The appearance of fine structure

Consider first a molecule that contains two spin- nuclei A and X. Suppose the spin of X is a, then A will resonate at a certain frequency as a result of the 

The levels on the left apply in the absence of spin-spin coupling. Those on the right are the result of allowing for spin-spin coupling. The only allowed transitions differ in frequency by/. 

neglect spin-spin coupling. The total energy of two protons in a magnetic field S is the sum of two terms like eqn 13.11 but with (Bq modified to 

Here cta and Tx are the shielding constants of A and X, respectively. The four energy levels predicted by this formula are shown on the left of Fig. 13.10. The spin-spin coupling energy is normally written 

There are four possibilities, depending on the values of the quantum numbers 

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Molecular vibrations and, very rarely, rotations cause the appearance of fine structure upon the molecular bands. 

It was shown by Strauss et ai [St 77] that in frozen methanol the O—H vibration bands become narrower, and in frozen methanol solutions of alkali metal salts the solute causes the appearance of fine structure in the spectrum. Appropriate assignment of the distinct bands has contributed to the understanding of the solvation processes. With a series of detailed examinations employing this method, Symons et al [St 76, St 77, Sy 75a, Sy 75b, Sy 75c] investigated the structures of alcoholic solutions of alkali metal and tetraalkylammonium halides. 

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