Clausius-Mosotti model

One of the weaknesses of the classical Clausius-Mosotti model is that it refers to the electronic polarizability a(cu) only at frequency (0 = 0. However, associated with a single chemical bond jk between atoms j and k one has excitation energies (in the case of a diatomic... 

Empirical models for the induced trace have also been obtained from (nonspectroscopic) measurements of the second virial dielectric coefficient of the Clausius-Mosotti and Lorentz-Lorenz expansions [30]. Excellent surveys with numerous references to the historical as well as the modern dielectric research activities were given by Buckingham [27], Kielich [89], and Sutter [143] in 1972 see also a recent review with a somewhat more spectroscopic emphasis [11]. 

The Born model with integral or partial charges assumes that the ions have zero polaris-ability. This is reasonable for small cations such as Li" or Mg + but can introduce significant errors for other systems. One pxropjerty that clearly demonstrates this is the high-frequency dielectric constant. At a suitably high frequency only the electrons can keep up with the external field and the dielectric constant is given by the Clausius-Mosotti relationship ... 

The shell model the ions are described by a core, including the nucleus and the inner electrons, and a zero-mass shell representing the valence electrons (Dick and Overhauser, 1958). The core and the shell bear opposite charges. They are harmonically coupled by a spring of stiffness k. The electric field / exerted by neighbouring ions shifts the shell with respect to the core position. If Y is the shell charge, induces a dipole moment equal to SY Ik. The ion polarizability ot in the model, is thus equal to o = Y jk. The value of k may be deduced from the value of the optical dielectric constant eClausius-Mosotti relationship ... 

The classical model of crystalline polarizabilities was introduced at least as early as 1850 by Mosotti, and discussed in an 1879 book by Clausius. The polarizability a of the medium is described in terms of a set of polarizability parameters a.j of the ions j in the crystal distributed in a unit cell of volume. The relation between a and the parameters ccj is (per unit cell)... 

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