Born model of solvation

The Born model of solvation overestimates solvation free energies but indicates the general trends correctly. Potential inversion, as observed in many other systems containing two identical oxidizable or reducible groups separated by an unsaturated bridge (Scheme 1.4), can be rationalized in the same manner. 

It might be anticipated that the intermolecular relaxation energies would be simply the static polarization energies of a molecular cation in the condepsed medium given, for example, by the Born model of solvation. That such cannot be the case is immediately evident upon noting that nonpolar polystyrene and condensed ethyl-benzene exhibit the same relaxation-energy shifts, E (inter)=1.5eV, polar poly(2-vinyl pyridine) and... 

The upshot is that the Born theory of solvation fails because it regards the solvent as a continuous dielectric, whereas in fact solute ions (especially metal cations with z > 1) often interact in a specific manner with solvent molecules. In any event the molecular dielectric is obviously very lumpy on the scale of the ions themselves. The Born theory and other continuous dielectric models work reasonably well when metal ion solute species are treated as solvent complexes such as Cr(OH2)63+ rather than naked ions such as Cr3+, but the emerging approach to solvation phenomena is to simulate solvation dynamically at the molecular level using computer methods. 

Bashford, D. and Case, D. A. 2000. Generalized Born Models of Macromolecular Solvation Effects Annu. Rev. Phys. Chem., 51, 129. 

Roux B, Hsiang-Ai Yu, Karplus M (1990) Molecular Basis for the Born Model of Ion Solvation. J. Phys. Chem. 94 4683 1688... 

Bashford D, Case DA (2000) Generalized born models of macromolecular solvation effects, Annu Rev Phys Chem, 51 129-152... 

On the basis of gas phase and solution data from their own and several other laboratories Aue, Webb and Bowers published a paper in 1976 in which they were able to assess solvent effects on the basicities of amines in quantitative terms by applying the Born electrostatic model of solvation [25]. By separating the en-thalpic and entropic contributions, they noted that solvation attenuates gas... 

Specifically, in the Born theory model of solvation, the intermolecular relaxation energy is (21)... 

Although polyhalide anions are most frequently studied in aqueous solution, they are in fact more stable in less polar solutions. For example, D(l2-I )=17 kJ/mol in aqueous solution, and 47 kJ/mol in acetone. While halide anions are spherical, the trihalide anions are oblate. The Born model is still reasonably accurate for these systems if a spherical ion approximation is used with either an experimental value of the radius or with the assumption that the volume of X is simply three times the volume of X . However, the model does not work for the pentahalide ions IJ and Br. Thus, application of the Born model to larger anions is an oversimplification. As more data become available, it may be possible to use more sophisticated models of solvation to correlate gas- and solution-phase data. 

Bashford, D., Case, D.A. Generalized Born models of macromolecular solvation effects. Ann. Rev. Phys. Chem. 2000,51,129-52. 

The Born ion is the simplest model of solvation It considers the solvation energy of a spherical, nonpolarizable (sp = 1) solute of radius R with a single point charge of magnitude z at its center. In this case, an analytical expression is available for the solvation energy ... 

In the simplest model of solvation, the solvent is treated as a structureless and continuous medium of dielectric constant e. In 1920, Born developed the earliest polarizable continuum model. He treated the ion as a point charge q located in the center of a hollow sphere with radius R. The hollow charged sphere is embedded in a classical dielectric continuum having a relative dielectric constant s. The electrostatic contribution to the free energy, evaluated in Section 11.1.1.1, is given by... 

The Electrostatic Contribution to the Free Energy of Solvation The Born and Onsager Models... 

One very popular technique is an adaptation of the Born model for orbital-based calculations by Cramer and Truhlar, et. al. Their solvation methods (denoted SMI, SM2, and so on) are designed for use with the semiempirical and ah initio methods. Some of the most recent of these methods have a few parameters that can be adjusted by the user in order to customize the method for a specific solvent. Such methods are designed to predict ACsoiv and the geometry in solution. They have been included in a number of popular software packages including the AMSOL program, which is a derivative of AMPAC created by Cramer and Truhlar. 

Using a set of (partial) atomic charges is often called the generalized Born model. It can be noted that the Born model predicts equal solvation for positive and negative ions of the same size, which is not the observed behaviour in solvents like H2O. 

Totrov [31] developed a model to estimate electrostatic solvation transfer energy AGd" in Eq. (1) based on the Generalized Born approximation, which considers the electrostatic contribution to the free energy of solvation as ... 

To obtain an estimate for the energy of reorganization of the outer sphere, we start from the Born model, in which the solvation of an ion is viewed as resulting from the Coulomb interaction of the ionic charge with the polarization of the solvent. This polarization contains two contributions one is from the electronic polarizability of the solvent molecules the other is caused by the orientation and distortion of the... 

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. 

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