Born charging energies

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. ... 

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... 

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.)...

Consider an alchemical transformation of a particle in water, where the particle s charge is changed from 0 to i) (e.g., neon sodium q = ). Let the transformation be performed first with the particle in a spherical water droplet of radius R (formed of explicit water molecules), and let the droplet then be transferred into bulk continuum water. From dielectric continuum theory, the transfer free energy is just the Born free energy to transfer a spherical ion of charge q and radius R into a continuum with the dielectric constant e of water ... 

A very simple version of this approach was used in early applications. An alchemical charging calculation was done using a distance-based cutoff for electrostatic interactions, either with a finite or a periodic model. Then a cut-off correction equal to the Born free energy, Eq. (38), was added, with the spherical radius taken to be = R. This is a convenient but ill-defined approximation, because the system with a cutoff is not equivalent to a spherical charge of radius R. A more rigorous cutoff correction was derived recently that is applicable to sufficiently homogeneous systems [54] but appears to be impractical for macromolecules in solution. 

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... 

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 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,... 

For phenol, PA (phenolate) = 350 kcalmol", AGt of the proton is about 260 kcalmol" and AGt((PhO ) — (PhOH)) may be roughly estimated assuming that it is mainly given by the Born free-energy of solvation of charged cavities immersed in a dielectric continuum (equation 16),... 

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... 

In the above calculations for the charging energy of an ion, we have actually integrated the energy of the electric field over the entire volume of the dielectric with the exception of the ion itself, which is the source of this field. Such an approach, which is quite natural for calculating the Born solvation energy for an isolated ion, has to be refined when we are dealing with a reaction between two ions, especially if the second ion is close to the first one (this actually is the most typical situation). Indeed, the field... 

In the generalised Born approach the total electrostatic energy is written as a sum of tin terms, the first of which is the Coulomb interaction between the charges in vacuo ... 

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