Operator field-dependent

A variety of methodologies have been implemented for the reaction field. The basic equation for the dielectric continuum model is the Poisson-Laplace equation, by which the electrostatic field in a cavity with an arbitrary shape and size is calculated, although some methods do not satisfy the equation. Because the solute s electronic strucmre and the reaction field depend on each other, a nonlinear equation (modified Schrddinger equation) has to be solved in an iterative manner. In practice this is achieved by modifying the electronic Hamiltonian or Fock operator, which is defined through the shape and size of the cavity and the description of the solute s electronic distribution. If one takes a dipole moment approximation for the solute s electronic distribution and a spherical cavity (Onsager s reaction field), the interaction can be derived rather easily and an analytical expression of theFock operator is obtained. However, such an expression is not feasible for an arbitrary electronic distribution in an arbitrary cavity fitted to the molecular shape. In this case the Fock operator is very complicated and has to be prepared by a numerical procedure. 

MIM or SIM [82-84] diodes to the PPV/A1 interface provides a good qualitative understanding of the device operation in terms of Schottky diodes for high impurity densities (typically 2> 1017 cm-3) and rigid band diodes for low impurity densities (typically<1017 cm-3). Figure 15-14a and b schematically show the two models for the different impurity concentrations. However, these models do not allow a quantitative description of the open circuit voltage or the spectral resolved photocurrent spectrum. The transport properties of single-layer polymer diodes with asymmetric metal electrodes are well described by the double-carrier current flow equation (Eq. (15.4)) where the holes show a field dependent mobility and the electrons of the holes show a temperature-dependent trap distribution. 

Obviously, the model is crude and does not take into account many of the factors operating in a real molecular stack. Lack of symmetry with respect to the polar axis and the fact that dipoles may not necessarily be situated in one plane represent additional complications. The angle a could also be field dependent which is ignored in the model. The model also requires that interactions between molecules in adjacent stacks be very weak in order for fields of 10 to 20KV/cm to overcome barriers for field induced reorientation. The cores are then presumably composed of a more or less ordered assembly of stacks with a structure similar to smectic liquid crystals. 

No field dependence in the electron relaxation time was ever found in the investigated region between 0.01 and 100 MHz of proton Larmor frequency, or at 800 MHz when high resolution is achieved (28). It was shown that Tie is essentially independent of the reorientational time of the macromolecule and the viscosity of the solution. Therefore, rotation independent mechanisms have to be operative. We also find that Tie decreases with increasing temperature, as also shown in Fig. 5. 

For the purposes of presentation, the velocity held is usually presented at regular intervals. This new scheme is very efficient and incorporates a vector validation procedure, making it independent of operator intervention. The time it takes to compute a vector field depends on the computer hardware and it ranges from 350 mesh points per second on a PC 150 MHz Pentium to 1400 mesh points per second on a 200-megahertz dual Pro. 

Note that the Breit-type operators are often neglected in quantum chemistry because they yield small energy contributions in comparison to the instantaneous Coulomb interaction. However, the effects may not be negligible in highly accurate quantum chemical calculations or for spin- or magnetic-field-dependent properties such as those measured by magnetic resonance spectroscopies. 

The success of field operations often depends on the investigator s ability to anticipate conditions at the field location. 

This algorithm may be viewed as direct, since the solution will yield the sought-after Hamiltonian Ho- Feedback is present here in that the information learned about the operator Ho in Eq. (7) will depend on the evolving state analogous to the same way that the field depends on the state in Eqs. (3), (4), or (5). 

In the field-dependent AO basis, an element of the PE potential operator becomes... 

Ignoring the field dependence of the dipole operator (MCSCF orbital connections are field independent) we write... 

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Permanent magnets are used for some of the less expensive spectrometers, but suffer from the disadvantage that the stability of the field depends on extremely accurate control of the temperature of the magnet enclosure this temperature may be affected by variable-temperature operations, unless the probe is thermally well-insulated.37... 

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