Rate Of Electronic Energy Transfer Research Articles

Exciton Transfer Between Extended Electronic States in Conjugated Inter-Polyelectrolyte Complexes.

Artificial light harvesting, a process that involves converting sunlight into chemical potential energy, is considered to be a promising part of the overall solution to address urgent global energy challenges. Conjugated polyelectrolyte complexes (CPECs) are particularly attractive for this purpose due to their extended electronic states, tunable assembly thermodynamics, and sensitivity to their local environment. Importantly, ionically assembled complexes of conjugated polyelectrolytes can act as efficient donor-acceptor pairs for electronic energy transfer (EET). However, to be of use in material applications, we must understand how modifying the chemical structure of the CPE backbone alters the EET rate beyond spectral overlap considerations. In this report we investigate the dependence of the EET efficiency and rate on the electronic structure and excitonic wave function of the CPE backbone. To do so, we synthesized a series of alternating copolymers where the electronic states are systematically altered by introducing comonomers with electron withdrawing and electron-rich character while keeping the linear ionic charge density nearly fixed. We find evidence that the excitonic coupling may be significantly affected by the exciton delocalization radius, in accordance with analytical models based on the line-dipole approximation and quantum chemistry calculations. Our results imply that care should be taken when selecting CPE components for optimal CPEC EET. These results have implications for using CPECs as key components in water-based light-harvesting materials, either as standalone assemblies or as adsorbates on nanoparticles and thin films.

Pressure effects on both fluorescent emission and charge transport properties of organic semiconductors: a computational study.

External pressure can regulate the photophysical property and charge transport performance of organic semiconductors, however, the underlying mechanism at the microscopic level is still elusive. Using thermal vibrational correlation function coupled quantum mechanics/molecular mechanics and full quantum charge transfer rate theory, we systematically explore the influence of pressure on fluorescence emission and charge transport behaviours of representative cyclooctatetrathiophene (COTh). It is found that, upon pressurization, the intramolecular configurations of COTh became more twisted, leading to the blue-shifted emission. The fluorescence quantum efficiency (FQE) of COTh crystals decreases monotonically in a wide pressure range of 0-4.38 GPa, because the increase of intermolecular electronic energy transfer rate constant (keet) is larger than the decrease of internal conversion rate constant (kic), and the variation of keet is dominant. The decrease in kic is attributed to the decreasing reorganization energy, reflecting the suppression of the low-frequency flipping vibrations of four thiophene rings and the high-frequency stretching vibrations of central cyclooctatetraene, while the keet increase is due to the simultaneous increase in exciton coupling and spectra overlap. Moreover, we predicted that the hole mobility of COTh increases monotonically by nearly an order of magnitude from 0.39 to 3.00 cm2 V-1 s-1 upon compression, because of the increase in transfer integral and the decrease of charged reorganization energy. Furthermore, its hole mobility exhibits obvious anisotropy. Our work systematically builds the external pressure, molecular packing, luminescence and transport properties relationships of organic semiconductors and provides theoretical guidance for the rational design of pressure responsive organic semiconductors with excellent photoelectric performance.

A Computational Study of the Electronic Energy and Charge Transfer Rates and Pathways in the Tetraphenyldibenzoperiflanthene/Fullerene Interfacial Dyad.

The electronic transition rates and pathways underlying interfacial charge separation in tetraphenyldibenzoperiflanthene:fullerene (DBP:C70) blends are investigated computationally. The analysis is based on a polarization-consistent framework employing screened range-separated hybrid functional in a polarizable continuum model to parametrize Fermi's golden rule rate theory. The model considers the possible transitions within the 25 lowest excited states of a DBP:C70 dyad that are accessible by photoexcitation. The different identified pathways contributing to charge carrier generation include electron and hole transfer and backtransfer, exciton transfer, and internal relaxation steps. The larger density of states of C70 appears to explain the previously observed larger efficiency for charge separation through hole transfer mechanism. We also analyze the validity of the high-temperature and short-time semiclassical approximations of the FGR theory, where both overestimated and underestimated Marcus theory based constants can be affected.

Biological Advantage of the Arrangements of C-Phycocyanin Chromophores in Phycobilisome from the Electronic Energy Transfer Viewpoint

Abstract In the present study, we report the electronic energy transfer (EET) rate and the EET dynamics in the hexamer of C-phycocyanin (C-PC). The EET rate for the Förster theory was calculated by a quantum chemical method and a master equation was used to describe the dynamics. Our calculation results suggest that the natural arrangements of phycocyanobilin (PCB) chromophores α84, β84, and β155 in C-PC are cooperatively well-adjusted to achieve the shortest EET time-length. It is the appropriate regular periodicity of the intermolecular distances and intermolecular angles of the ground and the first excited transition dipole moments of PCBs α84, β84, and β155, i.e., the three-fold symmetry and stacking order of their layers found in terrestrial plants and algae, that are some of the most important requisites in achieving such a highly efficient EET in PBS.

Estimation of the relative contributions to the electronic energy transfer rates based on Förster theory: The case of C-phycocyanin chromophores.

In the present study, we provide a reformulation of the theory originally proposed by Förster which allows for simple and convenient formulas useful to estimate the relative contributions of transition dipole moments of a donor and acceptor (chemical factors), their orientation factors (intermolecular structural factors), intermolecular center-to-center distances (intermolecular structural factors), spectral overlaps of absorption and emission spectra (photophysical factors), and refractive index (material factor) to the excitation energy transfer (EET) rate constant. To benchmark their validity, we focused on the EET occurring in C-phycocyanin (C-PC) chromophores. To this aim, we resorted to quantum chemistry calculations to get optimized molecular structures of the C-PC chromophores within the density functional theory (DFT) framework. The absorption and emission spectra, as well as transition dipole moments, were computed by using the time-dependent DFT (TDDFT). Our method was applied to several types of C-PCs showing that the EET rates are determined by an interplay of their specific physical, chemical, and geometrical features. These results show that our formulas can become a useful tool for a reliable estimation of the relative contributions of the factors regulating the EET transfer rate.

Ultrafast Through-Space Electronic Energy Transfer in Molecular Dyads Built around Dynamic Spacer Units.

A pair of complementary molecular dyads have been synthesized around a 1,2-diaminocyclohexyl spacer that itself undergoes ring inversion. Despite these conformational exchange processes, the donor and acceptor occupy quite restricted spatial regions, and they are not interchangeable. The donor and acceptor pair comprise disparate boron dipyrromethene dyes selected to display favorable electronic energy transfer (EET). Steady-state emission spectroscopy confirms that through-space EET from donor to acceptor is almost quantitative, aided by the relatively short separations. Ultrafast time-resolved fluorescence spectroscopy has allowed determination of the rates of EET for both dyads. Surprisingly, in view of the close proximity of donor and acceptor (center-to-center separations less than 20 Å), the EET dynamics are well-accounted for in terms of the computed molecular conformations and conventional Förster theory. One dyad appears as a single family of conformations, but EET for the second dyad corresponds to dual-exponential kinetics. In this latter case, an intramolecular hydrogen bond helps stabilize an open geometry, wherein EET is relatively slow.

Influence of Nanostructure on the Exciton Dynamics of Multichromophore Donor-Acceptor Block Copolymers.

We explore the synthesis and photophysics of nanostructured block copolymers that mimic light-harvesting complexes. We find that the combination of a polar and electron-rich boron dipyrromethene (BODIPY) block with a nonpolar electron-poor perylene diimide (PDI) block yields a polymer that self-assembles into ordered "nanoworms". Numerical simulations are used to determine optimal compositions to achieve robust self-assembly. Photoluminescence spectroscopy is used to probe the rich exciton dynamics in these systems. Using controls, such as homopolymers and random copolymers, we analyze the mechanisms of the photoluminescence from these polymers. This understanding allows us to probe in detail the photophysics of the block copolymers, including the effects of their self-assembly into nanostructures on their excited-state properties. Similar to natural systems, ordered nanostructures result in properties that are starkly different than the properties of free polymers in solution, such as enhanced rates of electronic energy transfer and elimination of excitonic emission from disordered PDI trap states.

Quantum chemical calculations of tryptophan → heme electron and excitation energy transfer rates in myoglobin.

The development of optical multidimensional spectroscopic techniques has opened up new possibilities for the study of biological processes. Recently, ultrafast two‐dimensional ultraviolet spectroscopy experiments have determined the rates of tryptophan → heme electron transfer and excitation energy transfer for the two tryptophan residues in myoglobin (Consani et al., Science, 2013, 339, 1586). Here, we show that accurate prediction of these rates can be achieved using Marcus theory in conjunction with time‐dependent density functional theory. Key intermediate residues between the donor and acceptor are identified, and in particular the residues Val68 and Ile75 play a critical role in calculations of the electron coupling matrix elements. Our calculations demonstrate how small changes in structure can have a large effect on the rates, and show that the different rates of electron transfer are dictated by the distance between the heme and tryptophan residues, while for excitation energy transfer the orientation of the tryptophan residues relative to the heme is important. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Ultrafast Electronic Energy Transfer Beyond the Weak Coupling Limit in a Proximal but Orthogonal Molecular Dyad.

Electronic energy transfer (EET) from a donor to an acceptor is an important mechanism that controls the light harvesting efficiency in a wide variety of systems, including artificial and natural photosynthesis and contemporary photovoltaic technologies. The detailed mechanism of EET at short distances or large angles between the donor and acceptor is poorly understood. Here the influence of the orientation between the donor and acceptor on EET is explored using a molecule with two nearly perpendicular chromophores. Very fast EET with a time constant of 120 fs is observed, which is at least 40 times faster than the time predicted by Coulombic coupling calculations. Depolarization of the emission signal indicates that the transition dipole rotates through ca. 64°, indicating the near orthogonal nature of the EET event. The rate of EET is found to be similar to structural relaxation rates in the photoexcited oligothiophene donor alone, which suggests that this initial relaxation brings the dyad to a conical intersection where the excitation jumps to the acceptor.

Enhance energy transfer between quantum dots by the surface plasmon of Ag island film

We observed enhanced energy transfer between quantum dots which were spin coated on the surface of Ag island film. By adjusting the thickness of Al2O3 spacer layer (4-16 nm) between quantum dots and Ag island film, we studied the distance dependence of the plasmon enhanced energy transfer. Experimental results showed the energy transfer efficiency increased as the quantum dots approached closer to the Ag film. A time-correlated single-photon counting system was also applied to study the dynamics of the plasmon enhanced energy transfer between quantum dots. Obvious decay rate increasing was discovered from time-resolve photoluminescence spectra of both the donor and accepter quantum dots, which clearly confirmed the existence of strong photon-exciton interaction. The theoretical analysis performed by the finite difference time domain method and COMSOL program, further revealed large electronic field and energy transfer rate enchantments on the surface of Ag island film, which uncovered the dominant reasons for the quantum dots’ enhanced energy transfer.

Structural and orientation effects on electronic energy transfer between silicon quantum dots with dopants and with silver adsorbates.

Starting from the atomic structure of silicon quantum dots (QDs), and utilizing ab initio electronic structure calculations within the Förster resonance energy transfer (FRET) treatment, a model has been developed to characterize electronic excitation energy transfer between QDs. Electronic energy transfer rates, KEET, between selected identical pairs of crystalline silicon quantum dots systems, either bare, doped with Al or P, or adsorbed with Ag and Ag3, have been calculated and analyzed to extend previous work on light absorption by QDs. The effects of their size and relative orientation on energy transfer rates for each system have also been considered. Using time-dependent density functional theory and the hybrid functional HSE06, the FRET treatment was employed to model electronic energy transfer rates within the dipole-dipole interaction approximation. Calculations with adsorbed Ag show that: (a) addition of Ag increases rates up to 100 times, (b) addition of Ag3 increases rates up to 1000 times, (c) collinear alignment of permanent dipoles increases transfer rates by an order of magnitude compared to parallel orientation, and (d) smaller QD-size increases transfer due to greater electronic orbitals overlap. Calculations with dopants show that: (a) p-type and n-type dopants enhance energy transfer up to two orders of magnitude, (b) surface-doping with P and center-doping with Al show the greatest rates, and (c) KEET is largest for collinear permanent dipoles when the dopant is on the outer surface and for parallel permanent dipoles when the dopant is inside the QD.

Through‐Space Electronic Energy Transfer Across Proximal Molecular Dyads

Energy transfer: For large electronic systems in close proximity it is shown that the coulombic mechanism accounts for the rates of electronic energy transfer for both linear and perpendicular geometries across distances from 36 to 16 Å. Replacing the ideal dipole approximation with either a revised extended dipole or atom-localized charges improves agreement between theory and experiment. As a service to our authors and readers, this journal provides supporting information supplied by the authors. Such materials are peer reviewed and may be re-organized for online delivery, but are not copy-edited or typeset. Technical support issues arising from supporting information (other than missing files) should be addressed to the authors. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Exploring Förster electronic energy transfer in a decoupled anthracenyl-based borondipyrromethene (bodipy) dyad

An anthracenyl-Bodipy dyad containing a triazole bridge, that acts to decouple the two units in the ground state, has been synthesised and structurally characterised. Efficient electronic energy transfer occurs from the anthracenyl-based unit to the Bodipy system in toluene in around 12 ps, and becomes faster in solvents of lower refractive index. The rate of electronic energy transfer is discussed in terms of Förster theory.

Quantum mechanical study of the solvent-dependence of electronic energy transfer rates in a Bodipy closely-spaced dyad

The ability of Förster theory to describe electronic energy transfer rates, and their solvent-dependence, have been studied theoretically in a series of 15 solvents of varying degrees of polarity for a rigid closely-spaced dyad, constituted by two boron dipyrromethene dyes, which was recently studied experimentally by Harriman & Ziessel, Photochem. Photobiol. Sci., 2010, 9, 960. We use time-dependent density functional theory calculations coupled to the polarizable continuum model to analyse the solvent-dependence of the spectroscopic and energy transfer properties of the system. This methodology allows us to examine the impact of the solvent on both electronic (solvent screening) and structural (dipole separation and orientation) factors by consistently incorporating solvent effects in the determination of molecular geometries, transition densities, and electronic couplings. In addition, we analyse the impact of bridge-mediated contributions to the electronic interaction between the dyes. We are therefore able to assess whether a Förster-type point-dipole approximation is valid for the molecular system studied.

Influence of the energy transfer in a single donor–acceptor pair on the photon distribution functions in its fluorescence

Fluorescence of a single donor–acceptor pair is considered. A donor molecule is described by a three-level energy scheme. It has a ‘dark’ state, which makes donor fluorescence blinking. An acceptor molecule is described by two-level scheme. Its fluorescence is of continuous type. Strong dependence of the distributions w N D ( T ) and w N A ( T ) for photons emitted by the donor and the acceptor on the electronic excitation energy transfer rate F between the two molecules is demonstrated. For instance, at F ≅ 1 / T D , where 1 / T D is the donor fluorescence rate, the fluorescence of the two-level acceptor starts blinking. The photon number distributions at F ≪ 1 / T D u F ≫ 1 / T D are considered as well.

Artificial light-harvesting antennae: electronic energy transfer by way of molecular funnels

Electronic energy transfer (EET) plays a critical role in many biological processes and is used by nature to direct energy to a site where chemical reactions need to be initiated. Such EET can occur over large distances and can involve many individual molecules of identical, similar or disparate chemical identity. Advances in spectroscopy and data processing have allowed the rates of EET to be measured on extremely fast timescales such that improved mechanistic insight becomes feasible. At the same time, highly sophisticated synthetic operations have been devised that facilitate the isolation and purification of elaborate multi-component molecular arrays. A key feature of these arrays concerns the logical positioning of individual units in a way that favours directed EET along the molecular axis or along some other preferred pathway. The availability of these novel molecular materials allows close examination of popular theoretical models and paves the way for the development of advanced molecular sensors, artificial light harvesters, fluorescent labels and sensitizers. Of particular interest is the spectacular growth in the application of boron dipyrromethene dyes as basic reagents in such artificial photon collectors and these compounds have dominated the market in recent years because of their synthetic versatility and valuable photophysical properties. In this article, recent developments in the field are highlighted in terms of synthesis and subsequent spectroscopic exploration.

Exploring the effects of solvent polarity on the rate of Förster-type electronic energy transfer in a closely-spaced molecular dyad

A rigid molecular dyad, comprising two disparate boron dipyrromethene dyes operating as terminals and being separated by a spirobifluorene connector, has been subjected to a detailed examination of how changes in solvent influence the rate of intramolecular electronic energy transfer (EET). In all solvents, the probability of EET exceeds 90% but the rate shows a clear increase in non-polar solvents. This effect is traced to small perturbations of the optical absorption spectrum of the acceptor, which affects the overlap integral for Förster-type EET and also disturbs the accompanying transition dipole moment. There is an additional subtle effect whereby the nature of the surrounding solvent affects the transition dipole density, which itself modifies the separation distance.

Length Dependence for Intramolecular Energy Transfer in Three- and Four-Color Donor−Spacer−Acceptor Arrays

A series of donor-spacer-acceptor triads has been synthesized and fully characterized. Both donor and acceptor units are built from boron dipyrromethene (BODIPY) dyes but they differ in their respective conjugation lengths, and thereby offer quite disparate optical properties. The spacer units comprise an oligomer of 1,4-phenylene-diethynylene repeat units and allow the boron-boron separation distance to be varied progressively from 18 to 38 A. A notable feature of this series is that each subunit can be selectively excited with monochromatic light. Highly efficacious electronic energy transfer (EET) occurs from the first-excited singlet state localized on the conventional BODIPY dye to its counterpart resident on the expanded BODIPY-based nucleus, but the rate constant follows a nonlinear evolution with separation distance. Overall, the rate of EET falls by only a factor of 4-fold on moving from the shortest to the longest spacer. This shallow length dependence is a consequence of the energy gap between donor and spacer units becoming smaller as the molecular length increases. Interestingly, a simple relationship exists between the measured electronic resistance of the spacer unit and the Huang-Rhys factor determined by emission spectroscopy. Both parameters relate to the effective conjugation length. Direct illumination of the spacer unit leads to EET to both terminals, followed by EET from conventional BODIPY to the expanded version. In each case, EET to the expanded dye involves initial population of the second-singlet excited state, whereas transfer from spacer to the conventional BODIPY dye populates the S(2) state for shorter lengths but the S(1) state for the longer analogues. The rate of EET from spacer to conventional BODIPY dye, as measured for the corresponding molecular dyads, is extremely fast (>10(11) s(-1)) and scales with the spectral overlap integral. The relative partitioning of EET from the spacer to each terminal is somewhat sensitive to the molecular length, with the propensity to populate the conventional BODIPY dye changing from 65% for N = 0 to 45% for N = 2. The most likely explanation for this behavior can be traced to the disparate spectral overlap integrals for the two dyes. These systems have been complemented by a molecular tetrad in which pyrene residues replace the fluorine atoms present on the conventional BODIPY-based dye. Here, rapid EET occurs from pyrene to the BODIPY dye and is followed by slower, long-range EET to the opposite terminal. Such materials are seen as highly attractive solar concentrators when dispersed in transparent plastic media and used under conditions where both inter- and intramolecular EET operate.

Intermolecular resonance energy transfer in the presence of a dielectric cylinder

Using a Green's tensor method, we investigate the rate of resonance electronic energy transfer between two molecules near a dielectric cylinder. Both the case of a real and frequency-independent dielectric constant $ϵ$ and the case of a Drude-Lorentz model for $ϵ(\ensuremath{\omega})$ are considered, the latter case including dispersion and absorption. If the donor is placed at a fixed position near the cylinder, we find that the energy transfer rate to the acceptor is enhanced compared to its vacuum value in a number of discrete hotspots, centered at the cylinder's surface. In the absence of dispersion and absorption the rate of energy transfer may be enhanced at most a few times. On the other hand, for the Drude-Lorentz model the enhancement may be huge (up to ${10}^{6}$) and the hotspots are sharply localized at the surface. We show that these observations can be explained from the fact that in the resonance region of the Drude-Lorentz dielectric surface plasmons occur, which play the dominant role in transferring the electronic energy between the donor and the acceptor. The dependence of the energy transfer rate on the molecular transition frequency is investigated as well. For small intermolecular distances, the cylinder hardly affects the transfer rate, independent of frequency. For larger distances, the frequency dependence is quite strong, in particular in the stop-gap region. The role of the intermolecular distance in the frequency dependence may be explained qualitatively using Heisenberg's uncertainty principle to calculate the spread in the frequencies of the intermediate photons.

Ideal dipole approximation fails to predict electronic coupling and energy transfer between semiconducting single-wall carbon nanotubes

The electronic coupling values and approximate energy transfer rates between semiconductor single-wall carbon nanotubes are calculated using two different approximations, the point dipole approximation and the distributed transition monopole approximation, and the results are compared. It is shown that the point dipole approximation fails dramatically at tube separations typically found in nanotube bundles ( approximately 12-16 A) and that the disagreement persists at large tube separations (>100 A, over ten nanotube diameters). When used in Forster resonance energy transfer theory, the coupling between two point transition dipoles is found to overestimate energy transfer rates. It is concluded that the point dipole approximation is inappropriate for use with elongated systems such as carbon nanotubes and that methods which can account for the shape of the particle are more suitable.