Electron Transfer Properties from Atomistic Simulations and Density Functional Theory

Abstract

Marcus theory of electron transfer is the quintessential example of a successful theory in physical chemistry. In this paper, we describe the theoretical approach we have adopted to compute key parameters in Marcus theory. In our method, based on molecular dynamics simulations and density functional theory, the redox center and its environment are treated at the same level of theory. Such a detailed atomistic model describes specific solvent-solute interactions, such as hydrogen bonding, explicitly. The quantum chemical nature of our computations enables us to study the effect of chemical modifications of the redox centers and deals accurately with the electronic polarization of the environment. Based on results of previous work, we will illustrate that quantitative agreement with experiment can be obtained for differences in redox potentials and solvent reorganization energies for systems ranging from small organic compounds to proteins in solution. Keywords: Density functional theory · Electron transfer · Marcus theory · Molecular dynamicsatomistic models using density functional Theory (DFT). The quantum chemical nature of DFT allows the effects of chemical modifications of the redox centers to be studied without a need for prior knowledge or empirical parameterization. This can thus make our method truly predictive. A key feature of ET reactions, or redox reactions in general, is the crucial role played by the environment. Indeed, oxidation (reduction) potentials are the condensed phase equivalents of ionization potentials (electron affinities) in the gas phase, and these quantities can differ significantly. Our atomistic models explicitly include the environment ( e.g. solvent and/or protein) so that not only dielectric properties but also specific interactions, such as hydrogen bonding or conformational changes are taken explicitly into account. Furthermore, the environment is far from being a static spectator. Its fluctuations bring donor and acceptor sites in an energy resonant state, triggering ET, and its ability to relax after ET influences significantly the energetics. In order to probe these fluctuations and relaxations in our computational setup, molecular dynamics is employed to generate a sufficiently large number of representative configurations of solute and solvent.A major step in the understanding of ET reactions was the formulation by Marcus [16,17] of the rate of electron transfer (k ET ) as a simple function of the reaction free energy ( Δ G), the solvent reorganization energy ( λ ) and a proportionality constant ( κ ) depending on the quantum coupling between donor and acceptor states.The fruitful concept that underlies this formula is the assumed harmonic nature of the free energy surface with respect to the reaction coordinate of electron transfer. This restricts the validity of this formula to the range of systems that fall in the linear response regime, which might thus exclude systems that undergo significant changes in conformation or solvation upon electron transfer. Ulti...

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