Lorenz-Lorentz theory

Lorenz-Lorentz theory addressed the issue by extending the approach of Clausius-Mossotti to optical frequency fields (12,13). This extension relies on a spherical cavity (compare with the need for a needle-shaped cavity) and takes into account the effect of other charges. The only thorny issue is that a spherical cavity is not the best choice for anisotropic molecules. Nevertheless, the Lorenz-Lorentz approach has been widely used in studying optical properties of polymers (14). The expression of the local field is given by... 

It is surprising that the mole refraction of the latter two compounds is not in agreement with the rules of Eisenlohr and Lorenz-Lorentz. No explanation has so far been given for the difference between experimental data and the theory. The Si—Si bond has not been found to have an abnormal increment. 

We show below how these inaccuracies in the Lorenz-Lorentz formula can be eliminated. We employ the local field method to modify this formula and apply it to anisotropic organic crystals of complex structure. We discuss below also a variety of their optical properties which were earlier analyzed in a less general form only in the framework of exciton theory. We explain how it has... 

Considerations of Maxwell-Gamett [273, 274] and Bragg and Pippard [275] based on Lorentz-Lorenz polarization theory have been put into the form for dielectric films composed of cylindrical columnar crystals by Harris, Macleod et al. [276] ... 

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... 

The crudest approximation to the density matrix for the system is obtained by assuming that there are no statistical correlations between the elementary excitations (perfect fluid), so that can be written as a simple product of molecular density matrices A. A better approximation is obtained if one does a quantum field theory calculation of the local field effects in the system which in a certain approximation gives the Lorentz-Lorenz correction L(TT) in terms of the refractive index n53). One then writes,... 

The calculated moment thus considerably exceeds the experimental value and furthermore represents the dipole as acting in the opposite direction the chlorine is represented as positive and the hydrogen negative. This result is clearly incorrect and Debye has shown that the error is due to the fact that the Lorentz-Lorenz equation is not valid at the small distances considered owing to the non-uniform character of the field. If the internuclear distances were of the order of 5 A, this type of calculation would be permissible. Attempts have been made to calculate the polarizability in a non-uniform electric field by the methods of wave mechanics , but have not yet been successful in producing a theory of the intermediate type of bond. 

The application of the Lorentz-Lorenz equation gives a convincing demonstration of the general similarity of the linear response in gas and liquid but its application in the liquid introduces an approximation which has not yet been quantified. A more precise objective for the theory would be to calculate the frequency dependent susceptibility or refractive index directly. For a continuum model this may lead to a polarizability rigorously defined through the Lorentz-Lorenz equation as shown in treatments of the Ewald-Oseen theorem (see, for example Born and Wolf, plOO),59 but the polarizability defined in this way need not refer to one molecule and would not be precisely related to the gas parameters. 

Among the few determinations of of molecular crystals, the CPHF/ INDO smdy of Yamada et al. [25] is unique because, on the one hand, it concerns an open-shell molecule, the p-nitrophenyl-nitronyl-nitroxide radical (p-NPNN) and, on the other hand, it combines in a hybrid way the oriented gas model and the supermolecule approach. Another smdy is due to Luo et al. [26], who calculated the third-order nonlinear susceptibility of amorphous thinmultilayered films of fullerenes by combining the self-consistent reaction field (SCRF) theory with cavity field factors. The amorphous namre of the system justifies the choice of the SCRF method, the removal of the sums in Eq. (3), and the use of the average second hyperpolarizability. They emphasized the differences between the Lorentz Lorenz local field factors and the more general Onsager Bbttcher ones. For Ceo the results differ by 25% but are in similar... 

Lorenz derived (1) by assuming that a material is made up of spherical molecules through which light travels slower than in the vacuum in which they are situated, while Lorentz proceeded logically from Maxwell s electromagnetic theory and was thus able to explain, in addition, the... 

In 1906, J. C. Maxwell Garnett used the Maxwell Garnett theory, equation (12), for the first time to descibe the color of metal colloids glasses and of thin metal films. Equation (12) can be deviated from the Rayleigh scattering theory for spherical particles [21], or from the Lorentz-Lorenz assumption for the electrical field of a sphere and the Clausius-Mossotti Equation by using the polarizability of an metal particle if only dipole polarization is considered [22]. 

It follows from Maxwell s theory of electromagnetic radiation that e = n, where s is the dielectric constant measured at the frequency for which the refractive index is n. Equation (9.8) thus leads immediately to the Lorentz-Lorenz equation... 

The apparent oscillator strength is proportional to the integrated intensity under the molar absorption curve. To derive the formula, Chako followed the elassieal dispersion theory with the Lorentz-Lorenz relation (also known as the Clausius-Mosotti relation), assuming that the solute molecule is located at the center of the spherical cavity in the continuous dielectric medium of the solvent. Hence, the factor derived by Chako is also called the Lorentz-Lorenz correction. Similar derivation was also presented by Kortiim. The same formula was also derived by Polo and Wilson from a viewpoint different from Chako. 

Applying the well known formula of Lorentz-Lorenz one finds a less good agreement. This formula is based on a theory which does not account for the influence of the internal field. The Gladstone and Dale equation is a purely empirical relation which seems to cover the actual behaviour of systems of this kind very satisfactorily. 

The relationship between a and the concentration of scattering centers is derived next (Tanford, 1961). The Lorentz-Lorenz formula (another aspect of electromagnetic theory) is... 

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