Antishielding

For nuclei that have perfect cubic site symmetry (e.g., those in an ideal rock salt, diamond, or ZB lattice) the EFG is zero by symmetry. However, defects, either charged or uncharged, can lead to non-zero EFG values in nominally cubic lattices. The gradient resulting from a defect having a point charge (e.g., a substitutional defect not isovalent with the host lattice) is not simply the quantity calculated from simple electrostatics, however. It is effectively amplified by factors up to 100 or more by the Sternheimer antishielding factor [25],... 

The EFGs for both 69,7 Ga and 14N have been calculated using the WIEN-97 program, and the results compare more favorably with the experimental results than do those from a simple point charge model including Stemheimer antishielding factors (note that the experimental 14N NQCC value used in the comparison was somewhat larger than the accurate value reported above) [52]. 

The nuclear quadrupole tensor of the Cu(II) ion is discussed in terms of the formalism outlined in Sect. 5.2.1. Kita et al.158) treated the Stemheimer antishielding factor (1 - as an adjustable parameter. The rhombicity of the measured quadrupole tensor was found to originate from the charge distribution on the ligands, the field gradient due to the copper valence electrons being nearly axially symmetric. 

The calculations show that the central contribution to the EFG, due to the valence electrons, is shielded rather than antishielded, but the effect is less pronounced. The shielding factor R is the density-weighted average of y(r), <7( ) "3>core,vaience/core,valence, where the average is to be taken separately over the core and valence shells, depending on the shell in which polarization is induced. 

If the electron density were known at high resolution, the antishielding effects would be represented in the experimental distribution, and the correction in Eq. (10.31a) would be superfluous. However, the experimental resolution is limited, and the frozen-core approximation is used in the X-ray analysis. Thus, for consistency, the Rcore shielding factor should be applied in the conversion of the... 

Though the peripheral contribution is considerably enhanced by the antishielding, it is nevertheless small relative to the central contribution, except for very short metal-ligand distances (Coppens 1990). 

Consider first the effect of the atomic electrons. A filled or half-filled electron shell has a spherically symmetric electron distribution, and as such gives rise to no electric field gradient (except through external deformation, i.e., Sternheimer antishielding). Thus, of all the atomic electrons, only the... 

The free water molecule was assumed to lie in the yz plane with its C2 axis pointing along the z-direction and with d(O-H) = 95.7 pm and ZHOH = 104.57°. A perfect agreement with experimental values is obtained for the asymmetry parameter and an antishielding factor (1 - yoo) = 22.7 is required for matching the coupling constant Cq. As for corundum, changing atomic radii alters only the y value. 

The distortion of closed shell electrons can be very significant in the case of charged species. The Stemheimer antishielding factor has been determined for sp3d2 hybridized sulphur by evaluation of the ion-water contribution to the 33S relaxation rate in aqueous SO4, 83 The value found (y, — —43.9) is in good agreement with the value reported for S2 (yrf, — —52.2) in the crystalline state.84... 

Isotope Spin Natural abundance (A) (%) vo at 9.4 T Relative receptivity" Quadrupole moment (fm2)7 Quadrupole broadening factor4 Stemheimer antishielding factor (70c) ... 

Stemheimer antishielding factor is given where meaningful calculations have been carried out for ions with closed-shell structure e.g. Al3+, Cr. Where possible given for a lattice,8 and if not for free ions. 

Table II.2. Antishielding factors for some closed shell ions, a Calculated for the free ion Calculated for the crystal" ion, the ion in the solid...

For an absolute agreement between the observed and calculated crystal field effects in such dipolar crystal lattices, the zero point vibrations have to be considered, as Bersohn pointed out. Furthermore, we think that the part of the solid state shift is due to the contribution of the quadrupole polarization (antishielding factor). The inner shell electrons of the atom considered experience an induced quadrupole moment under the influence of the external fields. This... 

Paschalis, E., and A. Weiss (1969). Hartree-Fock-Roothaan wave functions, electron density distributions, diamagnetic susceptibility, dipole polarizability and antishielding factor for ions in crystals. Theoret. Chim. Act. 13, 381-403. 

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