Equilibrium solvation in quadrupolar solvents

Ionic mobility driven by correlated van der Waals and electrostatic forces

Classical theories of dielectric friction make two critical assumptions: (i) friction due to van der Waals (vdW) forces is described by hydrodynamic drag and is independent of the ionic charge and (ii) vdW and electrostatic forces are statistically independent. Both assumptions turn out to be incorrect when tested against simulations of anions and cations with varying charge magnitude dissolved in water. Both the vdW and electrostatic components of the force variance scale linearly with the ionic charge squared. The two components are strongly anticorrelated producing simple relations for the total force variance in terms of self-variances. The inverse diffusion constant scales linearly with the charge squared. Solvation asymmetry between cations and anions extends to linear transport coefficients.

Electron transfer in nonpolar media

Electron transfer in nonpolar media violates the temperature scaling predicted by the fluctuation–dissipation theorem.

A spherical cavity model for quadrupolar dielectrics

The dielectric properties of a fluid composed of molecules possessing both dipole and quadrupole moments are studied based on a model of the Onsager type (molecule in the centre of a spherical cavity). The dielectric permittivity ε and the macroscopic quadrupole polarizability αQ of the fluid are related to the basic molecular characteristics (molecular dipole, polarizability, quadrupole, quadrupolarizability). The effect of αQ is to increase the reaction field, to bring forth reaction field gradient, to decrease the cavity field, and to bring forth cavity field gradient. The effects from the quadrupole terms are significant in the case of small cavity size in a non-polar liquid. The quadrupoles in the medium are shown to have a small but measurable effect on the dielectric permittivity of several liquids (Ar, Kr, Xe, CH4, N2, CO2, CS2, C6H6, H2O, CH3OH). The theory is used to calculate the macroscopic quadrupolarizabilities of these fluids as functions of pressure and temperature. The cavity radii are also determined for these liquids, and it is shown that they are functions of density only. This extension of Onsager's theory will be important for non-polar solutions (fuel, crude oil, liquid CO2), especially at increased pressures.

Molecular level approaches for investigation of electron transfer in nonpolar solvents

The authors extend their previous work published in Leontyev and TachiyaJ. Chem. Phys. 123, 224502 (2005) and study not only forward but also reverse electron transfer between pyrene and dimethylaniline in a nonpolar solvent, n-hexane. The distribution function methodology and molecular dynamics technique adopted in their previous work are used. Two algorithms (I and II) are formulated for obtaining the reorganization energy and the solvation free energy difference in the linear response approximation. The two algorithms are combined with different cutoff schemes and tested for polarizable and nonpolarizable solvent models. Agreement between the results obtained by the two algorithms was achieved only for simulations employing the particle mesh Ewald treatment. It is concluded that algorithm I provides a reliable scheme for evaluation of the reorganization energy and the solvation free energy difference. Moreover, a new algorithm referred to as the G-function algorithm is formulated which does not assume the linear response approximation, and is tested on evaluation of the solvation free energy difference. Agreement between the results from the G-function algorithm and those from algorithms I and II is fairly good, although it depends on the degree of statistical consistency of the simulations. In the case of nonpolar solvents the G-function method has practical importance because, unlike the conventional thermodynamic integration approach, it requires equilibrium molecular configuration ensembles only for the initial and final states of the system.

Solvent Reorganization Entropy of Electron Transfer in Polar Solvents

We report the results of molecular dynamics simulations of the solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile at varying temperatures. The simulations confirm the prediction of microscopic solvation theories of a positive reorganization entropy in polar solvents. The results of simulations are analyzed in terms of the splitting of the reorganization entropy into the contributions from the solute-solvent interaction and from the alteration of the solvent structure induced by the solute. These two contributions mutually cancel each other, resulting in the reorganization entropy amounting to only a fraction of each component.

Quadrupolar solvatochromism: 4-amino-phthalimide in toluene

We present calculations of the temperature dependence of the solvent reorganization energy of 4-amino-phthalimide chromophore in quadrupolar toluene. The reorganization energy is a sum of the contributions from quadrupolar and induction solvation. We employ several calculation formalisms in order to evaluate their performance against the experiment. The point-dipole and full atomic distributions of solute charge are compared to show that the point-dipole approximation works well for this chromophore. We also show that most of the reorganization entropy comes from the quadrupolar response. Induction solvation amounts to about 10% of the entropy. Both the reorganization energy and the reorganization entropy are greatly affected by the local solute-solvent density profile (density reorganization) which contributes about half of their values. The induction reorganization energy is strongly affected by the microscopic, nonlocal nature of the density fluctuations of the solvent around the solute.

Solvent reorganization of electron transitions in viscous solvents

We develop a model of electron transfer reactions at conditions of nonergodicity when the time of solvent relaxation crosses the observation time window set up by the reaction rate. Solvent reorganization energy of intramolecular electron transfer in a charge-transfer molecule dissolved in water and acetonitrile is studied by molecular dynamics simulations at varying temperatures. We observe a sharp decrease of the reorganization energy at a temperature identified as the temperature of structural arrest due to cage effect, as discussed by the mode-coupling theory. This temperature also marks the onset of the enhancement of translational diffusion relative to rotational relaxation signaling the breakdown of the Stokes-Einstein relation. The change in the reorganization energy at the transition temperature reflects the dynamical arrest of the slow, collective relaxation of the solvent related to the relaxation of the solvent dipolar polarization. An analytical theory proposed to describe this effect agrees well with both the simulations and experimental Stokes shift data. The theory is applied to the analysis of charge-transfer kinetics in a low-temperature glass former. We show that the reorganization energy is substantially lower than its equilibrium value for the low-temperature portion of the data. The theory predicts the possibility of discontinuous changes in the dependence of the electron transfer rate on the free energy gap when the reaction switches between ergodic and nonergodic regimes.

The reorganization energy of electron transfer in nonpolar solvents: Molecular level treatment of the solvent

The intermolecular electron transfer in a solute pair consisting of pyrene and dimethylaniline is investigated in a nonpolar solvent, n-hexane. The earlier elaborated approach [M. Tachiya, J. Phys Chem. 97, 5911 (1993)] is used; this method provides a physically relevant background for separating inertial and inertialess polarization responses for both nonpolarizable and polarizable molecular level simulations. The molecular-dynamics technique was implemented for obtaining the equilibrium ensemble of solvent configurations. The nonpolar solvent, n-hexane, was treated in terms of OPLS-AA parametrization. Solute Lennard-Jones parameters were taken from the same parametrization. Solute charge distributions of the initial and final states were determined using ab initio level [HF/6-31G(d,p)] quantum-chemical calculations. Configuration analysis was performed explicitly taking into account the anisotropic polarizability of n-hexane. It is shown that the Gaussian law well describes calculated distribution functions of the solvent coordinate, therefore, the rate constant of the ET reaction can be characterized by the reorganization energy. Evaluated values of the reorganization energies are in a range of 0.03-0.11 eV and significant contribution (more then 40% of magnitude) comes from anisotropic polarizability. Investigation of the reorganization energy lambda dependence on the solute pair separation distance d revealed unexpected behavior. The dependence has a very sharp peak at the distance d=7 A where solvent molecules are able to penetrate into the intermediate space between the solute pair. The reason for such behavior is clarified. This new effect has a purely molecular origin and cannot be described within conventional continuum solvent models.