Molecules internal fields

In deriving this equation, the effect of the surroundings of a molecule (internal field) is taken into account by assuming that it resides within a spherical cavity (Lorenz field). This assumption can restrict the applicability of this equation. The macroscopic quantity, P, is related to the microscopic quantity, the molecular polarizability (assumed in this case to be isotropic so that a and P are scalar quantities)... 

The internal field is that microwave field which is generally the object for solution when MaxweU s equations are appUed to an object of arbitrary geometry and placed in a certain electromagnetic environment. The is to be distinguished from the local field seen by a single molecule which is not necessarily the same (22). The dielectric permittivity as a function of frequency can be described by theoretical models (23) and measured by weU-developed techniques for uniform (homogeneous) materials (24). 

Gaussian probability, linear thermodynamics quadratic expansion, 12-13 regression theorem, 17-20 Gaussian-type orbitals (GTOs), 257-258 Gauss s law, diatomic molecules, internal electric field computations, 249-250... 

Based on the fundamental dipole moment concepts of mesomeric moment and interaction moment, models to explain the enhanced optical nonlinearities of polarized conjugated molecules have been devised. The equivalent internal field (EIF) model of Oudar and Chemla relates the j8 of a molecule to an equivalent electric field ER due to substituent R which biases the hyperpolarizabilities (28). In the case of donor-acceptor systems anomalously large nonlinearities result as a consequence of contributions from intramolecular charge-transfer interaction (related to /xjnt) and expressions to quantify this contribution have been obtained (29). Related treatments dealing with this problem have appeared one due to Levine and Bethea bearing directly on the EIF model (30), another due to Levine using spectroscopically derived substituent perturbations rather than dipole moment based data (31.) and yet another more empirical treatment by Dulcic and Sauteret involving reinforcement of substituent effects (32). 

Any external electric field is minute in comparison with the internal field generated by the system of electrons and nuclei inside a molecule. The effect of the operator (8.4) is therefore always much smaller than the electronic energy of the molecule. In most cases, the effects of electric-field perturbations are also much smaller than the vibrational energy of the molecule. The interaction with an external DC field can thus be treated as a perturbation to the vibronic energy levels of molecules. 

Accounting for the effect of the host material on the interactions between the dipoles involves the refractive index, the relative orientation of the charges, and the local or internal field. The local or internal field problem is associated with the fact that molecules in a host medium occupy a particular volume or a cavity . This cavity description has been used to formalize the description of interactions between dipoles. The region occupied by the molecule results in an additional correction so the field acting on the molecule will be an effective local field rather than the mean macroscopic field. The field acting on the molecule may be an applied electromagnetic field (such as in absorption), the effect of another dipole or a combination of the two. 

The internal field Fk is assumed to be the same for the segments and the solvent molecules. 

Next, use is made of the simple hypothesis that all the positions of the molecules and segments are equally probable, and, following tradition, we shall formulate an expression for the internal field as a field within a spherical cavity (Vleck 1932 Frohlich 1958)... 

The effective Eeld E, is the sum between the macroscopic field Eo and the internal field due to the other molecules of the medium. The latter can be calculated by adding the individual contributions of the other molecules close to the selected one, Elncal, and subtracting the contribution from the same molecules treated in an average continuum approximation described by the polarization P ... 

In order to obtain the dynamic matrix, a good representation of the potential is needed. Supposing that the internal field is known from the investigation of the isolated molecule, the components of the above-mentioned intermolecular potential must be described. 

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