Solvation effects analytic equations

A computationally efficient analytical method has been developed for the crucial calculation of Born radii, which is required for each atom of the solute that carries a (partial) charge, and the Gpoi term has been parameterized to fit atomic polarization energies obtained by Poisson-Boltzmann equation [57]. The GB/SA model is thus fully analytical and affords first and second derivatives allowing for solvation effects to be included in energy minimizations, molecular dynamics, etc. The Gpoi term is most important for polar molecules and describes the polarization of the solvent by the solute. As force fields in general are not polarizable, it does not account for the polarization of the solute by the solvent. This is clearly an important limitation of this type of calculations. 

Equation (1-7) shows that in an ideal case the selectivity of the system is only dependent on the difference in the analytes interaction with the stationary phase. It is important to note that the energetic term responsible for the eluent interactions was canceled out, and this means that the eluent type and the eluent composition in an ideal case does not have any influence on the separation selectivity. In a real situation, eluent type and composition may influence the analyte ionization, solvation, and other secondary equilibria effects that will have effect on the selectivity, but this is only secondary effect. 

Solvation energies for other multipoles inside a spherical cavity, including corrections due to salt effects, can be found, for example in Ref. 29. Analytical solutions of the Poisson equation for some other cavities, such as ellipse or cylinder, are also known [2] but are of little use in solvation calculations of biomolecules. For cavities of general shape only numerical solution of the Poisson and Poisson-Boltzmann equations is possible. There are two well-established approaches to the numerical solution of these equations the finite difference and the finite element methods. 

General analysis of the binary solvent mixtures formed by two solvate active components (these solvents are often used in analytical and electrochemistry) was conducted to evaluate their effect on H-acids. The analysis was based on an equation which relates the constant of ion association, K, of the solvent mixture and constants of ion association of the acid Kj and K of each component of the mixed solvent, using equilibrium constants of scheme [9.105] - heteromolecular association constant, ionization constant of the... 

Dielectric saturation produces "irrotational bounding of the solvent molecules surroimding the ion and hence yields solvation numbers. Pottel et al.25,58 use the empirical Bruggeman relation for the estimation of the "effective" volume fraction of the solvent. Comparision with its "analytical" value yields solvation numbeiTS Zp. Lestrade et al.30 39 use the Kirkwood Frohlich equation with the Kirkwood parameter assumed independent of electrolyte concentration, to calculate solvation numbers Zl Ly means of the number of molecules per unit volume required to explain the limiting slope of the permittivity depression. A siu vey of solvation numbers Zp and obtained from these methods and their critical discussion is given in Ref. 14. 

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