Splitting diagrams quartet

As a more complicated example, let s consider the case in which three hydrogens (HJ on one carbon are coupled to two hydrogens (H ) on an adjacent carbon. The following splitting diagram shows that the signal for Ha is split into four peaks, a quartet, with relative heights of 1 3 3 1 ... 

A splitting diagram for a quartet of triplets. The number of peaks actually observed when a signal is split by two sets of protons depends on the relative magnitudes of the two coupling constants. 

As a result for such levels the inner and outer branches of the Zeeman profile will be interchanged with respect to the normal quartet splitting. For this reason we have denoted this case as an inside out or inverted quartet [72], The pseudoscalar multiplication which relates the two types of quartet splitting corresponds to a Weyl reflection in the root diagram of SO (5). In the center of this reflection we meet a third case of Zeeman isotropy, which we have called a pseudodoublet. Since this case is invariant under the Weyl reflection inner and outer branches of the splitting pattern will coalesce. The V level thus will split in only two sublevels, each of which is pseudo-degenerate. Evidently this case is observed for any 2E state, since the -type orbital component of this state cannot contribute to the Zeeman splitting. It also occurs for a U ( E) state. 

A complex, first-order multiplet differs from a simple, first-order multiplet in that several different coupling constants are involved in the complex multiplet. The requirement that A vIJ be greater than about 8 still holds, but Pascal s triangle does not hold for the complex multiplet. An example is presented later in Figure 3.37 where it can be seen in the expanded splitting pattern that the multiplet consists of a quartet of doublets the stick pattern is shown in the text and consists of a sequence of two simple multiplets. Some dexterity with stick diagrams will be required throughout. Section 3.5.5 provides a more sophisticated treatment. 

The Hb signal is split into 12 peaks, a quartet of triplets. The number of peaks actually seen for the signal depends on the relative size of the coupling constants, J b and Jbe- When Jab bc. as drawn in this diagram, all 12 lines of the pattern are visible. When Jgb and J c are similar in magnitude, peaks overlap and fewer lines are observed. 

This pattern could also be analyzed as a quartet of doublets by reversing the order in which the couplings are considered. Try drawing the tree diagram for this splitting. See Problem 1 at the end of this chapter. 

PRACTICE PROBLEM 9.7 Draw a splitting tree diagram for a quartet by adding one more level to the diagram... 

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