Reorganization Energy Of Electron Transfer Research Articles

Theoretical study of long range electron transfer in Phthalimide–Peptide–Methyl Aminoacetate Model molecules

Long-range electron transfer (ET) matrix elements ( V PS), rate constants ( k ET) and reorganization energies for ET from phthalimide radical (pha) moiety to methyl aminoacetate radical (aa) moiety in pa–(gly) n = 0–6 –aa (pa = C 6H 4(CO) 2N–(CH 2CO), gly = glycine, aa = HNCH 2COOCH 3) ionic molecules have been investigated using two-state variational method (TSVM) and classical rate model. Calculations on V PS reveal that the overlap between the frontier orbitals of two diabatic states is quite small, which leads to a small value of V PS. k ET has a minimum at the range n = 1–3 for β-strand conformation, but linearly increases as the peptide chain length ( n) increases for pro II-helix conformation. These results are in good agreement with the experimental predictions. Relevant ET mechanisms are elucidated. The transition energies for charge transfer in such systems are also calculated to test the influences of local dipoles on the potentials of the donor and acceptor. For comparison electron couplings in [pa–(gly) n = 1,3 –aa] + cations are calculated and the effects of electron correlation on inner reorganization energies in pha + pha −/+ self-exchange reactions are examined at different levels of theory respectively. Calculated results are discussed also.

A priori evaluation of the solvent contribution to the reorganization energy accompanying intramolecular electron transfer: Predicting the nature of the Creutz–Taube ion

The solvent contribution to the reorganization energy is one of the key physical properties controlling electron-transfer processes. A priori computational schemes have been developed that can predict realistic values for all other properties controlling charge transfer such as electronic couplings, vibronic couplings for intramolecular modes, the effects of asymmetry, and the effects of symmetric modes, but robust schemes for treating solvation remain elusive. In recent years, excited-state quantum chemical electronic-structure packages have gained the ability to calculate non-equilibrium solvation effects without the need to treat solvent explicitly, establishing the core of the required technology. While quantum chemical schemes involving excited-states represented as perturbed ground states can readily be applied in such calculations, they in general fail to include sufficient inactive-electron correlation to properly describe the excited-state manifold of charge transfer states, states for which only multi-reference procedures may robustly be applied. We develop computational procedures by which complete-active-space self-consistent-field (CASSCF) and related multi-reference calculations may be applied to electron-transfer systems whose energetics are controlled by the solvent–solute interaction. This is tested through the evaluation of the reorganization energy for electron-transfer in the bis-pentaammineruthenium complexes of α,ω-dipyridyl trans-polyenes in aqueous solution. Predictions are then made for the Creutz–Taube ion that place it clearly in the region of maximum breakdown of the Born–Oppenheimer approximation for which both the localized and delocalized diabatic descriptions of its electronic structure become inappropriate. This result is in qualitative agreement with conclusions drawn over the last four years based on a number of sources.

Effects of DNA on driving force dependence of photoinduced electron transfer from the excited state of tris(2,2-bipyridine)ruthenium(II) to intercalators in DNA: Distinction between intra- and inter-DNA pathways

Photoinduced electron transfer (ET) dynamics from the excited state of a ruthenium complex [Ru(bpy) 3 2+ (bpy = 2,2′-bipyridine)] to a series of intercalators in DNA, 9-substituted-10-methylacridinium ions (AcrR +, R = H, CH 2Ph, Pr i and Ph), 3-substituted-1-methylquinolinium ions (RQuH +, R = H, Me, CN and Br) and 4- and 5-methylphenanthridinium ions (4- and 5-MePhen +), were examined from the emission decay profiles of Ru(bpy) 3 2+ in the absence and presence of DNA in an aqueous solution. Intercalation of AcrH + to DNA is found to result in inhibition of hydride transfer from an NADH model compound, 1-benzyl-1,4-dihydronicotinamide, to AcrH +. In contrast, the rate constants of photoinduced ET of intercalated molecules to DNA become much larger than those of free intercalators in solution due to the positive shift in the one-electron reduction potentials by the intercalation into DNA. The intramolecular pathway of photoinduced ET from Ru(bpy) 3 2+* bound electrostatically to DNA to intercalators bound to the same DNA molecule has been distinguished from the intermolecular pathway of photoinduced ET of intercalators bound to a different DNA molecule. The occurrence of photoinduced ET is examined by laser flash photolysis experiments which show the transient absorption spectra of the one-electron reduced intercalator when the ET is exergonic. The resulting data were analyzed in light of the Marcus theory of ET to determine reorganization energies of ET in DNA as well as in an aqueous solution.

Drastic Difference in Lifetimes of the Charge-Separated State of the Formanilide−Anthraquinone Dyad versus the Ferrocene−Formanilide−Anthraquinone Triad and Their Photoelectrochemical Properties of the Composite Films with Fullerene Clusters

A long-lived charge-separated (CS) state, which can be observed even at 900 mus after laser excitation, has been attained in the formanilide-anthraquinone dyad (FA-AQ) in dimethyl sulfoxide, whereas the CS lifetime is shortened significantly to 20 ps in the ferrocene-formanilide-anthraquinone triad (Fc-FA-AQ). Such a drastic decrease in the CS lifetime by the addition of a ferrocene moiety to the FA-AQ dyad is ascribed to a decrease in the driving force of back electron transfer and an increase in the reorganization energy of electron transfer despite the longer charge-separation distance. The FA-AQ dyad and the Fc-FA-AQ triad have been employed as components of photovoltaic cells, where composite molecular nanoclusters of the FA-AQ dyad or the Fc-FA-AQ triad with fullerene (C60) are assembled onto a SnO2 electrode using an electrophoretic method. The composite films of the Fc-FA-AQ triad exhibit 10 times smaller values of an incident photon-to-photocurrent efficiency (IPCE) as compared with those of the FA-AQ dyad in accordance with a drastic decrease of the CS lifetime by addition of a ferrocene moiety to the FA-AQ dyad.

New formulation for nonequilibrium solvation: a consistent expression of electrostatic free energy by different methods and its application to solvent reorganization energy and spectral shifts in solution

We present an overview of the current status of the theories of nonequilibrium solvation and their generalizations in modern chemistry. Based on the continuous medium theory, the nonequilibrium electrostatic free energy has been reformulated. We adopt three different methods, the multi-step charging approach, the field superposition principle, and the interaction energy method, to achieve the consistent expression of electrostatic free energy of nonequilibrium. The misunderstandings on the interaction energy between the polarization field and its source (free) charge have been made clear. Derivations reveal a significant feature that this interaction energy is quite different from that between two independent fields. In the present work, the solvation free energy is found entirely contributed from the interaction between the solvent polarization and its source charge, whereas the self-energy of the polarization field is deduced to zero. The spectral shifts for light absorption and emission, and solvent reorganization energy for electron transfer in solution, have been derived to new forms differing from the conventional ones. The newly developed two-sphere model for electron transfer has been employed to investigation of the intramolecular electron transfer in Closs–Miller system.

Inner-Sphere Electron-Transfer Reorganization Energies of Zinc Porphyrins

Inner-sphere electron-transfer reorganization energies of Zn(protoporphyrin IX) and Zn(octaethylporphyrin) are determined from band-shape analyses of the first ionization obtained by gas-phase valence photoelectron spectroscopy. The experimentally determined total inner-sphere reorganization energies for self-exchange (120-140 meV) indicate that structural changes upon oxidation are largely confined to the porphyrin ring, and substituents on the ring or solvent and other environmental factors make smaller contributions. Computational estimates by different models vary over a wide range and are sensitive to numerical precision factors for these low reorganization energies. Of current computational models that are widely available and practical for molecules of this size, functionals that contain a mixture of Hartree-Fock exchange and DFT exchange-correlation appear to be the most applicable.

Oxygen Isotope Effects on Electron Transfer to O2Probed Using Chemically Modified Flavins Bound to Glucose Oxidase

Apo-glucose oxidase has been reconstituted with flavins modified in the 7 and 8 positions and characterized with regard to the catalytic rate of O(2) reduction and oxygen-18 isotope effects on this process. Kinetic studies as a function of driving force indicate a reorganization energy for electron transfer to O(2) of lambda = 28 kcal mol(-)(1) at optimal pH, which is similar to the value obtained earlier from temperature dependencies of rates (Roth, J. P.; Klinman, J. P. Proc. Natl. Acad. Sci. U.S.A. 2003, 100, 62-67). For the various enzyme-bound flavins, competitive oxygen-18 kinetic isotope effects fall within the narrow range of 1.0266(5) to 1.0279(6), apparently because of the dominant contribution of outer-sphere reorganization to the activation barrier; within the context of semiclassical and quantum mechanical electron transfer theories, the magnitude of the isotope effects reveals the importance of nuclear tunneling.

Porphyrin—Fullerene Linked Systems as Artificial Photosynthetic Mimics

AbstractFor Abstract see ChemInform Abstract in Full Text.

Role of the Conserved Arginine Pair in Proton and Electron Transfer in Cytochrome c Oxidase

A hydrogen-bonded network is observed above the hemes in all of the high-resolution crystal structures of cytochrome oxidases. It includes water and a pair of arginines, R481 and R482 (Rhodobacter sphaeroides numbering), that interact directly with heme a and the heme a(3) propionates. The hydrogen-bonded network provides potential pathways for proton release. The arginines, and the backbone peptide bond between them, have also been proposed to form part of a facilitated electron transfer route between Cu(A) and heme a. Our studies show that mutations of R482 (K, Q, and A) and R481 (K) retain substantial activity and are able to pump protons, but at somewhat reduced rates and stoichiometries. A slowed rate of electron transfer from cytochrome c to Cu(A) suggests a change in the orientation of cytochrome c binding in all but the R to K mutants. The mutant R482P is more perturbed in its structure and is altered in the redox potential difference between heme a and Cu(A): +18 mV for R482P and +46 mV for the wild type (heme a - Cu(A)). The electron transfer rate between Cu(A) and heme a is also altered from 93000 s(-1) in the wild type to 50 s(-1) in the oxidized R482P mutant, reminiscent of changes observed in a Cu(A)-ligand mutant, H260N. In neither case is the approximately 2000-fold change in the rate accounted for by the altered redox potentials, suggesting that both cause a major modification in the path or reorganization energy of electron transfer.

Molecular dynamics investigation of ferrous-ferric electron transfer in a hydrolyzing aqueous solution: calculation of the pH dependence of the diabatic transfer barrier and the potential of mean force.

We present a molecular model for ferrous-ferric electron transfer in an aqueous solution that accounts for electronic polarizability and exhibits spontaneous cation hydrolysis. An extended Lagrangian technique is introduced for carrying out calculations of electron-transfer barriers in polarizable systems. The model predicts that the diabatic barrier to electron transfer increases with increasing pH, due to stabilization of the Fe3+ by fluctuations in the number of hydroxide ions in its first coordination sphere, in much the same way as the barrier would increase with increasing dielectric constant in the Marcus theory. We have also calculated the effect of pH on the potential of mean force between two hydrolyzing ions in aqueous solution. As expected, increasing pH reduces the potential of mean force between the ferrous and ferric ions in the model system. The magnitudes of the predicted increase in diabatic transfer barrier and the predicted decrease in the potential of mean force nearly cancel each other at the canonical transfer distance of 0.55 nm. Even though hydrolysis is allowed in our calculations, the distribution of reorganization energies has only one maximum and is Gaussian to an excellent approximation, giving a harmonic free energy surface in the reorganization energy F(DeltaE) with a single minimum. There is thus a surprising amount of overlap in electron-transfer reorganization energies for Fe(2+)-Fe(H2O)6(3+), Fe(2+)-Fe(OH)(H2O)5(2+), and Fe(2+)-Fe(OH)2(H2O)+ couples, indicating that fluctuations in hydrolysis state can be viewed on a continuum with other solvent contributions to the reorganization energy. There appears to be little justification for thinking of the transfer rate as arising from the contributions of different hydrolysis states. Electronic structure calculations indicate that Fe(H2O)6(2+)-Fe(OH)n(H2O)(6-n)(3-n)+ complexes interacting through H3O2- bridges do not have large electronic couplings.

Effects of Solvent and Solute Polarizability on the Reorganization Energy of Electron Transfer

We report Monte Carlo simulations of the effect of solute and solvent polarizability on the solvent reorganization energy of intramolecular electron transfer. In the first set of simulations, the polarizability of the solvent is varied at constant permanent dipole of the solvent molecules (high-frequency dielectric constants is in the range 1−2.5). The reorganization energy is calculated on the solvent configurations around a nonpolar solute (charge separation transition) and around a dipolar solute (charge recombination transition). In both cases, the variation of the solvent reorganization energy does not exceed 30%, a change much smaller than predicted by dielectric continuum models. In the second set of simulations, the solute polarizability in the charge-separated state was varied while keeping the initial state for charge separation at zero dipole moment and polarizability. The gap between the charge-separation and charge recombination reorganization energies widens substantially with increasing dif...

New formulation for non-equilibrium solvation: dielectric constant change during charging process and influence of slow response of polarization upon solvent reorganization energy of electron transfer

Based on continuous medium theory, a new expression for electrostatic free energy of non-equilibrium state is deduced. Considering the change of the dielectric constant of medium during the establishment of the non-equilibrium state, a less familiar but more rational formula is employed in calculating the difference of electrostatic free energy. Both the two-step method and the field superposition approach give a consistent result for non-equilibrium, that is, G 2 non =(1/2) ∫ V dVρ 2Φ 2 non . The direct calculation of the electrostatic free energy has been performed for the polarization field, which can represent the non-equilibrium state in charge recombination process. The result of zero coincides with that judged by using the new expression. In the present form of G 2 non, no quantity of intermediate equilibrium is explicitly involved, hence it satisfies the request of the thermodynamics. Starting from the electrostatic free energy, generalized formulations for solvent reorganization energy of electron transfer (ET) have been deduced. Application to the two-sphere case yields new formulas estimating this quantity. A significant feature of the present two-sphere model is the dependency of solvent reorganization energy on the direction of reaction and the charges initially brought by the donor and acceptor spheres. Results in this work reveal that the previous theory seems to overestimate the solvent reorganization energy of ET by a factor of about two. A qualitative analysis indicates that the considerable discrepancies between the theoretical predication and the experimental observation in the literatures will be solved fairly well, if the new formulations are applied.

Porphyrin-fullerene linked systems as artificial photosynthetic mimics.

We have prepared a variety of porphyrin-fullerene linked systems to mimic photoinduced energy and electron transfer (ET) processes in photosynthesis. Photodynamical studies on porphyrin and analogs-fullerene linked systems have revealed the acceleration of photoinduced electron transfer and charge-shift and the deceleration of charge recombination, which is reasonably explained by the small reorganization energies of electron transfer in fullerenes. In this context, we have proposed two strategies, photoinduced single-step and multi-step electron transfers, for prolonging the lifetime of a charge-separated state in donor-acceptor linked systems. The single-step ET strategy allowed a zinc chlorin-fullerene linked dyad to extend the lifetime up to 120 seconds in frozen PhCN at 123 K, which is the longest value of charge separation ever reported for donor-acceptor linked systems. Unfortunately, however, the quantum yield of formation of the charge-separated state was as low as 12%, probably due to the decay of the precursor exciplex state to the ground state rather than to the favorable complete charge-separated state. In contrast, the multi-step ET strategy has been successfully applied to porphyrin-fullerene linked triads, tetrads, and a pentad. In particular, a ferrocene-porphyrin trimer-fullerene pentad revealed formation of a long-lived charge-separated state (0.53 s in frozen DMF at 163 K) with an extremely high quantum yield (83%), which is comparable to natural bacterial reaction centers. These results not only provide valuable information for a better understanding of photoinduced energy and electron transfer processes in photosynthesis, but also open the door for the development of photoinitiated molecular devices and machines.

Reorganization Energy Induced by Noncovalent Bonding Interaction in Electron Transfer Reactions

A simple model is proposed to calculate a component of the electron-transfer reorganization energy derived from the reversible process of noncovalnt bond formation/dissociation between the reactant and hydrogen bonding donor or ligand. In the model, the reorganization of the formation/dissociation of the noncovalent-bonded complex is estimated by considering the chemical equilibrium change during the electron-transfer reaction. The effects of the hydrogen bonding and the ligand binding on the reorganization energies are calculated for the one-electron reduction processes of quinones, flavin, and the hem-fragment of cytochrome c based on the formation/dissociation constants of the noncovalent-bonded complexes in the liquid phase.

Proton-coupled electron transfer in a model for tyrosine oxidation in photosystem II.

Theoretical calculations of a model for tyrosine oxidation in photosystem II are presented. In this model system, an electron is transferred to ruthenium from tyrosine, which is concurrently deprotonated. This investigation is motivated by experimental measurements of the dependence of the rates on pH and temperature (Sjödin et al. J. Am. Chem. Soc. 2000, 122, 3932). The mechanism is proton-coupled electron transfer (PCET) at pH < 10 when the tyrosine is initially protonated and is single electron transfer (ET) for pH > 10 when the tyrosine is initially deprotonated. The PCET rate increases monotonically with pH, whereas the single ET rate is independent of pH and is 2 orders of magnitude faster than the PCET rate. The calculations reproduce these experimentally observed trends. The pH dependence for the PCET reaction arises from the decrease in the reaction free energies with pH. The calculations indicate that the larger rate for single ET arises from a combination of factors, including the smaller solvent reorganization energy for ET and the averaging of the coupling for PCET over the reactant and product hydrogen vibrational wave functions (i.e., a vibrational overlap factor in the PCET rate expression). The temperature dependence of the rates, the solvent reorganization energies, and the deuterium kinetic isotope effects determined from the calculations are also consistent with the experimental results.

Metal ion-promoted intramolecular electron transfer in a ferrocene-naphthoquinone linked dyad. Continuous change in driving force and reorganization energy with metal ion concentration.

Thermal intramolecular electron transfer from the ferrocene (Fc) to naphthoquinone (NQ) moiety occurs efficiently by the addition of metal triflates (M(n)()(+): Sc(OTf)(3), Y(OTf)(3), Eu(OTf)(3)) to an acetonitrile solution of a ferrocene-naphthoquinone (Fc-NQ) linked dyad with a flexible methylene and an amide spacer, although no electron transfer takes place in the absence of M(n)()(+). The resulting semiquinone radical anion (NQ(*)(-)) is stabilized by the strong binding of M(n)()(+) with one carbonyl oxygen of NQ(*)(-)( )()as well as hydrogen bonding between the amide proton and the other carbonyl oxygen of NQ(*)(-). The high stability of the Fc(+)()-NQ(*)(-)/M(n)()(+)() complex allows us to determine the driving force of electron transfer by the conventional electrochemical method. The one-electron reduction potential of the NQ moiety of Fc-NQ is shifted to a positive direction with increasing concentration of M(n)()(+), obeying the Nernst equation, whereas the one-electron oxidation potential of the Fc moiety remains the same. The driving force dependence of the observed rate constant (k(ET)) of M(n)()(+)-promoted intramolecular electron transfer is well evaluated in light of the Marcus theory of electron transfer. The driving force of electron transfer increases with increasing concentration of M(n)()(+) [M(n)()(+)], whereas the reorganization energy of electron transfer decreases with increasing [M(n)()(+)] from a large value which results from the strong binding between NQ(*)(-) and M(n)()(+).

Nonequilibrium solvation theory: Comparison, modification and application

Faults existing in the current theories of nonequilibrium solvation have been clarified in this report. Based on a novel expression of solvation free energy for nonequilibrium, generalized formulations of solvent reorganization energy for electron transfer and of solvation shift for spectrum have been established. Furthermore, a new form of solvent reorganization energy for electron transfer in two-sphere case, which greatly differs from the one by Marcus, has been deduced. A single-sphere model for solvation shift of spectrum has been put forward both by deducing the generalized formulations and by showing the correct forms of self-energy of reaction field. It has been concluded that the current theories overestimate the solvent reorganization energy and the solvation shift by a factor of about 2. By applying the models established, the discrepancies between the theory and experiments before have been perfectly explained.

Exploring Charge Migration in Light-Harvesting Complexes Using Electron Paramagnetic Resonance Line Narrowing

The light-harvesting protein complex 1 (LH1) of the purple bacterium Rhodobacter sphaeroides exhibits EPR signals upon treatment with oxidizing reagents such as potassium ferricyanide. These signals are assigned to radical cations of the LH1's bacteriochlorophyll pigments, B880•+. An intriguing feature of the B880•+ EPR spectrum is the narrow line width exhibited relative to in vitro monomeric BChla•+ and the primary donor radical cation of the photosynthetic reaction center's “special pair”, P•+. In this paper, we investigate the temperature and oxidant concentration dependence of the B880•+ EPR spectrum with the aim of elucidating the mechanism for spectral line narrowing. The experimental data are interpreted in terms of EPR line narrowing that accompanies charge migration and spin exchange. For charge migration, the line-narrowing models are driven by standard, nonadiabatic electron transfer assisted by vibronic coupling. The results are consistent with a hypothesis that, in LH1, the EPR spectral shape is dominated by electron transfer instead of spin exchange. In addition, the electronic and energetic factors governing the inter-BChla cryogenic charge transport are explored. Using standard treatments, large reorganization energy and weak electronic coupling are obtained for the charge migration process. The EPR results support the view that highly delocalized radical cation states similar to that observed for the primary donor BChlas of the special pair of the photosynthetic reaction center do not occur in oxidized LH1 complexes in the 6−300 K temperature range. However, the EPR results are compatible with a highly asymmetrical version of the special pair. The unrealistically high value of reorganization energy for electron transfer is attributed to treating the charge migration process as if electron transfer were homogeneous. A more realistic value of reorganization energy is predicted to result if free-energy heterogeneity were to be included in modeling electron transfer in LH1.

Studies of the solvent effects on the internal reorganization energy for electron transfer of uracil and its anion with ONIOM

In this paper, the aqueous adiabatic electron affinity (AEA) of Uracil (U) and internal reorganization energy λ i of the self-exchange electron transfer (ET) reaction between Uracil and Uracil anion radical (U − ) in aqueous solution were studied. The effect of the solvation was studied with the recently developed hybrid quantum molecular chemical method, ONIOM. In all calculations, the geometrical optimization for U and U − was performed at B3LYP/6-31++G(d) level. As for the solvent surroundings, the seven water molecules as the first hydration shell were adopted and treated with B3LYP, PM3 and AMBER methods, namely, ONIOM (B3LYP:B3LYP), ONIOM (B3LYP:PM3) and ONIOM (B3LYP:Amber) methods, respectively. The values of AEA for Uracil, predicted by the above three methods, are small positive ones. The geometrical differences between neutral and anion radical molecules of U originate mainly from those of dihedral angles. According to the corresponding dipole moment values, the excess electron in U − should be trapped dominantly by dipole-bound way. The calculated λ i values by ONIOM (B3LYP:B3LYP) and ONIOM (B3LYP:PM3) are close to each other within 0.89%. The λ i value from ONIOM (B3LYP:Amber) is in agreement with the one from SCRF-CPCM very well. Finally, the calculation results of the detailed geometries and molecular interaction mode effect of U and U − and related water molecules in the hydration shell were discussed.

N-isotope effects on the Raman spectra of Fe(2)S(2) ferredoxin and Rieske ferredoxin: evidence for structural rigidity of metal sites.

The diiron ferredoxins have a common diamond-core structure with two bridging sulfides, but differ in the nature of their terminal ligands: either four cysteine thiolates in the Fe(2)S(2) ferredoxins or two cysteine thiolates and two histidine imidazoles in the Rieske ferredoxins. Contributions of the bridging (b) and terminal (t) ligands to the resonance Raman spectra of the Fe(2)S(2) ferredoxins have been distinguished previously by isotopic substitution of the bridging sulfides. We now find that uniform (15)N-labeling of Anabaena Fe(2)S(2) ferredoxin results in shifts of -1 cm(-1) in the Fe-S(t) stretching modes at 282, 340, and 357 cm(-1). The (15)N dependence is ascribed to kinematic coupling of the Fe-S(Cys) stretch with deformations of the cysteine backbone, including the amide nitrogen. No (15)N dependence occurs for the nu(Fe-S(b)) modes at 395 and 426 cm(-1). Similar effects are observed for the Rieske center in T4MOC ferredoxin from the toluene-4-monooxygenase system of Pseudomonas mendocina. Upon selective (15)N-labeling of the alpha-amino group of cysteine, the vibrational modes at 321, 332, 350, and 362 cm(-1) all undergo shifts of -1 to -2 cm(-1), thereby identifying them as combinations of nu(Fe-S(t)) and delta(Cys). These same four modes undergo similar isotope shifts when T4MOC ferredoxin is selectively labeled with (15)N-histidine ((15)N in either the alpha1,delta1 or delta1,epsilon2 positions). Thus, the Fe-S(Cys) stretch must also be undergoing kinematic coupling with vibrations of the Fe-His moiety. The extensive kinematic coupling of iron ligand vibrations observed in both the Fe(2)S(2) and Rieske ferredoxins presumably arises from the rigidity of the protein framework and is reminiscent of the behavior of cupredoxins. In both cases, the structural rigidity is likely to play a role in minimizing the reorganization energy for electron transfer.