Outer solvation sphere

The Marcus-Hush (MH) formalism is an attempt to better account for changes in the outer solvation sphere during an electron transfer process. It incorporates the... 

The above discussion shows that the electrostatic free energy of solvation can be divided into an coordination shell or inner solvation sphere in which eA is close to 1, where the Pu interaction depends only on - xAa, and an outer solvation sphere where the PA interaction depends to a good approximation on Eqs. (55)-(57), but in which the electrostatic Gibbs energy may be approximated by the integral in Eq. (58), which resembles the Bom charging equation, but it is obtained in a different way with a more definite physical meaning. 

Fig. 5. Schematic representation of mechanism for replacement of NH3 in Ni(HEEDTA)(NH3) by a solvent molecule to give Ni(HEEDTA)S" where S is either H2O or CH3OH. The solid circles represent the outer solvation sphere. (From Shu and Rorabacher [122], by courtesy of the American Chemical Society.)...

Solvation effects have been incorporated into the calculations of anionic proton transfer potentials in a number of ways. The simplest is the microsolvation model where a few solvent molecules are included to form a supermolecular system that is directly characterized by quantum mechanical calculations. This has the advantage of high accuracy, but is limited to small systems. Moreover, one must assume that a limited number of solvent molecules can adequately model a tme solution. A more realistic approach is to explicitly describe the inner solvation shell with quantum calculations and then treat the outer solvation sphere and bulk solvent as a continuum (infinite polarizable dielectric medium). In this way, the specific interactions can be treated by high-level calculations, but the effect of the bulk solvent and its dielectric is not neglected. An ej tension of this approach is to characterize the reaction partners by quantum mechanics and then treat the solvent with a molecular mechanics approach (hybrid quantum mechanics/molecular mechanics QM/MM). The low-cost of the molecular mechanics treatment allows the solvent to be involved in molecular dynamics simulations and consequently free energies can be calculated. In more recent work, solvent also has been treated with a frozen or constrained density functional theory approach. ... 

Mechanism by outer sphere. The coordination sphere in these cases remains intact and only the outer solvation spheres overlap. In this case the rate law corresponds to... 

Schmickler, W. 1976. A dipole model for the outer solvation sphere and its application to outer sphere electron transfer reactions. Ber. Bunsenges. Phys. Chem. 80 834—838. 

But if we examine the localized near the donor or the acceptor crystal vibrations or intra-molecular vibrations, the electron transition may induce much larger changes in such modes. It may be the substantial shifts of the equilibrium positions, the frequencies, or at last, the change of the set of normal modes due to violation of the space structure of the centers. The local vibrations at electron transitions between the atomic centers in the polar medium are the oscillations of the rigid solvation spheres near the centers. Such vibrations are denoted by the inner-sphere vibrations in contrast to the outer-sphere vibrations of the medium. The expressions for the rate constant cited above are based on the smallness of the shift of the equilibrium position or the frequency in each mode (see Eqs. (11) and (13)). They may be useless for the case of local vibrations that are, as a rule, high-frequency ones. The general formal approach to the description of the electron transitions in such systems based on the method of density function was developed by Kubo and Toyozawa [7] within the bounds of the conception of the harmonic vibrations in the initial and final states. 

It is conventional to classify electrochemical reactions as outer-sphere and inner-sphere. The former involve the outer coordination sphere of a reacting ion. Thus, little if any change inside the ion solvate shell occurs they proceed without breaking-up intramolecular bonds. But in the latter, involving the inner coordination sphere, electron transfer is accompanied by breaking up or formation of such bonds. Often the inner-sphere reactions are complicated by adsorption of reactants and/or reaction products on the electrode surface. The electron transfer in the Fc(CN)62 /4 system is example of an outer-sphere reaction (with due reservation for some complications... 

These terms are based on a simple geometric model of the interface. One distinguishes between an inner and an outer Helmholtz layer. The inner Helmholtz layer comprises all species that are specifically adsorbed on the electrode surface. If only one type of molecule or ion is adsorbed, and they all sit in equivalent positions, then their centers define the inner Helmholtz plane. The outer Helmholtz layer comprises the ions that are closest to the electrode surface, but are not specifically adsorbed. They have kept their -> solvation spheres intact, and are bound only by electrostatic forces. If all these ions are equivalent, their centers define the outer Helmholtz plane. 

The role of the outer solvation shell in mixed solvents was also studied using the CoEn system as a model [302] (En = ethylenediamine). In this system the inner sphere of the substrate (CoEn ) and the product (CoEnl ) was not changed in the course of the one-electron electrode reaction. Therefore, the changes in the rate constant (determined by chronocoulometric method), observed when the composi-... 

The peak in the X-ray RDF at 5 A (fig. 4) was assigned to Ln-O distances for water molecules in the second (outer) hydration sphere. Curve B in fig. 6 shows the dependency of the position of this peak on the lanthanide radius. Both ion pair interactions [Ln(H20) (] -Cl and secondary solvation [Ln(H20) ] -H20 are expected to be responsive to differences in ionic radii of the lanthanide ions as well as to changes in the inner-sphere hydration. The decrease in the Ln H2O distance between La " and Lu " " (including the hydration change offset) is 0.24 A (fig. 6, curve A), in good agreement with the difference of 0.22 A for the peak at ca. 5 A. 

A spectroscopic study of Eu -Br showed that the increase in the Br concentration causes a larger enhancement in the intensity and band area of the -> transitions than for the Fj -> transitions. These modifications in the spectra were attributed to changes in the structure and nature of the inner solvation sphere of Eu in the excited state as compared to that of the ground state (Marcantonatos et al. 1984). The differences in intensity between absorption and emission bands would, therefore, reflect formation of inner-sphere complexes by Br in the excited state while outer-sphere complexation would dominate the ground state. It was proposed (Marcantonatos et al. 1981, 1982) that excitation of Eu " ion to the state would result in an expansion of the 4f and a shrinkage of the 5p orbitals with an overall decrease in the metal ion radius. The consequent contraction of the iimer shell would be expected to produce more compact and less easily disrupted outer hydration spheres for both ( Dj) Eu(H20)g and ( Di)Eu(H20)g with a possible increase in kobs-... 

Fig. 6.2.6 Values of the solvation parameter / o for CH3CN as a function of the mol fraction of CH3CN. / o is the number of solvent molecules in the outer coordination sphere (solvation sphere) in a mixed solvent compared to that in the pure solvent (from Ref. N62).

The zinc atom is in the distorted trigonal-bip5rramidal environment of the N- and 0-atoms of the molecule of the nitrilo-tris-methylene phos-phonic acid. The complex anions are dimerized by the Zn-0 bonds. The outer coordination sphere contains sodium ions in the distorted trigonal-bipyramidal and octahedral environment of oxygen atoms and the molecules of solvation water. 

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