Born electrostatic contribution

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

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 ... 

We can exploit the new results for packing contributions to reconsider the outer shell contribution in Eq. (33). For ionic solutes, the outer shell term would represent the Born contribution because it describes a hard ion stripped of any inner shell ligands. A Born model based on a picture of a dielectric continuum solvent is reasonable (see Section III,B, and Fig. 9, color insert). With that motivation, we first separate the outer shell term into an initial packing contribution and an approximate electrostatic contribution as... 

The electrostatic contributions, identified as /t x born and modeled on the basis of a dielectric continuum, are typically a substantial part of the... 

Assuming that the electrostatic contributions are given by Born theory and that the solvated ions, irrespective of the composition of the solvation shell, have the same radii, then Equation 19, utilizing the assumptions embodied in Equations 25, 26, and 27, simplifies to... 

AGpse7n derived from these data. To use Equation 67 it is necessary to estimate the electrostatic contributions. A first approximation to these will be given by the Born treatment (8). Thus for a molar standard state,... 

Figure 6. Free energy of transfer of sodium chloride from water to methanol-water mixtures. O emf derived values (28) — predicted values including electrostatic contribution estimated from the Born equation (69) with n = 4 (Na +), 8 (Cl ) NMR contribution for Na + ion ...

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... 

But in general, the Born equation in its original form is used quite often to estimate the electrostatic contribution to the free energy of transfer of large ions 4nd entities which consist of an ion with several solvent molecules ... 

It is a serious drawback that it is not possible to determine the transfer activity coefficient of the proton (or of any other single-ion species) directly by thermodynamic methods, because only the values for both the proton and its counterion are obtained. Therefore, approximation methods are used to separate the medium effect on the proton. One is based on the simple sphere-in-continuum model of Born, calculating the electrostatic contribution of the Gibb s free energy of transfer. This approach is clearly too weak, because it does not consider solvation effects. Different ex-trathermodynamic approximation methods, unfortunately, lead not only to different values of the medium effect but also to different signs in some cases. Some examples are given in the following log yH+ for methanol -1-1.7 (standard deviation 0.4) ethanol -1-2.5 (1.8), n-butanol -t-2.3 (2.0), dimethyl sulfoxide -3.6 (2.0), acetonitrile -1-4.3 (1.5), formic acid -1-7.9 (1.7), NH3 -16. From these data, it can be seen that methanol has about the same basicity as water the other alcohols are less basic, as is acetonitrile. Di-... 

A comparison of anion solvation by methanol, a protic solvent, and dimethylformamide, a dipolar aprotic solvent, is instructive. The electrostatic contribution, d/i , to the Gibbs free energy of solvation per mole of an ion is sometimes estimated quite successfully (Stokes, 1964) from the Bom model, in which a charged sphere of radius r is transferred from vacuum to a medium of uniform dielectric constant, c. The Bom equation (17) suggests that an anion should be similarly solvated in methanol and in DMF, because these solvents have effectively the same dielectric constant (33-36). The Born equation makes no allowance for chemical interactions, such as hydrogen-bonding and mutual... 

The addition of the ECPs to the cluster gives a better representation of the electrostatic potential hence of the electrostatic contribution to the surface bonding. What is still missing from this simplified approach is the polarization of the host crystal induced by an adsorbed species or by the presence of a defect. This effect can be particularly important for charged adsorbates or defects. The polarization, Epoi, induced by a charge on the surrounding lattice can be estimated by means of the classical Born formula [56] ... 

Therefore, we would expeet a tt bond to be weaker than a a bond, and so a double bond should be less than twice as strong as a single bond. This expectation is borne out for carbon-carbon bonds. However, many factors, such as lone-pair repulsions, bond polarities, and other electrostatic contributions, affect overlap and the relative strength of c and tt bonds between other pairs of atoms. Thus, as a rough approximation, a double bond is about twice as strong as a single bond, and a triple bond is about three times as strong. 

The simplest starting point for the quantitative treatment of the electrostatic part of the medium effect is the Born model of rigid spherical ions in a continuous dielectric. For a molecular acid whose ions have a mean radius r, the Born estimate of the electrostatic contribution to the medium effect is... 

Despite the simplifying assumptions in the derivation, such as assuming that the medium, water, is a continuum with no structure, and that the only work is electrostatic, and even more assumptions in calculating the properties of individual ions from the measured properties of electrolytes, as estimated by the Born function comes reasonably close to the measured Gibbs energy of ion solvation, as shown in Figure 6.7. Other thermodynamic properties such as the volume, entropy and enthalpy of solvation can also be obtained by appropriate differentiation of Equation (6.5). As a result, ever since its inception the Born equation has been used as a primitive model for the electrostatic contribution to the properties of an ion in a dielectric solvent. 

A modified Born model (uniform continuum solvent), in that it included the effect of waters of hydration about OH , was used to extrapolate the Kbha data[12]. The electrostatic contribution to the ion-solvation may be represented by the Born equation ... 

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... 

SASA), a concept introduced by Lee and Richards [9], and the electrostatic free energy contribution on the basis of the Poisson-Boltzmann (PB) equation of macroscopic electrostatics, an idea that goes back to Born [10], Debye and Htickel [11], Kirkwood [12], and Onsager [13]. The combination of these two approximations forms the SASA/PB implicit solvent model. In the next section we analyze the microscopic significance of the nonpolar and electrostatic free energy contributions and describe the SASA/PB implicit solvent model. 

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