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Excitonic interactions and Stark fluorescence spectra
The Journal of Chemical Physics
Abstract
We develop the theory for the Stark fluorescence (SF) of molecular aggregates by taking into account the mixing of the excited states [including the states with charge-transfer (CT) characters]. We use the sum-over-state approach and modified rotating wave approximation to describe interactions of the static and optical fields with the permanent and transition dipoles of the excited states. The SF spectral profiles are calculated using the standard and modified Redfield theories for the emission lineshapes. The resulting expression allows an interpretation of the SF response based on the calculation of only one-exciton states (i.e., the calculation of two-exciton states is not needed). The shape and amplitude of the SF spectrum can exhibit dramatic changes in the presence of the CT states, especially when the CT state is mixed with the red-most emitting exciton levels. In this case, the SF responses are much more sensitive to the exciton-CT mixing as compared with the usual Stark absorption. The limitation of the proposed theory is related to the simplified nature of the Redfield picture, which neglects the dynamic localization within the mixed exciton-CT configuration.
... There is a debate concerning the applicability of the standard Liptay formalism as a mathematical tool for simulating the Stark spectra of systems with appreciably large static dipole moments in their excited states, such as different pigment-protein complexes of photosynthetic organisms (Novoderezhkin et al. 2007;Gottfried et al. 1991;Somsen et al. 1998;Moore et al. 1999;Braver et al. 2021). However, as far as the analysis of Stark data is concerned, no other effective substitutes for the Liptay formalism have been developed so far that can be used independently to analyze the data and yield detailed information about the associated electrostatic parameters (which is the ultimate goal in analyzing Stark data), although some recent theoretical investigations attempted to do so (Braver et al. 2021;Novoderezhkin 2023). Thus, regardless of the size of their excited state static dipole moments, the conventional Liptay formalism serves as the fundamental To gain some qualitative inference about the emission contribution of PSII subunit, we carried out a systematic analysis of the observed F IsiAMem (see Fig. 2). ...
In this work, we applied Stark fluorescence spectroscopy to an iron-stressed cyanobacterial membrane to reveal key insights about the electronic structures and excited state dynamics of the two important pigment-protein complexes, IsiA and PSII, both of which prevail simultaneously within the membrane during iron deficiency and whose fluorescence spectra are highly overlapped and hence often hardly resolved by conventional fluorescence spectroscopy. Thanks to the ability of Stark fluorescence spectroscopy, the fluorescence signatures of the two complexes could be plausibly recognized and disentangled. The systematic analysis of the SF spectra, carried out by employing standard Liptay formalism with a realistic spectral deconvolution protocol, revealed that the IsiA in an intact membrane retains almost identical excited state electronic structures and dynamics as compared to the isolated IsiA we reported in our earlier study. Moreover, the analysis uncovered that the excited state of the PSII subunit of the intact membrane possesses a significantly large CT character. The observed notably large magnitude of the excited state CT character may signify the supplementary role of PSII in regulative energy dissipation during iron deficiency.
Lhca4 is one of the peripheral antennae of higher plant photosystem I and it is characterized by the presence of chlorophyll a with absorption and emission bands around 30 nm red-shifted compared to those of the other chlorophylls associated with plant complexes. In this work we have investigated the origin of this red shift by using the recent structure of Lhca4 (Qin et al., Science, 2015, 348, 989) to build an exciton model that includes a charge-transfer (CT) state mixed with the excited-state manifold. A simultaneous quantitative fit of absorption, linear dichroism, fluorescence, and Stark absorption spectra of the wild-type Lhca4 and NH mutant (where the sites involved in CT are affected) enables us to determine the origin of the CT state and explore its spectral signatures. A huge borrowing of dipole strength by the CT, accompanied by anomalous broadening and red-shifting of the fluorescence as well as dramatic changes in the Stark spectrum, can be accounted for by a model implying an exciton-type mixing between excited states and CT states.
Understanding how specific protein environments affect the mechanisms of non-radiative energy dissipation within densely assembled chlorophylls in photosynthetic protein complexes is of great interest to the construction of bioinspired solar energy conversion devices. Mixing of charge-transfer and excitonic states in excitonically interacting chlorophylls was implicated in shortening excited states’ lifetimes, but its relevance to active control of energy dissipation in natural systems is under considerable debate. Here we show that the degree of fluorescence quenching in two similar pairs of excitonically interacting bacteriochlorophyll derivatives is directly associated with increasing charge-transfer character in the excited state, and that the protein environment may control non-radiative dissipation by affecting the mixing of charge-transfer and excitonic states. The capability of local protein environments to determine the fate of excited states, and thereby to confer different functionalities to excitonically coupled dimers substantiates the dimer as the basic functional element of photosynthetic enzymes.
We propose an optimized tight-binding electron–hole model of the photosystem II (PSII) reaction center (RC). Our model incorporates two charge separation pathways and spatial correlations of both static disorder and fast fluctuations of energy levels. It captures the main experimental features observed in time-resolved two-dimensional (2D) optical spectra at 77 K: peak pattern, lineshapes and time traces. Analysis of 2D spectra kinetics reveals that specific regions of the 2D spectra of the PSII RC are sensitive to the charge transfer states. We find that the energy disorder of two peripheral chlorophylls is four times larger than the other RC pigments.
Diatoms are characterized by very efficient photoprotective mechanisms where the excess energy is dissipated as heat in the main antenna system constituted by fucoxanthin-chlorophyll (Chl) protein complexes (FCPs). We performed Stark fluorescence spectroscopy on FCPs in their light-harvesting and energy dissipating states. Our results show that two distinct emitting bands are created upon induction of energy dissipation in FCPa and possibly in FCPb. More specifically one band is characterized by broad red shifted emission above 700 nm and bears strong similarity with a red shifted band we detected in the dissipative state of the major light-harvesting complex II (LHCII) of plants (Wahadoszamen et al. PCCP 2012. 14(2): p. 759-766). We discuss the results in the light of different mechanisms proposed to be responsible for photosynthetic photoprotection.
A theory for four-wave-mixing signals from molecular aggregates, which includes effects of two-exciton states, static disorder, and coupling to a phonon bath with an arbitrary spectral density, is developed. The third-order polarization is rigorously partitioned into a coherent and a sequential contribution. The latter is given by a sum of an exciton-hopping and a ground state (bleaching) terms, both expressed using the doorway-window representation. Applications are made to photon-echo and pump-probe spectroscopies of the B850 system of the LH2 antenna in purple bacteria. © 1998 American Institute of Physics.
In order to cope with the deleterious effects of excess light, photosynthetic organisms have developed remarkable strategies where the excess energy is dissipated as heat by the antenna system. In higher plants one main player in the process is the major light harvesting antenna of Photosystem II (PSII), LHCII. In this paper we applied Stark fluorescence spectroscopy to LHCII in different quenching states to investigate the possible contribution of charge-transfer states to the quenching. We find that in the quenched state the fluorescence displays a remarkable sensitivity to the applied electric field. The resulting field-induced emission spectra reveal the presence of two distinct energy dissipating sites both characterized by a strong but spectrally very different response to the applied electric field. We propose the two states to originate from chlorophyll-chlorophyll and chlorophyll-carotenoid charge transfer interactions coupled to the chlorophyll exciton state in the terminal emitter locus and discuss these findings in the light of the different models proposed to be responsible for energy dissipation in photosynthesis.
The excited state dynamics and relaxation of electrons and holes in the photosynthetic reaction center of photosystem II are simulated using a two-band tight-binding model. The dissipative exciton and charge carrier motions are calculated using a transport theory, which includes a strong coupling to a harmonic bath with experimentally determined spectral density, and reduces to the Redfield, the Förster, and the Marcus expressions in the proper parameter regimes. The simulated third order two-dimensional signals, generated in the directions -k(1)+k(2)+k(3), k(1)-k(2)+k(3), and k(1)+k(2)-k(3), clearly reveal the exciton migration and the charge-separation processes.
A theory for calculating time– and frequency–domain optical spectra of pigment–protein complexes is presented using a density matrix approach. Non-Markovian effects in the exciton–vibrational coupling are included. A correlation function is deduced from the simulation of 1.6 K fluorescence line narrowing spectra of a monomer pigment–protein complex (B777), and then used to calculate fluorescence line narrowing spectra of a dimer complex (B820). A vibrational sideband of an excitonic transition is obtained, a distinct non-Markovian feature, and agrees well with experiment on B820 complexes. The theory and the above correlation function are used elsewhere to make predictions and compare with data on time–domain pump–probe spectra and frequency–domain linear absorption, circular dichroism and fluorescence spectra of Photosystem II reaction centers.
Stark spectroscopy has been applied to a wide range of molecular systems and materials. A generally useful method for obtaining electronic and vibrational Stark spectra that does not require sophisticated equipment is described. By working with frozen glasses it is possible to study nearly any molecular system, including ions and proteins. Quantitative analysis of the spectra provides information on the change in dipole moment and polarizability associated with a transition. The change in dipole moment reflects the degree of charge separation for a transition, a quantity of interest to a variety of fields. The polarizability change describes the sensitivity of a transition to an electrostatic field such as that found in a protein or an ordered synthetic material. Applications to donor-acceptor polyenes, transition metal complexes (metal-to-ligand and metal-to-metal mixed valence transitions), and nonphotosynthetic biological systems are reviewed.
External electric field effects on state energy and photoexcitation dynamics have been examined for para-substituted and unsubstituted all-trans-diphenylpolyenes doped in a film, based on the steady-state and picosecond time-resolved measurements of the field effects on absorption and fluorescence. The substitution dependence of the electroabsorption spectra shows that the dipole moment of the substituted stilbene in the Franck-Condon excited state becomes larger with increasing difference between the Hammet constants of the substituents. Fluorescence quantum yields of 4-(dimethylamino)-4'-nitrostilbene and 4-(dimethylamino)-4'-nitrodiphenylbutadiene are markedly reduced by an electric field, suggesting that the rates of the intramolecular charge transfer (CT) from the fluorescent state to the nonradiative CT state are accelerated by an external electric field. The magnitude of the field-induced decrease in fluorescence lifetime has been evaluated. The isomerization of the unsubstituted all-trans-diphenylpolyenes to the cis forms is shown to be a significant nonradiative pathway even in a film. Field-induced quenching of their fluorescence as well as field-induced decrease in fluorescence lifetime suggests that the trans to cis photoisomerization is enhanced by an electric field.
We model the energy transfer dynamics in the Lhca4 peripheral antenna of photosystem I from higher plants. Equilibration between the bulk exciton levels of the antenna and the red-shifted charge-transfer (CT) states is described using the numerically inexpensive Redfield-Förster approach and exact hierarchical equation (HEOM) method. We propose a compartmentalization scheme allowing a quantitatively correct description of the dynamics with the Redfield-Förster theory, including the exciton-type relaxation within strongly coupled compartments and hopping-type migration between them. The Redfield-Förster method gives the kinetics close to the HEOM solution when treating the CT state as dynamically localized. We also demonstrate that the excited states strongly coupled with the CT should be considered as localized as well.
Photosystem II (PSII) is the only biological system capable of splitting water to molecular oxygen. Its reaction center (RC) is responsible for the primary charge separation that drives the water oxidation reaction. In this work, we revisit the spectroscopic properties of the PSII RC using the complex time-dependent Redfield (ctR) theory for optical lineshapes [A. Gelzinis et al., J. Chem. Phys. 142, 154107 (2015)]. We obtain the PSII RC model parameters (site energies, disorder, and reorganization energies) from the fits of several spectra and then further validate the model by calculating additional independent spectra. We obtain good to excellent agreement between theory and calculations. We find that overall our model is similar to some of the previous asymmetric exciton models of the PSII RC. On the other hand, our model displays differences from previous work based on the modified Redfield theory. We extend the ctR theory to describe the Stark spectrum and use its fit to obtain the parameters of a single charge transfer state included in our model. Our results suggest that ChlD1+PheoD1- is most likely the primary charge transfer state, but that the Stark spectrum of the PSII RC is probably also influenced by other states.
Linear absorption is the most basic optical spectroscopy technique that provides information about the electronic and vibrational degrees of freedom of molecular systems. In simulations of absorption lineshapes, often diagonal fluctuations are included using the cumulant expansion, and the off-diagonal fluctuations are accounted for either perturbatively, or phenomenologically. The accuracy of these methods is limited and their range of validity is still questionable. In this work, a systematic study of several such methods is presented by comparing the lineshapes with exact results. It is demonstrated that a non-Markovian theory for off-diagonal fluctuations, termed complex time dependent Redfield theory, gives good agreement with exact lineshapes over a wide parameter range. This theory is also computationally efficient. On the other hand, accounting for the off-diagonal fluctuations using the modified Redfield lifetimes was found to be inaccurate.
When cyanobacteria are grown under iron-limited or other oxidative stress conditions the iron stress inducible pigment-protein IsiA is synthesized in variable amounts. IsiA forms aggregates inside the photosynthetic membrane that strongly dissipate chlorophyll excited state energy. In this paper we applied Stark fluorescence (SF) spectroscopy at 77K to IsiA aggregates to gain insight into the nature of the emitting and energy dissipating state(s). Our study shows that two emitting states are present in the system, one emitting at 684nm and the other emitting at about 730nm. The new 730nm state exhibits strongly reduced fluorescence (F) together with a large charge transfer character. We discuss these findings in the light of the energy dissipation mechanisms involved in the regulation of photosynthesis in plants, cyanobacteria and diatoms. Our results suggest that photosynthetic organisms have adopted common mechanisms to cope with the deleterious effects of excess light under unfavorable growth conditions.
Copyright © 2015 Elsevier B.V. All rights reserved.
The fluorescence intensity from randomly oriented, immobilized Rb. sphaeroides reaction centers at 77 K increases in the presence of an externally applied electric field. We have proposed that this increase is due to a net decrease in the rate of the forward electron transfer reaction which competes with the prompt fluorescence. This decrease results from the change in the free energy difference between the reactant and very dipolar product state in the presence of the electric field. Because the free energy change and thus the electron transfer rate for a given reaction center depends on its orientation relative to the field, the intensity of the competing fluorescence likewise becomes orientation dependent. An expression is derived relating the degree of this electric field induced fluorescence anisotropy to the angle ζet between the fluorescence transition moment and the effective dipole moment whose interaction with the field results in the change in the rate of the electron transfer reaction which competes with fluorescence. ζet is determined to be about 69°. This angle can be estimated from the x‐ray crystal structure coordinates for possible identities of the initial electron acceptor. The results are inconsistent with a two‐step hopping mechanism in which the bacteriochlorophyll on the L side is the initial electron acceptor whose formation competes with fluorescence. Effects of an electric field on the electronic coupling for a superexchange mechanism are discussed. The theoretical and experimental approach should be generally applicable for studying long‐range electron transfer reactions.
A closed expression for the Stark signal of molecular aggregates, which does not suffer from singularities when the exciton states are nearly degenerate and avoids the calculation of two-exciton states, is derived from the third order response to the total (static + optical) field, treating intermolecular interactions within the local field approximation. Transitions between one-exciton states play an important role and generally reduce the magnitude of the signal with respect to monomer spectra. The experimental Stark spectrum from the B820 dimer subunit of LH1 is consistent with simulations for a dimer of parallel pigments. The spectra of LH1 and LH2 cannot be explained by excitonic interactions alone. This supports the idea that charge-transfer states may play an important role in the spectroscopy of photosynthetic pigment proteins.
We studied the fluorescence dynamics of the light-harvesting-2 complex of Rhodopseudomonas acidophila both with and without an externally applied electric field. The fluorescence emission spectrum of the complex shows (small) spectral shifts of the average emission wavelength on a time scale of 300 ps. The shifts are temperature dependent and result from a combination of the (a) dielectric relaxation, or solvation, of the excited states by the protein, which causes a red shift of the emission, and (b) nonradiative loss processes occurring in a subset of the ensemble of complexes. These two processes compete with delocalization and energy transfer around the ring and are shown to be sensitive to an external electric field. The experiments illustrate how nature has prevented the above-mentioned loss processes in vivo by having fast energy transfer around a symmetric structure. Local protein relaxation is slow for the delocalized (or fast-hopping) excited states. However, once localized, localization and (dielectric) relaxation act in a cooperative way. Therefore, at low temperatures (<100 K), the nonradiative loss processes are more prominent. In a more general way, the experiments demonstrate how, by looking at the effects of an external electric field on the fluorescence dynamics, one can identify the nature of the relaxation processes; that is, the electric field is a probe for solvation and relaxation processes. These first experiments demonstrate the promising potential of the approach presented here for studies on ultrafast solvation processes.
Electron-transfer reactions are expected to be particularly sensitive to externally applied electric fields because of the presence of charge-separated, dipolar states, and the effects of the field on photoinduced reactions can be determined by monitoring the competing emission. The rates of photoinduced electron-transfer reactions between a donor and acceptor are often measured by comparing the quantum yield of the competing emission from the state undergoing the reaction in the presence and absence of electron transfer. Calculations are presented for the fluorescence line shape and amplitude changes expected for isotropic and oriented samples of molecules undergoing electron transfer in an applied electric field. The calculations are based on a model that includes the expected effects of the field on both the fluorescence transition energy and the rate of the competing electron-transfer reaction. These model calculations indicate that a surprisingly wide range of electric-field-modulated line shapes are possible and that the line shape is very sensitive to key parameters that characterize the electron-transfer reaction. An example of these effects has been obtained in a structurally characterized donor/acceptor system, the bacterial photosynthetic reaction center, whose electric-field-modulated fluorescence changes have been characterized in detail. Information on the magnitude and direction of the dipole moment of the emitting state and on the mechanism and rate versus free energy curve for this picosecond long-distance electron-transfer reaction are obtained by comparing the experimental data with the results of the model calculations.
IntroductionReduced-Density-Matrix TheoryNumerical Solution of the Redfield EquationApplications of the Stochastic ModelCanonical Transformations: Reducing the Strength of the System-Bath CouplingConclusions
The fluorescence intensity from randomly oriented Rhodobacter (Rb.) sphaeroides photosynthetic reaction centers at 77 K increases in an applied electric field. This is ascribed to a net reduction in the rate of the initial electron transfer reaction which competes with fluorescence due to the effect of the field on the free energy of charge separation. Quantitative analysis of the fluorescence change in an electric field indicates that the difference in permanent dipole moment between the ground and initially formed excited state is greater than between the ground and emitting state.
We explore the possibility of virtual transfer in the primary charge separation of photosynthetic bacteria within the context of several types of experimental data. We show that the peak that might be expected in the virtual rate as electric fields vary the intermediate state energy is severely broadened by coupling to high-frequency modes. The Stark absorption kinetics data are thus consistent with virtual transfer in the primary charge separation. High-frequency coupling also makes the temperature dependence weak over a wide range of parameters. We demonstrate that Stark fluorescence anisotropy data, usually taken as evidence of virtual transfer, can in fact be consistent with two-step transfer. We suggest a two-pulse excitation experiment to quantify the contributions from two-step and virtual transfer. We show that virtual absorption into a charge transfer state can make a substantial contribution to the Stark absorption spectrum in a way that is not related to any derivative of the absorption spectrum.
1. Introduction 563
2. Obtaining rate constants from molecular-dynamics simulations 564
2.1 General relationships between quantum electronic structures and reaction rates 564
2.2 The transition-state theory (TST) 569
2.3 The transmission coefficient 572
3. Simulating biological electron-transfer reactions 575
3.1 Semi-classical surface-hopping and the Marcus equation 575
3.2 Treating quantum mechanical nuclear tunneling by the dispersed-polaron/spin-boson method 580
3.3 Density-matrix treatments 583
3.4 Charge separation in photosynthetic bacterial reaction centers 584
4. Light-induced photoisomerizations in rhodopsin and bacteriorhodopsin 596
5. Energetics and dynamics of enzyme reactions 614
5.1 The empirical-valence-bond treatment and free-energy perturbation methods 614
5.2 Activation energies are decreased in enzymes relative to solution, often by electrostatic effects that stabilize the transition state 620
5.3 Entropic effects in enzyme catalysis 627
5.4 What is meant by dynamical contributions to catalysis? 634
5.5 Transmission coefficients are similar for corresponding reactions in enzymes and water 636
5.6 Non-equilibrium solvation effects contribute to catalysis mainly through Δ g [Dagger], not the transmission coefficient 641
5.7 Vibrationally assisted nuclear tunneling in enzyme catalysis 648
5.8 Diffusive processes in enzyme reactions and transmembrane channels 651
6. Concluding remarks 658
7. Acknowledgements 658
8. References 658
Obtaining a detailed understanding of the dynamics of a biochemical reaction is a formidable challenge. Indeed, it might appear at first sight that reactions in proteins are too complex to analyze microscopically. At room temperature, even a relatively small protein can have as many as 10 ³⁴ accessible conformational states (Dill, 1985). In many cases, however, we have detailed structural information about the active site of an enzyme, whereas such information is missing for corresponding chemical systems in solution. The atomic coordinates of the chromophore in bacteriorhodopsin, for example, are known to a resolution of 1–2 Å. In addition, experimental studies of biological processes such as photoisomerization and electron transfer have provided a wealth of detailed information that eventually may make some of these processes classical problems in chemical physics as well as biology.
Peridinin, the carotenoid in the peridinin chlorophyll a protein (PCP), was studied by Stark (electroabsorption) spectroscopy to determine the change in electrostatic properties produced on excitation within the absorption band, in methyl tetrahydrofuran (MeTHF) versus ethylene glycol (EG), at 77 K. Strikingly, a large change in the permanent dipole moment (|Deltamu|) was found between the ground state, S(0) (1(1)A(g)(-)), and the Franck-Condon region of the S(2) (1(1)B(u)(+)) excited state, in both MeTHF (22 D) and EG (approximately 27 D), thus revealing the previously unknown charge transfer (CT) character of this pi-pi transition in peridinin. Such a large |Deltamu| produced on excitation, we suggest, facilitates the bending of the lactone moiety, toward which charge transfer occurs, and the subsequent formation of the previously identified intramolecular CT (ICT) state at lower energy. This unexpectedly large S(2) dipole moment, which has not been predicted even from high-level electronic structure calculations, is supported by calculating the shift of the peridinin absorption band as a function of solvent polarity, using the experimentally derived result. Overall, the photoinduced charge transfer uncovered here is expected to affect the excited-state reactivity of peridinin and, within the protein, be important for efficient energy transfer from the carotenoid S(2) and S(1)/ICT states to the chlorophylls in PCP.
Fluorescence spectra and electrofluorescence spectra (plots of the electric field-induced change in fluorescence intensity as a function of wavelength) have been measured at different temperatures for pyrene butyric acid (PBA) in a PMMA film at different concentrations. At a low concentration of 0.5 mol % where fluorescence emitted from the locally excited state of PBA (LE fluorescence) is dominant, LE fluorescence spectra show only the Stark shift in the presence of an electric field (F), which results from the difference in molecular polarizability between the ground and emitting states. At a high concentration of 10 mol % where the so-called sandwich-type excimer fluorescence (EX(1)) is dominant, both EX(1) and LE fluorescence are quenched by F. Another fluorescence assigned to a partially overlapped excimer (EX(2)) also exists at room temperature, and this emission is enhanced by F. As the temperature decreases, three fluorescence emissions whose electric field effects are different from each other become clear besides EX(1) and LE fluorescence, indicating that at least five fluorescence components exist at high concentrations at low temperatures. At a medium concentration of 5 mol % where EX(1) is comparable in intensity to the LE fluorescence, the intensity of EX(1) is not affected by F at any temperature, but LE fluorescence and EX(2) are markedly influenced by F at room temperature, and four fluorescence emissions are confirmed at low temperatures.
We propose an exciton model for the Photosystem II reaction center (RC) based on a quantitative simultaneous fit of the absorption, linear dichroism, circular dichroism, steady-state fluorescence, triplet-minus-singlet, and Stark spectra together with the spectra of pheophytin-modified RCs, and so-called RC5 complexes that lack one of the peripheral chlorophylls. In this model, the excited state manifold includes a primary charge-transfer (CT) state that is supposed to be strongly mixed with the pure exciton states. We generalize the exciton theory of Stark spectra by 1), taking into account the coupling to a CT state (whose static dipole cannot be treated as a small parameter in contrast to usual excited states); and 2), expressing the line shape functions in terms of the modified Redfield approach (the same as used for modeling of the linear responses). This allows a consistent modeling of the whole set of experimental data using a unified physical picture. We show that the fluorescence and Stark spectra are extremely sensitive to the assignment of the primary CT state, its energy, and coupling to the excited states. The best fit of the data is obtained supposing that the initial charge separation occurs within the special-pair PD1PD2. Additionally, the scheme with primary electron transfer from the accessory chlorophyll to pheophytin gave a reasonable quantitative fit. We show that the effectiveness of these two pathways is strongly dependent on the realization of the energetic disorder. Supposing a mixed scheme of primary charge separation with a disorder-controlled competition of the two channels, we can explain the coexistence of fast sub-ps and slow ps components of the Phe-anion formation as revealed by different ultrafast spectroscopic techniques.
Stark spectroscopy of photosynthetic systems
- Amesz
Dipole moments and polarizabilities of molecules in excited electronic states
- Lim