Nuclear screening constant

As for all nuclei, the 33S nuclear screening constant a can be approximated as the sum of two independent terms of opposite sign, the diamagnetic and the paramagnetic contribution 32... 

Within the last two decades, significant progress has been achieved in the theoretical computation of NMR spectroscopic parameters,110 particularly of nuclear screening constants. Theoretical calculations of 33S NMR parameters have received a certain attention for two main reasons (i) they can help in identifying and elucidating the structural properties of sulphur-containing molecules, and (ii) they can provide important information on the electron distribution and bonding situation around the sulphur atom. 

It is not reasonable to expect of any theoretical treatment of nuclear screening constants that it exactly reproduces experimental values. Theoretical estimates are usually based upon an isolated molecule as a model. In contrast to this many experimental values are reported for liquid samples in which solvent effects may be present. Additionally the experimental results may be in considerable error, this being especially true for broad resonances. However, even if solvent effects and experimental errors are eliminated the observed relative screening... 

We have seen that the magnetic field R, required to obtain the resonance crmdition for nucleus i at a particular irradiating rf field (Ri) is not equal to the applied static field Rq, but is instead R, = Ro(l — a) [see Eq. (20.9)], where the nuclear screening constant, a, depends on the chemical structural environment of nucleus /. The local electron density in the vicinity of the nucleus shields it from the applied field Bo by producing small local magnetic fields (diamagnetic currents). Any structural feamre that alters the electronic environment of a nucleus will affect its screening constant a and lead to an alteration in its resonance frequency or chemical shift 5,. 

CSA reflects the anisotropy inherent in the distribution of electronic currents about nuclei which screen (tr) them fi om the applied magnetic field Bo- The local magnetic field experienced by a nucleus is anisotropic and therefore three dimensional, so the nuclear screening constant tr is in fact a tensor and may be described [1,32] by... 

K. A. K. Ebraheem and G. A. Webb. Calculation of some boron nuclear screening constants. Org. Mapi. Resonance, 1977, 10, 258. 

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... 

For an ion of nuclear charge Ze, the size-screening constant for a given electron is... 

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... 

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. 

Table 5.2 Oitoital energies, effective nuclear charges, and screening constants for n=3 orbitals In sodnim...

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