Shielded nuclei

A transition metal with the configuration t/ is an example of a hydrogen-like atom in that we consider the behaviour of a single (d) electron outside of any closed shells. This electron possesses kinetic energy and is attracted to the shielded nucleus. The appropriate energy operator (Hamiltonian) for this is shown in Eq. (3.4). 

Now consider a d ion as an example of a so-called many-electron atom. Here, each electron possesses kinetic energy, is attracted to the (shielded) nucleus and is repelled by the other electron. We write the Hamiltonian operator for this as follows ... 

The difference in resonance NMR frequency of a chemically shielded nucleus measured relative to that of a suitable reference compound is termed chemical shift [164,165], and is a measure of the immediate electromagnetic environment of a nucleus. While the chemical shift depends on the Bo field, J does not. Chemical shifts, which cover a range of about 10 ppm for protons (i.e. 600 Hz in case of a 14.1 kG magnetic field) and 250 ppm for 13C, are the substance of NMR. 

Now, by its very definition, the global hardness rj is a measure of the HOMO-LUMO gap of a compound. Consequently, it seems reasonable to assume that the AEE AE should scale with the global hardness. The <(ag/r)3> term describes the p-orbital expansion or contraction as electrons are added or removed from the shielded nucleus. Using effective atomic numbers Znp and Slater rules ... 

The group in the Periodic Table with the least complicated chemistry is almost certainly the alkali-metal group lithium (Z — 3), sodium (Z 11), potassium (Z = 19), rubidium (Z 37), cesium (Z = 55), and the recently discovered francium (Z = 87). These elements follow directly after the inert gases and thus have one single valence electron beyond a well-shielded nucleus. 

A measure of how slowly the nuclear spins return to their normal state after an RF pulse near their resonance frequency. Alternatively, the evening after a chemistry exam. (p. 612) Surrounded by electrons whose induced magnetic field opposes the externally applied magnetic field. The effective magnetic field at the shielded nucleus is less than the applied magnetic field, (p. 568)... 

A nucleus that absorbs at 6.50 8 is less shielded than a nucleus that absorbs at 3.20 8 and thus requires a weaker applied field to come into resonance. A shielded nucleus feels a smaller effective field, and a stronger applied field is needed to bring it into resonance. 

O A is a shielding constant tensor of the nucleus A. Due to this shielding, nucleus A feels a local field Hioc = (l < a)H — H — a aH instead of the external field H applied (due to the tensor character of o a, the vectors Hioc and H may differ by their length and direction). The formula assumes that the shielding is proportional to the external magnetic field intensity that causes the shielding. Thus, the first term in the Hamiltonian ii may also be written asa YaHJ Ja-... 

PRINCIPLE ENll (of Allred-Rochow) The electronegativity of an atom is given by the attraction force between the shielded nucleus and the electron found at a distance equal with the covalent radius and is expressed as follows ... 

This principle states the introduction of the force concept in explaining the chemical bonds and in defining the electronegativity. In the last relation the effective charge of the shielded nucleus, Z = = Z-s,h calculated... 

The NMR signal of a shielded nucleus appears more upheld than the signal for a deshielded nucleus. (11.7)... 

The use of the removal cross section involves the idea of a thin shield inside a hydrogenous infinite medium. This means that a fast neutron, once colliding with a nucleus in the shield penetrates into the moderating medium, slows down and is absorbed. This collision with a shield nucleus is the concept of "removing" the neutron from the fast energy group. ... 

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