Marcus Theory Of Electron Transfer Research Articles

Nuclear tunneling effects of charge transport in rubrene, tetracene, and pentacene

The mechanism of charge transport in organic materials is still controversial from both experimental and theoretical perspectives. At room temperature, molecular deformations interact strongly with the charge carrier both through intermolecular and intramolecular phonons, suggesting a thermally activated hopping mechanism as described by the Marcus electron transfer theory. However, several experimental measurements have indicated that the electronic transport behaves in a ``bandlike'' manner, as indicated by a decrease in mobility with increasing temperature, in contradiction to the Marcus description. Bandlike first-principles calculations based on the Holstein-Peierls model tend to overestimate the charge mobility by about 2 orders of magnitude. Here, a hopping model is derived that not only quantitatively describes the charge mobility but also explains the observed bandlike behavior. This model uses the quantum version of charge-transfer theory coupled with a random-walk simulation of charge diffusion. The results bridge the gap between the two extreme mechanisms. This first-principles method predicts the room-temperature hole mobilities to be 2.4, 2.0, and $0.67\text{ }{\text{cm}}^{2}/\text{V}\text{ }\text{s}$, for rubrene, pentacene, and tetracene, respectively, in good agreement with experiment.

Quantitative modeling of the role of surface traps in CdSe/CdS/ZnS nanocrystal photoluminescence decay dynamics.

Charge carrier trapping is an important phenomenon in nanocrystal (NC) decay dynamics because it reduces photoluminescence (PL) quantum efficiencies and obscures efforts to understand the interaction of NC excitons with their surroundings. Particularly crucial to our understanding of excitation dynamics in, e.g., multiNC assemblies, would be a way of differentiating between processes involving trap states and those that do not. Direct optical measurement of NC trap state processes is not usually possible because they have negligible transition dipole moments; however, they are known to indirectly affect exciton photoluminescence. Here, we develop a framework, based on Marcus electron transfer theory, to determine NC trap state dynamics from time-resolved NC exciton PL measurements. Our results demonstrate the sensitivity of PL to interfacial dynamics, indicating that the technique can be used as an indirect but effective probe of trap distribution changes. We anticipate that this study represents a step toward understanding how excitons in nanocrystals interact with their surroundings: a quality that must be optimized for their efficient application in photovoltaics, photodetectors, or chemical sensors.

Charge transfer rates in organic semiconductors beyond first-order perturbation: From weak to strong coupling regimes

Semiclassical Marcus electron transfer theory is often employed to investigate the charge transport properties of organic semiconductors. However, quite often the electronic couplings vary several orders of magnitude in organic crystals, which goes beyond the application scope of semiclassical Marcus theory with the first-order perturbative nature. In this work, we employ a generalized nonadiabatic transition state theory (GNTST) [Zhao et al., J. Phys. Chem. A 110, 8204 (2004)], which can evaluate the charge transfer rates from weak to strong couplings, to study charge transport properties in prototypical organic semiconductors: quaterthiophene and sexithiophene single crystals. By comparing with GNTST results, we find that the semiclassical Marcus theory is valid for the case of the coupling <10 meV for quaterthiophene and <5 meV for sexithiophene. It is shown that the present approach can be applied to design organic semiconductors with general electronic coupling terms. Taking oligothiophenes as examples, we find that our GNTST-calculated hole mobility is about three times as large as that from the semiclassical Marcus theory. The difference arises from the quantum nuclear tunneling and the nonperturbative effects.

Structural, electronic, and optical properties of phenol‐pyridyl boron complexes for light‐emitting diodes

AbstractThe coordination chemistry of polydentate chelating ligands that contain mixed pyridinephenol donor sets has been a sought‐after target of study and is a possible extension to the chemistry of polypyridines. In this article, seven compounds, which are the four‐coordinate boron complexes containing the mixed phenol‐pyridyl group, have been studied by theoretical calculation. They can function as charge transport materials and emitters, with high efficiency and stability. To reveal the relationship between the structures and properties of these bifunctional or multifunctional electroluminescent materials, the ground and excited state geometries were optimized at the B3LYP/6‐31G(d), HF/6‐31G(d), and CIS/6‐31G(d) levels, respectively. The ionization potentials (IPs) and electron affinities (EAs) were computed. The mobilities of hole and electron in these compounds were studied computationally based on the Marcus electron transfer theory. The lowest excitation energies, and the maximum absorption and emission wavelengths of these compounds were calculated by time‐dependent density functional theory method. As a result of these calculations, the values of HOMO, LUMO, energy gaps, IPs, EAs, and the balance between the hole‐ and electron‐transfer are greatly improved with the substitution of carbazole in compound 6. The calculated emission spectra of the seven studied molecules can almost cover the full UV‐vis range (from 447.4 to 649.3 nm). Also, the Stokes shifts are unexpectedly large, ranging from 139.4 to 335.1 nm. This will result in the relatively long fluorescence lifetimes. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

Reorganization Energies of Diprotonated and Saddle-Distorted Porphyrins in Photoinduced Electron-Transfer Reduction Controlled by Conformational Distortion

Kinetics of photoinduced electron transfer from a series of electron donors to the triplet excited states of a series of nonplanar porphyrins, hydrochloride salts of saddle-distorted dodecaphenylporphyrin ([H(4)DPP]Cl(2)), tetrakis(2,4,6-trimethylphyenyl)porphyrin ([H(4)TMP]Cl(2)), tetraphenylporphyrin ([H(4)TPP]Cl(2)), and octaphenylporphyrin ([H(4)OPP]Cl(2)), were investigated in comparison with those of a planar porphyrin, zinc [tetrakis(pentafluorophenyl)]porphyrin [Zn(F(20)TPP)(CH(3)CN)], in deaerated acetonitrile by laser flash photolysis. The resulting data were evaluated in light of the Marcus theory of electron transfer, allowing us to determine reorganization energies of electron transfer to be 1.21 eV for [H(4)TMP]Cl(2), 1.29 eV for [H(4)TPP]Cl(2), 1.45 eV for [H(4)OPP]Cl(2), 1.69 eV for [H(4)DPP]Cl(2), and 0.84 eV for [Zn(F(20)TPP)(CH(3)CN)]. The reorganization energies exhibited a linear correlation relative to the out-of-plane displacements, which represent the degree of nonplanarity. The rate of electron-transfer reduction of diprotonated porphyrins is significantly slowed down by conformational distortions of the porphyrin ring. This indicates that the reorganization energy of electron transfer is governed by structural change, giving a larger contribution of inner-sphere bond reorganization energy rather than outer-sphere solvent reorganization energy.

Solvent effects on photophysical properties of copper and zinc porphyrins

The photophysics of Zn(tetraphenylporphyrin,TPP), Zn(tetra-2,4,6-trimethylphenyl porphyrin, TMP), Zn (tetra-(o-dichlorophenyl) porphyrin, TPPCl8), Cu(tetraphenylporphyrin,TPP), Cu(tetra-2,4,6-trimethylphenyl porphyrin,TMP), and Cu(tetra-(o-dichlorophenyl) porphyrin, TPPCl8, TPPCl8) in several solvents have been investigated on steady state and time-resolved spectroscopy. The Cu(TPPCl8 ) is normal and shows no evidence of CT transition in the visible or near UV regions in nonpolar solvent. However, Cu(TPPCl8)shows a blue shift in the absorption spectrum and intramolecular CT bands at absorption spectra in polar solvent, which shows a fluorescence maximum emission at 650 nm and 8.4 ns lifetime. The reason can be attributed to two points. Firstly, the increase of solvent polarity can enlarge outer reorganisational energy, which is favorable to reduce the activation free energy of charger-transfer transition based on Marcus theory of electron transfer. Moreover, the internal heavy-atom effect on Cu(TPPCl8) is encouraging to stabilize the 2T1 state also, which increases the possibility of population to CT band from 2T1 state. This result is in accord with an earlier estimate of a 10 ns lifetime and CT absorption at 640 nm bands for the CT state of Cu (II) octethylporphyrins. Other possible reasons arousing unusual fluorescence like H-bonding, axial ligands, molecular aggregation are excluded.

Theoretical Study on Photophysical Properties of Multifunctional Electroluminescent Molecules with Different π-Conjugated Bridges

The photophysics of a series of molecular organic light-emitting diodes (OLEDs) has been studied by theoretical calculation. These molecular OLEDs have been integrated by an electron- and hole-transporting components as well as an emitting components into the donor-pi-acceptor (D-pi-A) structures: 2-carbazolyl-7-dimesitylboryl-9,9-diethylfluorene (1), trans-4'-N-carbazolyl-4-dimesitylborylstilbene (2), and trans-2-[(4'-N-carbazolyl)styryl]-5-dimesitylborylthiophene (3). To reveal the relationship between the structures and properties of these multifunctional electroluminescent materials, the ground- and excited-state geometries were optimized at the B3LYP/6-31G(d), HF/6-31G(d), and CIS/6-31G(d) levels, respectively. The ionization potentials and electron affinities were computed. The mobilities of hole and electron in these compounds were studied computationally based on the Marcus electron transfer theory. The lowest excitation energies (E(g)) and the maximum absorption and emission wavelengths of these compounds were calculated by time-dependent density functional theory methods. The solvent effect on the emission spectra of these compounds was considered by a polarizable continuum model. As a result of these calculations, it was concluded that the electron injections of these compounds are much easier than Mes(2)B[p-4,4'-biphenyl-NPh(1-naphthyl)], and the diethylfluorene-based compound has higher electron mobility and better equilibrium properties as compared to the stilbene-based and styrylthiophene-based compounds.

Mechanism of electron transfer in fusion protein cytochrome b 5—NADH-cytochrome b 5 reductase

In the present work we summarize results on construction of expression plasmid, heterologous expression in Escherichia coli, isolation and purification, as well as physicochemical characterization of chimeric protein consisting of hydrophilic domain of cytochrome b(5) and truncated from the N-terminal sequence (Delta(23)) form of NADH-cytochrome b(5) reductase. The kinetics and mechanism of electron transfer between NADH-cytochrome b(5) reductase and cytochrome b(5) in the frames of fusion protein consisting of cytochrome b(5) (94 amino acids) and truncated form of NADH-cytochrome b(5) reductase (277 amino acids) have been studied. It is shown that electron transfer takes place between redox partners belonging to two different molecules of the chimeric protein. Using computer modeling, we built the model of the tertiary structure of the fusion protein, which is in agreement with experimental data. By using Marcus theory of electron transfer in polar media, we demonstrate the inability of the hypothesis of electrostatic repulsions to explain the increase of electron transfer rate on increase of ion concentration in media due to elimination of the repulsion of similar charges. The real reason for the increase of the first order rate constant in some oxidation-reduction reactions between proteins, as shown in the present work, is a decrease of the media reorganization energy resulting in decrease of activation energy for oxidation-reduction reactions.

Theoretical Study of DNA Damage Recognition via Electron Transfer from the [4Fe-4S] Complex of MutY

The mechanism of site-specific recognition of DNA by proteins has been a long-standing issue. The DNA glycosylase MutY, for instance, must find the rare 8-oxoguanine-adenine mismatches among the large number of basepairs in the DNA. This protein has a [4Fe-4S] cluster, which is highly conserved in species as diverse as Escherichia Coli and Homo sapiens. The mixed-valent nature of this cluster suggests that charge transfer may play a role in MutY's function. We have studied the energetics of the charge transfer in Bacillus stearothermophilus MutY-DNA complex using multiscale calculation including density functional theory and molecular dynamics. The [4Fe-4S] cluster in MutY is found to undergo 2+ to 3+ oxidation when coupling to DNA through hole transfer, especially when MutY is near an oxoguanine modified base (oxoG). Employing the Marcus theory for electron transfer, we find near optimal Frank-Condon factors for electron transfer from MutY to oxoguanine modified base. MutY has modest selectivity for oxoguanine over guanine due to the difference in oxidation potential. The tunneling matrix element is significantly reduced with the mutation R149W, whereas the mutation L154F reduces the tunneling matrix element as well as the Frank-Condon factor. Both L154F and R149W mutations are known to dramatically reduce or eliminate repair efficiency. We suggest a scenario where the charge transfer leads to a stabilization of the specific binding conformation, which is likely the recognition mode, thus enabling it to find the damaged site efficiently.

Long-lived charge-separated states of simple electron donor-acceptor dyads using porphyrins and phthalocyanines

Control of electron-transfer processes is described for a number of electron donor-acceptor dyads containing porphyrins or phthalocyanines as models for the photosynthetic reaction center. The rates for intramolecular electron transfer in the dyads are controlled by the driving force and reorganization energy of electron transfer. The small reorganization energy of electron transfer reactions and large driving force of charge recombination are required to form long-lived charge-separated states. A directly linked zinc chlorin-fullerene dyad, especially, has the longest lifetime of charge-separated state at 120 s at -150 °C, which is a much longer lifetime and higher energy than those of natural photosynthetic reaction centers. On the other hand, the charge-separated states of the phthalocyanine-based donor-acceptor dyads (silicon phthalocyanine-fullerene, and zinc phthalocyanine-perylenebisimide) are short-lived since charge recombination forms the low-lying triplet excited state of the chromophore. The energy of the charge-separated state of a zinc phthalocyanine-perylenebisimide dyad is decreased by binding of metal ions to the radical anion moiety in order to be lower than the triplet excited state. This results in formation of a long-lived charge-separated state. The mechanistic viability of formation of long-lived charge-separated states is demonstrated by a variety of examples based on the Marcus theory of electron transfer.

Reaction coordinate in electron transfer: What physical quantity should we use for it?

In the Marcus theory of electron transfer the reaction coordinate due to solvent motion plays a central role. In 1991,Zhu and Rasaiah [J. Chem. Phys.95, 3325 (1991)] tried to define the reaction coordinate in terms of the solvent orientational polarization function. However, their definition is not consistent with the associated free energy curves as functions of the reaction coordinate. The appropriate definition of the reaction coordinate and the associated free energy curves are presented.

Effect of Size on Electron Transfer to Silver Clusters

The electronic properties of silver clusters containing up to eight atoms and adsorbed to a positive kink on the (001) surface of silver bromide in contact with aqueous solution are calculated. The necessary reorganization energies and standard free energies of reaction are computed so that the activation energy for transferring an electron from a reducing molecule in solution to silver clusters could be determined with diabatic Marcus electron transfer theory for different cluster sizes. The activation energy oscillates between odd- and even-sized neutral clusters and decreases with increasing size. In the presence of aqueous silver ions, a minimum cluster size of four atoms can be deduced for electron transfer from several reducing agents. These calculated results are discussed in relation to many experimental results. The calculations involve a self-consistent density functional method used to obtain solid state properties of the adsorbed silver clusters and a continuum solvation model (IEF-PCM) used t...

Theoretically Rational Designs of Transport Organic Semiconductors Based on Heteroacenes

AbstractA Marcus electron transfer theory coupled with an incoherent polaron hopping and charge diffusion model in combining with first‐principle quantum chemistry calculation was applied to investigating the effects of heteroatom on the intermolecular charge transfer rate for a series of heteroacene molecules. The influences of intermolecular packing and charge reorganization energy were discussed. It was found that the sulphur and nitrogen substituted heteroacenes were intrinsically hole‐transporting materials due to the reduced hole reorganization energy and the enhanced overlap between HOMOs. For the oxygen‐substituted heteroacene, it was found that both the electronic couplings and the reorganization energies for holes and electrons were comparative, indicating the application potential of ambipolar devices. Most interestingly, for the boron‐substituted heteroacenes, theoretical calculations predicted a promising electron‐transport material, which is rare for organic materials. These findings provide insights into rationally designing organic semiconductors with specific properties.

First Principles Study of Alkali-Tyrosine Complexes: Alkali Solvation and Redox Properties.

The oxidation of alkali-tyrosinate to radical alkali-tyrosine in aqueous solution is studied using ab initio Car-Parrinello molecular dynamics (CPMD). The aim is to investigate the cation-π interactions between alkali cations M and the aromatic ring of tyrosine, in gas phase and in aqueous solution, using the influence of the cation M on the reaction M(+)(Tyr(-)) → M(+)(Tyr(∗)) + e(-) as a probe. To this end, we calculate the redox potential and the reorganization free energy using a CPMD-based method derived from the Marcus theory of electron transfer. We discuss the redox properties of Tyr, Na(+)(Tyr), and K(+)(Tyr), in reduced and oxidized states, by analyzing selected interatomic distances, coordination numbers, and charge populations. Our results confirm the known inversion in the relative stabilities of Na(+)(Tyr) and K(+)(Tyr) in going from gas phase to solution and point to a stronger cation-π affinity of K(+) in solution.

Theoretical comparative studies of charge mobilities for molecular materials: Pet versus bnpery

Charge mobility is the most important issue for organic semiconductors. We calculate the electron and hole mobilities for prototypical polycyclic hydrocarbon molecules, perylothiophene (pet) and benzo( g, h, i)-perylene (bnpery) using Marcus electron transfer theory coupled with a diabatic model and a homogeneous diffusion assumption to obtain the charge mobility. The first-principles DFT calculations show that the hole mobility is about an order of magnitude higher than the electron mobility in pet. However, we find that for bnpery, the electron and hole transports are balanced, namely, very close in mobility, indicating the possible application in light-emitting field-effect transistor. The crystal packing effects on the frontier orbital coupling are found to be essential to understand such differences in transport behaviors.

Influences of Crystal Structures and Molecular Sizes on the Charge Mobility of Organic Semiconductors: Oligothiophenes

Both crystal packing and molecular size have strong influences on the charge mobility for organic semiconductors. The crystal structures for oligothiophene (nT) can be roughly classified into two types: the Z = 2 (two molecules in one unit cell) or high temperature (HT) phase and the Z = 4 or low temperature (LT) phase. Through first-principles calculations within the Marcus electron transfer theory coupled with random walk simulation for room temperature charge diffusion constants, we found that the hole mobility of the HT phase is about 3–4 times larger than that of the LT phase because the molecular packing in the HT phase favors the hole transfer (i.e., the frontier orbital wave function phases of the dimer are constructive, which tends to maximize the overlap), while for the LT phase, the molecules are packed in a position that reduces the intermolecular orbital overlap due to phase cancellation. As the molecular size increases from 2T to 8T, the hole mobility tends to increase because the reorganiza...

Face‐to‐Face Pacman‐Type Porphyrin–Fullerene Dyads: Design, Synthesis, Charge‐Transfer Interactions, and Photophysical Studies

Pacman-type face-to-face zinc-porphyrin-fullerene dyads have been newly synthesized and studied. Owing to the close proximity of the donor and acceptor entities, strong pi-pi intramolecular interactions between the porphyrin and fullerene entities resulted in modulating the spectral and electrochemical properties of the dyads. New absorption and emission bands that correspond to the charge-transfer interactions were observed in the near-IR region. Time-resolved transient absorption studies revealed efficient photoinduced electron transfer from the singlet excited porphyrin to the fullerene entity. The rate constants for photoinduced electron transfer are analyzed in terms of the Marcus theory of electron transfer, which afforded a large electron coupling matrix element (V=140 cm(-1)) for the face-to-face dyads. As a consequence of the large charge-recombination driving force in the Marcus inverted region, a relatively long lifetime of the charge-separated state has been achieved.

Fundamental Electron-Transfer Properties of Non-heme Oxoiron(IV) Complexes

Electron-transfer kinetics for the reduction of non-heme oxoiron(IV) complexes by a series of ferrocene derivatives were examined in deaerated acetonitrile, and the resulting data were evaluated in light of the Marcus theory of electron transfer to determine the reorganization energies of electron transfer and the one-electron reduction potentials of non-heme oxoiron(IV) complexes. The electron-transfer properties of non-heme oxoiron(IV) complexes are featured by the larger reorganization energies of electron transfer and the lower one-electron reduction potentials as compared with those of heme oxoiron(IV) complexes.

Photoinduced bimolecular electron transfer kinetics in small unilamellar vesicles

Photoinduced electron transfer (ET) from N,N-dimethylaniline to some coumarin derivatives has been studied in small unilamellar vesicles (SUVs) of the phospholipid, DL-alpha-dimyristoyl-phosphatidylcholine, using steady-state and time-resolved fluorescence quenching, both below and above the phase transition temperature of the vesicles. The primary interest was to examine whether Marcus inversion [H. Sumi and R. A. Marcus, J. Chem. Phys. 84, 4894 (1986)] could be observed for the present ET systems in these organized assemblies. The influence of the topology of SUVs on the photophysical properties of the reactants and consequently on their ET kinetics has also been investigated. Absorption and fluorescence spectral data of the coumarins in SUVs and the variation of their fluorescence decays with temperature indicate that the dyes are localized in the bilayer of the SUVs. Time-resolved area normalized emission spectra analysis, however, reveals that the dyes are distributed in two different microenvironments in the SUVs, which we attribute to the two leaflets of the bilayer, one toward bulk water and the other toward the inner water pool. The microenvironments in the two leaflets are, however, not indicated to be that significantly different. Time-resolved anisotropy decays were biexponential for all the dyes in SUVs, and this has been interpreted in terms of the compound motion model according to which the dye molecules can experience a fast wobbling-in-cone type of motion as well as a slow overall rotating motion of the cone containing the molecule. The expected bimolecular diffusion-controlled rates in SUVs, as estimated by comparing the microviscosities in SUVs (determined from rotational correlation times) and that in acetonitrile solution, are much slower than the observed fluorescence quenching rates, suggesting that reactant diffusion (translational) does not play any role in the quenching kinetics in the present systems. Accordingly, clear inversions are observed in the correlation of the fluorescence quenching rate constants k(q) with the free energy change, DeltaG(0) of the reactions. However, the coumarin dyes, C152 and C481 (cf. Scheme 1), show unusually high k(q) values and high activation barriers, which is not expected from Marcus ET theory. This unusual behavior is explained on the basis of participation of the twisted intramolecular charge transfer states of these two dyes in the ET kinetics.

Theoretical modelling of carrier transports in molecular semiconductors: molecular designof triphenylamine dimer systems

Charge transport in molecular systems and biosystems can be different from that ininorganic, rigid semiconductors. The electron–nuclear motion couplings play animportant role in the former case. We have developed a theoretical scheme toemploy the Marcus electron transfer theory coupled with a direct diabatic dimermodel and the Brownian diffusion assumption to predict the carrier mobility formolecular materials. For triphenylamine, a typical molecular transport material, thedesign strategies regarding the formation a cyclic or a linear dimer are evaluatedfrom theoretical calculations for the carrier mobility. We made a comparisonbetween the mobility and the electrical polarizability. It is found that in the case oftriphenylamine dimer, these two quantities have different trends. The fact that themacrocycle possesses higher mobility but lower polarizability than the linear chainis due to the difference in the reorganization energy. The theoretical predictedtemperature dependences are analysed within the hopping mechanism. The calculatedroom-temperature mobilities are in reasonable agreement with experimental values.