Solvation energy, Born model

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

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... 

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. 

The simplest approach to describing the interactions of metal cations dissolved in water with solvent molecules is the Born electrostatic model, which expresses solvation energy as a function of the dielectric constant of the solvent and, through transformation constants, of the ratio between the squared charge of the metal cation and its effective radius. This ratio, which is called the polarizing power of the cation (cf Millero, 1977), defines the strength of the electrostatic interaction in a solvation-hydrolysis process of the type... 

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]. 

Solvation in Ligand Binding Free Energy Calculations Using the Generalized-Born Model. 

Jayaram B, Sprous D, Beveridge DL (1998) Solvation free energy of biomacromolecules parameters for a modified generalized born model consistent with the AMBER force field, J Phys Chem B, 102 9571-9576... 

By changing the reference potential in a series of redox monitors, it is then possible to determine the dependence of the cluster potential on the nuclearity. The general trend of increasing redox potential with nuclearity is the same for all metals in solution as it is illustrated in Fig. 2 in the case of E°(AgVAg,) q. However, in gas phase, the variation of the ionization potential IV(Ag ) exhibits the opposite trend versus the nuclearity n. Indeed, since the Fermi potential of the normal hydrogen electrode (NHE) in water is 4.5 eV, and since the solvation free energy of Ag decreases with size as deduced from the Born model, one can explain the two opposite variations with size of F°(Ag /AgJ q and IP (AgJ as illustrated in Fig. 2. 

The so-called mean spherical approximation (MSA) treatment of the solvation energy should also be mentioned. Within the frame work of that model the electrostatic energy of ions is given by a Born-like expression [25], where the effective radius of the ion is considered to be the sum of the ionic radius and a correction term which depends not only on the solvent molecule diameter but also on the dielectric permittivity. Thus, the effective radius is a function of the frequency of the electromagnetic field. 

Zou, X., Sun, Y., Kuntz, I.D. Inclusion of solvation in ligand binding free energy calculations using the generalized-Born model. J. Am. Chem. Soc. 1999, 121, 8033 3. 

The Born model [11] provides a means of estimating the Gibbs energy of solvation for an ion in an infinitely dilute solution. It is based on a continuum description of the solvent as a uniform dielectric with a relative permittivity of The work of transferring the ion from vacuum to the dielectric medium is estimated on the basis of the following three-step process (a) the ion is reversibly discharged in vacuum (b) the discharged ion, which is assumed to be a sphere of radius, r, is... 

Table 3.4 Experimental Value and Estimates According to the Born Model and Mean Spherical Approximation for the Gibbs Energy and Entropy of Solvation of the Alkali Metal Cations and Halide Anions at 25°C...

The Gibbs energy of solvation according to the Born model is given by equation (3.4.6). The constant AlCo /Stiso is equal to 6.945 x lO Jmmol" The radius of Na" " according to Shannon and Prewitt is 116 pm (table 3.1). The factor (1 — l/Sj) is equal to 0.972. The resulting value of AjGi is -581.9 kJmor ... 

Nitromethane (NM) is a polar solvent with a relative permittivity of 35.8 at 25°C. It has a diameter of 431pm when represented as a sphere. Estimate the Gibbs energy of solvation of K, whose diameter is 276 pm, in NM according to the Born model and MSA at 25°C. Compare these estimates with the experimental estimate, which is -300kJmor. ... 

At a microscopic level, solutes in polar solvents undergo strong solvation. For example, the Born model predicts that the Gibbs free energy of an ion with charge q (in Coulombs) and radius r will be changed in the solvent compared with the gas phase by an amount... 

Among the many approximate models for solvation free energy evaluation, the most frequently used is the generalized Born (GB) model. It evaluates the solvation energy using the following equation ... 

Figure 19. Free energies of solvation of halide and trihalide anions as a function of inverse ionic radius, in accordance with the Born Model. The arrow indicates an upper limit on the trifluoride solvation energy.

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