Effective screening constant

Later methods, especially that of Gordy (1955), and later Allred and Rochow (1958) make use of screening constants of the electron strucmre for the nuclear charge of each atom. This determines die attraction between the nucleus of the atom and an electron outside the normal electron complement, and is die effective nuclear charge. The empirical equation for the values of electronegativity obtained in this manner by Allred and Rochow is... 

A similar model for many-electron atoms has been developed,6 by considering each electron to be hydrogen-like, but under the influence of an effective nuclear charge (Z — Ss)e, in which Ss is called the size-screening constant. It is found that atoms and ions containing only 5 electrons (with the quantum number l equal to zero) and completed sub-groups of... 

It is customary to express the empirical data concerning term values in the X-ray region by introducing an effective nuclear charge Zeff e in the place of the true nuclear charge Ze in an equation theoretically applicable only to a hydrogen-like atom. Often a screening constant S is used, defined by the equation... 

It has been suggested that this spherical layer of charges effectively screens water from the external electric field, leading to an apparent dielectric constant much lower than that of bulk water [35,91,95,96]. 

It is, of course, usual in discussing the electrochemical interface to use a dielectric constant, which is the ratio of the electric displacement to the electric field. By Fourier transforming the dielectric function e(k), one would obtain an effective dielectric constant, which would, however, depend on position. In fact,48 the screening... 

As required by (36), the variational parameter k is calculated to vary between k = 2 at R = 0 and k = 1 at R > 5ao- The parameter k is routinely interpreted as either a screening constant or an effective nuclear charge, as if it had real physical meaning. In fact, it is no more than a mathematical artefact, deliberately introduced to remedy the inadequacy of hydrogenic wave functions as descriptors of electrons in molecular environments. No such parameter occurs within the Burrau [84] scheme. 

The displacement in the magnetic resonance frequency of a nucleus as a consequence of the electronic environment in which the nucleus resides. Because moving electrons generate their own magnetic fields, a nucleus surrounded by these electrons experiences an effective field, Neff, which is defined by (1 - a)No, where a is the so-called screening constant and No is the applied magnetic field. A chemical shift is typically reported as a dimensionless displacement (units = parts per million, or simply ppm) from a reference standard. If the magnetic field is varied while the radio frequency v is held constant, then the chemical shift (ppm) equals [//sample ... 

This simple method can easily be refined for our present purpose. All the electrons are involved but the effect is predominantly due to the outermost shell fory is (in the hydrogen-like approximation) proportional to the fourth power of the principal quantum number n and inversely as the square of the effective shielded charge Y which is least (and y therefore greatest) for the outermost electrons. The small correction for the inner electrons can therefore be made by screening-constant approximations (15). This simple method suffers from two disadvantages ... 

The effective atomic number is considered to be the difference between the actual atomic number, Z, and a screening constant, S, which is estimated by the use of Slater s rules. These represent an approximate method of calculating the value of S, leading to an estimate of the effective atomic number, ZelT, given by Z - S. The value of S is obtained from the following rules. 

Our problem is to estimate A . It is the mean repulsive energy of a pair of charges at a distance or1 from each other. This will depend on the effective dielectric constant of the electron gas. This should be large for weak Anderson localization and will effectively screen out the repulsion, except when both electrons are in the same atom. We therefore write... 

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