NMR SHIELDING AND COUPLING CONSTANTS - DERIVATION

This section is for those who do not fully believe the author, and want to check whether the final formulae for the shielding and coupling constants in nuclear magnetic resonance are indeed valid (Chapter 12). 

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In the first, quantum mechanics can be used to calculate the NMR coupling constant between two nuclear spins in the molecular environment or the NMR shielding constant. Jensen [8] in Chapter 10 of the reference provides a comprehensive introduction to the methods for calculating these molecular properties. The NMR coupling constant, KAB, is related to the second derivative of the energy with respect to the internal magnetic moments, /u, arising from the nuclear spin of the two atoms, A and B. 

We apply this technique to study the effect of the spin-orbit coupling on an NMR shielding tensor and the shielding polarizability of the xenon atom. The shielding polarizabilities are defined as the second derivatives of nuclear shielding constants with respect to an electric field E... 

A careful analysis of the H and - C NMR spectral parameters (H,H coupling constants and shielding effects) established that the predominant conformation of the hetero ring for diexo-d ca- and d/ejco-l,2,3,4,4a,5,8,8a-octahydro-5,8-methano-3,l-benzoxazines is the endo-ho i 339A, whereas that for the corresponding diendo derivatives is the exo-boat 339B (85T5159). 

Before discussing the methods used for ab initio calculations of the spin-spin coupling constants we will shortly present the basic theory of these NMR parameters. The quantum mechanical expressions for the NMR shielding constant and the spin-spin coupling constant were first derived by Ramsey In this chapter a notation of Ref. is employed. 

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