Spectral analysis of electron transfer kinetics. I. Symmetric reactions

Correlating Interfacial Charge Transfer Rates with Interfacial Molecular Structure in the Tetraphenyldibenzoperiflanthene/C70 Organic Photovoltaic System

Organic photovoltaics (OPV) is an emerging solar cell technology that offers vast advantages such as low-cost manufacturing, transparency, and solution processability. However, because the performance of OPV devices is still disappointing compared to their inorganic counterparts, better understanding of how controlling the molecular-level morphology can impact performance is needed. To this end, one has to overcome significant challenges that stem from the complexity and heterogeneity of the underlying electronic structure and molecular morphology. In this Letter, we address this challenge in the context of the DBP/C₇₀ OPV system by employing a modular workflow that combines recent advances in electronic structure, molecular dynamics, and rate theory. We show how the wide range of interfacial pairs can be classified into four types of interfacial donor-acceptor geometries and find that the least populated interfacial geometry gives rise to the fastest charge transfer (CT) rates.

The dynamics of charge transfer with and without a barrier: A very simplified model of cyclic voltammetry

Using the Anderson-Holstein model, we investigate charge transfer dynamics between a molecule and a metal surface for two extreme cases. (i) With a large barrier, we show that the dynamics follow a single exponential decay as expected; (ii) without any barrier, we show that the dynamics are more complicated. On the one hand, if the metal-molecule coupling is small, single exponential dynamics persist. On the other hand, when the coupling between the metal and the molecule is large, the dynamics follow a biexponential decay. We analyze the dynamics using the Smoluchowski equation, develop a simple model, and explore the consequences of biexponential dynamics for a hypothetical cyclic voltammetry experiment.

Molecular dynamics and charge transport in organic semiconductors: a classical approach to modeling electron transfer

Organic photovoltaics (OPVs) are a promising carbon-neutral energy conversion technology, with recent improvements pushing power conversion efficiencies over 10%. A major factor limiting OPV performance is inefficiency of charge transport in organic semiconducting materials (OSCs). Due to strong coupling with lattice degrees of freedom, the charges form polarons, localized quasi-particles comprised of charges dressed with phonons. These polarons can be conceptualized as pseudo-atoms with a greater effective mass than a bare charge. We propose that due to this increased mass, polarons can be modeled with Langevin molecular dynamics (LMD), a classical approach with a computational cost much lower than most quantum mechanical methods. Here we present LMD simulations of charge transfer between a pair of fullerene molecules, which commonly serve as electron acceptors in OSCs. We find transfer rates consistent with experimental measurements of charge mobility, suggesting that this method may provide quantitative predictions of efficiency when used to simulate materials on the device scale. Our approach also offers information that is not captured in the overall transfer rate or mobility: in the simulation data, we observe exactly when and why intermolecular transfer events occur. In addition, we demonstrate that these simulations can shed light on the properties of polarons in OSCs. Much remains to be learned about these quasi-particles, and there are no widely accepted methods for calculating properties such as effective mass and friction. Our model offers a promising approach to exploring mass and friction as well as providing insight into the details of polaron transport in OSCs.

ESR-Investigations on the Dynamic Solvent Effects of Degenerate Electron Exchange Reactions. Part I: Cyanobenzenes

The rates of degenerate electron exchange (electron self-exchange) of various cyanobenzenes have been measured by EPR line broadening technique in nine different solvents at room temperature. The molecules studied comprise besides benzene-1,2-dicarbonitrile, benzene-1,4-dicarbonitrile and benzene-1,2,4,5-tetracarbonitrile, the two isomeric tricyanobenzenes, benzene-1,2,3-tricarbonitrile and benzene-1,2,4-tricarbonitrile, the anion radicals of which have not been characterized before.

The experimentally observed rates vary from 4.5 × 108 to 44.0 × 108 M−1 s−1 and show the pronounced dependence on the longitudinal relaxation times, τL, of the solvents. The solvent dynamical effect so manifested is confirmed with remarkable clarity using solvents spanning a wide range of τL-values, which comprise acetonitrile (0.2 ps) and o-dichlorobenzene (6.0 ps) at its extremes. The rate constants are compared with Marcus theory using the continuum model (CM) and the mean spherical approximation (MSA) for the outer sphere reorganization energies and Nelson’s method for the inner sphere reorganization energies. Furthermore, an estimation of the resonance splitting energies, V RP, is given based on the experimental rates.

Variation of the resonant transfer rate when passing from nonadiabatic to adiabatic electron transfer

Two competing theories are used for bridging the gap between the nonadiabatic and the deeply adiabatic electron transfer between symmetric parabolic wells. For the high friction limit, a simple analytic interpolation is proposed as a reasonable alternative to them, well-fitted to the results of numerical simulations. It provides a continuous description of the electron transfer rate in the whole range of variation of the nonadiabatic coupling between the diabatic states. For lower friction, the original theories are used for the same goal. With an increase in coupling, the cusped barrier transforms into the parabolic one. Correspondingly, the pre-exponent of the Arrhenius transfer rate first increases with coupling, then levels off approaching the "dynamic solvent effect" plateau but finally reduces reaching the limit of the adiabatic Kramers theory for the parabolic barrier. These changes proceeding with a reduction in the particle separation affect significantly the spatial dependence of the total transfer rate. When approaching the contact distance, the exact rate becomes smaller than in the theory of dynamical solvent effects and much smaller than predicted by perturbation theory (golden rule), conventionally used in photochemistry and electrochemistry.

Single molecule photon emission statistics for non-Markovian blinking models

The statistics of photon emission from a single molecule under continuous wave excitation are considered. In particular, we study stochastic model systems where photon emission rates evolve in time with non-Markovian dynamics. Our calculations are based on the recently introduced generalized optical Bloch equation (GBE) formalism, but with numerical complications beyond those seen in previous Markovian stochastic models. A spectral representation is introduced to facilitate the numerical solution of the GBE equations for these more challenging cases.

Theoretical analysis and computer simulation of fluorescence lifetime measurements. I. Kinetic regimes and experimental time scales

The configuration-controlled regime and the diffusion-controlled regime of conformation-modulated fluorescence emission are systematically studied for Markovian and non-Markovian dynamics of the reaction coordinate. A path integral simulation is used to model fluorescence quenching processes on a semiflexible chain. First-order inhomogeneous cumulant expansion in the configuration-controlled regime defines a lower bound for the survival probability, while the Wilemski-Fixman approximation in the diffusion-controlled regime defines an upper bound. Inclusion of the experimental time window of the fluorescence measurement adds another dimension to the two kinetic regimes and provides a unified perspective for theoretical analysis and experimental investigation. We derive a rigorous generalization of the Wilemski-Fixman approximation [G. Wilemski and M. Fixman, J. Chem. Phys. 60, 866 (1974)] and recover the 1/D expansion of the average lifetime derived by Weiss [G. H. Weiss, J. Chem. Phys. 80, 2880 (1984)].