Clausius-Mosotti-Debye equation

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

The quantity sr is directly sensitive to the detailed chemical composition of the sample. However, the quantitative theory that relates the observed er to the concentrations and dipole moments of the various polar segments present has proved quite difficult to use. The simplest approach is based on the Clausius-Mosotti equation as modified for permanent moments by Debye28). The Debye approach, although overly simple, revealed that sr should decrease with increasing temperature, and should reflect changing concentrations of polar constituents during a reaction. 

Onsager equation — (b) The Onsager equation is an extension of the Debye-Clausius-Mosotti equation, and it relates the - dielectric constant er with the -> dipole moment p ... 

It remains now to relate the molecular quantities ccq and p to the macroscopic polarizability or dielectric constant, which can be measured experimentally. This is a very difficult task and will not be carried out in a rigorous fashion here. Rather, we start our discussion with an approximate equation, given by Debye, which describes the complex dielectric constant in terms of molecular properties. We rationalize the form of the equation through the Clausius-Mosotti equation and then show how e (o)) and s"((o) can be derived from this expression. Additional factors that were not included in Debye s original work, such as the effect of the reaction field and orientation correlation-which are important in condensed phases-will also be discussed... 

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