Field-induced quantities

Field-Induced Quantities Obtained as Properties of Resonance States in the framework of the CESE-SSA... 

FIELD-INDUCED QUANTITIES OBTAINED AS PROPERTIES OF RESONANCE STATES IN THE FRAMEWORK OF THE CESE-SSA... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

Inhomogeneity of the field-induced change in the characteristics of the medium, the complex dielectric permittivity esc = ei + >n particular (here e1>2 are real quantities), is a distinguishing feature of electrooptic effects in the space-charge region. The ranges of such inhomogeneities (10 4-10 5 cm)... 

The drawback of Eq. (14c) is that the integrands comprise a dynamic quantity p (f) and an induced distribution F( y). Both are perturbed by radiation field and therefore depend on its complex amplitude E. Because of that further calculations become cumbersome [18]. It is possible to overcome this drawback on the basis of a linear-response approximation. The field-induced difference 8p of the law of motion p (f) from the steady-state law p (f) is proportional to the field amplitude E. The same is supposed with respect to the difference F(y) — 1 of induced and homogeneous distributions (for the latter F = 1). A steady-state dipole s trajectory does not depend on phase y and therefore does not contribute (at F = 1) to the integral (14c). Then in a linear approximation we may represent the average7 of p (f)F(y) over y as a sum... 

In Eq. (10), all quantities are set or measured independently except p. and Po, which can therefore in principle be deduced from the experimental I(VD, VG) curves. In fact, the field-effect mobility thus obtained may differ from the microscopic bulk mobility for a variety of reasons, such as confinement effects in the conducting channel or change in the transport properties near the surface. More important, a complete analysis must allow for the presence of surface states and of traps in the bulk and the distribution of total field-induced charge among them. The elements of this analysis are given in Ref. 230. 

The magnetic field in the vicinity of a nucleus is altered by the surrounding electrons, from Bo to a value o ), in which the quantity o is called the shielding (Figure 3-1 a and b). Because the magnetic field induced by the electrons opposes the static B field, the effect is said to be diamagnetic (or and is directly proportional to the electron density. 

Atom-Atom Interactions. - The methods applied, usually to interactions in the inert gases, are a natural extension of diatomic molecule calculations. From the interaction potentials observable quantities, especially the virial coefficients can be calculated. Maroulis et al.31 have applied the ab initio finite field method to calculate the interaction polarizability of two xenon atoms. A sequence of new basis sets for Xe, especially designed for interaction studies have been employed. It has been verified that values obtained from a standard DFT method are qualitatively correct in describing the interaction polarizability curves. Haskopoulos et al.32 have applied similar methods to calculate the interaction polarizability of the Kr-Xe pair. The second virial coefficients of neon gas have been computed by Hattig et al.,33 using an accurate CCSD(T) potential for the Ne-Ne van der Waals potential and interaction-induced electric dipole polarizabilities and hyperpolarizabilities also obtained by CCSD calculations. The refractivity, electric-field induced SHG coefficients and the virial coefficients were evaluated. The authors claim that the results are expected to be more reliable than current experimental data. 

Only the static values of the electronic contributions are available at the same level of theory. These are compared with the static, electro-optic effect ft and field induced SHG y, which are experimentally relevant quantities. 

Diffuse dispersive attractions and hydrophobic effects One may easily imagine that many different, inhomogeneous electric fields are present in supramolecular assemblies. These fields induce new electric fields, which may also be decomposed into electrostatic multipoles (for instance, dipole moments may be induced depending on the strength of the inducing permanent field and the (local) polarizability of the system, which is the material specific quantity). Interactions based on these effects are usually denoted van der Waals interactions. But note that the induced fields themselves will induce new polarization effects and so on. 

The Kerr and Cotton-Mouton experiments stand apart from the others in the sense that it is the electric-field-induced anisotropy in the refractive index which is measured (i.e. the difference in two quantities) rather than a single quantity such as an intensity. This means that, e.g., for the Cotton-Mouton effect, the experimentally-useful quantity is... 

In addition to orienting dipoles, electric fields induce dipole moments in molecules, since electrons and nuclei experience forces in opposite directions in the same electric field and since electrons, being less massive, move much more easily than nuclei in a field. The quantity that measures the ease with which the electron cloud in a certain molecule can be distorted is the molecular polarizability ccq. The magnitude of an induced dipole is given as... 

In conclusion, the discussion, the results, and the accompanying references of fhis chapter have documented, explained, and justified a set of formalisms and methods that can be used for the ab initio computation of fime-independenf and fime-dependent polyelectronic wavefunctions and for fhe quanfifafive undersfanding of basic quantities connected to a variety of field-free and field-induced unstable states (resonances) in the continuous spectra of afoms and molecules. 

In this case, the external field induces a time-dependent perturbation of the electron density of the cluster, Sn(r,t% with Fourier components 5n(r,linear response regime is the dynamic susceptibility (( , r ), which relates the individual components, 5n(r,o>), of the induced density to those of the applied field ... 

Since the chemical shift is dictated by field-induced paramagnetic and diamagnetic circulation of electrons, its quantity is dependent upon the external magnetic field or, more accurately, proportional to the latter. With the displacements being of the order of a few parts per million or often only a fraction of a part per million, it is essential to conduct the experiments at a sufficiently high field in order to resolve resonances of various nuclei pertaining to a molecule. 

The utility of a series of different inorganic bases, including LHMDS, NaHMDS, KHMDS, f-BuONa, f-BuOK, f-BuOLi, LTMP, LDA, PhOLi, MeONa, and EtONa for the alkylation of cyclohexanone with benzyl bromide in a microreactor was studied. The microreactor employed a field-induced electro-kinetic flow acting as apump. To achieve a sufficient electrokinetic mobilization, the inorganic bases had to be solubilized by the addition of stoichiometric quantities of the appropriate crown ethers. With a single exception (LHMDS with 12-crown-4 ether), the desired electrokinetic mobility was reached with aU other bases under these conditions. 

Traditionally, the term electroconvection is used in at least four different physical contexts, of which three pertain to flows of liquid dielectrics. Thus, it is used to describe the electric field-induced flow of nematic liquid crystals, the flow of liquid dielectrics caused by the action of electric field on the space charge of ions of the appropriate sign injected in a low quantity into a fluid, or the effects of an electric field acting on the surface charge accumulated at the interface between two weakly conducting fluids. The latter process was studied by G. I. Taylor, who in the mid-1960s introduced the leaky dielectric model... 

Note that the field-induced changes in the physical quantities of the material found in the above equations (including Aa) have a quadratic dependence with the electric field (Equation 19.25). A quadratic dependence on applied field is indeed generally found for the EA signal in experiments. 

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