Shielding Sternheimer

Quantum mechanical calculations of 33S nuclear quadrupole coupling constants are not an easy matter (not only for the 33S nucleus, but for all quadrupolar nuclei). Indeed, the electric field gradient is a typical core property, and it is difficult to find wave functions correctly describing the electronic distribution in close proximity to the nucleus. Moreover, in the case of 33S, the real importance of the Sternheimer shielding contribution has not been completely assessed, and in any case the Sternheimer effect is difficult to calculate. 

Table 3. Sternheimer shielding in atoms electronic configurations labelled a and b correspond to two slightly different Hartree-Fock functions used as basis functions... 

In those days electric field gradients could not be evaluated to a high degree of accuracy and correction factors for relativistic effects and polarization of the atomic core (Sternheimer shielding) had to be applied transferring this inaccuracy to the final NQM values. 

AR = change in nuclear radius Rq, -Roe = Sternheimer shielding factors Rfim =distancefrommthtonthion n = radial coordinate of ith electron rtj = distance from ith to /th nucleus [Pg.389]

The nuclear electric quadrupole moment may also interact with the electric field gradient arising from the non-spherical distribution of the 4f electrons when the lanthanide ion is situated in a solid. The general form of the quadrupole interaction has been given in section 1.3.2. The principal value of the field gradient tensor, due to the 4f electrons is given by (18.73) in section 2.1.1.2, and as indicated there in (18.72) should be multiplied by the Sternheimer shielding factor (I-Rq) to take account of the distortion of the inner closed shells of the lanthanide ion by the open 4f shell. Other contributions to the total... 

The gradient eq will be shielded by core electrons. This is expressed by the inner Sternheimer shielding factor R. This shielding is much less severe than the antishielding described by y. Values of R vary between 0.2 and 0.4. A measurement for Np [R = 0.35) has been published by Dunlap et al. (1971). 

Calculated free-ion hyperfine fields and ionic electric field gradients (without Sternheimer shielding) in the lanthanides and actinides of interest. 

Fowler, P W., Lazzeretti, P, Steiner, E., Zanasi, R. (1989). The theory of Sternheimer shielding in molecules in external fields. Chemical Physics, 133, 221. 

For some quadrupolar nuclei with a very small quadrupolar moment, the dipole-dipole mechanism contributes significantly to relaxation, e.g. 7Li. 87Rb has a very large quadrupolar moment and Sternheimer anti-shielding factor, and thus, quadrupolar relaxation dominates completely the same is true of 23Na and 39K. The Sternheimer anti-shielding factor describes how sensitive the NMR relaxation of a nucleus is to its electronic environment.37... 

A detailed review and summary of the experimental data as well as the results of calculations of the efg in the heavy lanthanide metals at low temperatures has been given by Pelzl (1972). It was found that in the metal the radial averages r of the 4f electrons appropriate to the quadrupole interaction are 10% smaller than in ionic compounds. In comparison with the magnetic hyperfine interaction (section 2.1.1.1) the additional reduction arises from increased closed shell shielding (1 Rq) in the metallic case. In addition, the conduction electrons increase the antishielding of the lattice efg due to their greater density outside the atomic sphere via the factor (1 + F) and to an increased Sternheimer factor (1 - 7 ) in the metal. 

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