Solvent infinite frequency permittivity

In the first equality, is the static permittivity of the solvent, its infinite frequency permittivity, is the ratio of the dynamic coupling and the Kirkwood dipole... 

Solvent permittivity — is an index of the ability of a solvent to attenuate the transmission of an electrostatic force. This quantity is also called the -> dielectric constant. -> permittivity decreases with field frequency. Static (related to infinite frequency) and optical op (related to optical frequencies) permittivities are used in numerous models evaluating the solvation of ions in polar solvents under both static and dynamic conditions. Usually the refractive index n is used instead of op (n2 = eop), as these quantities are available for the majority of solvents. The theory of permittivity was first proposed by Debye [i]. Systematic description of further development can be found in the monograph of Frohlich [ii]. Various aspects of application to reactions in polar media and solution properties, as well as tabulated values can be found in Fawcetts textbook [iii]. 

For the spectroscopic applications, it would be again instructive to separate the noninertial and inertial components of the electrostatic polarization of the dielectric medium. The first of them corresponds to the electrostatic polarization of the electron charge distribution in the solvent that is supposedly instantaneous as compared to any electronic or conformational transition of the solute. The second component arises from the orientational polarization of the solvent molecules in the electrostatic field of the solute. The noninertial polarization can be described by the optical dielectric permittivity of the solvent that corresponds to the infinite frequency of external electromagnetic field (e Ud) whereas the inertial polarization represents the slow, orientational part of the total dielectric constant of the solvent, s. In order to separate the noninertial polarization, it is helpful to determine the solute charge density as the sum of the respective nuclear and electronic parts... 

Here is the permittivity at infinite frequency of the alternating electric field it expresses the inability of the molecular dipoles of the solvent to orient themselves in the direction of the field. Then only the electronic orientation within the atoms remains dependent on the electric field, which is expressed by the refractive index squared, nl, approximated as Equation 3.16 can be simplified by expressing it as a power series in E, truncated after the second term, resulting in Equation 2.13 e(E) = e(0) + PE. Values of the coefficient p have been compiled by Marcus and Hefter [4] but are known for only some of the solvents listed in the tables of this chapter. 

The two dielectric constants in Eq. [6] warrant some discussion. The quantity e, which is sometimes called simply the dielectric constant (often denoted e instead of e ) is more precisely the static or zero-frequency dielectric constant. (Even more precisely, it is the scalar electric permittivity relative to that of vacuum, and is therefore dimensionless.) This quantity includes the effects of both orientational and electronic polarization. For a vertical ionization process, however, the solvent s orientational degrees of freedom are frozen, but the electron densities of individual solvent molecules can adjust on the same timescale on which the ionization process occurs. Such considerations lead to a correction involving the optical (infinite-frequency) dielectric constant, where denotes the solvent s index of refraction. 

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