Dmitry V. Matyushov

Solvent reorganization energy of electron-transfer reactions in polar solvents

A microscopic theory of solvent reorganization energy in polar molecular solvents is developed. The theory represents the solvent response as a combination of the density and polarization fluctuations of the solvent given in terms of the density and polarization structure factors. A fully analytical formulation of the theory is provided for a solute of arbitrary shape with an arbitrary distribution of charge. A good agreement between the analytical procedure and the results of Monte Carlo simulations of model systems is achieved. The reorganization energy splits into the contributions from density fluctuations and polarization fluctuations. The polarization part is dominated by longitudinal polarization response. The density part is inversely proportional to temperature. The dependence of the solvent reorganization energy on the solvent dipole moment and refractive index is discussed.

Calculation of Lennard-Jones energies of molecular fluids

In view of the ever increasing awareness of the importance of dispersion forces to chemical solvent effects, reliable liquid Lennard‐Jones (LJ) energies are eagerly required in order to assess the dispersion component of nonionic solvation. For this purpose two major methods of calculating LJ energies—one based on nonpolar gases solubilities and the other on the generalized van der Waals (GvdW) equation of state—are critically reexamined and updated by applying modern liquid state theories. The former method is improved over previous evaluations by including the cavity formation term according to the Boublik–Mansoori–Carnahan–Starling–Leland equation and by a molecular‐based calculation of the solute solvation energy due to both dispersion and induction forces. For the second approach, the attraction parameter of the GvdW equation of state is separated into the contributions of (i) dipole–dipole (permanent and induced) and (ii) dispersion interactions. The first part (i) is treated in the Wertheim theory ...

Modeling the free energy surfaces of electron transfer in condensed phases

We develop a three-parameter model of electron transfer (ET) 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 model). The exact analytical solution for the ET free energy surfaces demonstrates the following features: (i) the range of ET reaction coordinates is limited by a one-sided fluctuation band, (ii) the ET free energies are infinite outside the band, and (iii) 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 ...

Reorganization energy of electron transfer in polar liquids. Dependence on reactant size, temperature and pressure

Abstract The solvent reorganization energy of outer sphere electron transfer in polar liquids is derived in a molecular treatment. The reorganization energy is shown to be the sum of two contributions: the reorganization energy of reorientation of liquid permanent dipoles and and the energy of reorganization of the liquid density. Reorientation of the dipoles gives the main contribution to the solvent reorganization energy, whereas reorganization of the density contributes mainly to the activation entropy which is positive in the normal and negative in the inverted regions of electron transfer. The reorganization energy of the liquid density contains an explicit temperature dependence which causes the non-Arrhenius temperature dependence of the rate constant. Entropy, enthalpy and volume of activation are found for several solvents.

Cavity formation energy in hard sphere fluids: An asymptotically correct expression

Exact geometrical relations valid for hard sphere (HS) fluids are used to derive analytical expressions for the cavity formation energy equal to the free energy cost of insertion of a HS solute into a HS solvent and the contact value of the solute-solvent pair distribution function (PDF) in the limit of the infinite solute dilution. In contrast to existing relations from the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL) equation of state, the derived expressions are self-consistent and result in correct asymptotics when the solute size goes to infinity. The proposed equations are tested against Monte Carlo simulations at diameter ratios d in the range 1⩽d⩽3.5 and three reduced densities 0.7, 0.8, and 0.9. The BMCSL theory is shown to systematically underestimate contact PDF values as compared to simulations both for finite solute concentrations and in the infinite dilution limit calculated by extrapolation of the results obtained at several concentrations. These infinite-dilution values of the solute-...

Ferroelectric Hydration Shells around Proteins: Electrostatics of the Protein-Water Interface

Numerical simulations of hydrated proteins show that protein hydration shells are polarized into a ferroelectric layer with large values of the average dipole moment magnitude and the dipole moment variance. The emergence of the new polarized mesophase dramatically alters the statistics of electrostatic fluctuations at the protein-water interface. The linear response relation between the average electrostatic potential and its variance breaks down, with the breadth of the electrostatic fluctuations far exceeding the expectations of the linear response theories. The dynamics of these non-Gaussian electrostatic fluctuations are dominated by a slow (approximately = 1 ns) component that freezes in at the temperature of the dynamical transition of proteins. The ferroelectric shell propagates 3-5 water diameters into the bulk.

Energetics and kinetics of primary charge separation in bacterial photosynthesis.

We report the results of molecular dynamics (MD) simulations and formal modeling of the free-energy surfaces and reaction rates of primary charge separation in the reaction center of Rhodobacter sphaeroides. Two simulation protocols were used to produce MD trajectories. Standard force-field potentials were employed in the first protocol. In the second protocol, the special pair was made polarizable to reproduce a high polarizability of its photoexcited state observed by Stark spectroscopy. The charge distribution between covalent and charge-transfer states of the special pair was dynamically adjusted during the simulation run. We found from both protocols that the breadth of electrostatic fluctuations of the protein/water environment far exceeds previous estimates, resulting in about 1.6 eV reorganization energy of electron transfer in the first protocol and 2.5 eV in the second protocol. Most of these electrostatic fluctuations become dynamically frozen on the time scale of primary charge separation, resulting in much smaller solvation contributions to the activation barrier. While water dominates solvation thermodynamics on long observation times, protein emerges as the major thermal bath coupled to electron transfer on the picosecond time of the reaction. Marcus parabolas were obtained for the free-energy surfaces of electron transfer by using the first protocol, while a highly asymmetric surface was obtained in the second protocol. A nonergodic formulation of the diffusion-reaction electron-transfer kinetics has allowed us to reproduce the experimental results for both the temperature dependence of the rate and the nonexponential decay of the population of the photoexcited special pair.

Dipole solvation in dielectrics

This paper presents an exact solution for the free energy of linear solvation of a dipolar solute in an arbitrary dielectric material with a microscopic spectrum of polarization fluctuations. The solution is given in terms of wave vector-dependent longitudinal and transverse structure factors of the polarization fluctuations in the pure dielectric. Good agreement with computer simulations of dipole solvation in dipolar and dipolar--quadrupolar liquids is achieved.

A perturbation theory and simulations of the dipole solvation thermodynamics: Dipolar hard spheres

Pade truncation of the thermodynamic perturbation theory is used to calculate the solvation chemical potential of a dipolar solute in a model fluid of dipolar hard spheres. Monte Carlo simulations of the solvation thermodynamics are carried out over a wide range of solute and solvent dipoles in order to address the following major issues: (i) testing the performance of the Pade perturbation theory against simulations, (ii) understanding the mechanism of nonlinear solvation, and (iii) elucidating the fundamental limitations of the dielectric continuum picture of dipole solvation. The Pade form of the solvation chemical potential constructed in the paper agrees with the whole body of simulation results within an accuracy of 3%. Internal energy and entropy of solvation are also accurately described by the perturbation treatment. Simulations show a complex nonlinear solvation mechanism in dipolar liquids: At low solvent polarities the solvation nonlinearity is due to orientational saturation that switches to ...

Glassy Protein Dynamics and Gigantic Solvent Reorganization Energy of Plastocyanin

We report the results of molecular dynamics simulations of electron-transfer activation parameters of plastocyanin metalloprotein involved as an electron carrier in natural photosynthesis. We have discovered that slow, non-ergodic conformational fluctuations of the protein, coupled to hydrating water, result in a very broad distribution of donor-acceptor energy gaps far exceeding those observed for commonly studied inorganic and organic donor-acceptor complexes. The Stokes shift is not affected by these fluctuations and can be calculated from solvation models in terms of the linear response of the solvent dipolar polarization. The non-ergodic character of large-amplitude protein/water mobility breaks the strong link between the Stokes shift and the reorganization energy characteristic of equilibrium (ergodic) theories of electron transfer. This mechanism might be responsible for fast electronic transitions in natural electron-transfer proteins characterized by low reaction free energy.