Born charging

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. ... 

The energy curves in Figure 22 are closely related to the Marcus-Hush theory for electron transfer. The formalism we employ emphasizes a dipole model for the solute solvent interaction, i.e., an Onsager cavity model. However, a Born charge model based on ion solvation as something in between [135] would be essentially equivalent because we do not attempt to calculate Bop and Bor but rather determine them empirically. 

Moelwyn-Hughes93 examined the ion-solvent interaction energy outside of the first coordination shell or Inner Sphere by a non-Born charging method using the same Inner Sphere induction term as Bemal and Fowler16 and Eley and Evans,92 i.e., -ae(EA)2/2 = with eA =... 

If the dielectric constant of water at 298 K is 78.3, estimate its rate of change with temperature at this temperature. Also calculate the percent error introduced in the Born charging term if the dielectric constant is assumed to be independent of temperature. Consider = 181 pm and = 138 pm. (Contractor)... 

Estimate the error introduced by ignoring the size of the solvent molecules in calculating the heat of the Born-charging process of a Cs ion interaction with water-water = 169 pm). (Contractor)... 

If we view our process as charging the sphere such that we go from a single strand to a double strand then we have a Born charging model of the Free Energy, G, of binding DNA near a surface. This can be adjusted for both dielectric and metallic surfaces. Given the free energy we can then calculate entropy and enthalpy via the familiar derivatives,... 

Neither Equation (1.4) nor Equation (1.7) can explain these results. It is a gas-phase phenomenon, since it vanishes in solution, where the expected orders are found for H2O, H2S and fhSc. The simplest explanation is that the inverted order is the result of the classical charging energy for a sphere. This energy (the Born charging energy) is given by... 

This behavior for I and A can be predicted on classical grounds. The work function for bulk metal would be modified for small spherical samples by the Born charging energy. The ionization potential would be increased and the electron affinity would be decreased by the same amount... 

In the case of such large ions as the metalloporphyrin complexes with their rigid planar structure, to a first approximation the entropy change will be given by the difference in the Born charging entropy of the two valency forms. The Born charging entropy of an ion is given by ... 

Electrostatic solvation (Born charging) is probably significant for ions of very different size and shape but is probably a minor factor in differentiating among organic ammonium and oxonium ions. 

Fig. 4. The principal reactions of the carrier model. M denotes a metal ion. S denotes the uncomplexed carrier. MS devotes the complex. The reactions in the top line are heterogeneous An ion in the aqueous phase joins or leaves a carrier in the membrane phase. The reactions in the lower line are homogeneous Complexation or dissociation takes place between a carrier and an ion in the same phase. (Ions cannot exist in the membrane phase because of high Born charging energy.)...

Figure 8 Koopmans energies (bold lines) and corrected vertical energies (doited lines) of CH3SH, CH3S"(H20)n (n=l-4) in gas phase and aqueous solution calculated at the ROHF/6-31G basis set. The results in aqueous phase are obtained through the use of the SCRF model and the Born charge term. The calculated vertical values were scaled to experiment [164]. Reproduced with permission from ref. [164].

Optical Born energy of the electron. This contribution is due to the interaction of the electron with the second layer of solvent molecules. Apparently, this type of interaction is quite complicated to evaluate hence this second layer is considered to be a continuum. This means that the electron derives energy from the continuum due to optical Born charging according to... 

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