Higher multiplet effects

NMR spectrometers of the late 1960s did not permit the detection of higher spin orders for sensitivity reasons, so no new name was coined for them the term used today is "higher multiplet effects". More importantly, with the cw instruments ubiquitous at that time a separation of different spin orders n was principally impossible. The advent of pulsed and Fourier transform spectrometers reduced that to a trivial task Because for a weakly coupled spin system the amplitude of the detectable signal is proportional to sim cos i , one simply has to acquire spectra with different flip angles i9 and form suitable linear combinations (e.g. one- and two-spin orders are separated by adding and subtracting two spectra acquired with = 45° and = 135°). ... 

As will be explained in Section 3.2, multiplet and higher multiplet effects are much more prominent at low fields. For that reason, CIDNP net effects prevail on today s high-field spectrometers. 

As has long been known, CIDNP net effects, multiplet effects, and higher multiplet effects (i.e. 1-spin order, 2-spin order, etc.) can be separated through their dependence on the flip angle This is normally done by recording spectra... 

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.

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. 

In some ions, such as Sm3+ and Eu3+, because of the close proximity of the excited multiplets to the ground state, it is necessary to include one or more of the higher multiplets in evaluating the magnetic and related properties. Recent papers by Malik et al. (2) and de Wijn et al (2) provide excellent information on the details of the calculations. However, we give below some salient features of the effects of J mixing. 

If the perturbation function shows cubic symmetry, and in certain other special cases, the first-order perturbation energy is not effective in destroying the orbital magnetic moment, for the eigenfunction px = = i py leads to the same first-order perturbation terms as pi or pv or any other combinations of them. In such cases the higher order perturbation energies are to be compared with the multiplet separation in the above criterion. 

If the Ln3+ centre is a Kramers ion, the spectra can be interpreted in terms of a doublet with largely anisotropic effective -values. If one neglects the admixture of higher lying/ multiplets and considers an axial symmetry, the effective g values will be... 

Core electron ejection normally yields only one primary final state (aside from shake-up and shake-off states). However, if there are unpaired valence electrons, more than one final state can be formed because exchange interaction affects the spin-up and spin-down electrons differently. If a core s electron is ejected, two final states are formed. If a core electron of higher angular momentum, such as a 2p electron, is ejected, a large number of multiplet states can result. In this case it is difficult to resolve the separate states, and the usual effect of unpaired valence electrons is... 

Within L-S coupling the ground state multiplet is leading to an effective moment Heff = 3.38 Xb (see Table 3) which is slightly higher than the experimental value Peff = 3.2 Pb thus J mixing is small and the ground state is essentially H4 (Chan and Lam ... 

The product of escape from the cage (6) shows the opposite effect (Figure A 1.9). Here the spin states aA/3x and /3Aax have abnormally high populations, and the lower field members of the multiplets exhibit enhanced absorption while the higher field members show emission, A/E. 

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