Multiplet, definition splitting

Protons are magnetically equivalent if they have the same chemical shift and are coupled equally to otiier equivalent nuclei in die molecule. This is similar to chemical equivalence but is a more rigorous definition of equivalence. For example, the methyl protons of isobutane are chemically and magnetically equivalent since they absorb at die same frequency and are all coupled equally to the methine proton (which should be split into a 10-line multiplet ). Likewise die two mediyl groups of /i-xylene are chemically and magnetically equivalent because they are coupled equally (J = 0) to the aromatic protons both ortho and meta to diem. 

In atomic spectroscopy the term values depend primarily on electronic quantum numbers and the process of analysis consists of reducing a number of measurements to a term scheme. The confidence in an analysis increases as the system becomes more overdetermined, and the process becomes more definite as the accuracy of the measurements improves. Other information is also used to facilitate the assignments of the lines, e.g., relative intensities, the observation of certain lines in absorption, the splittings of lines by magnetic fields theoretical calculations of terms and multiplet splittings may sometimes be helpful. 

We note in passing that this definition of a strong field is not the one found in textbooks, which relates to the relative strengths of the Zeeman splitting and multiplet structure (the Paschen-Back effect). A field capable of inducing angular-momentum uncoupling can still be a weak field under the present definition.2... 

The Lande s interval rule underlies the definition of the spin-orbit operator Yvrhich first acts on atomic one-electron fimctions. Indeed, a single-electron spin-orbit interaction obeys this rule, which means that the Lande s average of a multiplet coincides with the non-split term [39]. For a given I symmetry, taking the non-split term as a reference, one defines a zero-diagonal operator in relation to the reference... 

The exact assigmnent of the multiplets in the allylic group depends not only on their chemical shift values, but also on the splitting patterns observed. Some initial analysis must be done before any assignments can be definitely made. 

Auzel had first introduced a slightly different definition foriVv, omitting the factor It can be shown that under some assumptions can be correlated to the maximum crystal field splitting of distinct multiplets. The relation between and the maximum splittings of the I9/2, I11/2, I13/2 and I15/2 multiplets of Nd " is linear in a good approximation. 

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