Vibrational Relaxations and Dephasing in Electron-Transfer Reactions

Electron transfer in a crystalline cytochrome with four hemes

Diffusion of electrons over distances on the order of 100 μm has been observed in crystals of a small tetraheme cytochrome (STC) from Shewanella oneidensis [J. Huang et al. J. Am. Chem. Soc. 142, 10459-10467 (2020)]. Electron transfer between hemes in adjacent subunits of the crystal is slower and more strongly dependent on temperature than had been expected based on semiclassical electron-transfer theory. We here explore explanations for these findings by molecular-dynamics simulations of crystalline and monomeric STC. New procedures are developed for including time-dependent quantum mechanical energy differences in the gap between the energies of the reactant and product states and for evaluating fluctuations of the electronic-interaction matrix element that couples the two hemes. Rate constants for electron transfer are calculated from the time- and temperature-dependent energy gaps, coupling factors, and Franck-Condon-weighted densities of states using an expression with no freely adjustable parameters. Back reactions are considered, as are the effects of various protonation states of the carboxyl groups on the heme side chains. Interactions with water are found to dominate the fluctuations of the energy gap between the reactant and product states. The calculated rate constant for electron transfer from heme IV to heme Ib in a neighboring subunit at 300 K agrees well with the measured value. However, the calculated activation energy of the reaction in the crystal is considerably smaller than observed. We suggest two possible explanations for this discrepancy. The calculated rate constant for transfer from heme I to II within the same subunit of the crystal is about one-third that for monomeric STC in solution.

Charge transport through DNA with energy-dependent decoherence

Modeling charge transport in DNA is essential to understand and control the electrical properties and develop DNA-based nanoelectronics. DNA is a fluctuating molecule that exists in a solvent environment, which makes the electron susceptible to decoherence. While knowledge of the Hamiltonian responsible for decoherence will provide a microscopic description, the interactions are complex and methods to calculate decoherence are unclear. One prominent phenomenological model to include decoherence is through fictitious probes that depend on spatially variant scattering rates. However, the built-in energy independence of the decoherence (E-indep) model overestimates the transmission in the bandgap and washes out distinct features inside the valence or conduction bands. In this study, we introduce a related model where the decoherence rate is energy-dependent (E-dep). This decoherence rate is maximum at energy levels and decays away from these energies. Our results show that the E-dep model allows for exponential transmission decay with the DNA length and maintains features within the bands' transmission spectra. We further demonstrate that we can obtain DNA conductance values within the experimental range. Our model can help study and design nanoelectronics devices that utilize weakly coupled molecular structures such as DNA.

Electron Transfer Rates in Solution: Toward a Predictive First Principle Approach

Using a very recently proposed theoretical model, electron transfer rates in solution are calculated from first principles for different donor-acceptor pairs in tetrahydrofuran. We show that this approach, which integrates tunneling effects into a classical treatment of solvent motion, is able to provide reliable rate constants and their temperature dependence, even in the case of highly exergonic reactions, where Marcus’ theory usually fails.

Electron Transfer Rates in Polar and Non-Polar Environments: a Generalization of Marcus' Theory to Include an Effective Treatment of Tunneling Effects

A multistep kinetic model in which solvent motion is treated in the framework of Marcus theory and the rates of the elementary electron transfer step are evaluated at full quantum mechanical level is proposed and applied to the calculation of the rates of intramolecular electron transfer reactions in rigidly spaced D-Br-A (D = 1,1'-biphenyl radical anion, Br = androstane) compounds, for five acceptors (A) in three organic solvents with different polarity. The calculated rates agree well with experimental ones, and their temperature dependence is almost quantitatively reproduced.

Reorganization Energies, Entropies, and Free Energy Surfaces for Electron Transfer

Reorganization energies for an intramolecular self-exchange electron-transfer reaction are calculated by quantum-classical molecular dynamics simulations in four solvents with varying polarity and at temperatures ranging from 250 to 350 K. The reorganization free energies for polar solvents decrease systematically with increasing temperature, indicating that they include substantial contributions from entropy changes. The variances of the energy gap between the reactant and product states have a major component that is relatively insensitive to temperature. Explanations are suggested for these observations, which appear to necessitate rethinking the free energy functions of a distributed coordinate that frequently are used in discussions of reaction dynamics.

Dynamics of the Excited State in Photosynthetic Bacterial Reaction Centers

In the initial charge-separation reaction of photosynthetic bacterial reaction centers, a dimer of strongly interacting bacteriochlorophylls (P) transfers an electron to a third bacteriochlorophyll (B_L). It has been suggested that light first generates an exciton state of the dimer and that an electron then moves from one bacteriochlorophyll to the other within P to form a charge-transfer state (P_L⁺P_M^-), which passes an electron to B_L. This scheme, however, is at odds with the most economical analysis of the spectroscopic properties of the reaction center and particularly with the unusual temperature dependence of the long-wavelength absorption band. The present paper explores this conflict with the aid of a simple model in which exciton and charge-transfer states are coupled to three vibrational modes. It then uses a similar model to show that the main experimental evidence suggesting the formation of P_L⁺P_M^- as an intermediate could reflect pure dephasing of vibrational modes that modulate stimulated emission.

The Dynamics of Hole Transfer in DNA

High-energy radiation and oxidizing agents can ionize DNA. One electron oxidation gives rise to a radical cation whose charge (hole) can migrate through DNA covering several hundreds of Å, eventually leading to irreversible oxidative damage and consequent disease. Understanding the thermodynamic, kinetic and chemical aspects of the hole transport in DNA is important not only for its biological consequences, but also for assessing the properties of DNA in redox sensing or labeling. Furthermore, due to hole migration, DNA could potentially play an important role in nanoelectronics, by acting as both a template and active component. Herein, we review our work on the dynamics of hole transfer in DNA carried out in the last decade. After retrieving the thermodynamic parameters needed to address the dynamics of hole transfer by voltammetric and spectroscopic experiments and quantum chemical computations, we develop a theoretical methodology which allows for a faithful interpretation of the kinetics of the hole transport in DNA and is also capable of taking into account sequence-specific effects.

Transient and Enduring Electronic Resonances Drive Coherent Long Distance Charge Transport in Molecular Wires

It is shown that the yields of oxidative damage observed in double-stranded DNA oligomers consisting of two guanines separated by adenine-thymine (A:T) _n bridges of various lengths are reliably accounted for by a multistep mechanism, in which transient and nontransient electronic resonances induce charge transport and solvent relaxation stabilizes the hole transfer products. The proposed multistep mechanism leads to results in excellent agreement with the observed yield ratios for both the short and the long distance regime; the almost distance independence of yield ratios for longer bridges ( n ≥ 3) is the consequence of the significant energy decrease of the electronic levels of the bridge, which, as the bridge length increases, become quasi-degenerate with those of the acceptor and donor groups (enduring resonance). These results provide significant guidelines for the design of novel DNA sequences to be employed in organic electronics.

Effects of Free Energy and Solvent on Rates of Intramolecular Electron Transfer in Organic Radical Anions

Rates of intramolecular electron transfer from a 1,1'-biphenylyl radical anion to six different acceptors on an androstane scaffold are examined with the aid of a theory that was developed recently to include effects of vibrational relaxations and dephasing. The electronic-interaction matrix element and other parameters needed for the theory are obtained by quantum-mechanical/molecular-mechanical simulations of the reactions in five solvents ranging from iso-octane to methyltetrahydrofuran. Intramolecular vibrational modes that are coupled to electron transfer are resolved in simulations in iso-octane and cyclohexane. The energies and coupling factors for these modes allow extension of the theory to incorporate transitions to and from excited vibrational levels. The calculated rates of electron transfer agree well with experimental measurements from the literature, except for reactions in which excited electronic states of the products become important.