Unified Theory on Rates for Electron Transfer Mediated by a Midway Molecule, Bridging between Superexchange and Sequential Processes

Photosynthetic reaction center variants made via genetic code expansion show Tyr at M210 tunes the initial electron transfer mechanism

Photosynthetic reaction centers (RCs) from Rhodobacter sphaeroides were engineered to vary the electronic properties of a key tyrosine (M210) close to an essential electron transfer component via its replacement with site-specific, genetically encoded noncanonical amino acid tyrosine analogs. High fidelity of noncanonical amino acid incorporation was verified with mass spectrometry and X-ray crystallography and demonstrated that RC variants exhibit no significant structural alterations relative to wild type (WT). Ultrafast transient absorption spectroscopy indicates the excited primary electron donor, P*, decays via a ∼4-ps and a ∼20-ps population to produce the charge-separated state P⁺H_A ^- in all variants. Global analysis indicates that in the ∼4-ps population, P⁺H_A ^- forms through a two-step process, P*→ P⁺B_A ^-→ P⁺H_A ^-, while in the ∼20-ps population, it forms via a one-step P* → P⁺H_A ^- superexchange mechanism. The percentage of the P* population that decays via the superexchange route varies from ∼25 to ∼45% among variants, while in WT, this percentage is ∼15%. Increases in the P* population that decays via superexchange correlate with increases in the free energy of the P⁺B_A ^- intermediate caused by a given M210 tyrosine analog. This was experimentally estimated through resonance Stark spectroscopy, redox titrations, and near-infrared absorption measurements. As the most energetically perturbative variant, 3-nitrotyrosine at M210 creates an ∼110-meV increase in the free energy of P⁺B_A ^- along with a dramatic diminution of the 1,030-nm transient absorption band indicative of P⁺B_A ^- formation. Collectively, this work indicates the tyrosine at M210 tunes the mechanism of primary electron transfer in the RC.

Charge Transfer through Redox Molecular Junctions in Nonequilibrated Solvents

Molecular conduction operating in dielectric solvent environments is often described using kinetic rates based on the Marcus theory of electron transfer at a molecule-metal electrode interface. However, the successive nature of charge transfer in such a system implies that the solvent does not necessarily reach equilibrium in such processes. Here we generalize the theory to account for solvent nonequilibrium and consider a molecular junction consisting of an electronic donor-acceptor system coupled to two metallic electrodes and placed in a polarizable solvent. We determine the nonequilbrium distribution of the solvent by solving diffusion equations in the strong- and weak-friction limits and calculate the charge current and its fluctuating behavior. In extreme limits, the absence of the solvent or fast solvent relaxation, the charge-transfer statistics is Poissonian, while it becomes correlated by the dynamic solvent between these limits. A Kramers-like turnover of the nonequilibrium current as a function of the solvent damping is found. Finally, we propose a way to tune the solvent-induced damping using geometrical control of the solvent dielectric response in nanostructured solvent channels.

Electron Transfer Methods in Open Systems

Utilization of electron transfer methods for description of quantum transport is popular due to simplicity of the formulation and its ability to account for basic physics of electron exchange between the system and baths. At the same time, the necessity to go beyond simple golden rule-type expressions for rates was indicated in the literature and ad hoc formulations were proposed. Similarly, kinetic schemes for quantum transport beyond the usual second-order Lindblad/Redfield considerations were discussed. Here we utilize recently introduced the nonequilibrium Hubbard Green's function diagrammatic technique to analyze the construction of rates in open systems. We show that previous considerations for rates of second and fourth order can be obtained as a particular case of zero- and second-order Green's function diagrammatic series with bare diagrams. We discuss limitations of previous considerations, stress advantages of the Hubbard Green's function approach in constructing the rates, and indicate that standard dressing of the diagrams is a natural way to account for additional baths/degrees of freedom in the formulation of generalized expressions for the rates.

Vibronic couplings and coherent electron transfer in bridged systems

A computational strategy to analyze the dynamics of coherent electron transfer processes in bridged systems, involving three or more electronic states, is presented.

Multistate treatments of the electronic coupling in donor-bridge-acceptor systems: insights and caveats from a simple model

We use a simple one-dimensional delta function electronic structure model (dfm) to investigate the results of a pair of multistate diabatization techniques (i.e., based on n states, with n ≥ 2) for linear DBA and DBBA (donor-bridge-acceptor) electron-transfer systems. In particular, we focus on the physical meaning of the couplings obtained from multistate methods and their relationship to two-state (n = 2) coupling elements. On the basis of the simple dfm approach, which allows exact as well as finite basis set treatment and has no many-electron effects, we conclude that for orthogonal diabatic states, it is difficult to assign clear physical significance to multistate matrix elements for coupling beyond nearest-neighbor contacts. The implications of these results for more complex multistate many-electron treatments are discussed. It is emphasized that physically meaningful coupling elements must involve states that are orthogonal, either explicitly or implicitly.

Energetics of bacterial photosynthesis

We report the results of extensive numerical simulations and theoretical calculations of electronic transitions in the reaction center of Rhodobacter sphaeroides photosynthetic bacterium. The energetics and kinetics of five electronic transitions related to the kinetic scheme of primary charge separation have been analyzed and compared to experimental observations. Nonergodic formulation of the reaction kinetics is required for the calculation of the rates due to a severe breakdown of the system ergodicity on the time scale of primary charge separation, with the consequent inapplicability of the standard canonical prescription to calculate the activation barrier. Common to all reactions studied is a significant excess of the charge-transfer reorganization energy from the width of the energy gap fluctuations over that from the Stokes shift of the transition. This property of the hydrated proteins, breaking the linear response of the thermal bath, allows the reaction center to significantly reduce the reaction free energy of near-activationless electron hops and thus raise the overall energetic efficiency of the biological charge-transfer chain. The increase of the rate of primary charge separation with cooling is explained in terms of the temperature variation of induction solvation, which dominates the average donor-acceptor energy gap for all electronic transitions in the reaction center. It is also suggested that the experimentally observed break in the Arrhenius slope of the primary recombination rate, occurring near the temperature of the dynamical transition in proteins, can be traced back to a significant drop of the solvent reorganization energy close to that temperature.

PNA versus DNA: effects of structural fluctuations on electronic structure and hole-transport mechanisms

The effects of structural fluctuations on charge transfer in double-stranded DNA and peptide nucleic acid (PNA) are investigated. A palindromic sequence with two guanine bases that play the roles of hole donor and acceptor, separated by a bridge of two adenine bases, was analyzed using combined molecular dynamics (MD) and quantum-chemical methods. Surprisingly, electronic structure calculations on individual MD snapshots show significant frontier orbital electronic population on the bridge in approximately 10% of the structures. Electron-density delocalization to the bridge is found to be gated by fluctuations of the covalent conjugated bond structure of the aromatic rings of the nucleic bases. It is concluded, therefore, that both thermal hopping and superexchange should contribute significantly to charge transfer even in short DNA/PNA fragments. PNA is found to be more flexible than DNA, and this flexibility is predicted to produce larger rates of charge transfer.

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.

Conformationally averaged score functions for electronic propagation in proteins

We explore the influence of conformational dynamics on protein-mediated electron donor-acceptor interactions. We introduce a thermally averaged score function to characterize electronic propagation from redox cofactors into the protein and solvent. The score function is explored for myoglobin at the extended-Hückel level, and the results are compared with those of simpler models. The conformationally averaged quantum results are consistent with the empirical analysis of the Pathways model. Notably, subtle effects of quantum interference among multiple coupling pathways that arise in static structures are largely averaged out when protein thermal motion is included. Propagation through bulk water near the single-protein interface decays rapidly with distance.

Multifunctional molecular carbon materials--from fullerenes to carbon nanotubes

This critical review covers the timely topic of carbon nanostructures-fullerenes and carbon nanotubes-in combination with metalloporphyrins as integrative components for electron-donor-acceptor ensembles. These ensembles are typically probed in condensed media and at semi-transparent electrode surfaces. In particular, we will present a comprehensive survey of a variety of covalent (i.e., nanoconjugates) and non-covalent linkages (i.e., nanohybrids) to demonstrate how to govern/fine-tune the electronic interactions in the resulting electron-donor-acceptor ensembles. In the context of covalent bridges, different spacers will be discussed, which range from pure "insulators" (i.e., amide bonds, etc.) to sophisticated "molecular wires" (i.e., p-phenylenevinylene units, etc.). Furthermore, we will elucidate the fundamental impact that these vastly different spacers may exert on the rate, efficiency, and mechanism of short- and long-range electron transfer reactions. Additionally, a series of non-covalent motifs will be described: hydrogen bonding, complementary electrostatics, pi-pi stacking and metal coordination-to name a few. These motifs have been successfully employed by us and our collaborators en route towards novel architectures (i.e., linear structures, tubular structures, rotaxanes, catenanes, etc.) that exhibit unique and remarkable charge transfer features.

Superexchange and sequential mechanisms in charge transfer with a mediating state between the donor and acceptor

The rate of intramolecular charge transfer from biphenyl to naphthalene was determined for the radical anions and radical cations of molecules with the general structure: (2-naphthyl)-(steroid spacer)-(4-biphenylyl). Varied degrees of unsaturation (one double bond, NSenB; two double bonds, NSen(2)B; and the b-ring completely aromatized, NSarB) were incorporated into the steroid spacer to examine the effect it would have on the charge transfer rate. The charge transfer rate, as inferred from the decay of the biphenyl radical ion absorption, increased in all cases relative to the completely saturated 3-(2-naphthyl)-16-(4-biphenylyl)-5alpha-androstane (NSB) reference molecule. For the anion charge transfer, the decay rates increased by factors of 1.4, 4.2, and 5.1, respectively, and for the cation, the decay rates increased by factors of 5, 276, and 470. To explain the results, the charge-transfer process was viewed as a combination of two independent mechanisms: a single-step, superexchange mechanism, and a two-step, sequential charge transfer. Using a low level of theory, simple models of the superexchange and two-step mechanisms were developed to elucidate the nature and differences between the two mechanisms. The critical variable for this analysis is the free energy of formation (DeltaG(I) degrees ) of the intermediate state: (2-naphthyl)-[spacer](1)+/--(4-biphenylyl). The conclusion from this treatment is that superexchange is the dominant mechanism when DeltaG(I) degrees is large, but at small DeltaG(I) degrees , the sequential mechanism will dominate. This is because the superexchange rate is shown to have a weak dependence on DeltaG(I) degrees , changing 10-fold for a change in DeltaG(I) degrees of 2 eV, compared to the sequential mechanism in which the rate can change over 10(3) for 0.5 V.

Protein dynamics and electron transfer: electronic decoherence and non-Condon effects

We compute the autocorrelation function of the donor-acceptor tunneling matrix element <T(DA)(t)T(DA)(0)> for six Ru-azurin derivatives. Comparison of this decay time to the decay time of the time-dependent Franck-Condon factor {computed by Rossky and coworkers [Lockwood, D. M., Cheng, Y.-K. & Rossky, P. J. (2001) Chem. Phys. Lett. 345, 159-165]} reveals the extent to which non-Condon effects influence the electron-transfer rate. <T(DA)(t)T(DA)(0)> is studied as a function of donor-acceptor distance, tunneling pathway structure, tunneling energy, and temperature to explore the structural and dynamical origins of non-Condon effects. For azurin, the correlation function is remarkably insensitive to tunneling pathway structure. The decay time is only slightly shorter than it is for solvent-mediated electron transfer in small organic molecules and originates, largely, from fluctuations of valence angles rather than bond lengths.

A phenomenological model of dynamical arrest of electron transfer in solvents in the glass-transition region

A phenomenological model of electron transfer reactions in solvents undergoing glass transition is discussed. The reaction constant cuts off slow polarization modes from the spectrum of nuclear thermal motions active on the observation time scale. The arrest of nuclear solvation in turn affects the reaction activation barrier making it dependent on the rate. The resultant rate constant is sought from a self-consistent equation. The model describes well the sharp change in the solvent Stokes shift of optical lines in the glass-transition region. It is also applied to describe the temperature dependence of primary charge separation and reduction of primary pair in photosynthetic reaction centers. The model shows that a weak dependence of the primary charge separation rate on temperature can be explained by dynamical arrest of nuclear solvation on the picosecond time scale of electron transfer. For reduction of primary pair by cytochrome, the model yields a sharp turnover of the reaction kinetics at the transition temperature when nuclear solvation freezes in.

Evidence Against the Hopping Mechanism as an Important Electron Transfer Pathway for Conformationally Constrained Oligopeptides

The rate constant of intramolecular electron transfer through oligopeptides based on the alpha-aminoisobutyric acid residue was determined as a function of the peptide length and found to depend weakly on the donor-acceptor separation. By measuring the electron-transfer activation energy and estimating the energy gap between donor and bridge, we were able to discard the electron hopping mechanism.

Understanding Electron Transfer across Negatively-Charged Aib Oligopeptides

The physicochemical effects modulating the conformational behavior and the rate of intramolecular dissociative electron transfer in phthalimide-Aibn-peroxide peptides (n = 0-3) have been studied by an integrated density functional/continuum solvent model. We found that three different orientations of the phthalimide ring are possible, labeled Phihel, PhiC7, and PhipII. In the condensed phase, they are very close in energy when the system is neutral and short. When the peptide chain length increases and the system is negatively charged, Phihel becomes instead the most stable conformer. Our calculations confirm that the 3(10)-helix is the most stable secondary structure for the peptide bridge. However, upon charge injection in the phthalimide end of the phthalimide-Aib3-peroxide, the peptide bridge can adopt an alpha-helix conformation as well. The study of the dependence of the frontier orbitals on the length and on the conformation of the peptide bridge (in agreement with experimental indications) suggests that for n = 3 the process could be influenced by a 3(10) --> alpha-helix conformational transition of the peptide chain.

Dendronized Perylenetetracarboxdiimides with Peripheral Triphenylamines for Intramolecular Energy and Electron Transfer

Novel perylene-3,4,9,10-tetracarboxdiimides (PDI) dyes functionalized with polyphenylene dendrimers attached at the bay region are reported. Derivatives of PDI bearing polyphenylene dendrimers up to the second generation, substituted with an increasing number of triphenylamine (TPA) moieties at the periphery, as well as a related nondendronized model compound were prepared. Intramolecular energy transfer was demonstrated by the observation of PDI emission on excitation of the triphenylamines, and electron transfer was detected by comparing photoluminescence quenching in solvents of different polarity.

Anomalous distance dependence of electron transfer across peptide bridges

The first investigation on the distance dependence of a dissociative electron transfer process across peptide bridges is reported. This study was carried out by using a series of donor-peptide-acceptor systems in which the donor is a phthalimido moiety, the peptide bridges are provided by alpha-aminoisobutyric acid (Aib) homooligomers, and the acceptor is a peroxide functional group. The intramolecular electron transfer from the electrogenerated phthalimido radical anion to the peroxide was studied in comparison with the thermodynamic and kinetic information obtained with models of the acceptor and the donor. The intramolecular rate constants were determined in N,N-dimethylformamide by taking into account the corresponding intermolecular values. The experimental results point to an unusual non-exponential dependence of the intramolecular electron transfer rate on the number of bridge units. The same trend could be verified also by taking into account the actual donor-acceptor edge-to-edge distance. The peculiar distance dependence that was observed for the intramolecular electron transfer rate is attributed to the mediating effect of the intramolecular C=O...H-N hydrogen bonds.

2-Aminopurine: a probe of structural dynamics and charge transfer in DNA and DNA:RNA hybrids

Spectroscopic techniques are employed to probe relationships between structural dynamics and charge transfer (CT) efficiency in DNA duplexes and DNA:RNA hybrids containing photoexcited 2-aminopurine (Ap). To better understand the variety of interactions and reactions, including CT, between Ap and DNA, the fluorescence behavior of Ap is investigated in a full series of redox-inactive as well as redox-active assemblies. Thus, Ap is developed as a dual reporter of structural dynamics and base-base CT reactions in nucleic acid duplexes. CD, NMR, and thermal denaturation profiles are consistent with the family of DNA duplexes adopting a distinct conformation versus the DNA:RNA hybrids. Fluorescence measurements establish that the d(A)-r(U) tract of the DNA:RNA hybrid exhibits enhanced structural flexibility relative to that of the d(A)-d(T) tract of the DNA duplexes. The yield of CT from either G or 7-deazaguanine (Z) to Ap in the assemblies was determined by comparing Ap emission in redox-active G- or Z-containing duplexes to otherwise identical duplexes in which the G or Z is replaced by inosine (I), the redox-inactive nucleoside analogue. Investigations of CT not only demonstrate efficient intrastrand base-base CT in the DNA:RNA hybrids but also reveal a distance dependence of CT yield that is more shallow through the d(A)-r(U) bridge of the A-form DNA:RNA hybrids than through the d(A)-d(T) bridge of the B-form DNA duplexes. The shallow distance dependence of intrastrand CT in DNA:RNA hybrids correlates with the increased conformational flexibility of bases within the hybrid duplexes. Measurements of interstrand base-base CT provide another means to distinguish between the A- and B-form helices. Significantly, in the A-form DNA:RNA hybrids, a similar distance dependence is obtained for inter- and intrastrand reactions, while, in B-DNA, a more shallow distance dependence is evident with interstrand CT reactions. These observations are consistent with evaluations of intra- and interstrand base overlap in A- versus B-form duplexes. Overall, these data underscore the sensitivity of CT chemistry to nucleic acid structure and structural dynamics.