Onsager reaction factor

The experimental data reported in the Table for gas phase have been extracted from measurements in dioxane solution by applying the Onsager reaction field model to eliminate the solvent effect [37], By contrast, the cyclohexane experimental dipole moments have been obtained from those reported in Ref. [37] re-including the proper reaction field factors. Once recalled these facts, we note that the observed solvent-induced changes on both ground and excited state dipole moments are quantitatively reproduced by the calculations. 

In case (I), the theory that has been used to describe the EFISH analysis in earlier sections, the isolated molecule calculation provides the pz value and the internal field factors adjust the fields to allow for the polarization on the cavity surface. The elfect of reaction fields due to the additional polarization on the cavity walls induced by the permanent and induced dipoles on the central molecule is implicitly included in the low frequency Onsager field factor through the dielectric constant values. The choice of the high frequency dielectric constant ( o) in this formulation is rather ill defined and no account is taken of changes in the static or dynamic polarizabilities of the molecule as a result of the surrounding fields. 

Here, N stands for the molecular packing density, h = 3el(2e+ 1) is the cavity field factor, e = (ej + 2e )/3 is the averaged dielectric constant, F is the Onsager reaction field, < //> and are the principal elements of the molecular polarizability tensor. 

The internal field factors are now in general to be adjusted to take account of the differing environments of the molecules of the two species. In particular the reaction field introduced in the Onsager field will be different, even in very dilute solution, in the cavity surrounding the polar solute as compared to that of a non-polar solvent. 

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... 

The Clausius-Mossotti equation is based on the simplest (Lorentz) form of the local field. In reality, the induced dipole in the selected molecule also creates an additional, reaction field that modifies the cavity field. On account of these factors Onsager has obtained the following equation for dielectric permittivity... 

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