Orbital shielding

Let us start with the field-free SO effects. Perturbation by SO coupling mixes some triplet character into the formally closed-shell ground-state wavefunction. Therefore, electronic spin has to be dealt with as a further degree of freedom. This leads to hyperfine interactions between electronic and nuclear spins, in a BP framework expressed as Fermi-contact (FC) and spin-dipolar (SD) terms (in other quasirelativistic frameworks, the hyperfine terms may be contained in a single operator, see e.g. [34,40,39]). Thus, in addition to the first-order and second-order ct at the nonrelativistic level (eqs. 5-7), third-order contributions to nuclear shielding (8) arise, that couple the one- and two-electron SO operators (9) and (10) to the FC and SD Hamiltonians (11) and (12), respectively. Throughout this article, we will follow the notation introduced in [58,61,62], where these spin-orbit shielding contributions were denoted... 

An increase in the donicity of the solvent results in an increase in the isomer shift of the antimony, which is indicative of a decrease in the electron density at the site of the antimony nucleus. (An increase in the donicity of the coordinated solvent molecules increases the electron density in the d and p orbitals shielding the s electrons, which causes a decrease in the electron density at the nucleus, and hence an increase in the isomer shift.)... 

If dimethylformamide is added to a carbon tetrachloride solution of tin(IV) iodide, a precipitate of composition Snl4(DMF)2 is obtained, the isomer shift of which is considerably smaller than that of the non-solvated Snl4 molecule. This shows that the coordination of DMF results in a large decrease in the electron density at the tin nucleus, owing to the higher occupation of the 5p and 5d orbitals shielding the s orbitals. 

The electrons in lower (inner) layers more strongly shield the electrons in the outer layers than do the electrons on the same subshell or orbital shield, or they reject each... 

The orbital shielding tensor cr, Ae electronic paramagnetic resonance g tensor, and the hyperfine coupling tensor A have been introduced previously. 

The last term which is required to evaluate the average in Eq. 4.34 is a mixed derivative with respect to the magnetic field strength B and nuclear magnetic moment flj, namely the orbital shielding tensor ... 

The two primary causes of shielding by electrons are diamagnetism and temperature-independent paramagnetism (TIP). Diamagnetism arises from the slight unpairing of electron orbits under the influence of the magnetic field. This always occurs so as to oppose the field and was first analysed by Lamb [7]. A simplified version of his fomuila. 

Carbon—carbon composites are used in high temperature service for aerospace and aircraft appHcations as weU as for corrosion-resistant industrial pipes and housings. AppHcations include rocket nozzles and cases, aircraft brakes, and sateUite stmctures. Carbonized phenoHc resin with graphite fiber functioned effectively as the ablative shield in orbital re-entry vehicles for many years (92). 

Uranium is the fourth element of the actinide (SJ series. In the actinide series the electrons are more effectively shielded by the Is and 7p electrons relative to the 4f electrons (shielded by 6s, 6p) in the lanthanide (4p series. Thus, there is a greater spatial extension of 5f orbitals for actinides than 4f orbitals for lanthanides. This results in a small energy difference between and 5/ 6d7s electronic configurations, and a wider range of oxidation states is... 

The /rans-fiised decalin system is conformationally rigid, and the stereochemistry of the product indicates that the initial addition of the trichloromethyl radical is from the axial direction. This would be expected on stereoelectronic grounds, because the radical should initially interact with the n orbital. The axial trichloromethyl group then shields the adjacent radical position enough to direct the bromine abstraction in the trans sense. 

Exact solutions to the electronic Schrodinger equation are not possible for many-electron atoms, but atomic HF calculations have been done both numerically and within the LCAO model. In approximate work, and for molecular applications, it is desirable to use basis functions that are simple in form. A polyelectron atom is quite different from a one-electron atom because of the phenomenon of shielding", for a particular electron, the other electrons partially screen the effect of the positively charged nucleus. Both Zener (1930) and Slater (1930) used very simple hydrogen-like orbitals of the form... 

The shielding constant s is calculated, for any of the sets of orbitals, from... 

---