The Absolute Shielding Tensor

NUCLEAR MAGNETIC SHIELDING AND THE CHEMICAL SHIFT I.l. The Absolute Shielding Tensor 

The chemical shift (as defined by lUPAC) in terms of measured frequencies 

The term magnetic shielding implies that any magnetic dipole of very small magnitude, such as that of a nucleus placed at that selected point, would be shielded from the full effect of B by the influence of the induced electronic motions. For free atoms a is always positive because this circulation generates a shielding field which opposes the applied field. In a molecule the presence of other nuclei hinders this circulation to an extent which depends on the electronic distribution and may even lead to a negative a. 

The components of the magnetic shielding at a nucleus in the molecule are defined as follows  

That is, the induced field in the a direction due to the currents induced in the molecular electrons by a uniform field in the / direction is given by In general 

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In the preceding, the magnetic shielding of the nucleus relative to that for the bare nucleus, and consequently are known as the components of the absolute shielding tensor. Experimentally, one measures the principal components of the chemical shift (CS) tensor relative to the frequency of a standard sample. 

This relation is of great importance for NMR spectroscopy because it allows us to determine the absolute shielding tensor by a combination of the measured spin rotation tensor with its nuclear contribution, which can easily be calculated from the nuclear coordinates, and a calculated diamagnetic contribution... 

Absolute Shielding Scales. - For lighter elements, the way to the absolute shielding involves a non-relativistically valid relation between the spin-rotation constant, C, and shielding a, applied to at least one primary reference molecule. A review of how spin-rotation constants relate to shielding constants was provided by Bryce and Wasylishen. The C and a tensors for the primary reference are corrected for rovibrational effects and then connected to a commonly used secondary reference (usually a neat liquid substance) via an NMR measurement in the gas phase at the limit of zero density and in the liquid... 

Vaara J, Lotmilla J, Ruud K, Helg er T (1998) Rovibiational effects, temperature dependence, and isotrop effects on the nuclear shielding tensors of water a new 0 absolute shielding scale. J Chem Phys 109 8388-8397... 

While the computational methods yield the asymmetric absolute shielding tensor, the usually observable quantity is related to the symmetrized tensor (eq 5). 

Method4 For a linear molecule measured anisotropy Aa and a theoretically calculated diamagnetic term [Pg.57]

Table VIII. Absolute O NMR shielding tensors (values in ppm) for the free water molecule (AEE = 56.1 eV) and a crystalline tungstate K2W04 (AEE = t ) assuming that <(a0/r)3> = 5.0 + q(O). Parametrization for K1WOd was r t(W) =...

A microwave study of the spin-rotation tensor of GaF in the gas phase has been reported by Wasylishen et al This provides spin-rotation constants for both the F and the Ga nucleus. A value of (an — aj ) = 945 35 ppm for Ga is derived from the experimental spin-rotation constant. The absolute Ga isotropic shielding obtained from the experimental spin-rotation constant at the ground vibrational state of GaF is... 

Table 21 Comparison Between Experimental and Calculated Absolute C and 0 Chemical Shielding Tensor Components (ppm) for the CO Molecule and Group 6 Transition Metal Carbonyls... 

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