Kirkwood-Onsager theory

The traditional treatment regarding medium effects is the dielectric continuum model in the Kirkwood-Onsager theory [76]. This simple model assumes that the solvation energy arises from the electrostatic interaction between the solutes and... 

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... 

However, recalculating the value of y using the method described in the paper for the field factors, gives the value in brackets. The unbracketed value, for the overall microscopic nonlinearity, converts to 2859 au. In the case of associating liquids the authors argue that equation (7) can be used in modified form with the inclusion of a factor, g, which they deduce from the Kirkwood-Frohlich modification of the Onsager theory,... 

More recently, Harris and Alder,24 keeping the general principles of Kirkwood s theory, have tried to calculate the polarization effects more rigorously. Unfortunately their final equation does not coincide as it should, with Onsager s equation when it is assumed that there are no short-range interactions cos y) — 0). This is because some of Kirkwood s equations are only valid when the assumptions of the author are justified, and cannot be used as was done by Harris and Alder, when a deformation polarization is superimposed on the orientation polarization. For instance, in presence of deformation effects boundary conditions cannot be introduced in the same manner as in Kirkwood s model (cf. Frdhlich 21). 

For such a comparison one has to consider the step of the density at the phase transition. All the other relations which connect molecular parameters such as the molecular dipole moment /i, the polarizability a and the angle between the molecular long axis and fj, with each other have a general problem the calculation of the internal field and its anisotropy. Therefore, all the equations given in Vol. 1, Chap. VII.2 are necessary and useful but one has to take always into account the limitations of the models. Nevertheless, the Onsager theory [27] (basis for the Maier-Meier model [28]) and Kirkwood-Frbhlich model [29] have been... 

In the Onsager theory of isotropic dielectrics as well as in its extension to the nematic phase given by Maier and Meier the short range dipole-dipole correlations w e ignored. Therefore the dipole moment p in EQNS (1) - (3) cannot be identified with its value measured in the state [16]. The dipole-dipole correlations were considered in the theory developed by Frdtdich [17] who generalised the former Kirkwood approach [18]. Frdhlich has introduced the dipole-dipole correlation factor (known as the Frdhlich-Kirkwood g-factor) in the form... 

Continuum models have a long and honorable tradition in solvation modeling they ultimately have their roots in the classical formulas of Mossotti (1850), Clausius (1879), Lorentz (1880), and Lorenz (1881), based on the polarization fields in condensed media [32, 57], Chemical thermodynamics is based on free energies [58], and the modem theory of free energies in solution is traceable to Bom s derivation (1920) of the electrostatic free energy of insertion of a monatomic ion in a continuum dielectric [59], and Kirkwood and Onsager s... 

Solvent continuum models are now routinely used in quantum mechanical (QM) studies to calculate solvation effects on molecular properties and reactivity. In these models, the solvent is represented by a dielectric continuum that in the presence of electronic and nuclear charges of the solute polarizes, creating an electrostatic potential, the so-called reaction field . The concept goes back to classical electrostatic schemes by Martin [1], Bell [2] and Onsager [3] who made fundamental contributions to the theory of solutions. Scholte [4] and Kirkwood [5] introduced the use of multipole moment distributions. The first implementation in QM calculations was reported in a pioneer work by Rivail and Rinaldi [6,7], Other fundamental investigations were carried out by Tapia and Goscinski [8], Hilton-McCreery et al. [9] and Miertus et al. [10], Many improvements have been made since then (for a review,... 

The first theoretical treatment of infrared solvent shifts was given in 1937 by Kirkwood [166] and by Bauer and Magat [167], Eq. (6-8) - known as the Kirkwood-Bauer-Magat (KBM) relationship - has been derived on the basis of Onsager s reaction field theory [80] using the simple model of a diatomic oscillator within a spherical cavity in an isotropic medium of macroscopic relative permittivity r. 

The classical treatment of nonpolar dielectric materials is expressed by the Clausius-Mossotti equation. Polar materials in nonpolar solvents are better handled by Debye s modification, which allows for the permanent dipole of the molecule. Onsager made the next major step by taking into account the effect of the dipole on the surrounding medium, and finally Kirkwood treated the orientation of neighboring molecules in a more nearly exact manner. (See Table 2-1.) The use of these four theoretical expressions can be quickly narrowed. Because of their limitations to nonpolar liquids or solvents, the Clausius-Mossotti and Debye equations have little application to H bonded systems. Kirkwood s equation has great potential interest, but in the present state of the theory of liquids the factor g is virtually an empirical constant. The equation has been applied in only a few cases. 

Dipole moments may also be derived by a consideration of the dielectric constant data themselves. Since amino acids and proteins are soluble only in polar solvents, the treatment which is applicable to dilute solutions of polar molecules in a non-polar medium cannot be applied here. However, the general theory of polar liquids developed by Onsager (S7) and Kirkwood (67) [see also Kirkwood in Cohn and Edsall [16), Chapter 12], is applicable here. According to Kirkwood s treatment, the dipole moment (/z) of an individual molecule in the liquid is in general different from its moment in the gaseous state because the attractions... 

Onsager s equation has been used for slightly polar solvents such as toluene. With strongly polar solvents, chloroform for instance, Kirkwood s or Frohlich s theories must be resorted to, and no value of the dipole moment can be obtained unless the correlation factor g is known by independent data concerning the structure of the solution. 

Molecular theories for the static permittivity bq of dipolar liquids developed originally by Onsager, Kirkwood, and Frohlich were adapted for linear bulk... 

Using the fundamental continuum theories (of Born, Onsager, Kirkwood), a direct calculation is in fact made not of the solvation energy but rather of the free solvation energy. Since, however, in most publications on this theme the calculated free solvation energy is stubbornly called the solvation energy, we shall retain this customary term. 

Dr. Franck indicated that the Calusius-Mosottieffect had been treated using the Onsager-Kirkwood corrections with agreement between experiment and theory that is only satisfactory. 

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