Semiclassical Electron Transfer Research Articles

Spin-phonon coupling in a double-stranded model of DNA.

We address the electron-spin-phonon coupling in an effective model Hamiltonian for DNA to assess its role in spin transfer involved in the Chiral-Induced Spin Selectivity (CISS) effect. The envelope function approach is used to describe semiclassical electron transfer in a tight-binding model of DNA at half filling in the presence of intrinsic spin-orbit coupling. Spin-phonon coupling arises from the orbital-configuration dependence of the spin-orbit interaction. We find spin-phonon coupling only for the acoustic modes, while the optical modes exhibit electron-phonon interaction without coupling to spin. We derive an effective Hamiltonian whose eigenstates carry spin currents that are protected by spin-inactive stretching optical modes. As optical phonons interact more strongly than acoustic phonons, side buckling and tilting optical base modes will be more strongly associated with decoherence, which allows for the two terminal spin filtering effects found in CISS.

Prediction of Internal Reorganization Energy in Photoinduced Electron Transfer Processes of Molecular Dyads.

A novel theoretical methodology is proposed to estimate the magnitude of internal reorganization energy for electron transfer and charge recombination processes in donor-bridge-acceptor (D-B-A) type molecular dyads. The potential energy surface for each process is plotted for the shortest path by assuming a displaced but slightly distorted harmonic oscillator model. Structural changes occurring upon photoexcitation and ionization were exploited to calculate the activation energies needed for electron transfer reactions with the aid of involved vibrational modes. D-B-A dyads consisting of octathiophene (T8) paired with three (di)imide acceptors (naphthalene diimide (NDI), benzene diimide (BDI), and naphthalimide (NI)) were studied as model systems for theoretical calculations. It has been found that T8NDI and T8BDI possess very low activation energies for both forward electron transfer and charge recombination, and hence the rates for relevant processes should be very rapid. In contrast, the activation energies for such processes for T8NI were found to be relatively large, and free energy estimations predict that the charge recombination mechanism in T8NI falls into the inverted regime of Marcus semiclassical electron transfer theory. All of the calculated properties of the dyads are in very good agreement with the available experimental data, suggesting the suitability of the proposed theoretical approach in revealing the photoinduced electron transfer mechanisms of molecular dyads.

Light-Activated Electron Transfer and Turnover in Ru-Modified Aldehyde Deformylating Oxygenases.

Conversion of biological molecules into fuels or other useful chemicals is an ongoing chemical challenge. One class of enzymes that has received attention for such applications is aldehyde deformylating oxygenase (ADO) enzymes. These enzymes convert aliphatic aldehydes to the alkanes and formate. In this work, we prepared and investigated ADO enzymes modified with RuII(tris-diimine) photosensitizers as a starting point for probing intramolecular electron transfer events. Three variants were prepared, with RuII-modification at the wild type (WT) residue C70, at the R62C site in one mutant ADO, and at both C62 and C70 in a second mutant ADO protein. The single-site modification of WT ADO at C70 using a cysteine-reactive label is an important observation and opens a way forward for new studies of electron flow, mechanism, and redox catalysis in ADO. These Ru-ADO constructs can perform the ADO catalytic cycle in the presence of light and a sacrificial reductant. In this work, the Ru photosensitizer serves as a tethered, artificial reductase that promotes turnover of aldehyde substrates with different carbon chain lengths. Peroxide side products were detected for shorter chain aldehydes, concomitant with less productive turnover. Analysis using semiclassical electron transfer theory supports proposals for hopping pathway for electron flow in WT ADO and in our new Ru-ADO proteins.

Photoinduced Electron Transfer in Naphthalene Diimide End-Capped Thiophene Oligomers

A series of linear thiophene oligomers containing 4, 6, 8, 10, and 12 thienylene units were synthesized and end-capped with naphthalene diimide (NDI) acceptors with the objective to study the effect of oligomer length on the dynamics of photoinduced electron transfer and charge recombination. The synthetic work afforded a series of nonacceptor-substituted thiophene oligomers, Tn, and corresponding NDI end-capped series, TnNDI2 (where n is the number of thienylene repeat units). This paper reports a complete photophysical characterization study of the Tn and TnNDI2 series by using steady-state absorption, fluorescence, singlet oxygen sensitized emission, two-photon absorption, and nanosecond-microsecond transient absorption spectroscopy. The thermodynamics of photoinduced electron transfer and charge recombination in the TnNDI2 oligomers were determined by analysis of photophysical and electrochemical data. Excitation of the Tn oligomers gives rise to efficient fluorescence and intersystem crossing to a triplet excited state that is easily observed by nanosecond transient absorption spectroscopy. Bimolecular photoinduced electron transfer from the triplet states, 3Tn*, to N,N-dimethylviologen (MV2+) occurs, and by using microsecond transient absorption it is possible to assign the visible region absorption spectra for the one electron oxidized (polaron) states, Tn+•. The fluorescence of the TnNDI2 oligomers is quenched nearly quantitatively, and no long-lived transients are observed by nanosecond transient absorption. These findings suggest that rapid photoinduced electron transfer and charge recombination occurs, NDI-1(Tn)*-NDI → NDI-(Tn)+•-NDI-• → NDI-Tn-NDI. Preliminary femtosecond-picosecond transient absorption studies on T4NDI2 reveal that both forward electron transfer and charge recombination occur with k > 1011 s-1, consistent with both reactions being nearly activationless. Analysis with semiclassical electron transfer theory suggests that both reactions occur at near the optimum driving force where -ΔG ∼ λ.

Quantum ergodicity breaking in semi-classical electron transfer dynamics.

Can the statistical properties of single-electron transfer events be correctly predicted within a common equilibrium ensemble description? This fundamental in nanoworld question of ergodic behavior is scrutinized within a very basic semi-classical curve-crossing problem. It is shown that in the limit of non-adiabatic electron transfer (weak tunneling) well-described by the Marcus-Levich-Dogonadze (MLD) rate the answer is yes. However, in the limit of the so-called solvent-controlled adiabatic electron transfer, a profound breaking of ergodicity occurs. Namely, a common description based on the ensemble reduced density matrix with an initial equilibrium distribution of the reaction coordinate is not able to reproduce the statistics of single-trajectory events in this seemingly classical regime. For sufficiently large activation barriers, the ensemble survival probability in a state remains nearly exponential with the inverse rate given by the sum of the adiabatic curve crossing (Kramers) time and the inverse MLD rate. In contrast, near to the adiabatic regime, the single-electron survival probability is clearly non-exponential, even though it possesses an exponential tail which agrees well with the ensemble description. Initially, it is well described by a Mittag-Leffler distribution with a fractional rate. Paradoxically, the mean transfer time in this classical on the ensemble level regime is well described by the inverse of the nonadiabatic quantum tunneling rate on a single particle level. An analytical theory is developed which perfectly agrees with stochastic simulations and explains our findings.

Interfacial Electronic Structure in Graded Shell Nanocrystals Dictates Their Performance for Optical Gain

The interface of semiconductor nanocrystals is a critical factor for determining their performance in light emissive applications. Traditional nanocrystals have an abrupt termination of the core/shell interface. Recent synthetic work has focused upon developing graded core/shell interfaces via alloying. Here, we employ femtosecond state-resolved pump/probe spectroscopy, temperature-dependent photoluminescence spectroscopy, and a microscopic theory of interfacial charge trapping to reveal the manner in which a graded interface controls the main optical gain metrics: threshold, bandwidth, and lifetime in the CdSe/Cd,Zn,S core/shell system. Photoluminescence spectroscopy in conjunction with semiclassical electron transfer theory reveals the absence of an interfacial electronic state. This absence of a surface/interfacial state is unique to these nanocrystals with a graded shell structure, enabling trap free performance. Excitonic state-resolved pump/probe spectroscopy reveals that the higher excitons do not ...

Confronting surface hopping molecular dynamics with Marcus theory for a molecular donor-acceptor system.

We investigate the performance of fewest switches surface hopping (SH) in describing electron transfer (ET) for a molecular donor-acceptor system. Computer simulations are carried out for a wide range of reorganisation energy (λ), electronic coupling strength (Hab) and driving force using our recently developed fragment orbital-based SH approach augmented with a simple decoherence correction. This methodology allows us to compute SH ET rates over more than four orders of magnitude, from the sub-picosecond to the nanosecond time regime. We find good agreement with semi-classical ET theory in the non-adiabatic ET regime. The correct scaling of the SH ET rate with electronic coupling strength is obtained and the Marcus inverted regime is reproduced, in line with previously reported results for a spin-boson model. Yet, we find that the SH ET rate falls below the semi-classical ET rate in the adiabatic regime, where the free energy barrier is in the order of kBT in our simulations. We explain this by first signatures of non-exponential population decay of the initial charge state. For even larger electronic couplings (Hab = λ/2), the free energy barrier vanishes and ET rates are no longer defined. At this point we observe a crossover from ET on the vibronic time scale to charge relaxation on the femtosecond time scale that is well described by thermally averaged Rabi oscillations. The extension of the analysis from the non-adiabatic limit to large electronic couplings and small or even vanishing activation barriers is relevant for our understanding of charge transport in organic semiconductors.

Connecting the Dots: The Kinetics and Thermodynamics of Hot, Cold, and Surface-Trapped Excitons in Semiconductor Nanocrystals

The excitonics of semiconductor nanocrystals (NC) depend upon temperature in a complex manner due to the interplay between the kinetics of hot exciton relaxation/trapping and the thermodynamics leading to cold exciton recombination. We apply a semiclassical electron transfer model of surface trapping to temperature-dependent absorption and emission data to elucidate a microscopic picture of the factors which govern the fate of hot and cold excitons. The linear absorption spectra reveal a unique temperature-dependence to the energies of higher excitonic states, while oscillator strength is shown to be temperature invariant. We identify the phonon based origin to the anomalous low temperature peak energy trend in photoluminescence (PL) spectra. PL intensities, PL lifetimes, and absorption spectra are used to demonstrate that variation of quantum yield with temperatures arises from the thermally controlled fraction of NC which emit, rather than from an activated nonradiative pathway common to all NCs. Experimental quantum yield spectra are shown for several NCs and we perform a much-needed analysis of the role of surface PL in quantum yield. Finally, we show that a semiclassical electron transfer model including hot excitonic effects can explain experimental quantum yield spectra and suggests how to probe kinetic trapping processes via simple steady-state spectroscopy.

Negative Resistance Region 10 nm Gate Length on FINFET

In this paper the physical characteristics of FINFET (fin-field effect transistor) transistor behavior are investigated. For the analysis, semi-classical electron transfer method was used based on drift diffusion approximation by TCAD (Tiber CAD) software. Simulations show that the output resistance of FINFET along very small gate (gate length and fin height of 50 nm) is negative. The negative resistance is used in oscillators.

Challenge to the deep-trap model of the surface in semiconductor nanocrystals

Temperature-dependent photoluminescence spectra of a range of semiconductor nanocrystals are presented which reveal an unanticipated thermodynamic relationship between the core excitonic states and the surface of the nanocrystal. These results challenge the widely held view of the surface emission arising from an energetically broad distribution of midgap defect states at the surface. We show that a simpler model based on semiclassical electron transfer and invoking only a single surface state uniquely describes all observables.

Temperature Dependence of Spin-Selective Charge Transfer Pathways in Donor−Bridge−Acceptor Molecules with Oligomeric Fluorenone and p-Phenylethynylene Bridges

The temperature dependence of spin-selective intramolecular charge recombination (CR) in a series of 2,7-fluorenone (FN(1-2)) and p-phenylethynylene (PE(1-2)P) linked donor-bridge-acceptor molecules with a 3,5-dimethyl-4-(9-anthracenyl) julolidine (DMJ-An) electron donor and a naphthalene-1,8:4,5-bis(dicarboximide) (NI) acceptor was studied using nanosecond transient absorption spectroscopy in the presence of a static magnetic field. Photoexcitation of DMJ-An into its charge transfer band and subsequent electron transfer to NI results in a nearly quantitative yield of (1)(DMJ(+•)-An-FN(n)-NI(-•)) and (1)(DMJ(+•)-An-PE(n)P-NI(-•)), which undergo rapid radical pair intersystem crossing (RP-ISC) to produce the triplet RPs, (3)(DMJ(+•)-An-FN(n)-NI(-•)) and (3)(DMJ(+•)-An-PE(n)P-NI(-•)), respectively. The CR rate constants, k(CR), in toluene were measured over a temperature range from 270 to 350 K, and a kinetic analysis of k(CR) in the presence of an applied static magnetic field was used to extract the singlet and triplet charge recombination rate constants, k(CRS) and k(CRT), respectively, as well as the intersystem crossing rate constant, k(ST). Plots of ln (kT(1/2)) versus 1/T for PE(1)P show a distinct crossover at 300 K from a temperature-independent singlet CR pathway to a triplet CR pathway that is positively activated with a barrier of 1047 ± 170 cm(-1). The singlet CR pathway via the FN(1) bridge displays a negative activation energy that results from donor-bridge and bridge-acceptor torsional motions about the single bonds joining them. In contrast, the triplet CR pathway via the FN(1-2) and PE(1-2)P bridges exhibits positive activation energies. The activation barriers to these torsional motions range from 1100 to 4500 cm(-1) and can be modeled by semiclassical electron transfer theory.

Intramolecular electron transfer in [4Fe-4S] proteins: estimates of the reorganization energy and electronic coupling in Chromatium vinosum ferredoxin.

The semi-classical electron transfer theory has been very successful in describing reactions occurring in biological systems, but the relevant parameters in the case of iron-sulfur proteins remain unknown. The recent discovery that 2[4Fe-4S] proteins homologous to Chromatium vinosum ferredoxin contain clusters with different reduction potentials now gives the opportunity to study the dependence of the intramolecular electron transfer rate between these clusters as a function of the driving force. This work shows how decreasing the reduction potential difference between the clusters by site-directed mutagenesis of C. vinosum ferredoxin modifies the rate of electron hopping between the two redox sites of the protein by measuring the line broadening of selected 1H NMR signals. Beside the shifts of the reduction potentials, no signs of large structural changes or of significant alterations of the intrinsic kinetic parameters among the different variants of C. vinosum ferredoxin have been found. A reorganization energy of less than 0.5 eV was deduced from the dependence of the electron transfer rates with the reduction potential difference. This small value is associated with a weak electronic coupling between the two closely spaced clusters. This set of parameters, determined for the first time in an iron-sulfur protein, may help to explain how efficient vectorial electron transfer occurs with a small driving force in the many enzymatic systems containing a 2[4Fe-4S] domain.

Lanthanide ions as redox probes of long-range electron transfer in proteins

Occupancy of the two calcium-binding sites of codfish parvalbumin by the redox-active probe ions Yb 3+ and Eu 3+ causes the average tryptophan (Trp) fluorescence lifetime in this protein to decrease and become non-exponential from the single exponential values found for Ca 2+ and La 3+ of 4.45 ns. These observations are interpreted in terms of an electron transfer (ET) deexcitation mechanism wherein excited singlet state Trp transfers an electron to the Ln 3+ ion, reducing it to the +2 oxidation state and producing a Trp cation radical. Back ET reestablishes the initial system. The driving forces, Δ G°, for the Eu 3+ and Yb 3+ ET systems are different, whereas the nuclear rearrangement factor, λ, and electron donor-acceptor coupling, H AB, of semiclassical ET theory should be nearly the same for both ions. This allows the λ-value to be determined from the measured rates (∼2.05 eV). Temperature dependence studies show that the rate constant for the Eu 3+ system is near the activationless maximum value. Yb 3+ and Eu 3+ are established as redox probes of long-range ET in proteins making Ln 3+-substituted calcium-binding proteins convenient model systems for studying the distance-dependence of ET.

Present status and future directions of research in electron-transfer mediated by DNA

This commentary article presents an overview of recent experimental results on DNA-mediated electron transfer (ET) from the perspective of semiclassical ET theory. The question concerning whether or not DNA can act as a wire is addressed. Much of the article focuses on a discussion of the decay of electronic coupling (β) between electron donors and acceptors with increasing donor/acceptor separation in DNA and in protein systems. In particular, the dependence of the electronic coupling itself (H AB) on the energy gap between the tunneling energy of the reactants and the virtual ionic states of the DNA bridge is highlighted. The article concludes by suggesting that future experimental and theoretical work in this field should focus on the tunneling gap energies of the systems studied and that special attention should be paid to systems that are likely to be in the "small tunneling gap" regime. It is these systems that are expected to exhibit enhanced electronic couplings and consequently enhanced rates of long-distance ET.

Electron Transfer Reactions in DNA

This paper introduces to an active and provocative area of current research. It describes motivations for studying electron transfer (ET) chemistry in general and ET reactions in DNA in particular. A rate expression for a semiclassical electron transfer model is given along with a description of appropriate conditions for its use. Formulas describing the distance dependence of electronic coupling (HAB) and solvent reorganization energy are also provided as a basis for understanding and interpreting recent experiments. Three different long-range ET experiments are presented, and their results are compared with one another and with the results of similar experiments in proteins. Discrepancies and difficulties are noted, and suggestions for new experiments are made.

Rates of Heme Oxidation and Reduction in Ru(His33)cytochrome c at Very High Driving Forces

The rates of Ru(His33)cytochrome c electron-transfer (ET) reactions have been measured over a driving-force range of 0.59 to 1.89 eV. The driving-force dependence of Fe2+ → Ru3+ ET in RuL2(im)(His33)cyt c [L = 2,2‘-bipyridine (bpy), 4,4‘,5,5‘-tetramethyl-2,2‘-bipyridine (4,4‘,5,5‘-(CH3)4-bpy), 4,4‘-dimethyl-2,2‘-bipyridine (4,4‘-(CH3)2-bpy), 4,4‘-bis(N-ethylcarbamoyl)-2,2‘-bipyridine (4,4‘-(CONH(C2H5))2-bpy), 1,10-phenanthroline (phen); im = imidazole] is well described by semiclassical ET theory with kmax = 2.7 × 106 s-1 (HAB = 0.095 cm-1) and λ = 0.74 eV. As predicted by theory, the rate of an exergonic (−ΔG° = 1.3 eV) heme reduction reaction, *Ru2+(bpy)2(im)(His) → Fe3+, falls in the inverted region (k = 2.0 × 105 s-1). In contrast, the rates of three highly exergonic heme reductions, *Ru2+(phen)2(CN)(His) → Fe3+ (2.0 × 105 s-1; 1.40 eV), Ru+(4,4‘-(CONH(C2H5))2-bpy)2(im)(His) → Fe3+ (2.3 × 105 s-1; 1.44 eV), and Ru+(phen)2(CN)(His) → Fe3+ (4.5 × 105 s-1; 1.89 eV), are much higher than expected for reac...

Ultraviolet Absorption of the Mixed System KCl-KBr

The ultraviolet absorption of thin evaporated layers and the edge absorption of single crystals of the mixed system KCl-KBr were measured at room temperature in the photon energy range from 6-11 ev. In the thin layers, both the ${\mathrm{Cl}}^{\ensuremath{-}}$ and the ${\mathrm{Br}}^{\ensuremath{-}}$ absorption bands are present in the mixtures and their heights depend on the relative concentrations of the two ions. The energy values of the bands generally shift with composition, although in contrast to all the other bands, the high-energy KBr band shifts very little. The results obtained for the low-energy absorption bands can be described by a simple semiclassical electron transfer model. The behavior of the high-energy KBr band is discussed.