Nonlinear solvation effects

DHS solvent, squares correspond to a liquid DHS solvent, and triangles indicate a nonpolarizable solute in a polarizable DHS liquid Pm2/ry3 = 1, a/a3 = 0.05, a is the solvent polarizability. 

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Solvation Effects. Many previous accounts of the activity coefficients have considered the connections between the solvation of ions and deviations from the DH limiting-laws in a semi-empirical manner, e.g., the Robinson and Stokes equation (3). In the interpretation of results according to our model, the parameter a also relates to the physical reality of a solvated ion, and the effects of polarization on the interionic forces are closely related to the nature of this entity from an electrostatic viewpoint. Without recourse to specific numerical results, we briefly illustrate the usefulness of the model by defining a polarizable cosphere (or primary solvation shell) as that small region within which the solvent responds to the ionic field in nonlinear manner the solvent outside responds linearly through mild Born-type interactions, described adequately with the use of the dielectric constant of the pure solvent. (Our comments here refer largely to activity coefficients in aqueous solution, and we assume complete dissociation of the solute. The polarizability of cations in some solvents, e.g., DMF and acetonitrile, follows a different sequence, and there is probably some ion-association.)... 

What is of interest here is the description of nonlinear dielectric effects with a linear procedure. Nonlinear dielectrics were introduced in the theory of liquids by Dogonatze and Kornyshev in the 1970s [21] the reformulation of the theory in more recent years by Basilevsky [22] permits its insertion in the whole machinery of the PCM version of the CS method. The reader is also referred to the contribution of Basilevsky and Chuev dedicated to non-local dielectric solvation models. 

Clearly, the MFI description does not capture all possible complicated mechanisms of ET activation in condensed phases. The general question that arises in this connection is whether we are able to formulate an extension of the mathematical MH framework that would (1) exactly derive from the system Hamiltonian, (2) comply with the fundamental linear constraint in Eq. [24], (3) give nonparabolic free energy surfaces and more flexibility to include nonlinear electronic or solvation effects, and (4) provide an unambiguous connection between the model parameters and spectroscopic observables. In the next section, we present the bilinear coupling model (Q model), which satisfies the above requirements and provides a generalization of the MH model. 

The revision of characteristic frequencies of nuclear modes is a general result of electronic delocalization holding for both the intramolecular vibrational modes and the solvent modes. The fact that this effect shows up already in the harmonic expansion term makes it much stronger compared to nonlinear solvation in respect to nonparabolic distortion of the free energy surfaces. 

When the external field has an oscillatory behavior, all these quantities depend on the frequency of such oscillations for a given 7 ") we have to consider the frequencies and phases of the various components of external fields that can be combined in all possible ways to give different electric molecular response. These elements constitute the essential part of the linear and nonlinear optics, a subject for which there is a remarkable interest to know the influence of solvation effects. 

The radii of organic ions are typically R = 4 A (see Section 4.2), which yields P = 0.925 eV. On a molecular scale, the ion is seen to be surrounded by shells of polarized solvent molecules (see Figure 20). Under the assumption that is independent of the electric field strength and that Rj n = Rsoivent/ can estimate the contribution of each shell to the total polarization energy by means of Equation 93. In the first shell 0.62 eV is expended, in the second shell 0.12 eV, and in the third shell 0.05 eV, or, in other words, 86% of the polarization energy is located within the first three layers of polarized molecules around the ionic core. If the nonlinear dielectric effect is taken into account (see Section 1.6), increases near the ionic core and an even greater fraction of the total polarization energy is concentrated in the first few solvation shells. 

Jain has also developed an empirically derived scoring function based on 34 diverse protein-ligand complexes. The primary terms of the function arise for hydrophobic and polar complementarity, with additional factors for entropic and solvation effects. From this, Jain has constructed a sufficiently fast continuously differentiable nonlinear function, such that optimization of alignment/conformation of the ligand within the receptor, based on the predicted affinity, may be readily achieved. 

Clearly, then, the chemical and physical properties of liquid interfaces represent a significant interdisciplinary research area for a broad range of investigators, such as those who have contributed to this book. The chapters are organized into three parts. The first deals with the chemical and physical structure of oil-water interfaces and membrane surfaces. Eighteen chapters present discussion of interfacial potentials, ion solvation, electrostatic instabilities in double layers, theory of adsorption, nonlinear optics, interfacial kinetics, microstructure effects, ultramicroelectrode techniques, catalysis, and extraction. 

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