Electric field static

As we have discussed earlier in the context of surfaces and interfaces, the breaking of the inversion synnnetry strongly alters the SFIG from a centrosynnnetric medium. Surfaces and interfaces are not the only means of breaking the inversion synnnetry of a centrosynnnetric material. Another important perturbation is diat induced by (static) electric fields. Such electric fields may be applied externally or may arise internally from a depletion layer at the interface of a semiconductor or from a double-charge layer at the interface of a liquid. 

Two states /a and /b that are eigenfunctions of a Hamiltonian Hq in the absence of some external perturbation (e.g., electromagnetic field or static electric field or potential due to surrounding ligands) can be "coupled" by the perturbation V only if the symmetries of V and of the two wavefunctions obey a so-called selection rule. In particular, only if the coupling integral (see Appendix D which deals with time independent perturbation theory)... 

Figure 1. Drawing showing how static electrical fields and microwave fields interact with the same electronic or ionic charge carriers and electrical dipoles.

Expressions for the sixth- through tenth-order coefficients are given in the Appendix. In ESHG experiments with the optical field polarized perpendicular to the static electric field, the measured second hyperpolarizability is [13]... 

Under the conditions of a static electric field, the Maxwell s field equations reduce to the Poisson equation [111,112,172,261], given by... 

The polarlsablllty of a molecule will vary during vibrations which change the Internuclear separations. Thus the vibrations of a molecule sitting In an electrical field will be coupled to the field via the polarlsablllty. This should be particularly noticeable for a molecule adsorbed on an electrode surface where the field strength Is typically In the range 10 -10 V cm, The dipole, perpendicular to the surface, Induced In the molecule by the static electric field will fluctuate In step with the normal mode vibrations of the molecule. 

Now the core functions are adapted to the static electric field of the broken symmetry situation, they are adapted for instance to the A+.-.Asituation while the symmetry-adapted solution optimized the cores in an qualitatively understand the... 

For real perturbations, e g., in the presence of a static electric field, which is the case studied in the present paper, the zero- and first-order orbitals can always be chosen real, so that also... 

The first term in the brackets represents a static electric field in the material and the second term represents a dipole oscillating at 2co, tvdce the frequency of the incident light. This is a process knovm as SHG. 

Formal Theory A small neutral particle at equilibrium in a static electric field experiences a net force due to DEP that can be written as F = (p V)E, where p is the dipole moment vector and E is the external electric field. If the particle is a simple dielectric and is isotropically, linearly, and homogeneously polarizable, then the dipole moment can be written as p = auE, where a is the (scalar) polarizability, V is the volume of the particle, and E is the external field. The force can then be written as ... 

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 energy Ustat is the interaction energy of the N induced dipoles with the static electric field,... 

More recently, Ponder and co-workers [40-48] developed the AMOEBA force field based on a modification of the formulation of Applequist [49] and Thole [50], It is based on a modification of Eq. (9-3) with the static electric field due to permanent charges replaced by permanent multipoles ... 

The diagonal elements of the matrix A are af1 and the off-diagonal elements of Aij are Ty. Equation (9-21) determines how the dipoles are coupled to the static electric field. There are three major methods to determine the dipoles matrix inversion, iterative methods and predictive methods. 

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.

Figure 4. The sample cell arrangement in the DCSHG experiment, where the sample solution was inserted between two glass slips (lop), and the optical design for the DCSHG dispersion experiment, where the compressed H gas medium was pumped by a tunable pulsed dye laser source for Stokes generation by stimulated Raman scattering (bottom). (E° is the static electric field.) Key beam guiding prisms P, Stokes...

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... 

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.

Fig. 17.9 Sketch of a typical setup for ion trap experiments on lasing microdroplets. The oscillating field between the inner and outer ring electrodes forms the trapping potential, and gravitational forces can he opposed by static electrical fields to move the droplet to the trap center with no micromotion...

A static electrical field in free space cannot have potential minima and hence cannot trap a charged particle. By using oscillating fields, a pseudopotential can be formed as illustrated in Fig. 17.8, where amass with a suitable charge to mass ratio can be trapped. 

Among the recently published works, the one which showed that the cyclic structures of water clusters open up to form a linear structure above a certain threshold electric field value a was a systematic ab initio study on the effect of electric field on structure, energetics, and transition states of trimer, tetramer, and pentamer water clusters (both cyclic and acyclic) [36], Considering c/.v-butadiene as a model system, the strength and the direction of a static electric field has been used to examine the delocalization energy, the probabilities of some local electronic structures, the behavior of electron pairs, and the electronic fluctuations [37]. Another recent work performed by Rai et al. focused on the studies using the DFT and its time-dependent counterpart of effects of uniform static electric field on aromatic and aliphatic hydrocarbons [38],... 

The response of the energy of a molecule to a static electric field along the z axis may be written as... 

The conventional approach used to describe the response of a molecule to a static electric field is either to perform pure electronic BO calculations or to perform calculations where the BO values are corrected for vibrational and rotational (thermal) motion of the nuclei. The vibrationally corrected polarizabilities usually do an excellent job of correcting the errors inherent in the pure electronic BO values. Bishop has written several excellent reviews on this topic [78-80]. 

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