Shielding, nuclear

The procedure [due to Ramsey (see also McWeeny )] for calculating o is to introduce the complete vector potential including that due to the nuclear magnetic moments, M r, of each nucleus. 

This modified vector potential has to be inserted into the Hamiltonian of equation (3) and additional terms giving the energy of the interaction of the total magnetic induction field with the nuclear moments and also the nuclear spin-nuclear spin interaction included. The total magnetic field is derived from equation (8) and (9) as 

If the solution of the modified Schrodinger equation is expressed as a sum over states, the second order energy is given by 

The experimental finding that the NMR resonance frequency of a particular nucleus depends on the chemical environment - the chemical shift - still forms the basis for a majority of applications of NMR spectroscopy. The chemical shift originates from the fact that in an atom or molecule the local magnetic field B sensed by the nucleus is different from the applied static magnetic field, B. The difference between the two fields is usually expressed by the equation 

The shielding constant is an expression of electronic effects generated by the applied magnetic field and its value is very nearly the same for all magnetic isotopes of the same element. 

The shielding constant of a nucleus in a particular compound cannot be directly measured in an NMR experiment - only the chemical shift , 6, which is the difference in shielding constant for the nucleus in two chemically different environments, can be obtained  

Chemical shifts are therefore usually reported relative to a common reference compound. In NMR studies of chlorine, bromine and iodine compounds chemical shifts are mostly measured relative to the corresponding halide ion in aqueous solution. Since the ion shifts themselves are dependent on the nature of the counter-ion, salt concentration and temperature they are not ideal references. 

As will be further discussed in Chapter 3 a is actually a tensor quantity. For a typical field strength (2 T). 

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Cold-roUed alloys of lead with 0.06 wt % teUurium often attain ultimate tensile strengths of 25—30 MPa (3625—5350 psi). High mechanical strength, excellent creep resistance, and low levels of alloying elements have made lead—teUurium aUoys the primary material for nuclear shielding for smaU reactors such as those aboard submarines. The aUoy is self-supporting and does not generate secondary radiation. 

Miscellaneous (nuclear shielding, metallurgy, corrosion control, leather tanning, flame-proofing, catalysts) 19% (26%)... 

Frenking s group showed that the Group 11 isocyanides M—NC (M = Cu, Ag and Au) are less well bound compared with the corresponding cyanides M—CN [276]. They also studied CO coordination on Cu, Ag+ and Au with Au(CO)2 being the most stable of all Group 11 dicarbonyl complexes [281]. Vaara et al. demonstrated the importance of relativistic effects in the 13-C NMR nuclear shielding constant in... 

Vaara, J., Malkina, O.L., Stoll, H., Malkin, V.G. and Kaupp, M. (2001) Study of relativistic effects on nuclear shieldings using density-functional theory and spin-orbit pseudopotentials. Journal of Chemical Physics, 114, 61-71. 

Lee, A. M., Handy, N. C., Colwell, S. M., 1995, The Density Functional Calculation of Nuclear Shielding Constants using London Atomic Orbitals , J. Chem. Phys., 103, 10095. 

The localized quantities of the IGLO results allow separation of the influences of the different bonds, of the inner shells and of the lone pairs on the shielding of the resonance nuclei. It is evident from Table 1 that the SiX bonds with different substituents X do mainly contribute to the chemical shifts. On the other hand, the substituents X have distinct influences on the chemically unchanged parts of the molecules as in system II and on the inner L shell which, on their parts, influence the nuclear shielding, too. 

Electrons that are in filled sets of orbitals between the nucleus and outer shell electrons shield the outer shell electrons partially from the effect of the protons in the nucleus this effect is called nuclear shielding. 

As we move from left to right along a period, the outer shell electrons do experience a progressively stronger force of attraction to the nucleus due to the combination of an increase in the number of protons and a constant nuclear shielding by inner electrons. As a result the atomic radii decrease. 

Figure 31 CNDO/MO-calculated 29Si nuclear shielding for the central Si in Si11H24 as a function of dihedral angle.287 Reprinted with permission from Takayama, T. J. Mol. Struct. 1998, 441, 101-117, 1998 Elsevier.

The first theoretical treatment of the nuclear shielding cta of a nucleus A was published by Ramsey (29) in 19S0. Shortly thereafter, Saika and Slichter proposed a more practical partition of crA into three components (30) ... 

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