Classical field effect

A through-space electrostatic effect (field effect) due to the charge on X. This model was developed by Kirkwood and Westheimer who applied classical electrostatics to the problem. They showed that this model, the classical field effect (CFE), depended on the distance d between X and Y, the cosine of the angle 6 between d and the X—G bond, the effective dielectric constant and the bond moment of X. 

It has long been known that a substituent X in an XGY system can exert an electrical effect on an active site Y. It is also well known that the electrical effect which results when X is bonded to an sp hybridized carbon atom differs from that observed when X is bonded to an sp or an sp hybridized carbon atom. As electron delocalization is minimal, in the first case, it has been chosen as the reference system. The electrical effect observed in systems of this type is a universal electrical effect which occurs in all systems. In the second type of system, a second effect (resonance effect) occurs due to delocalization, which is dependent both on the inherent capacity for delocalization and on the electronic demand of file active site. In systems of the second type the overall (total) electrical effect is assumed to be a combination of the universal and the delocalized electrical effects. For many years an argument has sometimes raged (and at other times whimpered) concerning the mode of transmission of the universal electrical effect. Two models were proposed originally by Derick, a through bond model (the inductive effect) and a through space model (the field effect). These proposals were developed into the classical inductive effect (CIE) and the classical field effect (CFE)" models. As the CIE model could not account... 

Kinetic and equilibrium acidities of bridgehead hydrogens in fluorinated norbornanes and bicyclo[2,2,2]octanes are accommodated by a classical field effect modelled on Kirkwood-Westheimer calculations. The stability of the donor-acceptor complexes of homoconjugated dienes e.g. norbornadiene) with tetracyanoethylene increases with increasing ionization potential of the donor hydrocarbon, and the IP values also correlate with the charge-transfer excitation energies. ... 

We present here a condensed explanation and summary of the effects. A complete discussion can be found in a paper by Hellen and Axelrod(33) which directly calculates the amount of emission light gathered by a finite-aperture objective from a surface-proximal fluorophore under steady illumination. The effects referred to here are not quantum-chemical, that is, effects upon the orbitals or states of the fluorophore in the presence of any static fields associated with the surface. Rather, the effects are "classical-optical," that is, effects upon the electromagnetic field generated by a classical oscillating dipole in the presence of an interface between any media with dissimilar refractive indices. Of course, both types of effects may be present simultaneously in a given system. However, the quantum-chemical effects vary with the detailed chemistry of each system, whereas the classical-optical effects are more universal. Occasionally, a change in the emission properties of a fluorophore at a surface may be attributed to the former when in fact the latter are responsible. 

In FFF, separation is determined by the combined action of the nonuniform flow profile and transverse field effects. The classical configuration assumes the FFF channel as two infinite parallel plates (see Figure 12.4), of which the accumulation wall lies at x=0, where x is the cross-channel axis (directed upward from the accumulation wall). Inside the channel, the carrier fluid, assumed to have a constant viscosity, has a velocity profile u(x) that takes the form... 

These properties of the d-shell chromophore (group) prove the necessity of the localized description of d-electrons of transition metal atom in TMCs with explicit account for effects of electron correlations in it. Incidentally, during the time of QC development (more than three quarters of century) there was a period when two directions based on two different approximate descriptions of electronic structure of molecular systems coexisted. This reproduced division of chemistry itself to organic and inorganic and took into account specificity of the molecules related to these classical fields. The organic QC was then limited by the Hiickel method, the elementary version of the HFR MO LCAO method. The description of inorganic compounds — mainly TMCs,— within the QC of that time was based on the crystal field... 

Abstract Optical techniques for three-dimensional micro- and nanostructuring of transparent and photo-sensitive materials are reviewed with emphasis on methods of manipulation of the optical field, such as beam focusing, the use of ultrashort pulses, and plasmonic and near-field effects. The linear and nonlinear optical response of materials to classical optical fields as well as exploitation of the advantages of quantum lithography are discussed. 

The underlying issue is broader Coherent control was originally conceived for closed systems, and it is a priori unclear to what extent it is applicable to open quantum systems, that is, systems embedded in their ubiquitous environment and subject to omnipresent decoherence effects. These may have different physical origins, such as the coupling of the system to an external environment (bath), noise in the classical fields controlling the system, or population leakage out of a relevant system subspace. Their consequence is always a deviation of the quantum-state evolution (error) with respect to the unitary evolution expected... 

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. 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

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. 

The most unsatisfactory features of our derivation of the molecular Hamiltonian from the Dirac equation stem from the fact that the Dirac equation is, of course, a single particle equation. Hence all of the inter-electron terms have been introduced by including the effects of other electrons in the magnetic vector and electric scalar potentials. A particularly objectionable aspect is the inclusion of electron spin terms in the magnetic vector potential A, with the use of classical field theory to derive the results. It is therefore of interest to examine an alternative development and in this section we introduce the Breit Hamiltonian [16] as the starting point. We eventually arrive at the same molecular Hamiltonian as before, but the derivation is more satisfactory, although fundamental difficulties are still present. 

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