Onsager model, polarizability

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 ... 

With this particular example of a located, invariable charge model, Barriol used a method that would be frequently used in his laboratory, particularly in the many studies on the Onsager model to work on a very simple model and to adjust it punctually for one case or another. Other authors calculated the atomic polarizability of a molecule according to a dynamic model based on absorption and dispersion infrared measurements. But the problem is to determine the charge value participating effectively in polarization. [36] Barriol, for his part, did work on the simple model of located, invariable charges, with very disputable hypotheses Things are certainly not like this, but there are some difficulties to find a more elaborated model, with which it would be possible to do calculations. [37]... 

The Onsager Model in the Non-linear Electric Field Effect. The non-linear dectric field theory of Debye disagrees with most of the measurements of Ac in liquids and thdr solutions. To Van Vleck is due the atten t to reduce the discrepandes by applying Onsager s local electric field model in the treatment of the field effect. Aiming at simplidty, he considered only the influence of reorientation of ri d (not polarizable) electric dipoles p,... 

The extension of continuum solvation modes to evaluate vibrational frequencies of molecular systems in solution was pioneered by RivaU and co-workers in the 1980s [150] by exploiting a semiempirical QM molecular model coupled with a continuum description of the medium. Further extension to ab initio QM methods, including the treatment of electron correlation effects and electrical and mechanical anharmonicities, was then proposed [151-153] in the framework of the polarizable continuum model (PCM). Wang et al. [154] used an ab initio self consistent reaction field (SCRF) Onsager model to compute vibrational frequencies at different levels of... 

In this section we compare the PCM formulation of the effective polarizabilities with the semiclassical Onsager-Wortmann-Bishop model [2] (from now on indicated as OWB). 

In contrast, the Onsager—Kirkwood model provides a polarizability in polar liquids larger than that in vapors.21 This is a result of the increase of the dipole moment by the strong electric field, which is generated when a molecule with a permanent dipole moment is introduced in a polarizable medium (Onsager), and the correlation between the orientations of neighboring molecules (Kirkwood).21... 

Onsager 0 equations (Section 5.10), one can extract the dipole moments of polar molecules and the polarizability of any solute molecule. One needs a capacitance cell whose electrodes are as close to each other as practical (for higher capacitances) and reasonable solubilities. If the shape of the solute is very different from the sphere used in the Debye model, then the ellipsoidal cavity has been treated theoretically [13] and applied to hypsochromism [14]. 

In the reaction field model (Onsager, 1936), a solute molecule is considered as a polarizable point dipole located in a spherical or ellipsoidal cavity in the solvent. The solvent itself is considered as an isotropic and homogeneous dielectric continuum. The local field E at the location of the solute molecule is represented by (78) as a superposition of a cavity field E and a reaction field (Boettcher, 1973). 

The effect of the solvent is usually modelled either by the use of the Onsager s self consistent reaction field (SCRF) [20] or by the polarizable continuum method (PCM) [21]. With regard to the relative stability of cytosine tautomers in aqueous solution, these methods provided results [14,15] which, in spite of some discrepancies, are in reasonable agreement with experimental data [3]. However, continuum-based methods do not explicitly take into consideration the local solvent-solute interaction which is instead important in the description of the proton transfer mechanism in hydrogen-bonded systems. A reasonable approach to the problem was recently proposed [22,23] in which the molecule of interest and few solvent molecules are treated as a supermolecule acting as solute, while the bulk of the solvent is represented as a polarizable dielectric. 

The cavity size in the Bom/Onsager/Kirkwood models strongly influences the calculated stabilization. Unfortunately, there is no consensus on how to choose the cavity radius. In some cases, the molecular volume is calculated from the experimental density of the solvent and the cavity radius is defined by equating the cavity volume to the molecular volume. Alternatively, the cavity size may be derived from the (experimental) dielectric constant and the calculated dipole moment and polarizability. In any case, the underlying assumption of these models is that the molecule is roughly spherical or ellipsoidal, which is only generally true for small compact molecules. 

The first is the direct calculation of polarization effects without the use of empirical values of a. Polarizability alone is not sufficient to achieve chemical accuracy better results can be obtained by using group polarizabilities (and hyperpolarizabilities) at the cost, however, of a proliferation in the number of parameters of dubious quality. The direct quantum mechanical calculation avoids these problems and introduces a new dimension to the model. The Schrodinger equation is, in fact, no longer linear this leads to a refinement of the model (We remark that in the Onsager formulation there was no influence on R of the polarizability enhancement of the solute dipole. This was introduced in 1938 by Bottcher [13], but was limited to the original dipole-only model.) and opens the way to robust extensions of the model to nonequilibrium problems. 

Onsager s SCRF is the simplest method for taking dielectric medium effects into account and more accurate approaches have been developed such as polarizable continuum modes, " continuum dielectric solvation models, - explicit-solvent dynamic-dielectric screening model, - and conductor-like screening model (COSMO). Extensive refinements of the SCRF method (spherical, elliptical, multicavity models) in conjunction with INDO/CIS were introduced by Zerner and co-workers ° as well. 

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