Onsager reaction

Kirkwood generalized the Onsager reaction field method to arbitrary charge distributions and, for a spherical cavity, obtained the Gibbs free energy of solvation in tenns of a miiltipole expansion of the electrostatic field generated by the charge distribution [12, 1 3]... 

The simplest SCRF model is the Onsager reaction field model. In this method, the solute occupies a fixed spherical cavity of radius Oq within the solvent field. A dipole in the molecule will induce a dipole in the medium, and the electric field applied by the solvent dipole will in turn interact with the molecular dipole, leading to net stabilization. 

The salient features of quantum formulation of Onsager reaction field model (dipole model) is described here. In this method, the reaction field is treated as perturbation to the Hamiltonian of the isolated molecule. If H0 is the Hamiltonian of the isolated molecule and HR[ is the reaction field [21], the Hamiltonian of the whole system (Hlol) is represented as... 

Porter has shown for several solvents a correlation between the cohesive energy density (CED) and the Onsager reaction field parameter... 

As a first approximation, solvent effects can be described by models where the solvent is represented by a dielectric continuum, e.g., the Onsager reaction-field model. 

In practice, empirical or semi-empirical interaction potentials are used. These potential energy functions are often parameterized as pairwise additive atom-atom interactions, i.e., Upj(ri,r2,..., r/v) = JT. u ri j), where the sum runs over all atom-atom distances. An all-atom model usually requires a substantial amount of computation. This may be reduced by estimating the electronic energy via a continuum solvation model like the Onsager reaction-field model, discussed in Section 9.1. 

The Kamlet-Taft u polarity/polarizability scale is based on a linear solvation energy relationship between the n it transition energy of the solute and the solvent polarity ( 1). The Onsager reaction field theory (11) is applicable to this type of relationship for nonpolar solvents, and successful correlations have previously been demonstrated using conventional liquid solvents ( 7 ). The Onsager theory attempts to describe the interactions between a polar solute molecule and the polarizable solvent in the cybotatic region. The theory predicts that the stabilization of the solute should be proportional to the polarizability of the solvent, which can be estimated from the index of refraction. Since carbon dioxide is a nonpolar fluid it would be expected that a linear relationship... 

The Cl relaxed density approach [18] should give a more accurate evaluation of the reaction field, but because of its more involved computational character it has been rarely applied in Cl solvation models. The only notably exception is the Cl methods proposed by Wiberg at al. in 1991 [19] within the framework of the Onsager reaction field model. In their approach, the electric dipole moment of the solute determining the solvent reaction field is not given by an expectation value but instead it is computed as a derivative of the solute energy with respect to a uniform electric field. 

A more general framework to treat local field effects in linear and nonlinear optical processes in solution has been pioneered, among others [45], by Wortmann and Bishop [46] using a classical Onsager reaction field model (see the contribution by the Cammi and Mennucci for more details). Such a model has not been extended to treat vibrational spectra. 

Probably the simplest quantum-mechanical operators that include interaction with a continuum are the Born and Onsager reaction field models. In the case of neutral solutes, the model could be express as... 

This is a generalization of the Onsager reaction field model for a point dipole inside a spherical cavity. For charged solutes, one should also include an ionic Born term, derived by... 

The experimental data reported in the Table for gas phase have been extracted from measurements in dioxane solution by applying the Onsager reaction field model to eliminate the solvent effect [37], By contrast, the cyclohexane experimental dipole moments have been obtained from those reported in Ref. [37] re-including the proper reaction field factors. Once recalled these facts, we note that the observed solvent-induced changes on both ground and excited state dipole moments are quantitatively reproduced by the calculations. 

The total local field FA is equal to the vector sum of the Onsager cavity field FA, and the Onsager reaction field.101 The latter is independent of EA, and results from the dipoles own fields.101 In the medium of dielectric constant n2, FA is ... 

Local ordering effects have long been recognised experimentally in measurements of dipole moments of polar solutes in non-polar solvents, where the value obtained on the basis of the simple model differs from the value obtained for the pure solute in the gas phase, even when the results are extrapolated to infinite dilution. This so-called solvent effect is due to the Onsager reaction field. If there is no strong local ordering, Onsager s formula (2.52) is valid and the apparent solution moment is related to the isolated molecule or gas moment by... 

Born—Kirkwood—Onsager Reaction Field The theory underlying the implementation of the BKO model at the semiempirical level is no different from that presented in Equations [22] and [23], although the approximations inherent to various levels of semiempirical theory make certain technicalities of the... 

C2H6, N2O and NH3 as a function of density, and have been analyzed using the Onsager reaction field function(15L i.e. L(n2)=(n2-l)/(2n2 +1) as shown in Figure 5. In order to explain the plot of n versus the reaction field, two straight lines were... 

Figure 6. Qustering of CHFj about (dimethylamino)benzonitrile at 50 C based on solvatochromic shifts in fluorescence (A data from ref. 26, — Onsager reaction field theory).

In addition, the molecules properties are changed due to the interaction with the surrounding medium. Several computational schemes have been proposed to address these effects. Tliey are essentially based on the extension of the Onsager reaction field cavity model and give effective hyperpolarizabilities, i.e. molecular hyperpolarizabilities induced by the external fields that include the modifications due to the surrounding molecules as well as local (cavity) field effects [40 2]. These condensed-phase effects have, however, not yet been included in the SFG hyperpolarizability calculations, which are therefore strictly gas-phase calculations. 

These conclusions were based on the severe curvature of the plots of chemical shift against reaction field calculated from both the simple Onsager and the more complex Diehl and Freeman equations. Fontaine et al. have found similar curvature in plots of for acetone versus the Onsager reaction field of cyclohexane-acetone mixtures. Some interesting results recently obtained show that if e is substituted for the dielectric function (e —l)/(e- - ) of equation (5), the curvature of these plots is effectively removed, especially for protons near the dipole location in the large molecules studies by Laszlo and Musher. No explanation for the dependence of on e has been offered. Deviations from linearity in plots of versus in some haloethylenes are explained by the occurrence of excess dispersion forces in the solvents producing the deviations. 

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