Onsager model, solvation

Key words Onsager model - Solvation methods -Models in chemistry... 

The Electrostatic Contribution to the Free Energy of Solvation The Born and Onsager Models... 

As the plot of AE indicates, the energy difference between the two forms decreases in more polar solvents, and becomes nearly zero in acetonitrile. The left plot illustrates the fact that the IPCM model (at the B3LYP/6-31+G(d) level of theory) does a much better job of reproducing the observed solvent effect than the two Onsager SCRF models. In contrast, the Onsager model at the MP2 level treats the solvated systems more accurately than it does the gas phase system, leading to a poorer value for the solvent effect. ... 

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. 

An Evaluation of the Debye-Onsager Model. The simplest treatment for solvation dynamics is the Debye-Onsager model which we reviewed in Section II.A. It assumes that the solvent (i) is well modeled as a uniform dielectric continuum and (ii) has a single relaxation time (i.e., the solvent is a Debye solvent ) td (Eq. (18)). The model predicts that C(t) should be a single... 

Ignoring the potential limitations of the dielectric data, we can evaluate the Debye-Onsager model for a number of apparently roughly Debye solvents, like propylene carbonate, the alkyl nitriles, the alkyl acetates, and other solvents. First of all, C( ) is often strongly nonmonoexponential, in contradiction to the theoretical prediction. Second, the observed average solvation time is often much different from xt. 

A number of theoretical models for solvation dynamics that go beyond the simple Debye Onsager model have recently been developed. The simplest is an extension of Onsager model to include solvents with a non-Debye like (dielectric continuum and the probe can be represented by a spherical cavity. Newer theories allow for nonspherical probes [46], a nonuniform dielectric medium [45], a structured solvent represented by the mean spherical approximation [38-43], and other approaches (see below). Some of these are discussed in this section. Attempts are made where possible to emphasize the comparison between theory and experiment. 

Bagchi and co-workers [47-50] have explored the role of translational diffusion in the dynamics of solvation by employing a Smoluchowski-Vlasov equation (see also Calef and Wolyness [37] and Nichols and Calef [42]). A significant contribution to polarization relaxation is observed in certain cases. It is found that the Onsager inverted snowball model is correct only when the rotational diffusion mechanism of solvation dominates the polarization relaxation. The Onsager model significantly breaks down when there is an important translational contribution to the polarization relaxation [47-50]. In fact, translational effects can rapidly accelerate solvation near the probe. In certain cases, the predicted behavior can actually approach the uniform continuum result that rs = t,. 

Correlation and solvation effects on heterocyclic equilibria in aqueous solution were analyzed with the use of SM2/AM1 and Onsager models. It was found that the Onsager model was inferior to SM2/AM1,because it underestimates the solvation of the syn -form. Local bond moments, as shown by SM2/AM1, had significant effects on the bulk electric polarizaton, even when they largely cancel in the net dipole moment. Moreover, the equilibrium shifts calculated with SM2 /AMI, due to the effects of methyl substitution on the isoxazole ring, were consistent with the available experimental data [79]. 

Still within continuum solvation models, Wang et al. [5] have used an ab initio SCRF Onsager model to compute vibrational frequencies at different levels of the ab initio QM molecular theory, the G-COSMO model has been used by Stefanovich and Truong to calculate vibrational frequencies at the DFT level [6], and the multipole SCRF model, developed by the group of Rivail, has been extended to the calculation of frequency shifts at the HF, MP2 and DFT levels, including nonequilibrium effects [7],... 

Models to describe frequency shifts have mostly been based on continuum solvation models (see Rao et al. [13] for a brief review). The most important steps were made in the studies of West and Edwards [14], Bauer and Magat [15], Kirkwood [16], Buckingham [17,18], Pullin [19] and Linder [20], all based on the Onsager model [21], which describes the solvated solute as a polarizable point dipole in a spherical cavity immersed in a continuum, infinite, homogeneous and isotropic dielectric medium. In particular, in the study of Bauer and Magat [15] the solvent-induced shift in frequency Av is given as ... 

Similar calculated changes in carbonyl frequencies have been observed by Wong et al. [98] using their Onsager model reaction field techniques. For formaldehyde, their calculated shifts in frequencies are similar across a wide variety of extended basis sets at the 6-31 G level, but are much smaller at the 3-21G and STO-3G level. The shifts in carbonyl frequency are an important test for the computational methods since this is the most sensitive probe for the effects of solvation [134,135. ... 

The exciplex or CIP is treated as a dipole of radius q and dipole moment p. The last term in Eq. (15) describes the energy of this dipole, based on the Kirkwood-Onsager model (assuming formation of a spherical complex) [14]. Thus, an exciplex or CIP is stabilized by Coulombic interactions and by solvation. The solvation energy is expected to be favored by increasing solvent polarity and a large dipole... 

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. 

The aqueous solvation free energies of the four tautomers available to the 5-(2H)-isoxazolone system have also been studied using a variety of continuum models (Table 7). Hillier and co-workers - " have provided data at the ab initio level using the Born-Kirkwood-Onsager model, the classical multipolar expansion model (up to I = 7), and an ab initio polarized continuum model. We examined the same BKO model with a different cavity radius and the AMl-SMl and AMl-SMla o- models, and Wang and Ford have performed calculations with the AMl-PCM model. 

The quantum Onsager model, which has also been termed the Self-Consistent Reaction Field (SCRF) method, is the simplest of the continuum models used in solvation studies. In this model, which dates from the work of Kirkwood[44] and Onsager[45] in the 1930s, the solvent is represented by a continuous rmifonn dielectric with a static dielectric constant, e, surrounding a solute in a spherical cavity[46] - [48]. 

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