Effect of high-frequency modes and hot transitions on free energy gap dependence of charge recombination rate

The charge recombination (CR) dynamics of geminate ion pairs formed by excitation of the ground-state donor-acceptor complexes in polar solvent have been investigated within the framework of stochastic approach. It is shown that for low exergonic reactions these dynamics critically depend on the reorganization energy of intramolecular high-frequency mode. Even moderate reorganization energies (0.1-0.2 eV) significantly accelerate the excited-state population decay making it nearly exponential. In the solvent-controlled regime, the majority of the excited donor-acceptor complexes recombine at nonthermal (hot) stage when the nonequilibrium initial wave packet passes through a number of term crossings corresponding to the transitions with creation of several vibrational quanta. Analysis of this mechanism allows to conclude (i) the CR in viscous solvents proceeds much faster than the diffusive relaxation of solvent, (ii) under certain conditions, the CR rate becomes practically independent of the diffusive component of solvent relaxation which is determined by solvent viscosity, (iii) in contrast to predictions of Marcus theory, the CR rate decreases monotonically with the rise of reaction exergonicity even at small free energy gaps, in accordance with experimental results. Two semiquantitative approaches providing rather simple analytical expressions for the hot charge recombination dynamics are suggested. These approximations give a good reproduction of the excited-state decay in the wide area of model parameters.     

Excited states of the high-frequency vibrational modes and kinetics of ultrafast photoinduced electron transfer

The effect of the carrier frequency of the exciting laser pulse on the kinetics of intramolecular photoinduced charge transfer in the multi-channel stochastic model is studied. It is shown that the population of different states of high-frequency intramolecular modes upon varying the frequency of the excitation pulse can considerably alter the rate constant of ultrafast charge transfer. It is found that a negative vibrational spectral effect is expected in the vicinity of a barrier-free area (the rate constant of photoinduced charge transfer decreases along with the carrier frequency of the excitation pulse), while a positive effect is predicted in areas of high and low exergonicity (an inverse dependence). It is concluded that the value of the spectral effect falls along with the time of vibrational relaxation. For ultrafast photo-induced charge transfer, however, it remains considerable up to relaxation times of 100 fs.     

Charge recombination versus charge separation in donor-bridge-acceptor systems

Optimizing the ratio of the rates for charge separation (CS) over charge recombination (CR) is crucial to create long-lived charge-separated states. Mastering the factors that govern the electron transfer (ET) rates is essential when trying to achieve molecular-scale electronics, artificial photosynthesis, and also for the further development of solar cells. Much work has been put into the question of how the donor-acceptor distances and donor-bridge energy gaps affect the electronic coupling, V(DA), and thus the rates of ET. We present here a unique comparison on how these factors differently influence the rates for CS and CR in a porphyrin-based donor-bridge-acceptor model system. Our system contains three series, each of which focuses on a separate charge-transfer rate-determining factor, the donor-acceptor distance, the donor-bridge energy gap, and last, the influence of the electron acceptor on the rate for charge transfer. In these three series both CS and CR are governed by superexchange interactions which make a CR/CS comparative study ideal. We show here that the exponential distance dependence increases slightly for CR compared to that for CS as a result of the increased tunneling barrier height for this reaction, in accordance with the McConnell superexchange model. We also show that the dependence on the tunneling barrier height is different for CS and CR. This difference is highly dependent on the electron acceptor and thus cannot solely be explained by the differences in the frontier orbitals of the electron donor in these porphyrin systems.     

Stepwise charge separation and charge recombination in ferrocene-meso,meso-linked porphyrin dimer-fullerene triad

A meso,meso-linked porphyrin dimer [(ZnP)(2)] as a light-harvesting chromophore has been incorporated into a photosynthetic multistep electron-transfer model for the first time, including ferrocene (Fc), as an electron donor and fullerene (C(60)) as an electron acceptor to construct the ferrocene-meso,meso-linked porphyrin dimer-fullerene system (Fc-(ZnP)(2)-C(60)). Photoirradiation of Fc-(ZnP)(2)-C(60) results in photoinduced electron transfer from the singlet excited state of the porphyrin dimer [(1)(ZnP)(2)] to the C(60) moiety to produce the porphyrin dimer radical cation-C(60) radical anion pair, Fc-(ZnP)(2)(*+)-C(60)(*-). In competition with the back electron transfer from C(60)(*-) to (ZnP)(2)(*+) to the ground state, an electron transfer from Fc to (ZnP)(2)(*+) occurs to give the final charge-separated (CS) state, that is, Fc(+)-(ZnP)(2)-C(60)(*-), which is detected as the transient absorption spectra by the laser flash photolysis. The quantum yield of formation of the final CS state is determined as 0.80 in benzonitrile. The final CS state decays obeying first-order kinetics with a lifetime of 19 micros in benzonitrile at 295 K. The activation energy for the charge recombination (CR) process is determined as 0.15 eV in benzonitrile, which is much larger than the value expected from the direct CR process to the ground state. This value is rather comparable to the energy difference between the initial CS state (Fc-(ZnP)(2)(*+)-C(60)(*-)) and the final CS state (Fc(+)-(ZnP)(2)-C(60)(*-)). This indicates that the back electron transfer to the ground state occurs via the reversed stepwise processes,that is, a rate-limiting electron transfer from (ZnP)(2) to Fc(+) to give the initial CS state (Fc-(ZnP)(2)(*+)-C(60)(*-)), followed by a fast electron transfer from C(60)(*-) to (ZnP)(2)(*+) to regenerate the ground state, Fc-(ZnP)(2)-C(60). This is in sharp contrast with the extremely slow direct CR process of bacteriochlorophyll dimer radical cation-quinone radical anion pair in bacterial reaction centers.     

Evaluation of the complexity of charge recombination kinetics in photosynthetic bacteria

Abstract Improvements in instrumentation and methodology have allowed us to collect data of high signal to noise and reliability on the kinetics of recovery of both light-induced absorbance changes and ESR signals at 95 K. The results obtained by the two methods are identical and can not be fit with a single exponential curve. The decay kinetics can be fit well with three exponential components which represent 85, 9 and 6% of the total change with rate constants of 29 s⁻¹, 69 s⁻¹ and 2.3 s⁻¹, respectively. An interesting effect by molecular oxygen on the relaxation time of the donor cation radical was found by ESR measurements at low temperatures and higher microwave power. This interaction with oxygen could be blocked by addition of small amounts (e.g. 0.05%) of organic solvents such as ethanol. A variety of systems were examined including R. rubrum whole cells and chromatophores prepared from R. rubrum and Rps. sphaeroides. R. rubrum chromatophore samples were examined at high and low light intensities, at pH values from 6 to 10, in the presence and absence of air and after equilibration in D₂O media. In all cases, the same decay kinetics were observed. It seems possible that the observed complex decay may be a characteristic of phototraps of all photosynthetic material and reflect fundamental structural and functional features yet to be uncovered.     

Effect of ions on the vibrational relaxation of liquid water

We study the relaxation of the O-H stretch vibration of water in aqueous salt solutions using femtosecond two-color pump-probe spectroscopy. The vibrational lifetimes are measured for a series of salts consisting of the anions Cl(-), Br(-), and I(-) and the cations Li(+), Na(+), and Mg(2+), for a range of concentrations from 0.5 M up to 6 M (chloride salts), 9 M (bromide salts), and 10 M (iodide salts). In addition to the previously found dependence of the vibrational lifetime on the nature of the anion, the lifetime is found to depend on concentration and is observed to show a small but significant dependence on the nature of the cation. We present a model in which all the effects of ions on the vibrational relaxaton of liquid water are accounted for.     

On the early charge separation and recombination processes in bacterial reaction centers

A new mechanism for the rapid initial charge separation in bacterial reaction centers is investigated. It can be characterized as a combined exciton-electron transfer mechanism. It involves as first step the deactivation of the initially excited dimer (BC_LPBC_MP)^* together with a charge transfer transition between the accessory monomer BC_LA and the pheophytine BP_L leading to the state BC⁺_LABP⁻_L. This first step is followed by a rapid electron transfer from the dimer to the cation BC⁺_LA. It is shown that this mechanism is consistent with the pertinent experimental facts from absorption and emission spectra as well as time resolved measurements related to the initial charge separation and subsequent recombination processes.     

Is it common for charge recombination to be faster than charge separation?

Attaining long-lived charge-transfer (CT) states is of the utmost importance for energy science, photocatalysis, and materials engineering. When charge separation (CS) is slower than consequent charge recombination (CR), formation of a CT state is not apparent, yet the CT process provides parallel pathways for deactivation of electronically excited systems. The nuclear, or Franck-Condon (FC), contributions to the CT kinetics, as implemented by various formalisms based on the Marcus transition-state theory, provide an excellent platform for designing systems that produce long-lived CT states. Such approaches, however, tend to underestimate the complexity of alternative parameters that govern CT kinetics. Here we show a comparative analysis of two systems that have quite similar FC CT characteristics but manifest distinctly different CT kinetics. A decrease in the donor-acceptor electronic coupling during the charge-separation step provides an alternative route for slowing down undesired charge recombination. These examples suggest that, while infrequently reported and discussed, cases where CR is faster than CS are not necessarily rare occurrences.     

Photoinduced charge separation and recombination in a conjugated polymer-semiconductor nanocrystal composite

Semiconductor nanocrystals and conjugated polymers are classes of well-known materials with optoelectronic properties. We demonstrate that in a nanocrystalline TiO₂/poly(p-phenylene vinylene) (PPV) composite, excitons photogenerated in the polymer can be dissociated at the interface between the components, with electrons transferred to the nanocrystals. We show this and also follow the subsequent recombination using a time-resolved microwave conductivity technique. Recombination proceeds in a complex manner with roughly half of the initial amplitude decaying in 600 ns and the remainder in a biexponential process with time constants and relative amplitudes of 4.3 (0.7) and 80 μs (0.3). Photovoltaic devices were made from the composite films and their properties are discussed in light of the measured recombination rate and a simple carrier transport model.     

Energetics and kinetics of primary charge separation in bacterial photosynthesis

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.     

The role of van der Waals molecules in vibrational relaxation kinetics

The relaxation kinetics of N₂O and CO₂ vibrationally excited molecules (VEM) in two-phase gas-cluster systems was investigated under conditions of supersonic expansion with condensation. The catalytic effect of clusters on the vibrational relaxation rate was revealed. The relaxation rate of clustered VEM, R_c, and the probability of relaxation of VEM per collision with a cluster, $\text{P}$, as functions of the average number of molecules in a cluster, $\text{N}$, were obtained. Values of R_c and $\text{P}$ increase rapidly with increasing $\text{N}$, and at $\text{N}$ = constant they decrease with decreasing cluster temperature.     

Time resolved infrared absorption studies of geminate recombination and vibrational relaxation in OClO photochemistry

Ultrafast time-resolved infrared absorption studies of aqueous chlorine dioxide (OClO) photochemistry are reported. Following photoexcitation at 401 nm, the evolution in optical density at frequencies between 1000 to 1100 cm(-1) is monitored to investigate vibrational energy deposition and relaxation along the asymmetric-stretch coordinate following the reformation of ground-state OClO via geminate recombination of the primary photofragments. The measured kinetics are compared to two proposed models for the vibrational-relaxation dynamics along the asymmetric-stretch coordinate. This comparison demonstrates that the perturbation model derived from molecular dynamics studies is capable of qualitatively reproducing the observed kinetics, where the collisional model employed in previous UV-pump, visible probe experiments demonstrates poor agreement with experiment. The ability of the perturbation model to reproduce the optical-density evolution observed in these studies demonstrates that for aqueous OClO, frequency dependence of the solvent-solute coupling is important in defining the level-dependent vibrational relaxation rates along the asymmetric-stretch coordinate. The absence of optical-density evolution corresponding to the population of higher vibrational levels (n>8) along the asymmetric-stretch coordinate suggests that following geminate recombination, energy is initially deposited into a local Cl-O stretch, with the relaxation of vibrational energy from this coordinate providing for delayed vibrational excitation of the asymmetric- and symmetric-stretch coordinates relative to geminate recombination, as previously observed.     

The anharmonic vibrational potential and relaxation pathways of the amide I and II modes of N-methylacetamide

We investigate the influence of isotopic substitution and solvation of N-methylacetamide (NMA) on anharmonic vibrational coupling and vibrational relaxation of the amide I and amide II modes. Differences in the anharmonic potential of isotopic derivatives of NMA in D2O and DMSO-d6 are quantified by extraction of the anharmonic parameters and the transition dipole moment angles from cross-peaks in the two-dimensional infrared (2D-IR) spectra. To interpret the effects of isotopic substitution and solvent interaction on the anharmonic potential, density functional theory and potential energy distribution calculations are performed. It is shown that the origin of anharmonic variation arises from differing local mode contributions to the normal modes of the NMA isotopologues, particularly in amide II. The time domain manifestation of the coupling is the coherent exchange of excitation between amide modes seen as the quantum beats in femtosecond pump-probes. The biphasic behavior of population relaxation of the pump-probe and 2D-IR experiments can be understood by the rapid exchange of strongly coupled modes within the peptide backbone, followed by picosecond dissipation into weakly coupled modes of the bath.     

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.     

Energy-gap dependence of photoinduced charge separation and subsequent charge recombination in 1,4-phenylene-bridged zinc--free-base hybrid porphyrins

A series of 1,4-phenylene-bridged ZP-HP hybrid porphyrins (ZP = zinc porphyrin, HP = free-base porphyrin) 1-8 ZH have been prepared in which an electron-donating ZP moiety is kept constant and electron-accepting HP moieties are varied by introducing electron-accepting substituents, so that the energy gap for charge separation, ZP-1HP*--> ZP(+)-HP-, covers a range of about 0.9 eV in DMF. Here selective excitation at the HP moiety was employed to avoid complication in the determination of electron transfer rates derived from energy transfer, 1ZP*-HP --> ZP-1HP*. Definitive evidence for the electron transfer has been obtained in three solvents (benzene, THF, and DMF) through picosecond-femtosecond transient absorption studies, which have allowed the determination of the rates of the photoinduced charge separation, ZP-1HP* --> ZP(+)-HP-, and subsequent thermal charge recombination ZP(+)-HP- --> ZP-HP. Dyad 1ZH in THF exhibits a biphasic fluorescence decay that indicates thermal repopulation of the ZP-1HP* from ZP(+)-HP-; this has been also supported by the transient absorption spectra. On this ground, the energy levels of the ZP(+)-HP- ion pairs have been estimated. Similar biphasic fluorescence decay has been observed for 5 ZH in benzene; this allows furhter estimation of the energy level of the ZP(+)-HP- ion pairs. The free-energy-gap dependence (energy-gap law) has been probed from the normal to the upper limit region for the rate of the charge separation alone, and only the inverted region for the rate of the charge recombination. It was not possible to reproduce both energy-gap dependencies of the charge separation and the charge recombination assuming common parameter values for the reorganization energy and electronic interaction responsible for the electron transfer with the classical Marcus equation. Although both energy-gap dependencies can be approximately reproduced by means of the simplified semiclassical equation, which takes into consideration the effect of the high-frequency vibrations replaced by one mode of averaged frequency, many features, which include the effects of solvent polarity, electron-tunneling matrix element, and so forth on the energy-gap law, are considerably different from those of the previous studied porphyrin-quinone systems with weaker inter-chromophore electronic interactions.     

Using meta conjugation to enhance charge separation versus charge recombination in phenylacetylene donor-bridge-acceptor complexes

A pair of donor-bridge-acceptor electron-transfer complexes, with a carbazole donor and a naphthalimide acceptor connected by either a para- or meta-conjugated phenylacetylene bridge, are synthesized and studied using time-resolved and steady-state spectroscopy. These experiments show that the charge separation times, which depend on the coupling of the donor and acceptor through the excited bridge moiety, are similar for the two molecules (Meta and Para). The charge recombination time, however, is a factor of 10 slower for Meta than for Para. These results are related to changes in the electronic coupling of the bridge depending on its electronic state, and show that meta-conjugated bridges provide a possible motif for the design of asymmetric molecular wires.     

Time-domain ab initio study of charge relaxation and recombination in dye-sensitized TiO2

In order to investigate the electron dynamics at the alizarin/I2-/TiO2 interface this study uses a novel state-of-the-art quantum-classical approach that combines time-dependent density functional theory with surface hopping in the Kohn-Sham basis. Representing the dye-sensitized semiconductor Gr?tzel cell with the I-/I3- mediator, the system addresses the problems of an organic/inorganic, molecule/bulk interface that are commonly encountered in molecular electronics, photovoltaics, and photoelectrochemistry. The processes studied include the relaxation of the injected electron inside the TiO2 conduction band (CB), the back electron transfer (ET) from TiO2 to alizarin, the ET from the surface to the electrolyte, and the regeneration of the neutral chromophore by ET from the electrolyte to alizarin. Developing a theoretical understanding of these processes is crucial for improving solar cell design and optimizing photovoltaic current and voltage. The simulations carried out for the entire system that contains many electronic states reproduce the experimental time scales and provide detailed insights into the ET dynamics. In particular, they demonstrate the differences between the optimized geometric and electronic structure of the system at 0 K and the experimentally relevant structure at ambient temperature. The relaxation of the injected electron inside the TiO2 CB, which affects the solar cell voltage, is shown to occur on a 100 fs time scale and occurs simultaneously with the electron delocalization into the semiconductor bulk. The transfer of the electron trapped at the surface to the ground state of alizarin proceeds on a 1 ps time scale and is facilitated by vibrational modes localized on alizarin. If the electrolyte mediator is capable of approaching the semiconductor surface, it can form a stable complex and short-circuit the cell by accepting the photoexcited electron on a subpicosecond time scale. The ET from TiO2 to both alizarin and the electrolyte diminishes the solar cell current. Finally, the simulations show that the electrolyte can efficiently regenerate the neutral chromophore. This is true even though the two species do not form a chemical bond and, therefore, the electronic coupling between them is weaker than in the TiO2-chromophore and TiO2-electrolyte donor-acceptor pairs. The chromophore-electrolyte coupling can occur both directly through space and indirectly through bonding to the semiconductor surface. The ET events involving the electrolyte are promoted primarily by the electrolyte vibrational modes.     

Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies

Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.     

Non-equilibrium vibrational kinetics and ‘hot atom'' models in the recombination of hydrogen atoms on surfaces

Non-equilibrium vibrational kinetics as recently developed for adlayers is applied to experimental data on H-atom recombination and abstraction at solid surfaces. This model allows one to fit vibrational and translational energy distribution functions of the excited diatoms leaving the surface. Eley–Rideal and Langmuir–Hinshelwood mechanisms involving vibrationally excited adatoms are presented together with a criterion for establishing their relative contribution to the total reaction rate. Analogies of this multilevel ‘hot atom' (HA) model with recently employed two and three levels HA kinetic schemes are presented and discussed.     

Surfactant charge effects on the location, vibrational spectra, and relaxation dynamics of cyanoferrates in reverse micelles

Ultrafast infrared spectroscopy has been used to measure vibrational energy relaxation (VER) and reorientation (Tr) times for the high frequency CN stretches of potassium ferrocyanide and ferricyanide and the NO stretch of sodium nitroprusside (SNP) in several reverse micelle (RM) systems using cationic, anionic, and nonionic surfactants. The confinement effects on anion vibrational spectra and dynamics in aqueous RMs depend on the charge of the surfactant that is used to form the RMs. Spectra and VER dynamics of ferrocyanide are not significantly altered in the limited number of RMs in which it could be solubilized. The static spectra of ferricyanide suggest an environment that is most bulklike in anionic RMs and least bulklike in cationic RMs. The dynamics of ferricyanide are slower in cationic RMs and indistinguishable from the bulk in nonionic RMs. The VER dynamics and static spectra of SNP are indistinguishable from the bulk in anionic RMs, but much slower in cationic RMs. This suggests a strong surfactant-solute repulsion in the former and an attraction in the latter. Broad static spectra and probe frequency dependent dynamics are seen for SNP in nonionic RMs, indicating an inhomogeneous distribution of environments. Similar measurements were carried out for SNP in mixtures of water and a model compound containing only the hydrophilic portion of the nonionic surfactants in which RMs are not formed. The results closely resemble those observed for SNP in nonionic RMs and provide evidence that in the latter water penetrates the interface and hydrates the ethylene oxide groups before forming a water pool. The results are consistent with the explanation that Coulombic forces determine the anion location. The anions are repelled to the interior of the water pool, which has a bulklike environment in anionic RMs, and are attracted to the interface in cationic RMs, resulting in a strong interaction with the surfactant. The solute location in the nonionic RMs depends on the hydrophilic nature of the probe, with ferrocyanide and ferricyanide being more hydrophilic than SNP. These results and the dependence on surfactant charge are similar to those reported for azide.