Onsager model, application

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Applications of the Born—Kirkwood-Onsager model at the ab initio level include investigations of solvation effects on sulfamic acid and its zwitterion,23i an examination of the infrared spectra of formamide and formamidic acid,222 and a number of studies focusing on heterocyclic tautomeric equilibria.222,232,233 a more detailed comparison of some of the heterocyclic results is given later. The gas phase dipole moment depends on basis set, and systematic studies of this dependence are available. Furthermore, the effects of basis set choice and level of correlation analysis have been explored in solvation studies as well,222,233 but studies to permit identification of particular trends in their impact on the solvation portion of the calculation are as yet insufficient. 

Easily obtaining the result is not sufficient to assure the popularity of a formulation. In the Onsager case a reason for the success is the physical robustness of the model. It may be modified with little effort and adapted to many different problems. Among these I quote its extension to describe solvent shifts in electronic spectra and to estimate dipole moments of molecules in their excited states. The chemical spectroscopic literature is full of applications of the Onsager model, both in the past (I quote here as examples the texts I have in my room, Refs. [8-10]) as well as at present. The popularity of this model has led to a phenomenon which occurs in several similar cases. There are few quotations of the original Onsager paper in this literature as the model s so often applied, there is no reason to quote its source. As a sort of compensation there is the adjective on-sagerian , which has found use in some specialized literature. 

Bokov, O. G. and Naberukhin, Y. L, Application of the Onsager model to the theory of the dielectric constant of nonpolar liquids, /. Chem. Phys., 75, 2357, 1981. 

F.2.3.3. Application of the Onsager Model. For this model, it is not clear at present how to take into account the fact that (M) is not parallel to H ff. We shall consider below only the (M) component parallel to... 

Onsager Theory for C(t) for Non-Debye Solvents. Generally solvents have more complex dielectric responses than described by the Debye equation (Eq. (18)). To obtain the time dependence of the reaction field R from Eqs. (12, (15), (16) and (7) an appropriate model for dielectric behavior of a specific liquid should be employed. One of the most common dielectric relaxation is given by the Debye-type form, which is applicable to normal alcohols. 

From the point of view of theory, the formulae of Table 2.6 are equally applicable to both gas and condensed phase samples, as they include the local field factors, which account for local modifications to the Maxwell fields due to bulk interactions within the Onsager-Lorentz model. 

Equations (2.6) as well as Eqs. (2.7) were obtained by use of some approximations. The approximations of the Flory method are connected with the lattice character of his model it is difficult to estimate the degree of their accuracy. The approximations of the Onsager method are due to (a) the application of the second virial approximation and (b) the application of the variational procedure. It is rather easy to eliminate the latter approximation by solving numerically with high degree of accuracy the integral equation which appears as a result of the exact minimization of expression (2.2). This has been done in Ref.30 the results are... 

The application of Blum s theory to experiment is unexpectedly impressive it can even represent conductance up to 1 mol dm . Figure 4.96 shows experimental data and both theories—Blum s theory and the Debye-Hiickel-Onsager first approximation. What is so remarkable is that the Blum equations are able to show excellent agreement with experiment without taking into account the solvated state of the ion, as in Lee and Wheaton s model. However, it is noteworthy that Blum stops his comparison with experimental data at 1.0 M. 

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