Local-fields effect

Here the ijk coordinate system represents the laboratory reference frame the primed coordinate system i j k corresponds to coordinates in the molecular system. The quantities Tj, are the matrices describing the coordinate transfomiation between the molecular and laboratory systems. In this relationship, we have neglected local-field effects and expressed the in a fomi equivalent to simnning the molecular response over all the molecules in a unit surface area (with surface density N. (For simplicity, we have omitted any contribution to not attributable to the dipolar response of the molecules. In many cases, however, it is important to measure and account for the background nonlinear response not arising from the dipolar contributions from the molecules of interest.) In equation B 1.5.44, we allow for a distribution of molecular orientations and have denoted by () the corresponding ensemble average ... 

Leventl-Peetz A, Krasovskll E E and Schattke W 1995 Dielectric function and local field effects of TISe2 Phys. Rev. B 51 17 965... 

G2, to G3, and to G4, the effective enhancement was 10%, 36%, and 35% larger than the value estimated by the simple addition of monomeric values. The enhancement included the local field effect due to the screening electric field generated by neighboring molecules. Assuming the chromophore-solvent effect on the second-order susceptibility is independent of the number of chro-mophore units in the dendrimers, p enhancement can be attributed to the inter-molecular dipole-dipole interaction of the chromophore units. Hence, such an intermolecular coupling for the p enhancement should be more effective with the dendrimers composed of the NLO chromophore, whose dipole moment and the charge transfer are unidirectional parallel to the molecular axis. 

Pnorm Ynorm normalized p and y values by volume fraction and local field effect, respectively. 

The SH signal directly scales as the square of the surface concentration of the optically active compounds, as deduced from Eqs. (3), (4), and (9). Hence, the SHG technique can be used as a determination of the surface coverage. Unfortunately, it is very difficult to obtain an absolute calibration of the SH intensity and therefore to determine the absolute number for the surface density of molecules at the interface. This determination also entails the separate measurement of the hyperpolarizability tensor jS,-, another difficult task because of local fields effects as the coverage increases [53]. However, with a proper normalization of the SH intensity with the one obtained at full monolayer coverage, the adsorption isotherm can still be extracted through the square root of the SH intensity. Such a procedure has been followed at the polarized water-DCE interface, for example, see Fig. 3 in the case of 2-( -octadecylamino)-naphthalene-6-sulfonate (ONS) [54]. The surface coverage 6 takes the form ... 

The y-facior. The 0-factor takes into account the fact that the local magnetic field experienced by a particular atom in a molecule may not be the same as the applied field owing to the existence of local field effects. In the absence of such effects, g for any particular radical would simply have the same value as that of the free electron, 2.0023, and all radicals would come into resonance at the same applied field for a given microwave frequency. We can thus express the resonance condition (equation 2.173) as ... 

The second explanation, based on Cardona s (1983) discussion of the local field effect, requires that the dielectric cavity have about the size of a monovacancy. 

For excited state calculations, significant progress has been made based on the GW method first introduced by Hybertsen and Louie. [29] By considering quasi-partide and local field effects, this scheme has allowed accurate calculations of band gaps, which are usually underestimated when using the LDA. This GW approach has been applied to a variety of crystals, and it yields optical spectra in good agreement with experiment. 

P. Ye and Y. R. Shen, Local field effect on linear and nonlinear optical properties of... 

The supporting medium (aqueous or organic solvents membrane-mimetic compartments) also has a profound influence on the optical and electro-optical properties of nanosized semiconductor particles. This dielectric confinement (or local field effect) originates, primarily, in the difference between the refractive indices of semiconductor particles and the surrounding medium [573, 604], In general, the refractive index of the medium is lower than that of the semiconductor particle, which enhances the local electric field adjacent to the semiconductor particle surface as compared with the incident field intensity. Dielectric confinement of semiconductor particles also manifests in altered optical and electro-optical behavior. 

The absorption spectrum is proportional to the imaginary part of the macroscopic dielectric function. Adopting the same level of approximation that we have introduced to obtain GW quasiparticle energies, i.e. neglecting the vertex correction by putting T = 55, we get the so called random phase approximation (RPA) for the dielectric matrix. Within this approximation, neglecting local field effects, the response to a longitudinal field, for q 0, is ... 

More recently, the PCM has been amply extended to the treatment of vibrational spectroscopies, by taking into account not only solvent-induced vibrational frequency shifts, but also vibrational intensities in a unified and coherent formulation. Thus, models to treat IR [8], Raman [9], IR linear dichroism [10], VCD [11] and VROA [12] have been proposed and tested, by including in the formulation local field effects, as well as an incomplete solute-solvent regime (nonequilibrium) and, when necessary, by extending the model to the treatment of specific solute-solvent (or solute-solute) effects. 

In order to formulate a theory for the evaluation of vibrational intensities within the framework of continuum solvation models, it is necessary to consider that formally the radiation electric field (static, Eloc and optical E[jc) acting on the molecule in the cavity differ from the corresponding Maxwell fields in the medium, E and Em. However, the response of the molecule to the external perturbation depends on the field locally acting on it. This problem, usually referred to as the local field effect, is normally solved by resorting to the Onsager-Lorentz theory of dielectric polarization [21,44], In such an approach the macroscopic quantities are related to the microscopic electric response of... 

A more general framework to treat local field effects in linear and nonlinear optical processes in solution has been pioneered, among others [45], by Wortmann and Bishop [46] using a classical Onsager reaction field model (see the contribution by the Cammi and Mennucci for more details). Such a model has not been extended to treat vibrational spectra. 

A nowadays more easily applicable framework to treat local field effects in optical processes involving pure liquids or solutions has been discussed at length elsewhere in this book, and it consists in resorting to dielectric continuum solvation models. In the last pages of this section some application of such models the study of birefringences in condensed phases will be briefly discussed. 

Nonequilibrium solvation model for the electric dipole polarizability. b Result corrected for local field effects. c Ref.[27], mean value for T between 283.1 5 and 293.1 5 K. 

The interactions between the molecule and the environment can lead to distortions in the electrical properties due to the susceptibility of the molecules and the properties of the host matrix. The refractive index of the matrix acts as a screening factor, modifying the optical spectra and interaction between charges or dipoles embedded within it. Local field effects change the interaction with an electromagnetic field and should be considered along with orientation factors in the dipolar interaction. 

Solvent effects on vibrational spectroscopies are analyzed by Cappelli using classical and quantum mechanical continuum models. In particular, PCM and combined PCM/discrete approaches are used to model reaction and local field effects. 

Equations (3) or (4), with refinements as necessary for "local field" effects, are an appropriate and useful basis for discussion of various models of non-conducting solutions of biological species considered in I. In many cases, however, solutions of interest have appreciable ionic concentrations in the natural solvent medium and the polymer or other solute species may also have net charges. Under these conditions, the electrical response is better considered in terms of the total current density Jfc(t) defined and expressed by linear response theory as... 

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,... 

Sipe JE, Boyd RW (2002) Nanocomposite materials for nonlinear optics based on local field effects, in optical properties of nanostructured random media, 82nd edn. Springer, Berlin, pp 1-19... 

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