Plane wave generators = charges

Usually a plane wave generator (PWG) consists of several different expl components, some or all of which are likely to be different expls from the main driver charge. Obviously the PWG contributes energy to projecting the plate, and an estimate of its contribution must be made before one can determine y/2E for the main driver charge. The procedure adopted in Ref 14 for correcting for the presence of a PWG is as follows. Let and h be the respective thicknesses of the main driver charge and the metal plate and pc and pm their respective densities. 

Second, there is a line of charge-ordering in the T -p plane, where the charge-charge correlation function begins to oscillate. This line, as established from GDH theory, passes close to the critical point and may generate a virtual tricritical state. A charge-density wave scenario also arises from r-dependent cavity interactions. 

A much better choice is to use the length of s to define the spin density . In the non-relativistic limit, the absolute value of the spin density of a one-electron system equals the charge density. While one cannot exactly retain this property in the relativistic case because of the small component contribution (except for single-particle plane waves, where s can be parallel to the momentum everywhere), the length of s equals the charge density for one-electron systems in the weakly relativistic limit and in two-component quasi-relativistic approaches. The same holds if there is one electron outside a closed-shell core. The non-collinear approach is not too difficult to implement [27], it generates a spin-dependent exchange-correlation potential of the form... 

As the frequency of voltage perturbation is increased, one may limit the penetration depth (D/jco) of a concentration wave generated by the redox reaction so that it is much smaller than the thickness of the electroactive polymer film. In this region, one measures the kinetics of the charge injection process at the surface (Region III). The impedance characteristic is a semicircle in the Zreal vs —Zjmag impedance plane plot. For the impedance measurement, one may obtain Rct, the charge transfer resistance, and the double layer capacitance Cdl- This procedure was used to calculate the... 

The LCAO total energy was evaluated using the variational expression (Eq. 7) with n obtained from a potential generated using superposition of carbon sp atomic charges. This and the fact that only 12 basis functions per atom were used account for the slight difference in the cohesive energy between the two calculations. We note that because of the localized nature of the carbon bond in diamond approximately 250 plane waves per atom were used for the plane wave basis. 

The numerical AO-based DFT code SIESTA [344] employs the same muneric pseudopotentials as plane-wave-based codes. An alternative approach is used in the Slater-orbital-based DFT code ADF [345], where so-called core functions are introduced. They represent the core-electron charge distribution, but are not variational degrees of freedom and serve as fixed core charges that generate the potential experienced by valence electrons [479]. 

The crystal orbitals were calculated by the DFT method in the plane-wave basis set with the CASTEP code [377] in the GGA density functional. A set of special points k in the Brillouin zone for all the crystals was generated by the snperceU method (see Chap. 3) with a 5 x 5 x 5 diagonal symmetric extension, which corresponds to 125 points. In all cases, the pseudopotentials were represented by the normconserving optimized atomic pseudopotentials [621], which were also used to calculate the atomic potentials of free atoms. In the framework of both techniques (A, B), the population analysis was performed in the minimal atomic basis set i.e. the basis set involved only occupied or partially occupied atomic orbitals of free atoms. It is well known that the inclusion of diffuse vacant atomic orbitals in the basis set can substantially change the results of the population analysis. For example, if the Mg 2p vacant atomic orbitals are included in the basis set, the charge calculated by technique A for the Mg... 

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