Molecular dynamics simulations are presented for condensed-phase electron transfer (ET) systems where the electronic polarizability of both the solvent and the solute is incorporated. The solute polarizability is allowed to change with electronic transition. The results display notable deviation from the standard free energy parabolas of traditional ET theories. A new three-parameter ET model is applied, and the theory is shown to accurately model the free energy surfaces. This paper presents conclusive evidence that the traditional theory for the free energy barrier of ET reactions requires modification.

We develop a three-parameter model of electron transfer ͑ET͒ in condensed phases based on the Hamiltonian of a two-state solute linearly coupled to a harmonic, classical solvent mode with different force constants in the initial and final states ͑a classical limit of the quantum Kubo-Toyozawa model͒. The exact analytical solution for the ET free energy surfaces demonstrates the following features: ͑i͒ the range of ET reaction coordinates is limited by a one-sided fluctuation band, ͑ii͒ the ET free energies are infinite outside the band, and ͑iii͒ the free energy surfaces are parabolic close to their minima and linear far from the minima positions. The model provides an analytical framework to map physical phenomena conflicting with the Marcus-Hush two-parameter model of ET. Nonlinear solvation, ET in polarizable charge-transfer complexes, and configurational flexibility of donor-acceptor complexes are successfully mapped onto the model. The present theory leads to a significant modification of the energy gap law for ET reactions.

The temperature dependence of the solvent reorganization energy for intramolecular electron transfer (ET) in acetonitrile is measured experimentally and calculated theoretically. The Stokes shifts for the charge transfer, optical transitions of (tetrahydro-4H-thiopyran-4-ylidene)propanedinitrile indicate that the solvent reorganization energy for ET decreases with temperature, whereas dielectric continuum theories of solvent reorganization predict an increase with temperature. A molecular alternative to the continuum description is proposed that models the solvent as a fluid of polarizable, dipolar hard spheres. Good agreement between the molecular theory and experiment is achieved for both the ET reorganization energy and equilibrium energy gap. The negative temperature slope of the solvent reorganization energy is understood in terms of its dissection into components arising from different solute-solvent interaction potentials and contributions from different solvent modes activating ET. In the first approach, we consider reorganization energy components from permanent and induced dipoles. In the second dissection, the orientational and density solvent fluctuations are considered. The analyses show that the molecular nature of the solvent, embodied in density fluctuations and associated translational motions of the solvent permanent dipoles, is the principal source of the negative temperature dependence of the solvent reorganization energy. This component is absent in the continuum picture. Its absence is the reason the continuum model fails to correctly predict the sign of the reorganization energy temperature dependence in polar solvents.

Despite its diversity, life universally relies on a simple basic mechanism of energy transfer in its energy chains-hopping electron transport between centers of electron localization on hydrated proteins and redox cofactors. Since many such hops connect the point of energy input with a catalytic site where energy is stored in chemical bonds, the question of energy losses in (nearly activationless) electron hops, i.e., energetic efficiency, becomes central for the understanding of the energetics of life. We show here that standard considerations based on rules of Gibbs thermodynamics are not sufficient, and the dynamics of the protein and the protein-water interface need to be involved. The rate of electronic transitions is primarily sensitive to the electrostatic potential at the center of electron localization. Numerical simulations show that the statistics of the electrostatic potential produced by hydration water are strongly non-Gaussian, with the breadth of the electrostatic noise far exceeding the expectations of the linear response. This phenomenon, which dramatically alters the energetic balance of a charge-transfer chain, is attributed to the formation of ferroelectric domains in the protein's hydration shell. These dynamically emerging and dissipating domains make the shell enveloping the protein highly polar, as gauged by the variance of the shell dipole which correlates with the variance of the protein dipole. The Stokes-shift dynamics of redox-active proteins are dominated by a slow component with the relaxation time of 100-500 ps. This slow relaxation mode is frozen on the time-scale of fast reactions, such as bacterial charge separation, resulting in a dramatically reduced reorganization free energy of fast electronic transitions. The electron transfer activation barrier becomes a function of the corresponding rate, self-consistently calculated from a non-ergodic version of the transition-state theory. The peculiar structure of the protein-water interface thus provides natural systems with two "non's"-non-Gaussian statistics and non-ergodic kinetics-to tune the efficiency of the redox energy transfer. Both act to reduce the amount of free energy released as heat in electronic transitions. These mechanisms are shown to increase the energetic efficiency of protein electron transfer by up to an order of magnitude compared to the "standard picture" based on canonical free energies and the linear response approximation. In other words, the protein-water tandem allows both the formation of a ferroelectric mesophase in the hydration shell and an efficient control of the energetics by manipulating the relaxation times.