Born solvation

The Born solvation equation is based on the difference in the energy needed to charge a sphere of radius r,- in a solvent of dielectric constant e, and in vacuum having a dielectric constant of unity. Thae are basic flaws in the concept of the Born solvation equation (5) on which the continuum theory of ET reactions is based. First, Bom Eq. (5) does not take into account the interaction of ions with a water solvent that has a dielectric constant of approximately 80 at room temperature. Hence, the Born solvation energy will have negligible contribution from solvents with high dielectric constants. Consequently, for solvents of high dielectric constant, Eq. (5) can be written as... 

These points indicate that the continuum theory expression of the free energy of activation, which is based on the Born solvation equation, has no relevance to the process of activation of ions in solution. The activation of ions in solution should involve the interaction energy with the solvent molecules, which depends on the structure of the ions, the solvent, and their orientation, and not on the Born charging energy in solvents of high dielectric constant (e.g., water). Consequently, the continuum theory of activation, which depends on the Born equation,fails to correlate (see Fig. 1) with experimental results. Inverse correlations were also found between the experimental values of the rate constant for an ET reaction in solvents having different dielectric constants with those computed from the continuum theory expression. Continuum theory also fails to explain the well-known Tafel linearity of current density at a metal electrode. ... 

Qy. = Born solvation term B = coulombic repulsion term Kh+ = adsorption constant for H ). An excellent correlation resulted between the experimentally determined and calculated pHp c for nine different solids, namely quartz, kaolinite, rutile, magnetite, goethite, hematite, corundum gibbsite and MgO. For the Fe oxides, the predicted (experimentally determined) values were magnetite 7.1 (6.6), hematite 8.47 (8.5) and goethite 9.0 (9.4). 

Some stability constants for ion pairs on Fe oxides are listed in Table 10.4. This model was applied by Davis and Leckie (1978, 1980) to adsorption of various cations and anions on ferrihydrite. The extended triple layer model of Sahai and Svenjensky (1997) incorporates recent advances in aqueous electrolyte chemistry which enable aqueous activity coefficients for electrolytes to be calculated over a wide range of ionic strengths. The model also considers the free energy of adsorption of an ion to be the sum of the contributions from an electrostatic term, a Born solvation term and a ion intrinsic term. This extended model has been applied to adsorption of Co and Cd on goethite. 

Fig. 6 compares the nuclearity effect on the redox potentials [19,31,63] of hydrated Ag+ clusters E°(Ag /Ag )aq together with the effect on ionization potentials IPg (Ag ) of bare silver clusters in the gas phase [67,68]. The asymptotic value of the redox potential is reached at the nuclearity around n = 500 (diameter == 2 nm), which thus represents, for the system, the transition between the mesoscopic and the macroscopic phase of the bulk metal. The density of values available so far is not sufficient to prove the existence of odd-even oscillations as for IPg. However, it is obvious from this figure that the variation of E° and IPg do exhibit opposite trends vs. n, for the solution (Table 5) and the gas phase, respectively. The difference between ionization potentials of bare and solvated clusters decreases with increasing n as which corresponds fairly well to the solvation free energy of the cation deduced from the Born solvation model [45] (for the single atom, the difference of 5 eV represents the solvation energy of the silver cation) [31]. 

What is the Born solvation energy of Fe3+ in water having a dielectric constant of 78, and what is its value when it is in ethanol, which has dielectric constant of 36 (b) What is the self-energy of Fe3+ in a vacuum (c) Is there any meaningful difference between the Born solvation energy and the self-energy of an Fe3+ ion The radius of this ion is 0.64 A and the diameter of water is 2.76 A. (c) Where do you think there is a possible flaw in Born s solvation equation (Khan)... 

Tsui V, Case DA (2001) Theory and applications of the generalized Born solvation model in macromolecular simulations, Biopolymers, 56 275-291... 

Tsui V, Case DA (2002) Molecular dynamic simulations of nucleic acids with a generalized born solvation model, J Am Chem Soc, 122 2489-2498... 

AHf = AHam + AHax + AHEi + AHAE + U0. Born solvation e"ergy - Born equation... 

Tetraphenylborate — A large, weakly solvated anion of tetrahedral shape used in electrochemical measurements as the anion of the -> supporting electrolyte in nonaqueous solutions. Due to its weak -> solvation (see -> hydration and -> Born solvation energy) it is especially... 

Since Eq. (28) was obtained under assumptions similar to those used by Born, the calculation of AGq suffers from the same limitations as the Born solvation model. The dielectric continuum model is valid for electron transfer in a structureless dielectric medium with a reactant approximated by a hard conducting sphere. It is obeyed when the specific solute-solvent interactions are negligible. 

The generalized Born solvation models o " " take account of specific water interactions explicitly and give excellent agreement in the AMl-SMl and PM3-SM3 cases AMl-SMl is less successful, albeit still improved over the most reasonable BKO treatment. Cavity radii are not an issue for these models. 

The energy required to reorganize the solvent, Ao, is obtained by a different procedure. The medium outside the reactant (or reactants) is treated as a dielectric continuum with the polarization made up of two parts, a relatively rapid electronic polarization and a slower vibrational-orientational one. The latter has to adjust to a nonequilibrium value appropriate to the final state, contrary to the former. On the basis of the Born solvation theory Aq (if one electron is transferred) is given by ... 

On the basis of the analysis described by Marcus [25], the Gibbs energy Gxo may be written as the difference between a Born solvation term at static frequencies and one at optical frequencies. Thus, from equation (7.8.26)... 

Tsui, V., Case, D.A. Molecular dynamics simulations of nucleic adds with a Generalized Born solvation model. J. Am. Chem. Soc. 2000,122,2489-98. 

A.V. Marenich, C.J. Cramer, and D.G. Truhlar, Generalized Born solvation model SM12, J. Chem. Theory Comput. 9 (2013), pp. 609-620. 

Generalized Born Solvation Model in Macromolecular Simulations. 

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