Use of Modern Electron Transfer Theories To Determine Electronic Coupling Matrix Elements in Intramolecular Systems

Photoinduced interfacial electron transfer from perovskite quantum dots to molecular acceptors for solar cells

Bandgap-engineered inorganic and hybrid halide perovskite (HP) films, nanocrystals, and quantum dots (PQDs) are promising for solar cells. Fluctuations of photoinduced electron transfer (PET) rates affect the interfacial charge separation efficiencies of such solar cells. Electron donor- or acceptor-doped perovskite samples help analyze PET and harvest photogenerated charge carriers efficiently. Therefore, PET in perovskite-based donor-acceptor (D-A) systems has received considerable attention. We analyzed the fluctuations of interfacial PET from MAPbBr₃ or CsPbBr₃ PQDs to classical electron acceptors such as 7,7,8,8-tetracyanoquinodimethane (TCNQ) and 1,2,4,5-tetracyanobenzene (TCNB) at single-particle and ensemble levels. The significantly negative Gibbs free energy changes of PET estimated from the donor-acceptor redox potentials, the donor-acceptor sizes, and the solvent dielectric properties help us clarify the PET in the above D-A systems. The dynamic nature of PET is apparent from the decrease in photoluminescence (PL) lifetimes and PL photocounts of PQDs with an increase in the acceptor concentrations. Also, the acceptor radical anion spectrum helps us characterize the charge-separated states. Furthermore, the PL blinking time and PET rate fluctuations (10⁸ to 10⁷ s^-1) provide us with single-molecule level information about interfacial PET in perovskites.

Functional and protective hole hopping in metalloenzymes

Electrons can tunnel through proteins in microseconds with a modest release of free energy over distances in the 15 to 20 Å range. To span greater distances, or to move faster, multiple charge transfers (hops) are required. When one of the reactants is a strong oxidant, it is convenient to consider the movement of a positively charged "hole" in a direction opposite to that of the electron. Hole hopping along chains of tryptophan (Trp) and tyrosine (Tyr) residues is a critical function in several metalloenzymes that generate high-potential intermediates by reactions with O2 or H2O2, or by activation with visible light. Examination of the protein structural database revealed that Tyr/Trp chains are common protein structural elements, particularly among enzymes that react with O2 and H2O2. In many cases these chains may serve a protective role in metalloenzymes by deactivating high-potential reactive intermediates formed in uncoupled catalytic turnover.

Quantum coherence in ultrafast photo-driven charge separation

Coherent interactions are prevalent in photodriven processes, ranging from photosynthetic energy transfer to superexchange-mediated electron transfer, resulting in numerous studies aimed towards identifying and understanding these interactions. A key motivator of this interest is the non-statistical scaling laws that result from coherently traversing multiple pathways due to quantum interference. To that end, we employed ultrafast transient absorption spectroscopy to measure electron transfer in two donor-acceptor molecular systems comprising a p-(9-anthryl)-N,N-dimethylaniline chromophore/electron donor and either one or two equivalent naphthalene-1,8:4,5-bis(dicarboximide) electron acceptors at both ambient and cryogenic temperatures. The two-acceptor compound shows a statistical factor of 2.1 ± 0.2 rate enhancement at room temperature and a non-statistical factor of 2.6 ± 0.2 rate enhancement at cryogenic temperatures, suggesting correlated interactions between the two acceptors with the donor and with the bath modes. Comparing the charge recombination rates indicates that the electron is delocalized over both acceptors at low temperature but localized on a single acceptor at room temperature. These results highlight the importance of shielding the system from bath fluctuations to preserve and ultimately exploit the coherent interactions.

Blinking Suppression in Highly Excited CdSe/ZnS Quantum Dots by Electron Transfer under Large Positive Gibbs (Free) Energy Change

Semiconductor quantum dots with stable photoluminescence are necessary for next generation optoelectronic and photovoltaic devices. Photoluminescence intensity fluctuations of cadmium and lead chalcogenide quantum dots have been extensively investigated since the first observation of blinking in CdSe nanocrystals in 1996. In a quantum dot, blinking originates from stochastic photocharging, nonradiative Auger recombination, and delayed neutralization. So far, blinking is suppressed by defect passivation, electron transfer, and shell preparation, but without any deep insight into free energy change of electron transfer. We report real-time detection of significant blinking suppression for CdSe/ZnS quantum dots exposed to N, N-dimethylaniline, which is accompanied by a considerable increase in the time-averaged photoluminescence intensity of quantum dots. Although the Gibbs (free) energy change (Δ G_et = +2.24 eV), which is estimated electrochemically and from density functional theory calculations, is unfavorable for electron transfer from N, N-dimethylaniline to a quantum dot in the minimally excited (band-edge) state, electron transfer is obvious when a quantum dot is highly excited. Nonetheless, Δ G_et crosses from the positive to negative scale as the solvent dielectric constant exceeds 5, favoring electron transfer from N, N-dimethylaniline to a quantum dot excited to the band-edge state. Based on single-molecule photoluminescence and ensemble electron transfer studies, we assign blinking suppression to the transfer of an electron from N, N-dimethylaniline to the hot hole state of a quantum dot. In addition to blinking suppression by electron transfer, complete removal of blinking is limited by short-living OFF states induced by the negative trion.

Coherent exciton-vibrational dynamics and energy transfer in conjugated organics

Coherence, signifying concurrent electron-vibrational dynamics in complex natural and man-made systems, is currently a subject of intense study. Understanding this phenomenon is important when designing carrier transport in optoelectronic materials. Here, excited state dynamics simulations reveal a ubiquitous pattern in the evolution of photoexcitations for a broad range of molecular systems. Symmetries of the wavefunctions define a specific form of the non-adiabatic coupling that drives quantum transitions between excited states, leading to a collective asymmetric vibrational excitation coupled to the electronic system. This promotes periodic oscillatory evolution of the wavefunctions, preserving specific phase and amplitude relations across the ensemble of trajectories. The simple model proposed here explains the appearance of coherent exciton-vibrational dynamics due to non-adiabatic transitions, which is universal across multiple molecular systems. The observed relationships between electronic wavefunctions and the resulting functionalities allows us to understand, and potentially manipulate, excited state dynamics and energy transfer in molecular materials.

Electron Transfer Rate Maxima at Large Donor-Acceptor Distances

Because of their low mass, electrons can transfer rapidly over long (>15 Å) distances, but usually reaction rates decrease with increasing donor-acceptor distance. We report here on electron transfer rate maxima at donor-acceptor separations of 30.6 Å, observed for thermal electron transfer between an anthraquinone radical anion and a triarylamine radical cation in three homologous series of rigid-rod-like donor-photosensitizer-acceptor triads with p-xylene bridges. Our experimental observations can be explained by a weak distance dependence of electronic donor-acceptor coupling combined with a strong increase of the (outer-sphere) reorganization energy with increasing distance, as predicted by electron transfer theory more than 30 years ago. The observed effect has important consequences for light-to-chemical energy conversion.

Fluoride binding to an organoboron wire controls photoinduced electron transfer

We demonstrate that the rates for long-range electron transfer can be controlled actively by tight anion binding to a rigid rod-like molecular bridge. Electron transfer from a triarylamine donor to a photoexcited Ru(bpy)32+ acceptor (bpy = 2,2'-bipyridine) across a 2,5-diboryl-1,4-phenylene bridge occurs within less than 10 ns in CH2Cl2 at 22 °C. Fluoride anions bind with high affinity to the organoboron bridge due to strong Lewis base/Lewis acid interactions, and this alters the electronic structure of the bridge drastically. Consequently, a large tunneling barrier is imposed on photoinduced electron transfer from the triarylamine to the Ru(bpy)32+ complex and hence this process occurs more than two orders of magnitude more slowly, despite the fact that its driving force is essentially unaffected by fluoride addition. Electron transfer rates in proteins could potentially be regulated via a similar fundamental principle, because interactions between charged amino acid side chains and counter-ions can modulate electronic couplings between distant redox partners. In artificial donor-bridge-acceptor compounds, external stimuli have been employed frequently to control electron transfer rates, but the approach of exploiting strong Lewis acid/Lewis base interactions to regulate the tunneling barrier height imposed by a rigid rod-like molecular bridge is conceptually novel and broadly applicable, because it is largely independent of the donor and the acceptor, and because the effect is not based on a change of the driving-force for electron transfer. The principle demonstrated here can potentially be used to switch between conducting and insulating states of molecular wires between electrodes.

Electron transfer triggered by optical excitation of phenothiazine-tris(meta-phenylene-ethynylene)-(tricarbonyl)(bpy)(py)rhenium(I)

We have investigated excited-state electron transfer in a donor-bridge-acceptor complex containing phenothiazine (PTZ) linked via tris(meta-phenylene-ethynylene) to a tricarbonyl(bipyridine)(pyridine)Re(I) unit. Time-resolved luminescence experiments reveal two excited-state (*Re) decay regimes, a multiexponential component with a mean lifetime of 2.7 ns and a longer monoexponential component of 530 ns in dichloromethane solution. The faster decay is attributed to PTZ → *Re electron transfer in a C-shaped PTZ-bridge-Re conformer (PTZ-Re ≈ 7.5 Å). We assign the longer lifetime, which is virtually identical to that of free *Re, to an extended conformer (PTZ-Re > 20 Å). The observed biexponential *Re decay requires that interconversion of PTZ-bridge-Re conformers be slower than 10(6) s(-1).

Electron flow through metalloproteins

Electron transfers in photosynthesis and respiration commonly occur between metal-containing cofactors that are separated by large molecular distances. Understanding the underlying physics and chemistry of these biological electron transfer processes is the goal of much of the work in our laboratories. Employing laser flash-quench triggering methods, we have shown that 20A, coupling-limited Fe(II) to Ru(III) and Cu(I) to Ru(III) electron tunneling in Ru-modified cytochromes and blue copper proteins can occur on the microsecond timescale both in solutions and crystals; and, further, that analysis of these rates suggests that distant donor-acceptor electronic couplings are mediated by a combination of sigma and hydrogen bonds in folded polypeptide structures. Redox equivalents can be transferred even longer distances by multistep tunneling, often called hopping, through intervening amino acid side chains. In recent work, we have found that 20A hole hopping through an intervening tryptophan is several hundred-fold faster than single-step electron tunneling in a Re-modified blue copper protein.

Theoretical characterization of the structural and hole transport dynamics in liquid-crystalline phthalocyanine stacks

We present a joint molecular dynamics (MD)/kinetic Monte Carlo (KMC) study aimed at the atomistic description of charge transport in stacks of liquid-crystalline tetraalkoxy-substituted, metal-free phthalocyanines. The molecular dynamics simulations reproduce the major structural features of the mesophases, in particular, a phase transition around 340 K between the rectangular and hexagonal phases. Charge transport simulations based on a Monte Carlo algorithm show an increase by 2 orders of magnitude in the hole mobility when accounting for the rotational and translational dynamics. The results point to the formation of dynamical structural defects along the columns.

Electron Flow through Proteins

Electron transfers in photosynthesis and respiration commonly occur between metal-containing cofactors that are separated by large molecular distances. Employing laser flash-quench triggering methods, we have shown that 20-Å, coupling-limited Fe(II) to Ru(III) and Cu(I) to Ru(III) electron tunneling in Ru-modified cytochromes and blue copper proteins can occur on the microsecond timescale both in solutions and crystals. Redox equivalents can be transferred even longer distances by multistep tunneling, often called hopping, through intervening amino acid side chains. Our work has established that 20-Å hole hopping through an intervening tryptophan is two orders of magnitude faster than single-step electron tunneling in a Re-modified blue copper protein.

Experimental evidence for water mediated electron transfer through bis-amino acid donor-bridge-acceptor oligomers

This work compares the photoinduced unimolecular electron transfer rate constants for two different solute molecules (D-SSS-A and D-SRR-A) in water and DMSO solvents. The D-SSS-A solute has a cleft between the electron donor and acceptor units, which is able to contain a water molecule but is too small for DMSO. The rate constant for D-SSS-A in water is significantly higher than that for D-SRR-A, which lacks a cleft, and significantly higher for either solute in DMSO. The enhancement of the rate constant is explained by an electron tunneling pathway that involves water molecule(s).

Charge hopping in organic semiconductors: influence of molecular parameters on macroscopic mobilities in model one-dimensional stacks

We present a Monte Carlo approach to estimate how molecular parameters impact hopping rates and charge mobilities in organic pi-conjugated materials. Our goal is to help in establishing structure-properties relationships. As a first step, our approach is illustrated by considering a model system made of a one-dimensional array of pentacene molecules; we describe the variations of the electron-transfer rates and of the resulting charge mobilities as a function of electric field and of the presence of molecular disorder and traps. The results highlight that there is no direct relationship between the degree of spatial overlap among adjacent molecules and charge mobility.

Two-state model based on the block-localized wave function method

The block-localized wave function (BLW) method is a variant of ab initio valence bond method but retains the efficiency of molecular orbital methods. It can derive the wave function for a diabatic (resonance) state self-consistently and is available at the Hartree-Fock (HF) and density functional theory (DFT) levels. In this work we present a two-state model based on the BLW method. Although numerous empirical and semiempirical two-state models, such as the Marcus-Hush two-state model, have been proposed to describe a chemical reaction process, the advantage of this BLW-based two-state model is that no empirical parameter is required. Important quantities such as the electronic coupling energy, structural weights of two diabatic states, and excitation energy can be uniquely derived from the energies of two diabatic states and the adiabatic state at the same HF or DFT level. Two simple examples of formamide and thioformamide in the gas phase and aqueous solution were presented and discussed. The solvation of formamide and thioformamide was studied with the combined ab initio quantum mechanical and molecular mechanical Monte Carlo simulations, together with the BLW-DFT calculations and analyses. Due to the favorable solute-solvent electrostatic interaction, the contribution of the ionic resonance structure to the ground state of formamide and thioformamide significantly increases, and for thioformamide the ionic form is even more stable than the covalent form. Thus, thioformamide in aqueous solution is essentially ionic rather than covalent. Although our two-state model in general underestimates the electronic excitation energies, it can predict relative solvatochromic shifts well. For instance, the intense pi-->pi* transition for formamide upon solvation undergoes a redshift of 0.3 eV, compared with the experimental data (0.40-0.5 eV).

Competing Electron-Transfer Pathways in Hydrocarbon Frameworks: Short-Circuiting Through-Bond Coupling by Nonbonded Contacts in Rigid U-Shaped Norbornylogous Systems Containing a Cavity-Bound Aromatic Pendant Group

This work explores electron transfer through nonbonded contacts in two U-shaped DBA molecules 1DBA and 2DBA by measuring electron-transfer rates in organic solvents of different polarities. These molecules have identical U-shaped norbornylogous frameworks, 12 bonds in length and with diphenyldimethoxynaphthalene (DPMN) donor and dicyanovinyl (DCV) acceptor groups fused at the ends. The U-shaped cavity of each molecule contains an aromatic pendant group of different electronic character, namely p-ethylphenyl, in 1DBA, and p-methoxyphenyl, in 2DBA. Electronic coupling matrix elements, Gibbs free energy, and reorganization energy were calculated from experimental photophysical data for these compounds, and the experimental results were compared with computational values. The magnitude of the electronic coupling for photoinduced charge separation, /V(CS)/, in 1DBA and 2DBA were found to be 147 and 274 cm(-1), respectively, and suggests that the origin of this difference lies in the electronic nature of the pendant aromatic group and charge separation occurs by tunneling through the pendant group, rather than through the bridge. 2DBA, but not 1DBA, displayed charge transfer (CT) fluorescence in nonpolar and weakly polar solvents, and this observation enabled the electronic coupling for charge recombination, /V(CR)/, in 2DBA to be made, the magnitude of which is approximately 500 cm(-1), significantly larger than that for charge separation. This difference is explained by changes in the geometry of the molecule in the relevant states; because of electrostatic effects, the donor and acceptor chromophores are about 1 A closer to the pendant group in the charge-separated state than in the locally excited state. Consequently the through-pendant-group electronic coupling is stronger in the charge-separated state--which controls the CT fluorescence process--than in the locally excited state--which controls the charge separation process. The magnitude of /V(CR)/ for 2DBA is almost 2 orders of magnitude greater than that in DMN-12-DCV, having the same length bridge as for the former molecule, but lacking a pendant group. This result unequivocally demonstrates the operation of the through-pendant-group mechanism of electron transfer in the pendant-containing U-shaped systems of the type 1DBA and 2DBA.

Free energy, entropy and volume of activation for electron transfer reactions in a polar solvent

A continuum theory with account of cavity size fluctuations is employed to study free energy, volume and entropy of activation for nonadiabatic electron transfer (ET) reactions in polar solvents. By using a two-sphere cavity description, model calculations are performed for charge separation and recombination processes in acetonitrile under ambient conditions. It is found that the cavity size at the transition state varies with the free energy of reaction as well as with the thermodynamic conditions. In contrast to the Marcus theory predictions, the volume and entropy of activation show a monotonic behavior with the free energy of reaction and a strong correlation with each other. For example, for a given ET process, the volume and entropy of activation have the same sign. Their values for the charge separation and recombination processes are opposite in sign. These findings are in good qualitative agreement with measurements.

Temperature- and Pressure-Dependence of the Outer-Sphere Reorganization Free Energy for Electron Transfer Reactions: A Continuum Approach

The outer-sphere reorganization free energy for electron-transfer reactions in polar solvents and its variations with temperature and pressure are studied in the dielectric continuum framework by extending the recent fluctuating cavity description [J. Chem. Phys. 2005, 123, 014504]. The diabatic free energies are obtained as a function of three variables, i.e., radii of two spherical cavities for the donor and acceptor moieties of an electron-transfer complex and a solvent coordinate that gauges an arbitrary configuration of solvent orientational polarization. Equilibrium cavities relevant to the reactant and product states are determined via the variational principle. This incorporates cavity size readjustment accompanying electron transfer and related electrostrictive effects. Another important consequence of the variational determination of equilibrium cavities is that their size depends on thermodynamic conditions. The application of the theoretical formulation presented here to electron self-exchange shows that in contrast to the prediction of the standard Marcus theory, the solvent reorganization free energy decreases with temperature. This is in excellent accord with a recent experiment on a mixed valence dinuclear iron complex in acetonitrile [J. Phys. Chem. A 1999, 103, 7888]. It is also found that electrostriction makes a significant contribution to outer-sphere reorganization. Model calculations for the dinuclear iron complex system show that about 25-30% of the total solvent reorganization free energy arises from cavity size changes, while solvent repolarization is responsible for the rest.

Ab Initio Characterization of Electron Transfer Coupling in Photoinduced Systems: Generalized Mulliken−Hush with Configuration-Interaction Singles

To calculate electronic couplings for photoinduced electron transfer (ET) reactions, we propose and test the use of ab initio quantum chemistry calculation for excited states with the generalized Mulliken-Hush (GMH) method. Configuration-interaction singles (CIS) is proposed to model the locally excited (LE) and charge-transfer (CT) states. When the CT state couples with other high lying LE states, affecting coupling values, the image charge approximation (ICA), as a simple solvent model, can lower the energy of the CT state and decouple the undesired high-lying local excitations. We found that coupling strength is weakly dependent on many details of the solvent model, indicating the validity of the Condon approximation. Therefore, a trustworthy value can be obtained via this CIS-GMH scheme, with ICA used as a tool to improve and monitor the quality of the results. Systems we tested included a series of rigid, sigma-linked donor-bridge-acceptor compounds where "through-bond" coupling has been previously investigated, and a pair of molecules where "through-space" coupling was experimentally demonstrated. The calculated results agree well with experimentally inferred values in the coupling magnitudes (for both systems studied) and in the exponential distance dependence (for the through-bond series). Our results indicate that this new scheme can properly account for ET coupling arising from both through-bond and through-space mechanisms.

Analysis of Charge-Transfer Absorption and Emission Spectra on an Absolute Scale: Evaluation of Free Energies, Matrix Elements, and Reorganization Energies

The relationship between the absorption and emission spectra of the charge-transfer complexes formed between a series of methyl-substituted benzene donors with 1,2,4,5-tetracyanobenzene as acceptor in 1,2-dichloroethane was examined in detail. The association constants for charge-transfer complex formation and the emission quantum yields for these complexes were used to place the experimental absorption and emission spectra on absolute scales. The simultaneous analysis of these spectra is valid only when the Mulliken two-state model is justified. For several of the complexes included in this study the electron-transfer parameters, including the electronic coupling matrix elements, obtained from the analysis of the individual absorption and emission spectra are in close agreement. The simultaneous analysis of the combined absorption and emission spectra leads to a well-defined set of electron-transfer parameters for these complexes. In other complexes, where the two-state model does not apply because of the influence of localized excited states on the absorption spectrum, analysis of the absorption and emission spectra led to significantly different sets of electron-transfer parameters. It is demonstrated that the electronic coupling matrix elements are a very sensitive indicator of the influence of localized excited states on these spectra.

Competition between Superexchange-Mediated and Sequential Electron Transfer in a Bridged Donor-Acceptor System

The temperature- and solvent-dependence of photoinduced electron-transfer reactions in a porphyrin-based donor-bridge-acceptor (DBA) system is studied by fluorescence and transient absorption spectroscopy. Two competing processes occur: sequential and direct superexchange-mediated electron transfer. In a weakly polar solvent (2-methyltetrahydrofuran), only direct electron transfer from the excited donor to the appended acceptor is observed, and this process has weak temperature dependence. In polar solvents (butyronitrile and dimethylformamide), both processes are observed and the sequential electron transfer shows strong temperature dependence. In systems where both electron transfer processes are observed, the long-range superexchange-mediated process is more than two times faster than the sequential process, even though the donor-acceptor distance is significantly larger in the former case.

Dynamic nature of the intramolecular electronic coupling mediated by a solvent molecule: a computational study

We present a combined Molecular Dynamics/Quantum Chemical study of the solvent-mediated electronic coupling between an electron donor and acceptor in a C-clamp molecule. We characterize the coupling fluctuations due to the solvent motion for different solvents (acetonitrile, benzene, 1,3-diisopropyl-benzene) for the charge separation and the charge recombination processes. The time scale for solvent-induced coupling fluctuation is approximately 0.1 ps. The effect of these fluctuations on the observed rate is discussed using a recently developed theoretical model. We show that, while the microscopic charge transfer process is very complicated and its computational modeling very subtle, the macroscopic phenomenology can be captured by the standard models. Analyzing the contribution to the coupling given by different solvent orbitals, we find that many solvent orbitals mediate the electron transfer and that paths through different solvent orbitals can interfere constructively or destructively. A relatively small subset of substrate-solvent configurations dominate contributions to solvent-mediated coupling. This subset of configurations is related to the electronic structure of the C-clamp molecule.