Marcus Parameters Research Articles

Charge Conduction in Polymer Dielectrics: Theoretical Perspectives and First-Principle Approaches

This review highlights the updated picture of charge transport in polymer dielectrics and offers suggestions for future research. It begins with the backgrounds of the various theoretical charge transport models and the underlying concepts of the physical quantities. The techniques for deriving the microscopic physical quantities, e.g., the Marcus parameters and the spectral density of bath, from first-principles methods are outlined for tutorial purposes. Our recent multi-scale simulation studies are presented to demonstrate how and why the macroscopic charge transfer behavior can be predicted from these microscopic quantities, without the use of phenomenological/ empirical models nor ad hoc parameters. Some new insights gained through the multiscale modeling technique are summarized, with a focus on the relation between the chemical structure of polymers and the carrier transport properties. Finally, what is further required for computer-aided (rational) dielectric polymer design is discussed.

First-principles determination of electronic charge transport properties in polymer dielectrics using a crystalline-based model system

There are various models for describing the charge transport in polymers but it is unclear how to choose the appropriate one for a given system. In this study, we determine the relevant charge transfer model for several insulating polymers by evaluating the Marcus parameters for electron and hole transfer with the aid of first-principles calculations. As expected, except for electron transfer in polyethylene and isotactic polypropylene, non-adiabatic (polaron) hopping takes place in most polymers, owing to the small inter-chain electronic interactions (10–100 meV) and large polaron formation energy (100–1000 meV). Therefore, the first-principles based parameter-free, multi-scale modeling approach, which we developed for evaluating the hole transfer property in polyethylene, can be used to study the electronic carrier transport properties in wide variety of polymers. The computed Marcus parameters imply that the electron and hole mobilities in syndiotactic polystyrene and polytetrafluoroethylene are larger than the hole mobility in polyethylene and isotactic polypropylene, which agrees with experimental data. The strong chain-length dependence of the computed Marcus parameters indicates that slight change in the polymer structure can result in significant variations in the charge mobility.

Exciton Dissociation within Quantum Dot–Organic Complexes: Mechanisms, Use as a Probe of Interfacial Structure, and Applications

This article reviews the structural and electronic features of colloidal quantum dot (QD)–organic complexes that influence the rate of photoinduced charge separation (PCS) across the interface between the inorganic core of the QD and its organic surface ligands. While Marcus theory can be used to describe the rate of PCS in QD–organic complexes, uncertainties in the exact atomic configuration of the inorganic–organic interface and heterogeneities in this interfacial structure within an ensemble of QDs complicate the determination of the most fundamental Marcus parameters—electronic coupling, reorganization energy, and driving force. This article discusses strategies for accounting for uncertainties and heterogeneities when using Marcus theory to interpret rates of PCS in QD–organic complexes and highlights how measurement of PCS rates can provide information about the interfacial structure of the QD surface. Recent progress in the application of mechanistic knowledge of PCS to harvest multiple charge carriers from QDs containing multiple excitons and extend the lifetime of the charge-separated state is also discussed.

Charge Transfer in Model Peptides: Obtaining Marcus Parameters from Molecular Simulation

Charge transfer within and between biomolecules remains a highly active field of biophysics. Due to the complexities of real systems, model compounds are a useful alternative to study the mechanistic fundamentals of charge transfer. In recent years, such model experiments have been underpinned by molecular simulation methods as well. In this work, we study electron hole transfer in helical model peptides by means of molecular dynamics simulations. A theoretical framework to extract Marcus parameters of charge transfer from simulations is presented. We find that the peptides form stable helical structures with sequence dependent small deviations from ideal PPII helices. We identify direct exposure of charged side chains to solvent as a cause of high reorganization energies, significantly larger than typical for electron transfer in proteins. This, together with small direct couplings, makes long-range superexchange electron transport in this system very slow. In good agreement with experiment, direct transfer between the terminal amino acid side chains can be dicounted in favor of a two-step hopping process if appropriate bridging groups exist.

Nonadiabatic QM/MM Simulations of Fast Charge Transfer in Escherichia coli DNA Photolyase

In this report, we study the photoactivation process in Escherichia coli DNA photolyase, involving long-range electron transport along a conserved chain of Trp residues between the protein surface and the flavin adenine dinucleotide (FAD) cofactor. Fully coupled nonadiabatic (Ehrenfest) quantum mechanics/molecular mechanics (QM/MM) simulations allow us to follow the time evolution of charge distributions over the natural time scale of multiple charge transfer events and conduct rigorous statistical analysis. Charge transfer rates in excellent agreement with experimental data are obtained without the need for any system-specific parametrization. The simulations are shown to provide a more detailed picture of electron transfer than a classical analysis of Marcus parameters. The protein and solvent both strongly influence the localization and transport properties of a positive charge, but the directionality of the process is mainly caused by solvent polarization. The time scales of charge movement, delocalization, protein relaxation and solvent reorganization overlap and lead to nonequilibrium reaction conditions. All these contributions are explicitly considered and fully resolved in the model used and provide an intricate picture of multistep biochemical electron transfer in a flexible, heterogeneous environment.

Pulse Radiolysis Studies of Temperature Dependent Electron Transfers among Redox Centers in ba3-Cytochrome c Oxidase from Thermus thermophilus: Comparison of A- and B-Type Enzymes.

The functioning of cytochrome c oxidases involves orchestration of long-range electron transfer (ET) events among the four redox active metal centers. We report the temperature dependence of electron transfer from the CuAr site to the low-spin heme-(a)bo site, i.e., CuAr + heme-a(b)o → CuAo + heme-a(b)r in three structurally characterized enzymes: A-type aa3 from Paracoccus denitrificans (PDB code 3HB3) and bovine heart tissue (PDB code 2ZXW), and the B-type ba3 from T. thermophilus (PDB codes 1EHK and 1XME). k,T data sets were obtained with the use of pulse radiolysis as described previously. Semiclassical Marcus theory revealed that λ varies from 0.74 to 1.1 eV, Hab, varies from ∼2 × 10-5 eV (0.16 cm-1) to ∼24 × 10-5 eV (1.9 cm-1), and βD varies from 9.3 to 13.9. These parameters are consistent with diabatic electron tunneling. The II-Asp111Asn CuA mutation in cytochrome ba3 had no effect on the rate of this reaction whereas the II-Met160Leu CuA-mutation was slower by an amount corresponding to a decreased driving force of ∼0.06 eV. The structures support the presence of a common, electron-conducting "wire" between CuA and heme-a(b). The transfer of an electron from the low-spin heme to the high-spin heme, i.e., heme-a(b)r + heme-a3o → heme-a(b)o + heme-a3r, was not observed with the A-type enzymes in our experiments but was observed with the Thermus ba3; its Marcus parameters are λ = 1.5 eV, Hab = 26.6 × 10-5 eV (2.14 cm-1), and βD = 9.35, consistent also with diabatic electron tunneling between the two hemes. The II-Glu15Ala mutation of the K-channel structure, ∼ 24 Å between its CA and Fe-a3, was found to completely block heme-br to heme-a3o electron transfer. A structural mechanism is suggested to explain these observations.

Direct Simulation of Electron Transfer Reactions in DNA Radical Cations

The electron transfer properties of DNA radical cations are important in DNA damage and repair processes. Fast long-range charge transfer has been demonstrated experimentally, but the subtle influences that experimental conditions as well as DNA sequences and geometries have on the details of electron transfer parameters are still poorly understood. In this work, we employ an atomistic QM/MM approach, based on a one-electron tight binding Hamiltonian and a classical molecular mechanics forcefield, to conduct nanosecond length MD simulations of electron holes in DNA oligomers. Multiple spontaneous electron transfer events were observed in 100 ns simulations with neighboring adenine or guanine bases. Marcus parameters of charge transfer could be extracted directly from the simulations. The reorganization energy lambda for hopping between neighboring bases was found to be ca. 25 kcal/mol and charge transfer rates of 4.1 x 10(9) s(-1) for AA hopping and 1.3 x 10(9) s(-1) for GG hopping were obtained.

Photoinduced electron transfer in fullerene triads bearing pyrene and fluorene

Photochemical properties of pyrene and fluorene appended fulleropyrrolidine triads (AH 1–C 60–AH 2; AH 1 = pyrene and fluorene; AH 2 = naphthalene and phenyl) are reported. Electrochemical studies using cyclic voltammetry technique and DFT calculations at B3LYP/3-21G( ∗) method revealed that the charge-separated states in pyrene and fluorene appended triads are pyrene + – C 60 - – AH 2 and fluorene + – C 60 - – AH 2 , respectively; however, no such charge-separated states could be established for naphthalene and phenyl appended triads. As demonstrated from the time resolved fluorescence, upon excitation of AH moiety in nonpolar solvents, energy transfer predominantly occurred from the singlet excited fluorophore to the C 60 moiety, whereas in polar DMF charge-separation also contributed to the fluorescence quenching. Additionally, charge separation also occurred from the singlet excited C 60 to the pyrene or fluorene entities of the triads in DMF. The rates and quantum yields of charge separation obtained by time-resolved emission studies were around 10 9 s −1 and 0.9–0.6 for pyrene–C 60–AH 2 and fluorene–C 60–AH 2 triads. Nanosecond transient absorption spectral studies performed by using 355 nm laser light on the triads, exhibited transient bands corresponding to the C 60 - and pyrene + or fluorene + , thus establishing the occurrence of electron transfer in these triads in DMF. The rates of charge recombination obtained by monitoring the decay of the C 60 - were found to be around 10 6 s −1 in DMF which resulted in the lifetimes of the radical ion pairs up to 1000 ns indicating charge stabilization in pyrene–C 60–AH 2 and fluorene–C 60–AH 2 triads. The formations of long-lived charge-separated states, pyrene + – C 60 - – AH 2 and fluorene + – C 60 - – AH 2 in DMF, were rationalized by evaluating the Marcus parameters from the temperature dependence of the charge-recombination rate constants.

Photoinduced Charge Separation and Charge Recombination in [60]Fullerene-(Benzothiadiazole-Triphenylamine) Based Dyad in Polar Solvents

The molecular dyad C60-(BTD-TPA) consisting of an electron donor triphenylamine-appended 2,1,3-benzothiadiazole chromophore (BTD-TPA) unit covalently linked to an electron acceptor [60]fullerene has been synthesized. The photoinduced electron transfer in C60-(BTD-TPA) has been studied in polar and nonpolar solvents using time-resolved transient absorption and fluorescence measurements. By fluorescence lifetime measurements in picosecond time regions, the excitation of the C60 moiety leads to the formation of C60•--(BTD-TPA)•+ efficiently via the singlet excited state of the C60 moiety. Excitation of the BTD-TPA moiety leads to initial energy transfer to 1C60*- (BTD-TPA), from which electron transfer occurs to form C60•--(BTD-TPA)•+. In the nanosecond time region, C60•--(BTD-TPA)•+ in which the radical cation (hole) delocalizes in the BTD-TPA moiety is persistent for 690 ns in DMF at room temperature. From the temperature dependence of the charge-recombination rate constants, which gave the Marcus parameters, we attempted to reveal the origins of long persistent C60•--(BTD-TPA)•+ in DMF.

Kinetics of Intramolecular Electron Transfer in Cytochrome bo3 from Escherichia coli

We have examined the temperature dependence of the intramolecular electron transfer (ET) between heme b and heme o 3 in CO-mixed valence cytochrome bo 3 (C bo) from Escherichia coli. Upon photolysis of CO-mixed valence C bo rapid ET occurs between heme o 3 and heme b with a rate constant of 2.2 × 10 5 s −1 at room temperature. The corresponding rate of CO recombination is found to be 86 s −1. From Eyring plots the activation energies for these two processes are found to be 3.4 kcal/mol and 6.7 kcal/mol for the ligand binding and ET reactions, respectively. Using variants of the Marcus equation the reorganization energy ( λ), electronic coupling factor (H AB), and the ET distance were found to be 1.4 ± 0.2 eV, (2 ± 1) × 10 −3 eV, and 9 ± 1 Å, respectively. These values are quite distinct from the analogous values previously obtained for bovine heart cytochrome c oxidase (C cO) (0.76 eV, 9.9 × 10 −5 eV, 13.2 Å). The differences in mechanisms/pathways for heme b/heme o 3 and heme a/heme a 3 ET suggested by the Marcus parameters can be attributed to structural changes at the Cu B site upon change in oxidation state as well as differences in electronic coupling pathways between Heme b and heme o 3.

Activation volumes for intramolecular electron transfer in Escherichia coli cytochrome bo3

In this report we describe the activation volumes associated with the heme–heme electron transfer (ET) and CO rebinding to the binuclear center subsequent to photolysis of the CO-mixed-valence derivative of Escherichia coli cytochrome bo3 (Cbo). The activation volumes associated with the heme–heme ET (k=1.2×105 s−1), and CO rebinding (k=57 s−1) are found to be +27.4 ml/mol and −2.6 ml/mol, respectively. The activation volume associated with the rebinding of CO is consistent with previous Cu X-ray absorption studies of Cbo where a structural change was observed at the CuB site (loss of a histidine ligand) due to a change in the redox state of the binuclear center. In addition, the volume of activation for the heme–heme ET was found to be quite distinct from the activation volumes obtained for heme–heme ET in bovine heart Cytochrome c oxidase. Differences in mechanisms/pathways for heme b/heme o3 and heme a/heme a3 ET are suggested based on the associated activation volumes and previously obtained Marcus parameters.

Intermolecular proton transfer in catalysis by carbonic anhydrase V

The dehydration of bicarbonate catalyzed by carbonic anhydrase is accompanied by the transfer of a proton from solution to the zinc-bound hydroxide. We have investigated the properties of proton transfer from donors in solution, mostly derivatives of imidazole and pyridine, to a truncated mutant of carbonic anhydrase V with replacements that render the active site cavity less sterically constrained, Tyr 64 →> Ala and Phe 65 →> Ala. Catalysis was measured by determining the rate of exchange of 18O between the CO2-HCO3- system and water, and rate constants for proton transfer were estimated as the rate-limiting step in the release of H218O from the enzyme to solution. Each proton donor enhanced catalytic activity in a saturable manner. The resulting rate constants for proton transfer when compared with the values of pKa of the donor and acceptor gave a Brønsted plot of high curvature. These data could also be described by Marcus theory which showed an intrinsic barrier for intermolecular proton transfer near 0.8 kcal/mol and a work term or thermodynamic contribution to the free energy of reaction near 10 kcal/mol. This low intrinsic kinetic barrier for proton transfer is very similar to nonenzymic bimolecular proton transfer between nitrogen and oxygen acids and bases in solution. However, the significant thermodynamic contribution suggests appreciable involvement of solvent and active-site organization prior to proton transfer. These Marcus parameters are very similar to those describing intramolecular proton transfer from His 64 in carbonic anhydrase, suggesting similarities in the intra- and intermolecular proton transfer processes.Key words: carbonic anhydrase, proton transfer, Marcus theory, carbon dioxide.

Intermolecular proton transfer in catalysis by carbonic anhydrase V

The dehydration of bicarbonate catalyzed by carbonic anhydrase is accompanied by the transfer of a proton from solution to the zinc-bound hydroxide. We have investigated the properties of proton transfer from donors in solution, mostly derivatives of imidazole and pyridine, to a truncated mutant of carbonic anhydrase V with replacements that render the active site cavity less sterically constrained, Tyr 64 →> Ala and Phe 65 →> Ala. Catalysis was measured by determining the rate of exchange of 18O between the CO2-HCO3- system and water, and rate constants for proton transfer were estimated as the rate-limiting step in the release of H218O from the enzyme to solution. Each proton donor enhanced catalytic activity in a saturable manner. The resulting rate constants for proton transfer when compared with the values of pKa of the donor and acceptor gave a Brønsted plot of high curvature. These data could also be described by Marcus theory which showed an intrinsic barrier for intermolecular proton transfer near 0.8 kcal/mol and a work term or thermodynamic contribution to the free energy of reaction near 10 kcal/mol. This low intrinsic kinetic barrier for proton transfer is very similar to nonenzymic bimolecular proton transfer between nitrogen and oxygen acids and bases in solution. However, the significant thermodynamic contribution suggests appreciable involvement of solvent and active-site organization prior to proton transfer. These Marcus parameters are very similar to those describing intramolecular proton transfer from His 64 in carbonic anhydrase, suggesting similarities in the intra- and intermolecular proton transfer processes.Key words: carbonic anhydrase, proton transfer, Marcus theory, carbon dioxide.

Properties of Intramolecular Proton Transfer in Carbonic Anhydrase III

We investigated the efficiency of glutamic acid 64 and aspartic acid 64 as proton donors to the zinc-bound hydroxide in a series of site-specific mutants of human carbonic anhydrase III (HCA III). Rate constants for this intramolecular proton transfer, a step in the catalyzed dehydration of bicarbonate, were determined from the proton-transfer-dependent rates of release of H 2 18O from the enzyme measured by mass spectrometry. The free energy plots representing these rate constants could be fit by the Marcus rate theory, resulting in an intrinsic barrier for the proton transfer of Δ G O ‡ = 2.2 ± 0.5 kcal/mol, and a work function or thermodynamic contribution to the free energy of reaction w r = 10.8 ± 0.1 kcal/mol. These values are very similar in magnitude to the Marcus parameters describing intramolecular proton transfer from His 64 and His 67 to the zinc-bound hydroxide in mutants of HCA III. That result and the equivalent efficiency of Glu 64 and Asp 64 as proton donors in the catalysis by CA III demonstrate a lack of specificity in proton transfer from these sites, which is indirect evidence of a number of proton conduction pathways through different structures of intervening water chains. The dominance of the thermodynamic contribution or work function for all of these proton transfers is consistent with the view that formation and breaking of hydrogen bonds in such water chains is a limiting factor for proton translocation.

Electron Transfer in Nitrogenase Analyzed by Marcus Theory: Evidence for Gating by MgATP

Nitrogenase-catalyzed substrate reduction reactions require electron transfer between two component proteins, the iron (Fe) protein and the molybdenum-iron (MoFe) protein, in a reaction that is coupled to the hydrolysis of MgATP. In the present work, electron transfer (Marcus) theory has been applied to nitrogenase electron transfer reactions to gain insights into possible roles for MgATP in this reaction. Evidence is presented indicating that an event associated with either MgATP binding or hydrolysis acts to gate electron transfer between the two component proteins. In addition, evidence is presented that the reaction mechanism can be fundamentally changed such that electron transfer becomes rate-limiting by the alteration of a single amino acid within the nitrogenase Fe protein (deletion of Leu 127, L127 Delta). These studies utilized the temperature dependence of intercomponent electron transfer within two different nitrogenase complexes: the wild-type nitrogenase complex that requires MgATP for electron transfer and the L127 Delta Fe protein-MoFe protein complex that does not require MgATP for electron transfer. It was found that the wild-type nitrogenase electron transfer reaction did not conform to Marcus theory, suggesting that an adiabatic event associated with MgATP interaction precedes electron transfer and is rate-limiting. Application of transition state theory provided activation parameters for this rate-limiting step. In contrast, electron transfer from the L127 Delta Fe protein variant to the MoFe protein (which does not require MgATP hydrolysis) was found to be described by Marcus theory, indicating that electron transfer was rate-limiting. Marcus parameters were determined for this reaction with a reorganization energy (lambda) of 2.4 eV, a coupling constant (HAB) of 0.9 cm-1, a free energy change (Delta G' degrees ) of -22.0 kJ/mol, and a donor-acceptor distance (r) of 14 A. These values are consistent with parameters deduced for electron transfer reactions in other protein-protein systems where electron transfer is rate-limiting. Finally, the electron transfer reaction within the L127 Delta Fe protein-MoFe protein complex was found to be reversible. These results are discussed in the context of models for how MgATP interactions might be coupled to electron transfer in nitrogenase.

Effect of reduction potential on the rate of reduction of nitroacridines by xanthine oxidase and by dihydro-flavin mononucleotide

The cytotoxicity of many nitroaromatic compounds is mediated by bioreduction. There is a correlation between the one-electron-reduction potentials and cytotoxic potencies of simple nitroheterocycles such as nitroimidazoles, but no such correlation is observed with DNA-binding nitroacridines related to the drug nitracrine. A study of the reduction of 1-nitroacridines by the enzyme xanthine oxidase and by reduced flavin mononucleotide, FMNH2(as a model of the enzyme's active site) has been undertaken to explore the redox dependence in this series. The values of Vmax,/Km for reduction by xanthine oxidase, XOD, and the second-order rate constants of reduction by FMNH2, analysed using Marcus electron-transfer theory, indicate a correlation between reduction potential and the rate of reduction, but suggest that the potential-energy barrier for electron transfer is small relative to that imposed by requirements for association, orientation and desolvation of the reactants. The close similarity in Marcus parameters for reduction by FMNH2 and by XOD suggests that reduction occurs by a similar mechanism in each case. The free-energy change for electron transfer, ΔG‡o, is only 1–2 kJ mol–1. It appears that the rate of reduction is unlikely to be the only determinant of hypoxic cytotoxicity for the nitroacridines, although the applicability of findings with XOD to other nitroreductases is uncertain.

The carbanion mechanism of olefin-forming elimination. VIII. Theoretical analysis of substituent and isotope effects in proton transfers from 2,2-Diaryl-1,1,1-trichloroethanes

Rate constants for the dehydrochlorination of the title compounds by anionic bases in alcoholic solvents are those for simple proton transfer. Rate and estimated equilibrium data for these reactions can be approximately analysed in terms of the Marcus theory of proton transfer. In one reaction series comprising the reactions of para-substituted Ar2CHCC13 compounds with NaOMe in MeOH, the work term (wr) and the intrinsic free energy of activation (ΔG?) are comparable and large. The change in kH/kD with variation in substituent can be quantitatively rationalized, and the fact that kH/kD does not pass through a maximum even though ΔpK = 0 within the series can be understood. Although the required rate-equilibrium parabolic relationship for a second series involving the reactions of (p-ClC6H4)2CHCCl3 with a series of bases is obtained, anomalous Marcus parameters are derived, and reasons for the anomalies are given. A revised set of approximate pKa values for Ar2CHCCl3 compounds is presented, and more precise experimental values of rate constants for the reactions of (p-NO2C6H4)2CHCC13 and (p-NO2C6H4)2CDCCl3 with NaOMe in MeOH are provided.