Magnetic fields and density functional theory Page: 42 of 244
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tem the asymmetry vanishes and the anisotropy becomes
60= 0- - O1. (1.60)
Axially or nearly axially symmetric systems are commonly encountered in experimen-
tal situations.
Another important physical effect to consider when comparing theoretical and
experimental shieldings is the effect of rovibrational averaging. [9] Te majority of
experiments are carried out at room temperature. However, theoretical shifts are
usually calculated at a fixed geometry. So to compare exactly a theoretical shift
and an experimental shift one should average the theoretical results over a chemical
shielding surface. A chemical shielding surface is a surface showing the shielding
for different nuclear geometries much like a potential energy surface, but with the
shieldings instead of the.energies plotted. In principle, one must do this for both the
zero-point and thermal vibrations. Now this can rarely be done at present due to the
computational cost of most theoretical treatments, which provides further motivation
for the development of new theoretical techniques.
The magnetic susceptibility is not really a NMR parameter as it is independent of
the nuclei and depends only on the electrons. However, as the Biot-Savart integrals
demonstrate it is related to the chemical shielding and hence should be examined.25
1.3 Nuclear Magnetic Resonance Parameters
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Salsbury Jr., Freddie. Magnetic fields and density functional theory, thesis or dissertation, February 1, 1999; Berkeley, California. (https://digital.library.unt.edu/ark:/67531/metadc709007/m1/42/: accessed May 6, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.