storage, and excitation-energy transfer (EET). EET takes place rapidly to and/or from optically forbidden exciton states, without total transition dipole, within the antenna system and to the reaction center. Such EETs cannot be rationalized by F?rster's formula, the traditional theory on EET, because it allows EET only between optically allowed states. The coherence in the excitons seems to prohibit rapid EET on this formula. The bacteria overcome this difficulty by circumventing the coherence, using the effects of the physical size of an aggregate that is larger than the shortest distance between pigments in the donor and pigments in the acceptor. The shortest-distance pair therein cannot detect whether the aggregate has a nonvanishing total transition dipole or not, since the pair see effectively only the transition dipole on the other pigment in themselves. The transition dipole facilitates rapid EET even to and/or from optically forbidden exciton states. Such EETs have enabled us to develop a general formula for the rate constant of EET. This is a formula in the weak-interaction limit, and so is F?rster's formula, but it correctly takes into account the above size effect.     

A reduced density-matrix theory of absorption line shape of molecular aggregate

A theory for the absorption line shape of molecular aggregates in condensed phase is formulated based on a reduced density-matrix approach. Intermolecular couplings in the aggregates are assumed to be weak (F?rster type of energy transfer mechanism). The spin-Boson model is employed to include the effect of electron-phonon coupling. Using the projection operator technique, we derive kinetic equations for the reduced electronic density matrix associated with the absorption spectrum. General expressions of time-dependent rate constants in the kinetic equations are derived by using the cumulant expansion technique. The resulting time-dependent kinetic equations are solved numerically. We illustrate the applicability of the present theory by calculating the line shape of a dimer (a pair of donor and acceptor of energy transfer). For a J-aggregate type of molecular pair (with excitonic redshift), a tail appears on the blue side of the absorption spectrum due to the existence of inhomogeneity in electronic state mixing which is originated from the electron-phonon coupling.     

Excitation Dynamics in Hetero‐bichromophoric Calixarene Systems

In this work, the dynamics of electronic energy transfer (EET) in bichromophoric donor–acceptor systems, obtained by functionalizing a calix[4]arene scaffold with two dyes, was experimentally and theoretically characterized. The investigated compounds are highly versatile, due to the possibility of linking the dye molecules to the cone or partial cone structure of the calix[4]arene, which directs the two active units to the same or opposite side of the scaffold, respectively. The dynamics and efficiency of the EET process between the donor and acceptor units was investigated and discussed through a combined experimental and theoretical approach, involving ultrafast pump–probe spectroscopy and density functional theory based characterization of the energetic and spectroscopic properties of the system. Our results suggest that the external medium strongly determines the particular conformation adopted by the bichromophores, with a direct effect on the extent of excitonic coupling between the dyes and hence on the dynamics of the EET process itself.     

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.     

Efficient exciton transport in layers of self-assembled porphyrin derivatives

The photosynthetic apparatus of green sulfur bacteria, the chlorosome, is generally considered as a highly efficient natural light-harvesting system. The efficient exciton transport through chlorosomes toward the reaction centers originates from self-assembly of the bacteriochlorophyll molecules. The aim of the present work is to realize a long exciton diffusion length in an artificial light-harvesting system using the concept of self-assembled natural chlorosomal chromophores. The ability to transport excitons is studied for porphyrin derivatives with different tendencies to form molecular stacks by self-assembly. A porphyrin derivative denoted as ZnOP, containing methoxymethyl substituents ({meso-tetrakis[3,5-bis(methoxymethyl)phenyl]porphyrinato}zinc(II)) is found to form self-assembled stacks, in contrast to a derivative with tert-butyl substituents, ZnBuP ({meso-tetrakis[3,5-bis(tert-butyl)phenyl]porphyrinato}zinc(II)). Exciton transport and dissociation in a bilayer of these porphyrin derivatives and TiO2 are studied using the time-resolved microwave conductivity (TRMC) method. For ZnOP layers it is found that excitons undergo diffusive motion between the self-assembled stacks, with the exciton diffusion length being as long as 15 +/- 1 nm, which is comparable to that in natural chlorosomes. For ZnBuP a considerably shorter exciton diffusion length of 3 +/- 1 nm is found. Combining these exciton diffusion lengths with exciton lifetimes of 160 ps for ZnOP and 74 ps for ZnBuP yields exciton diffusion coefficients equal to 1.4 x 10(-6) m2/s and 1 x 10(-7) m2/s, respectively. The larger exciton diffusion coefficient for ZnOP originates from a strong excitonic coupling for interstack energy transfer. The findings show that energy transfer is strongly affected by the molecular organization. The efficient interstack energy transfer shows promising prospects for application of such self-assembled porphyrins in optoelectronics.     

Rotationally resolved C2 symmetric conformers of bis-(4-hydroxyphenyl)methane: prototypical examples of excitonic coupling in the S1 and S2 electronic states

Rotationally resolved microwave and ultraviolet spectra of jet-cooled bis-(4-hydroxyphenyl)methane (b4HPM) have been obtained using Fourier-transform microwave and UV laser/molecular beam spectrometers. A recent vibronic level study of b4HPM [Rodrigo, C. P.; Mu?ller, C. W.; Pillsbury, N. R.; James, W. H., III; Plusquellic, D. F.; Zwier, T. S. J. Chem. Phys. 2011, 134, 164312] has assigned two conformers distinguished by the orientation of the in-plane OH groups and has identified two excitonic origins in each conformer. In the present study, the rotationally resolved bands of all four states have been well-fit to asymmetric rotor Hamiltonians. For the lower exciton (S(1)) levels, the transition dipole moment (TDM) orientations are perpendicular to the C(2) symmetry axes and consist of 41(2):59(2) and 34(2):66(2)% a:c hybrid-type character. The S(1) levels are therefore delocalized states of B symmetry and represent the antisymmetric combinations of the zero-order locally excited states of the p-cresol-like chromophores. The TDM polarizations of bands located at ≈132 cm(-1) above the S(1) origins are exclusively b-type and identify them as the upper exciton S(2) origin levels of A symmetry. The TDM orientations and the relative band strengths from the vibronic study have been analyzed within a dipole-dipole coupling model in terms of the localized TDM orientations, μ(loc), on the two chromophores. The out-of-the-ring plane angles of μ(loc) are both near 20° and are similar to results for diphenylmethane [Stearns, J. A.; Pillsbury, N. R.; Douglass, K. O.; Mu?ller, C. W.; Zwier, T. S.; Plusquellic, D. F. J. Chem. Phys. 2008, 129, 224305]. The in-plane angles are, however, rotated by 14 and 18° relative to DPM and, in part, explain the smaller than expected exciton splittings of these two conformers.     

Using circularly polarized luminescence to probe exciton coherence in disordered helical aggregates

Circularly polarized emission from helical MOPV4 aggregates is studied theoretically based on a Hamiltonian including excitonic coupling, exciton phonon coupling, and site disorder. The latter is modeled via a Gaussian distribution of site energies. The frequency dependence of the circularly polarized luminescence dissymmetry g(lum)(omega) contains structural information about the low-energy-neutral (excitonic) polaron from which emission originates. Near the 0-0 emission frequency, g(lum)(omega) provides a measure of the exciton coherence length, while at lower energies, in the vicinity of the sideband frequencies, g(lum)(omega) probes the polaron radius. The present work focuses on how the 0-0 dissymmetry, g(lum)(0-0), relates to the emitting exciton's coherence function, from which the coherence length is deduced. In the strong disorder limit where the exciton is localized on a single chromophore, g(lum)(0-0) is zero. As disorder is reduced and the coherence function expands, /g(lum)(0-0)/ increases more rapidly than the sideband dissymmetries, resulting in a pronounced surge in g(lum)(omega) near the 0-0 transition frequency. The resulting spectral shape of g(lum)(omega) is in excellent agreement with recent experiments on MOPV4 aggregates. In the limit of very weak disorder, corresponding to the motional narrowing regime, the coherence function extends over the entire helix. In this region, g(lum)(0-0) undergoes a surprising sign reversal but only for helices which are between n+12 and n+1 complete turns (n = 0,1,...). This unusual sign change is due to the dependence of the rotational line strength on long-range exciton coherences which are also responsible for a heightened sensitivity of g(lum)(omega) to long-range excitonic coupling.     

Coherent Exciton-Phonon Coupling in CdSe/ZnS Nanocrystals Studied by Two-Dimensional Electronic Spectroscopy

Coherent exciton-phonon coupling in CdSe/ZnS nanocrystals have been investigated by temperature-dependent two-dimensional electronic spectroscopy (2DES) measurements. Benefiting from the ability of 2DES to dissect assembles in nanocrystal films, we have clearly identified experimental evidences of coherent coupling between exciton and phonon in CdSe/ZnS nanocrystals. In time domain, 2DES signals of excitonic transitions beat at a frequency resonant to a longitudinal optical phonon mode; in energy domain, phonon side bands are distinct at both Stokes and anti-Stokes sides. When temperature increases, phonon-induced exciton dephasing is observed with dramatic broadening of homogeneous linewidth. The results suggest exciton-phonon coupling is essential in elucidating the quantum dynamics of excitonic transitions in semiconductor nanocrystals.     

Enhanced photogeneration of triplet excitons in an oligothiophene-fullerene blend.

Photoinduced and transient absorption spectroscopy is used to study triplet exciton dynamics in thin films of a new thiophene-based oligomer (DCV3T) and blends of DCV3T and fullerene C60. We find enhanced DCV3T triplet exciton generation in the blend layer, which is explained as an excitonic ping-pong effect: singlet energy transfer from DCV3T to C60, followed by immediate intersystem crossing to C60, and triplet exciton back-transfer. Estimations of the rate constants involved show that the ping-pong effect has an overall efficiency close to unity. The singlet-singlet energy transfer from DCV3T to C60 is demonstrated by efficient quenching of DCV3T luminescence in the blend, leading to sensitized emission of C60. We discuss a promising new concept of solar cells with an enlarged active-layer thickness based on potentially long-ranged triplet exciton diffusion in combination with efficient intersystem crossing.     

Resonant coupling of bound excitons with LO phonons in ZnO: excitonic polaron states and Fano interference

We report on a photoluminescence observation of robust excitonic polarons due to resonant coupling of exciton and longitudinal optical (LO) phonon as well as Fano-type interference in high quality ZnO crystal. At low enough temperatures, resonant coupling of excitons and LO phonons leads to not only traditional Stokes lines (SLs) but also up to second-order anti-Stokes lines (ASLs) besides the zero-phonon line (ZPL). The SLs and ASLs are found to be not mirror symmetric with respect to the ZPL, strongly suggesting that they are from different coupling states of exciton and phonons. Besides these spectral features showing the quasiparticle properties of exciton-phonon coupling system, the first-order SL is found to exhibit characteristic Fano lineshape, caused by quantum interference between the LO components of excitonic polarons and the continuous phonon bath. These findings lead to a new insight into fundamental effects of exciton-phonon interactions.     

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.     

Ultrafast exciton transfers in DNA and its nonlinear optical spectroscopy

We have calculated the nonlinear response function of a DNA duplex helix including the contributions from the exciton population and coherence transfers by developing an appropriate exciton theory as well as by utilizing a projector operator technique. As a representative example of DNA double helices, the B-form (dA)10-(dT)10 is considered in detail. The Green functions of the exciton population and coherence transfer processes were obtained by developing the DNA exciton Hamiltonian. This enables us to study the dynamic properties of the solvent relaxation and exciton transfers. The spectral density describing the DNA base-solvent interactions was obtained by adjusting the solvent reorganization energy to reproduce the absorption and steady-state fluorescence spectra. The time-dependent fluorescence shift of the model DNA system is found to be ultrafast and it is largely determined by the exciton population transfer processes. It is further shown that the nonlinear optical spectroscopic techniques such as photon echo peak shift and two-dimensional photon echo can provide important information on the exciton dynamics of the DNA double helix. We have found that the exciton-exciton coherence transfer plays critical roles in the peculiar energy transfer and ultrafast memory loss of the initially created excitonic state in the DNA duplex helix.