Quantum effects in electron transfer reactions with strong electronic coupling

Symmetry Effects in Photoinduced Electron Transfer in Chlorin‐Quinone Dyads: Adiabatic Suppression in the Marcus Inverted Region

In donor–acceptor dyads undergoing photoinduced electron transfer (PET), a direction or pathway for electron movement is usually dictated by the redox properties and the separation distance between the donor and acceptor subunits, while the effect of symmetry is less recognized. We have designed and synthesized two isomeric donor–acceptor assemblies in which electronic coupling between donor and acceptor is altered by the orbital symmetry control with the reorganization energy and charge transfer exothermicity being kept unchanged. Analysis of the optical absorption and luminescence spectra, supported by the DFT and TD‐DFT calculations, showed that PET in these assemblies corresponds to the Marcus inverted region (MIR) and has larger rate for isomer with weaker electronic coupling. This surprising observation provides the first experimental evidence for theoretically predicted adiabatic suppression of PET in MIR, which unambiguously controlled solely by symmetry.

Reorganization energies and spectral densities for electron transfer problems in charge transport materials

Various contributions to the outer reorganization energy of an electron transfer system and their theoretical and computational aspects have been discussed.

Quantum effect of intramolecular high-frequency vibrational modes on diffusion-controlled electron transfer rate: From the weak to the strong electronic coupling regions

The Sumi-Marcus theory is extended by introducing two approaches to investigate electron transfer reactions from weak-to-strong electronic coupling regime. One of these approaches is the quantum R-matrix theory, useful for dealing with the intramolecular vibrational motions in the whole electronic coupling domain. The other is the split operator approach that is employed to solve the reaction-diffusion equation. The approaches are then applied to electron transfer in the Marcus inverted regime to investigate the nuclear tunneling effect on the long time rate and the survival probabilities. The numerical results illustrate that the adiabatic suppression obtained from the R-matrix approach is much smaller than that from the Landau-Zener theory whereas it cannot be predicted by the perturbation theory. The jointed effects of the electronic coupling and solvent relaxation time on the rates are also explored.

Semiclassical Treatment of Thermally Activated Electron Transfer in the Inverted Region under the Fast Dielectric Relaxation

The previously formulated semiclassical theory (Zhao, Liang, and Nakamura, J. Phys. Chem. A 2006, 110, 8204) is used to study electron transfer in the Marcus inverted case by considering multidimensional potential energy surfaces of donor and acceptor. The Zhu-Nakamura formulas of nonadiabatic transition in the case of Landau-Zener type are incorporated into the approach. The theory properly takes into account the nonadiabatic transition coupled with the nuclear tunneling and can cover the whole range from weak to strong coupling regime uniformly under the assumption of fast solvent relaxation. The numerical calculations are performed for the 12-dimensional model of shifted harmonic oscillators and demonstrate that the reaction rate with respect to the electronic coupling shows a maximum, confirming the adiabatic suppression in the strong coupling limit. The adiabatic suppression is dramatically reduced by the effect of nuclear tunneling compared to the case that the Landau-Zener formula is used. The possible extension and applications to the case of the slow solvent dynamics are discussed.

Semiclassical Treatment of Thermally Activated Electron Transfer in the Intermediate to Strong Electronic Coupling Regime under the Fast Dielectric Relaxation

The generalized nonadiabatic transition-state theory (NA-TST) (Zhao, Y.; et al. J. Chem. Phys. 2004, 121, 8854) is used to study electron transfer with use of the Zhu-Nakamura (ZN) formulas of nonadiabatic transition in the case of fast dielectric relaxation. The rate constant is expressed as a product of the well-known Marcus formula and a coefficient which represents the correction due to the strong electronic coupling. In the case of general multidimensional systems, the Monte Carlo approach is utilized to evaluate the rate by taking into account the multidimensionality of the crossing seam surface. Numerical demonstration is made by using a model system of a collection of harmonic oscillators in the Marcus normal region. The results are naturally coincident with the perturbation theory in the weak electronic coupling limit; while in the intermediate to strong electronic coupling regime where the perturbation theory breaks down the present results are in good agreement with those from the quantum mechanical flux-flux correlation function within the model of effective one-dimensional mode.

Femtosecond studies of electron dynamics at interfaces

A delocalized electron at a metal-dielectric interface interacts with the adlayer and spatially localizes or self-traps on the femtosecond time scale into what is termed a small polaron. The dynamics can be studied by two-photon photoemission. Theoretical and experimental analyses reveal the interaction energy and the lattice vibrational mode that mediates electron localization. These results contribute to a fundamental understanding of electron behavior in weakly bonded solids and can lead to a better understanding of carrier dynamics in many different systems, including organic light-emitting diodes.

Exactly solvable quantum model for electrochemical electron-transfer reactions

We consider electron exchange between a metal electrode and a solvated reactant coupled to a harmonic oscillator bath. In the wide-band approximation the time development of the occupation probability for the reactant orbital can be calculated explicitly. From the behavior at long times we derive an expression for the reaction rate that is valid for all strengths of the electronic interaction between the metal and the reactant. The rate constant is related to the scattering matrix for electron exchange between a metal substrate and a scanning tunneling microscope via an electroactive adsorbate.

Effect of protein dynamics on biological electron transfer

Computer simulations of the effect of protein dynamics on the long distance tunneling mediated by the protein matrix have been carried out for a Ru-modified (His 126) azurin molecule. We find that the tunneling matrix element is a sensitive function of the atomic configuration of the part of the protein matrix in which tunneling currents (pathways) are localized. Molecular dynamics simulations show that fluctuations of the matrix element can occur on a time scale as short as 10 fs. These short time fluctuations are an indication of a strong dynamic coupling of a tunneling electron to vibrational motions of the protein nuclear coordinates. The latter results in a modification of the conventional Marcus picture of electron transfer in proteins. The new element in the modified theory is that the tunneling electron is capable of emitting or absorbing vibrational energy (phonons) from the medium. As a result, some biological reactions may occur in an activationless fashion. An analytical theoretical model is proposed to account for thermal fluctuations of the medium in long distance electron transfer reactions. The model shows that, at long distances, the phonon-modified inelastic tunneling always dominates over the conventional elastic tunneling.