Bridge-dependent electron transfer in porphyrin-based donor-bridge-acceptor systems.

Photoinduced electron transfer in donor-bridge-acceptor systems with zinc porphyrin (or its pyridine complex) as the donor and gold(III) porphyrin as the acceptor has been studied. The porphyrin moieties were covalently linked with geometrically similar bridging chromophores which vary only in electronic structure. Three of the bridges are fully conjugated pi-systems and in a fourth, the conjugation is broken. For systems with this bridge, the quenching rate of the singlet excited state of the donor was independent of solvent and corresponded to the rate of singlet energy transfer expected for a F?rster mechanism. In contrast, systems with a pi-conjugated bridging chromophore show a solvent-dependent quenching rate that suggests electron transfer in the Marcus normal region. This is supported by picosecond transient absorption measurements, which showed formation of the zinc porphyrin radical cation only in systems with pi-conjugated bridging chromophores. On the basis of the Marcus and Rehm-Weller equations, an electronic coupling of 5-20 cm(-)(1) between the donor and acceptor is estimated for these systems. The largest coupling is found for the systems with the smallest energy gap between the donor and bridge singlet excited states. This is in good agreement with the coupling calculated with quantum mechanical methods, as is the prediction of an almost zero coupling in the systems with a nonconjugated bridging chromophore.     

Conformationally constrained macrocyclic diporphyrin-fullerene artificial photosynthetic reaction center

Photosynthetic reaction centers convert excitation energy from absorbed sunlight into chemical potential energy in the form of a charge-separated state. The rates of the electron transfer reactions necessary to achieve long-lived, high-energy charge-separated states with high quantum yields are determined in part by precise control of the electronic coupling among the chromophores, donors, and acceptors and of the reaction energetics. Successful artificial photosynthetic reaction centers for solar energy conversion have similar requirements. Control of electronic coupling in particular necessitates chemical linkages between active component moieties that both mediate coupling and restrict conformational mobility so that only spatial arrangements that promote favorable coupling are populated. Toward this end, we report the synthesis, structure, and photochemical properties of an artificial reaction center containing two porphyrin electron donor moieties and a fullerene electron acceptor in a macrocyclic arrangement involving a ring of 42 atoms. The two porphyrins are closely spaced, in an arrangement reminiscent of that of the special pair in bacterial reaction centers. The molecule is produced by an unusual cyclization reaction that yields mainly a product with C(2) symmetry and trans-2 disubstitution at the fullerene. The macrocycle maintains a rigid, highly constrained structure that was determined by UV-vis spectroscopy, NMR, mass spectrometry, and molecular modeling at the semiempirical PM6 and DFT (B3LYP/6-31G**) levels. Transient absorption results for the macrocycle in 2-methyltetrahydrofuran reveal photoinduced electron transfer from the porphyrin first excited singlet state to the fullerene to form a P(?+)-C(60)(?-)-P charge separated state with a time constant of 1.1 ps. Photoinduced electron transfer to the fullerene excited singlet state to form the same charge-separated state has a time constant of 15 ps. The charge-separated state is formed with a quantum yield of essentially unity and has a lifetime of 2.7 ns. The ultrafast charge separation coupled with charge recombination that is over 2000 times slower is consistent with a very rigid molecular structure having a small reorganization energy for electron transfer, relative to related porphyrin-fullerene molecules.     

Driving force and electronic coupling effects on photoinduced electron transfer in a fullerene-based molecular triad

Tuning thermodynamic driving force and electronic coupling through structural modifications of a carotene (C) porphyrin (P) fullerene (C60) molecular triad has permitted control of five electron and energy transfer rate constants and two excited state lifetimes in order to prepare a high-energy charge-separated state by photoinduced electron transfer with a quantum yield of essentially unity (> or = 96%). Excitation of the porphyrin moiety of C-P-C60 is followed by a combination of photoinduced electron transfer to give C-P(.+)-C60.- and singlet-singlet energy transfer to yield C-P-1C60. The fullerene excited state accepts an electron from the porphyrin to also generate C-P(.+)-C60.-. Overall, this initial state is formed with a quantum yield of 0.97. Charge shift from the carotenoid to yield C(.+)-P-C60.- is at least 60 times faster than recombination of C-P(.+)-C60.-, leading to the overall quantum yield near unity for the final state. Formation of a similar charge-separate species from the zinc analog of the triad with a yield of 40% is also observed. Charge recombination of C(.+)-P-C60.- in 2-methyltetrahydrofuran yields the carotenoid triplet state, rather than the ground state. Comparison of the results for this triad with those for related triads with different structural features provides information concerning the effects of driving force and electronic coupling on each of the electron transfer steps.     

Theoretical investigation of the mechanism and dynamics of intramolecular coherent resonance energy transfer in soft molecules: a case study of dithia-anthracenophane

A computational study is conducted on dithia-anthracenophane (DTA), for which there is experimental evidence for coherent resonance energy transfer dynamics, and on dimethylanthracene (DMA), a molecule representing the energy donor and the acceptor in DTA. Electronic excitation energies are calculated by configuration interaction singles (CIS) and time-dependent density functional theory (TD-DFT) methods and are compared to experimental ones. Electronic coupling constants are calculated between two DMAs embedded into the ground-state structure of DTA employing methods based on transition densities. The resulting values of electronic coupling provide a more consistent interpretation of experiments than those based on one-half the level spacing of DTA excitation energies. Solvation effects are studied based on the polarizable continuum model (PCM). Solvent-induced polarization and screening effects are shown to make opposite contributions, and the net electronic coupling is little different from the value in a vacuum. The likelihood of coherent population transfer is assessed on the basis of a recently developed theory of coherent resonance energy transfer. The time scale of bath is shown to have an important role in sustaining the quantum coherence. The combination of quantum chemical and dynamical data suggests that the electronic coupling in DTA is in the range of 50-100 cm(-1). The presence of oscillatory excitation population dynamics can be understood from the picture of polaronic excitation moderately dressed with dispersive vibrational modes. The effect of torsional modulation on the excitation energies of DTA and electronic coupling is examined on the basis of optimized structures with the torsional angle constrained. The result suggests that inelastic effect due to torsional motion cannot be disregarded in DTA.     

Luminescence of Hybrid Nanostructures of InP@ZnS Colloidal Quantum Dots and <Emphasis Type="Italic">meso</Emphasis>-Tetra(3-pyridyl)porphyrin Molecules

The formation of hybrid nanostructures consisting of InP@ZnS colloidal quantum dots and mesotetra(3-pyridyl)porphyrin molecules adsorbed on the quantum dots has been studied. In such nanostructures, strong quenching of quantum dot luminescence and an increase in the emission intensity of porphyrin are observed due to nonradiative resonance energy transfer from colloidal quantum dots to porphyrin.     

Restricted and unrestricted Hartree–Fock approaches applied to spherical quantum dots in a magnetic field

The Roothaan and Pople–Nesbet approaches for real atoms are adapted to quantum dots in the presence of a magnetic field. Single‐particle Gaussian basis sets are constructed, for each dot radius, under the condition of maximum overlap with the exact functions. The chemical potential, charging energy, and total spin expected values are calculated, and we have verified the validity of the quantum dot energy shell structure as well as Hund's rule for electronic occupation at zero magnetic field. At finite field, we have observed the violation of Hund's rule and studied the influence of magnetic field on the closed and open energy shell configurations. We have also compared the present results with those obtained within the LS‐coupling scheme for low electronic occupation numbers. We focus only on ground‐state properties and consider quantum dots populated up to 40 electrons, constructed by GaAs or InSb nanocrystals. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Single particle versus ensemble average: from power-law intermittency of a single quantum dot to quasistretched exponential fluorescence decay of an ensemble

Light-induced diffusion-controlled electron transfer is proposed as an underlying mechanism for the intermittency (power law and breakdown) of a single quantum dot and ensemble-averaged fluorescence decay. The intensity decay can be approximated to a stretched exponential expression. The physical links to the free energy gap, reorganization energy, electronic coupling, and diffusion correlation times are discussed. A procedure is described for extracting these molecular-based parameters from experiments and is demonstrated with examples using existing data.     

Conformer-dependent electronic coupling for long-range triplet energy transfer in donor-bridge-acceptor porphyrin dimers

The electronic coupling for triplet energy transfer is calculated by time-dependent density functional theory (TD-DFT) for a set of tri-chromophoric systems based on a zinc(II) porphyrin donor and the corresponding free base acceptor covalently connected by different hydrocarbon bridging chromophores. The calculated electronic coupling, for systems with identical donor acceptor distances, is sensitive to the bridge electronic structure and shows a significant dependence for the bridge and donor-bridge conformations. The computational results compare quantitatively to measurements of triplet energy transfer rates in the corresponding donor-bridge-acceptor systems.     

Electronic coupling matrix elements from charge constrained density functional theory calculations using a plane wave basis set

We present a plane wave basis set implementation for the calculation of electronic coupling matrix elements of electron transfer reactions within the framework of constrained density functional theory (CDFT). Following the work of Wu and Van Voorhis [J. Chem. Phys. 125, 164105 (2006)], the diabatic wavefunctions are approximated by the Kohn-Sham determinants obtained from CDFT calculations, and the coupling matrix element calculated by an efficient integration scheme. Our results for intermolecular electron transfer in small systems agree very well with high-level ab initio calculations based on generalized Mulliken-Hush theory, and with previous local basis set CDFT calculations. The effect of thermal fluctuations on the coupling matrix element is demonstrated for intramolecular electron transfer in the tetrathiafulvalene-diquinone (Q-TTF-Q(-)) anion. Sampling the electronic coupling along density functional based molecular dynamics trajectories, we find that thermal fluctuations, in particular the slow bending motion of the molecule, can lead to changes in the instantaneous electron transfer rate by more than an order of magnitude. The thermal average, (<|H(ab)|(2)>)(1/2)=6.7 mH, is significantly higher than the value obtained for the minimum energy structure, |H(ab)|=3.8 mH. While CDFT in combination with generalized gradient approximation (GGA) functionals describes the intermolecular electron transfer in the studied systems well, exact exchange is required for Q-TTF-Q(-) in order to obtain coupling matrix elements in agreement with experiment (3.9 mH). The implementation presented opens up the possibility to compute electronic coupling matrix elements for extended systems where donor, acceptor, and the environment are treated at the quantum mechanical (QM) level.     

Temperature dependence of charge separation and recombination in porphyrin oligomer-fullerene donor-acceptor systems

Electron-transfer reactions are fundamental to many practical devices, but because of their complexity, it is often very difficult to interpret measurements done on the complete device. Therefore, studies of model systems are crucial. Here the rates of charge separation and recombination in donor-acceptor systems consisting of a series of butadiyne-linked porphyrin oligomers (n = 1-4, 6) appended to C(60) were investigated. At room temperature, excitation of the porphyrin oligomer led to fast (5-25 ps) electron transfer to C(60) followed by slower (200-650 ps) recombination. The temperature dependence of the charge-separation reaction revealed a complex process for the longer oligomers, in which a combination of (i) direct charge separation and (ii) migration of excitation energy along the oligomer followed by charge separation explained the observed fluorescence decay kinetics. The energy migration is controlled by the temperature-dependent conformational dynamics of the longer oligomers and thereby limits the quantum yield for charge separation. Charge recombination was also studied as a function of temperature through measurements of femtosecond transient absorption. The temperature dependence of the electron-transfer reactions could be successfully modeled using the Marcus equation through optimization of the electronic coupling (V) and the reorganization energy (λ). For the charge-separation rate, all of the donor-acceptor systems could be successfully described by a common electronic coupling, supporting a model in which energy migration is followed by charge separation. In this respect, the C(60)-appended porphyrin oligomers are suitable model systems for practical charge-separation devices such as bulk-heterojunction solar cells, where conformational disorder strongly influences the electron-transfer reactions and performance of the device.     

Single-molecule quantum-dot fluorescence resonance energy transfer.

Colloidal semiconductor quantum dots are promising for single-molecule biological imaging due to their outstanding brightness and photostability. As a proof of concept for single-molecule fluorescence resonance energy transfer (FRET) applications, we measured FRET between a single quantum dot and a single organic fluorophore Cy5. DNA Holliday junction dynamics measured with the quantum dot/Cy5 pair are identical to those obtained with the conventional Cy3/Cy5 pair, that is, conformational changes of individual molecules can be observed by using the quantum dot as the donor.     

Synthesis,Photophysical Properties and Computational Studies of beta‐Substituted Porphyrin Dyads

Beta‐pyrrole‐substituted porphyrin dyads connected by ethynyl linkage to N‐butylcarbazole or triphenylamine donors are reported. Donor‐π‐acceptor type beta‐substituted porphyrin dyads and their Zn(II) and Pd(II) complexes were characterized by MALDI‐MS, NMR, UV‐vis absorption, fluorescence and cyclic voltammetry techniques. The S₁ emission dynamics were analyzed by time‐resolved spectroscopy (TCSPC); dyads exhibited efficient energy transfer up to 93% from beta‐donors (N‐butylcarbazole or triphenylamine group) to the porphyrin core. The efficiency of energy transfer for the beta‐substituted porphyrin dyads were much higher than those of the corresponding meso‐substituted porphyrin dyads, reflecting enhanced communications between the beta‐donors and the porphyrin core. The Pd(II) dyads, showed characteristic phosphorescence in the near IR region and very efficient singlet oxygen quantum yields (53–60%); these dyads are promising candidates for photocatalytic oxidations of organic compounds. The donor‐acceptor interaction between the porphyrin core and the beta‐donors was supported by the DFT studies in the porphyrin dyads.     

Intramolecular energy-transfer processes in a bis(porphyrin)-ruthenium(II) bis(2,2':6',2'-terpyridine) molecular array

A molecular triad has been synthesized comprising two free-base porphyrin terminals linked to a central ruthenium(II) bis(2,2':6',2'-terpyridine) subunit via meso-phenylene groups. Illumination into the ruthenium(II) complex is accompanied by rapid intramolecular energy transfer from the metal-to-ligand, charge-transfer (MLCT) triplet to the lowest-energy pi-pi* triplet state localized on one of the porphyrin subunits. Transfer takes place from a vibrationally excited level which lowers the activation energy. The electronic coupling matrix element for this process is 73 cm(-1). Selective illumination into the lowest-energy singlet excited state (S1) localized on the porphyrin leads to fast singlet-triplet energy transfer that populates the MLCT triplet state with high efficiency. This latter process occurs via Dexter-type electron exchange at room temperature, but the activation energy is high and the reaction is prohibited at low temperature. For this latter process, the electronic coupling matrix element is only 8 cm(-1).     

Influence of environment induced correlated fluctuations in electronic coupling on coherent excitation energy transfer dynamics in model photosynthetic systems

Two-dimensional photon-echo experiments indicate that excitation energy transfer between chromophores near the reaction center of the photosynthetic purple bacterium Rhodobacter sphaeroides occurs coherently with decoherence times of hundreds of femtoseconds, comparable to the energy transfer time scale in these systems. The original explanation of this observation suggested that correlated fluctuations in chromophore excitation energies, driven by large scale protein motions could result in long lived coherent energy transfer dynamics. However, no significant site energy correlation has been found in recent molecular dynamics simulations of several model light harvesting systems. Instead, there is evidence of correlated fluctuations in site energy-electronic coupling and electronic coupling-electronic coupling. The roles of these different types of correlations in excitation energy transfer dynamics are not yet thoroughly understood, though the effects of site energy correlations have been well studied. In this paper, we introduce several general models that can realistically describe the effects of various types of correlated fluctuations in chromophore properties and systematically study the behavior of these models using general methods for treating dissipative quantum dynamics in complex multi-chromophore systems. The effects of correlation between site energy and inter-site electronic couplings are explored in a two state model of excitation energy transfer between the accessory bacteriochlorophyll and bacteriopheophytin in a reaction center system and we find that these types of correlated fluctuations can enhance or suppress coherence and transfer rate simultaneously. In contrast, models for correlated fluctuations in chromophore excitation energies show enhanced coherent dynamics but necessarily show decrease in excitation energy transfer rate accompanying such coherence enhancement. Finally, for a three state model of the Fenna-Matthews-Olsen light harvesting complex, we explore the influence of including correlations in inter-chromophore couplings between different chromophore dimers that share a common chromophore. We find that the relative sign of the different correlations can have profound influence on decoherence time and energy transfer rate and can provide sensitive control of relaxation in these complex quantum dynamical open systems.     

Triplet excitation energy transfer in porphyrin-based donor--bridge--acceptor systems with conjugated bridges of varying length: an experimental and DFT study

A series of donor--bridge--acceptor (D--B--A) systems with varying donor-acceptor distances have been studied with respect to their triplet energy transfer properties. The donor and acceptor moieties, zinc(II), and free-base porphyrin, respectively, were separated by 2-5 oligo-p-phenyleneethynylene units (OPE) giving rise to edge-to-edge separations ranging between 12.7 and 33.4 A. The study was performed in 2-MTHF at 150 K and it was established that triplet excitation energy transfer occurs with high efficiency in all of the studied D--B--A systems. The distance dependence was exponential with an attenuation factor, beta, equal to 0.45 +/- 0.015 A(-1). The experimental study was also supported by quantum mechanical DFT and TD-DFT calculations on a series of closely related model systems. A thorough analysis of the OPE-bridge conformational dynamics led to an equation that quantitatively models the distance dependence of the electronic coupling found in the experimental study.     

Laser control of double proton transfer in porphycenes: towards an ultrafast switch for photonic molecular wires

Electronic excitation energy transfer along a molecular wire depends on the relative orientation of the electronic transition dipole moments of neighboring chromophores. In porphycenes, this orientation is changed upon double proton transfer in the electronic ground state. We explore the possibility to trigger such a double proton transfer reaction by means of an infrared pump-dump laser control scheme. To this end, a quantum chemical characterization of an asymmetrically substituted porphycene is performed using density functional theory. Ground state geometries, the topology of the potential energy surface for double proton transfer, and \(\hbox{S}_0\rightarrow\hbox{S}_1\) transition energies are compared with the parent compound porphycene and a symmetric derivative. Employing a simple two-dimensional model for the double proton transfer, which incorporates sequential and concerted motions, quantum dynamics simulations of the laser-driven dynamics are performed which demonstrate tautomerization control. Based on the orientation of the transition dipole moments, this tautomerization may lead to an estimated change in the Förster transfer coupling of about 60%.     

Effects of Configurational Fluctuation on Electronic Coupling for Charge Transfer Dynamics

We advance a theory for the effects of bridge configurational fluctuations on the electronic coupling for electron transfer reactions in donor-bridge-acceptor systems. The theory of radiationless transitions was applied for activationless electron transfer, where the nuclear Franck–Condon constraints are minimized, with the initial vibronic state interacting directly with the final vibronic manifold, without the need for thermal activation. Invoking the assumption of energy-independent coupling, the time-dependent initial state population probability was analyzed in terms of a cumulant expansion. Two limiting situations were distinguished, i.e. the fast configurational fluctuation limit, where the electron transfer rate is given in terms of the configurational average of me squared electronic coupling, and the slow configurational fluctuation limit, where the dynamics is determined by a configurational averaging over a static distribution of electron transfer probability densities. The correlation times for configurational fluctuations of the electronic coupling will be obtained from the analysis of molecular dynamics, in conjunction with quantum mechanical calculations of the electronic coupling, to establish the appropriate limit for electron transfer dynamics.     

Electron transfer in porphyrin—quinone cyclophanes studied on the pico- and femto-second time scale

Electron transfer in porphyrin—quinone cyclophanes is investigated by fluorescence and absorption spectroscopy with pico- and femto-second pulses. In nonpolar solvents, the S₁ state of the porphyrin shows a lifetime from 300 ps up to several nanoseconds, depending upon the number of quinones and upon their electron affinity. Comparative measurements in polar solvents demonstrate very fast electron transfer on a time scale between 1 and 10 ps. The results are analyzed with the aid of quantum-chemical calculations which give the energy of the charge transfer states and the relevant coupling strengths. For nonpolar solvents, theory suggests fluctuation-induced charge separation and/or direct radiationless internal conversion from the porphyrin S₁ to the ground state. In polar solution, the molecules exist in a tilted configuration with strong electronic coupling and charge transfer states well below the S₁ level, resulting in fast electron transfer and subsequent charge recombination within 10–40 ps.     

The Synthesis and Characterisation of a Free‐Base Porphyrin–Perylene Dyad that Exhibits Electronic Coupling in Both the Ground and Excited States

A covalent dyad composed of a free‐base porphyrin and a perylene diimide ( 1 ) was synthesised and characterised by NMR, HRMS, UV/Vis and fluorometric methods. UV/Vis spectrophotometric analysis indicated a moderate coupling between the components in the ground state. Fluorescence spectroscopy revealed that the emissive properties of the dyad showed that the quantum yield of emission from the porphyrin Soret band increased dramatically and could not be rationalised by a straightforward photoinduced energy (and/or electron) transfer, but rather a coupling of excited states.