Diamagnetic current density

The scheme named continuos transformation of origin of the current density , see (27t21t22t28) proves that the transformed diamagnetic current density tensor,... 

Such a procedure amounts to killing everywhere the vector potential (2), appearing in the definition of the diamagnetic current density (42). However, it is impractical to regard this procedure as a continuous gauge transformation, as this would imply that also the second-order energies, Eq. (46) and second identity of Eq. (47), vanish. That s the reason why the denomination CTOCD seems preferable to CSGT. 

The diamagnetic current density terms defined in the new coordinate system, jf (r — r") and 7/ (r — r"), are formally annihilated in every point r, all over the molecular domain, choosing that point as origin, i.e., by setting r" = r, compare for equations (112) and (114), so that... 

Diamagnetic currents on the atom in question. This depends on the absolute electron density on, for example, the proton and gives a measure of the ionic character of the bond this is therefore of direct relevance to a discussion of cis and trans effects. 

Similarly, the monohomocyclooctatetraene di-anion, 74, (see Table 15) 212,218) deshielded peripheral protons, and a differential shielding of the methylene protons, whereby that proton situated above the ring (H(a), t 10.0) is more shielded than the "outer" proton (H(b), t 8.0). The chemical shifts of the peripheral protons (centered at ca. t 4.5 to 4.8) are shifted upfield from those of the parent hydrocarbon by only 0.4 to 0.7 ppm. As the upfield shift expected from charge density considerations alone is 2.5 ppm, a deshielding effect associated with a diamagnetic current is clearly implicated 218>. 

DFT [95] was generalized to include relativistic effects by MacDonald and Vosko [96] and by Ramana and Rajagopal.[97] By omitting small diamagnetic effects one-electron equations were obtained that contained a scalar effective potential as well as an effective magnetic field caused by the polarization. In cases where the paramagnetic currents cannot be neglected, it is necessary to resort to a current-density formalism.[98,99]... 

The current density is an observable which can be visualised for a molecule through oriented contour lines. Usually the applied field is perpendicular to the plane of the paper, and points inward. Clockwise circulation corresponds to a diamagnetic current since it induces an internal magnetic field pointing against the applied field [21]. 

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