The Multiplet Effect

As with the net E and A effects, the multiplet effects can also be rationalized on the basis of nonequilibrium spin state populations. Recall the AB spin system we discussed in 

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Kaptein s rule for the multiplet effect is useful for predicting the phase of each transition, and it is similar to... 

The remainder of equation (38) describes the multiplet effect, and it can be seen that whether an individual line in the multiplet corresponds to emission or absor ption depends on the signs of the hyperfine coupling constants but is independent of Hq. The nature of the hyperfine field is such that the integral over the whole multiplet is zero if Ag = 0. 

Figure A1.8 Nuclear spin states and spectrum for product 5. At the top the four states are again shown in an energy-level diagram. Heavy lines are the states with enhanced populations. A downward-pointing arrow indicates a net transfer of molecules from an overpopulated higher spin state to a less populated lower one, and corresponds to net emission. The spectrum shows the multiplet effect of type El A. From S. H. Pine, J. Chem. Educ., 49, 664 (1972). Reproduced by permission of the Division of Chemical Education.

The net effect and the multiplet effect may occur together. Figure A 1.10 shows how excess population in the lowest level of our AX system, and a smaller excess in the highest level, will yield a superposition of a net and a multiplet effect, A + EjA. 

Kaptein has worked out simple formulae for deciding the type of spectrum that will be obtained in a given set of circumstances/ Two parameters are defined, Tn and rm. Tn tells whether there will be a net enhanced absorption, A, or a net emission, E, and rm tells whether the multiplet effect will be of the EjA type or of the A/E type. The calculation of Tn and rm and their interpretation are given in Table Al.l. 

Figure A1.9 Nuclear spin states and spectrum for product 6. The conventions of the diagram are the same as for Figure A 1.7. The spectrum shows the multiplet effect of type AjE.

We saw in Section 11.9 how multiplet effects result from coupled spin states that become polarized. The type of multiplet effect (E/A or A/E) can be predicted in much the same way as the net effect [Eq. (11.2)], except that more parameters must be considered. The multiplet effect (Tm) is given by the sign of the product ... 

In many cases an NMR spectrum exhibits both net and multiplet CIDNP effects. In many of these cases the net For A effect is superimposed on the multiplet effect of a given signal. For example, when singlet radical pair 11-14 undergoes recombination to 11-15, the H spectrum of the CH2 group in the product shows an E/A multiplet effect superimposed on an E net effect3 ... 

The simulated INEPT 13C spectrum of 2-chlorobutane is shown in Figure 12.14. By comparing this to the corresponding undecoupled 13C spectrum (Figure 8.11), note how each multiplet is both intensified and divided at its center into positive and negative lines that no longer show the same relative intensities as in the undisturbed multiplet. The appearance of these multiplets is quite similar to the multiplet effect CIDNP spectra we saw in Section 11.9, and as was true there, the middle leg of a multiplet with an odd number of lines vanishes. 

From Fig. 2-8, we can see that the NMR signals appear as shown in Fig. 4-7. Let us consider the case when the product of fJ Ai Ap is positive. In this case, emissive signals appear at lower fields than Bj and enhanced absorptive ones at higher fields than 5, if 7 is positive as shown in Fig. 4-7(a). This is denoted by E/A. If Jip is negative, the reversed A/E signals can be observed as shown in Fig. 4-7(b). Thus, the phase of the multiplet effect of nucleus i coupled with several nuclei p which are located on the same radical ((i, p)) is given by the product of five signs. 

Similarly, the phase of the multiplet effect of nucleus i coupled with several nuclei k which are located on the counter radical (T (i,k)) is given by the product of five signs. 

Their spectral pattern are E/A, or slightly E /A. The slightly net emissive polarization can be explained by a slight contribution from the TM. The main E/A pattern can be explained by the multiplet effect due to the S-Tq mixing as given by Eq. (5-21). 

Problem 5-11. Calculate the HF intensity ratio of the CIDEP spectrum of the 2-hydroxy-2-propyl radical for the multiplet effect where Ag = 0 and p is positive. 

The multiplet effects are estimated to lower the Th and U atomic energies by 4.3 and 19.2 kcal/mol following the procedure described in Ref. 87. 

These vector models also show that the multiplet effects decrease when the Zeeman interaction has to be taken into accoimt, because the additional rotation causes the projections onto the singlet state to differ less. This explains why multiplet effects are much more important in low fields and for radical pairs with small g-value differences. 

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