Kirkwood-Westheimer model

The spherical cavity, dipole only, SCRF model is known as the OnMger model.The Kirkwood model s refers to a general multipole expansion, if the cavity is ellipsoidal the Kirkwood—Westheimer model arise." A fixed dipole moment of yr in the Onsager model gives rise to an energy stabilization. 

As shown in Figure 1,4a, most molecules are not spherical, and so use of a spherical cavity large enough to enclose the whole molecule may mean that solvent will be quite far away from the molecule in some directions. The Kirkwood-Westheimer model uses an ellipsoidal cavity, which comes closer to mimicking a true molecular surface. 

Kinetic balance, of basis sets, 214 Kirkwood model, solvation, 395 Kirkwood-Westheimer model, solvation, 395... 

W. H. Orttung. Extension of the Kirkwood-Westheimer model of substituent effects to general shapes, charges, and polarizabilities. Application to the substituted Biocyclo[2.2.2]octanes. J. Am. Chem. Soc., /00 4369-4375 (1978). 

Kirkwood-Westheimer model arise. A fixed dipole moment of fj, in the Onsager model gives rise to an energy stabilization. 

The inductive model assumes that substituent effects are propagated by the successive polarization of the bonds between the substituent and the reaction site. This effect is transmitted through both the a bond network (a inductive effect) and the Jt-bond network (jt inductive effect).10 The field effect model assumes that the polar effect originates in bond dipole moments and is propagated according to the classical laws of electrostatics. The appropriate description of this effect is the Kirkwood-Westheimer model, in which the molecule is treated as a cavity of low dielectric constant submerged in a solvent continuum. 

The simplest reaction field model, known as the Born model, consists of a spherical cavity where only the net charge and the dipole moment of the molecule are considered. When the solute is represented by a set of atomic charges the model is often called Generalized Born (GB) Model. Ellipsoidal cavities can also be employed as in the early Kirkwood-Westheimer model. The main advantage of these simple models is that [Eq. (7.12)] can be computed analytically. Unfortunately, they are of limited accuracy. 

The Kirkwood model refers to a general multipole expansion in a spherical cavity, while the Kirkwood-Westheimer model arises for an ellipsoidal cavity. ... 

Note that the separability of the two contributions of the polar effect is attained with difficulty in fact, attempts to separate the polar effect contributions have been unsuccessful, so they are usually considered together. However, from a theoretical point of view, field effects have been studied using the Kirkwood-Westheimer [Kirkwood and Westheimer, 1938 Westheimer and Kirkwood, 1938] and Tanford models [Tanford, 1957]. 

If all of the atoms and charges in the system of interest are explicitly represented and atomic polarization is included, the use of a dielectric constant other than unity would be inappropriate. A variety of models has been used, however, to approximate the dielectric behavior of a macromolecular system where the solvent was not explicitly included. Dielectric constants for the protein interior between 2 and 10 have been employed, as has a distance-dependent dielectric response equal to the distance in angstroms.78 Also, simple forms of the Kirkwood-Westheimer-Tanford model79 have been used to approximate the effect of the aqueous solvent. An approach that may improve our understanding in this area employs linear response theory to evaluate the spatially dependent dielectric response.80 In any such model it is necessary to consider the frequency dependence of the dielectric constant relative to the time scale of the dynamic process under consideration. 

The spiro [3,4]octane-2-carboxylic acids (1—4) have been prepared and used in experiments designed to test the applicability of either the field or inductive models for the effects of polar substituents. The experimentally determined ApK, values of these acids have been compared with values calculated using either spherical or ellipsoidal cavities in a modified Kirkwood-Westheimer expression. 

Kinetic and equilibrium acidities of bridgehead hydrogens in fluorinated norbornanes and bicyclo[2,2,2]octanes are accommodated by a classical field effect modelled on Kirkwood-Westheimer calculations. The stability of the donor-acceptor complexes of homoconjugated dienes e.g. norbornadiene) with tetracyanoethylene increases with increasing ionization potential of the donor hydrocarbon, and the IP values also correlate with the charge-transfer excitation energies. ... 

A through-space electrostatic effect (field effect) due to the charge on X. This model was developed by Kirkwood and Westheimer who applied classical electrostatics to the problem. They showed that this model, the classical field effect (CFE), depended on the distance d between X and Y, the cosine of the angle 6 between d and the X—G bond, the effective dielectric constant and the bond moment of X. 

The several continuum models used to evaluate the terms given are, in fact, different versions of the classical reaction field theory introduced by Kirkwood (Kirkwood, 1934 Westheimer and Kirkwood, 1938) and Onsa-ger (1936). The contributions of the first two terms A ajb and A AdBw) to the A a.b value are small and partially compensate each other. Calcula-... 

In a major contribution to the understanding of transmission of substituent effects in organic molecules, Westheimer and co-workers (Kirkwood and Westheimer, 1938 Westheimer and Kirkwood, 1938 Westheimer and Shookhoff, 1939 Westheimer et al., 1942) pointed out that the electrostatic field of a charged or dipolar substituent is at least partially transmitted through the molecule itself. Because the dielectric constant of an organic molecule is much smaller than that of a polar solvent such as water, substituent effects are attenuated with increasing distance to a much smaller extent than predicted by Equations (5) and (6). Kirkwood and Westheimer described methods for computation of the effective dielectric constant for a molecule-solvent system. The use of the effective dielectric constant (Dea) in place of the solvent s dielectric constant (D) in Equations (5) and (6) greatly improved the quantitative capabilities of electrostatic models of substituent effects. 

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