Bergman theory

In the statistic route, an effechve dielectric function e(v) is calculated from the dielectric funchon of the metal Enie(v) and the of polymer material po(v) by using a formula, the effective medium theory. The most general effective medium theory is the Bergman theory in which the nanostructure of the composite material can be considered by a spectral density function. The Bergman theory includes the soluhons from the Bruggeman theory and the Maxwell Garnett theory for spherical, parallel-oriented, and random-oriented ellipsoidal parhcles. 

The most popular effective medium theories are the Maxwell Garnett theory [18], which was derived from the classical scattering theory, and the Bruggeman theory [19]. With these theories, an effective dielectric function is calculated from the dielectric functions of both basic materials by using the volume filling factor. At some extensions of these theories, a unique particle shape for all particles is assumed. There is also an other concept based on borders for the effective dielectric functions. The borders are valid for a special nanostructure. Between these borders, the effective dielectric function varies depending on the nanostructure of the material. The Bergman theory includes a spectral density function g(x) that is used as fit function and correlates with the nanostructure of the material [20]. 

L.B. Kier, Molecular Orbital Theory in Drug Research. Academic Press, New York, 1971. P.S. Portoghese, In Molecular and Quantum Pharmacology (E.D. Bergman and B. Pullman, Eds.). Reidel, Dordrecht, 1974, pp. 352-353. 

Bergman effective medium theory, in conjunction with a model dielectric function for the particles, has been used. For the other layers the Bruggeman effective medium theory was used. After [Bel6]. 

Bergman, A., Winters, L., and Cornblatt, B. (1991). Methylphenidate effects on sustained attention. In Greenhill, L. and Osman, B., eds. Ritalin Theory and Patient Management. New York Mary Ann Liebert, Inc., pp. 223-231. 

Hooykaas, R., "Torbern Bergman s crystal theory, Lychnos, 1952, pp. 21-54. 

Lavoisier s ideas met initial resistance from the established chemical community. After all, phlogiston had been used for a century to explain chemistry, and natural philosophers had explained their work based on phlogiston theory. The leading chemists of the day, including Richard Kirwan (1733-1812), Priestley, Cavendish, andTor-bern Bergman (1735-1784), not only rejected Lavoisier s ideas, but they also were antagonistic toward him. This was not to say... 

Figure 9.9 Bergman cycloaromatization reactions for ltex-3-ett-l,5-diyne and its perfluorinated congener, as well as a photochemical reaction scheme for generating the perfluorinated diradical from an iodinated precursor. What spectral features would be expected to be most diagnostic of the different intermediates What levels of theory would be appropriate for predicting these spectral signatures (Note that equilibrium arrows of unequal length indicate which species predominates at equilibrium.)...

It is difficult, from a modern point of view, to understand why Scheele was not led on, by this clear comprehension of the nature of common air and of its relation to combustion, to see the unnecessary character of the phlogiston hypothesis, or at least to accept promptly the suggestion of Lavoisier to that effect. We can better understand the weight of authority of that theory, however, when we remember that Bergman (who prefaced Scheele s book), Kirwan and Priestley, who read and commentated it, also saw no reasons for abandoning that hypothesis, though Kirwan indeed some years later appreciated the logic of the facts. 

This theory was endorsed by Bergman, by de Morveau, and others. 

A theoretical study on the reaction mechanism for the Bergman cyclization from the perspective of the Electron Localization Function and Catastrophe Theory has been reported.175 The authors argue that topological analysis of electron localization function can be used to complement the molecular orbital- or valence bond-based methods. 

Bergman and Hynen (1997) developed a method similar to that of Box and Meyer (1986), but with a simple and exact distribution theory for inference from the test statistic. The important observation of Bergman and Hynen was that the residuals from the fitted location model could complicate inference for the Box-Meyer statistic in two ways. First, the residuals in the two sums of squares could be correlated. Second, the residuals at the high (low) level of factor j typically depend on the actual variances at both levels of the factor, not just the level at which the run was made. 

Dong, H. Chen, B.-Z. Huang, M.-B. Lindh, R. The Bergman cyclizations of the enediyne and its N-substituted analogs using multiconfigurational second-order perturbation theory, J. Comput. Chem. 2012, 33, 537-549. 

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