Electric fields static field 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... 

To obtain hyperpolarizabilities of calibrational quality, a number of standards must be met. The wavefunctions used must be of the highest quality and include electronic correlation. The frequency dependence of the property must be taken into account from the start and not be simply treated as an ad hoc add-on quantity. Zero-point vibrational averaging coupled with consideration of the Maxwell-Boltzmann distribution of populations amongst the rotational states must also be included. The effects of the electric fields (static and dynamic) on nuclear motion must likewise be brought into play (the results given in this section include these effects, but exactly how will be left until Section 3.2.). All this is obviously a tall order and can (and has) only been achieved for the simplest of species He, H2, and D2. Comparison with dilute gas-phase dc-SHG experiments on H2 and D2 (with the helium theoretical values as the standard) shows the challenge to have been met. 

Distortions due to magnetic and electric fields static theory 3.4.1 The Freedericksz effect... 

Permanent molecular electric dipole moments and static polarizability anisotropies can be obtained from electric-field splittings (Stark effects). Only a few dipole moments have been determined in recent years. 

As noted above with regard to ELF and VLF radiation, there is no evidence that electric fields have an effect on humans (except in cases where pacemakers are used). In fact, there are no common lab situations where laboratorians would be exposed to strong static electric fields. 

We now consider the process of director axis reorientation by an external static or low-frequency field. Optical field effects are discussed in Chapter 6. The following examples will illustrate some of the important relationships among the various torques and dynamical effects discussed in the preceding sections. We will consider the magnetic field as it does not involve complicated local field effects and other electric phenomena (e.g., conduction). The electric field counterparts of the results obtained here for the magnetic field can be simply obtained by the replacement of by AeE [cf Eq. (3.26) and (3.29)]. 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

The outer layer (beyond the compact layer), referred to as the diffuse layer (or Gouy layer), is a three-dimensional region of scattered ions, which extends from the OHP into the bulk solution. Such an ionic distribution reflects the counterbalance between ordering forces of the electrical field and the disorder caused by a random thermal motion. Based on the equilibrium between these two opposing effects, the concentration of ionic species at a given distance from the surface, C(x), decays exponentially with the ratio between the electro static energy (zF) and the thermal energy (R 7). in accordance with the Boltzmann equation ... 

The CCSD model gives for static and frequency-dependent hyperpolarizabilities usually results close to the experimental values, provided that the effects of vibrational averaging and the pure vibrational contributions have been accounted for. Zero point vibrational corrections for the static and the electric field induced second harmonic generation (ESHG) hyperpolarizability of methane have recently been calculated by Bishop and Sauer using SCF and MCSCF wavefunctions [51]. 

Vidal F, Busson B, Tadjeddine A, Peremans A. 2003. Effect of a static electric field on the vibrational and electronic properties of a compressed CO adlayer on Pt(l 10) in nonaqueous electrolyte as probed by infia ed reflection-absorption spectroscopy and infi ared-visible sum-fi equency generation spectroscopy. J Chem Phys 119 12492-12498. 

The general problem of the orienting effect of a static electric field (orientation of polar molecules) was first considered by Debye [6, 7], Frolich [8], and more recently Bottcher [9,10]. 

Fig. 1.2 A distribution of dipoles undergoing the effect of a static electric field.

Earlier sections of this review have already discussed results for quadrupolar nuclei in certain connections for Knight shifts (Sects. 3.4.3 and 3.4.4), for electric-field (Stark) effects upon NQCCs (Sect. 3.1), for measurements of NQCCs in GaN by static NMR and the effects of strain upon NQCCs (Sect. 3.2.1), for obtaining exchange couplings by MAS-NMR (Sect. 3.2.2), and for characterizing polytypes and defects in cubic polytypes by chemical shifts and NQCCs obtained from MAS-NMR (Sect. 3.3.2). This section will give some further examples of information about semiconductors obtained from the NMR of quadrupolar nuclei (see also [18]). 

When a strong static electric field is applied across a medium, its dielectric and optical properties become anisotropic. When a low frequency analyzing electric field is used to probe the anisotropy, it is called the nonlinear dielectric effect (NLDE) or dielectric saturation (17). It is the low frequency analogue of the Kerr effect. The interactions which cause the NLDE are similar to those of EFLS. For a single flexible polar molecule, the external field will influence the molecule in two ways firstly, it will interact with the total dipole moment and orient it, secondly, it will perturb the equilibrium conformation of the molecule to favor the conformations with the larger dipole moment. Thus, the orientation by the field will cause a decrease while the polarization of the molecule will cause an... 

Brownian motion, other mechanisms, as for instance, a decay of a local vibration into substrate phonons (see Chapter 4) or inhomogeneous broadening caused by static shifts of oscillator frequencies in random electric fields of a disordered dipole environment. A temperature dependence of a broadening arising from these additional effects should be considerably weaker than the exponential dependence in Eq. (A2.26) or (A2.4). The total broadening is therefore expressible as... 

Figure 9.3 Schematic illustration of second-order nonlinear optical effects, (a) Second-harmonic generation. Two light fields at frequency go are incident on medium with nonvanishing / 2. Nonlinear interaction with medium creates new field at frequency 2 go. (b) Frequency mixing. One light field at frequency GO and one at frequency go2 is incident on nonlinear medium. Nonlinear interaction with medium creates new field at frequency goi + go2. (c) electro-optic effect. Static electric field E (0) applied over nonlinear medium changes phase of an incoming light field.

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