Multiplet intensities

Number of equivalent protons to which nucleus is coupled Appearance of multiplet Intensities of lines in multiplet... 

For sets of spin- nuclei, the multiplet intensity ratios are simply the binomial coefficients found most easily from Pascal s triangle (Figure 2.11). 

The most recent calculations, however, of the photoemission final state multiplet intensity for the 5 f initial state show also an intensity distribution different from the measured one. This may be partially corrected by accounting for the spectrometer transmission and the varying energy resolution of 0.12, 0.17, 0.17 and 1,3 eV for 21.2, 40.8, 48.4, and 1253.6 eV excitation. However, the UPS spectra are additionally distorted by a much stronger contribution of secondary electrons and the 5 f emission is superimposed upon the (6d7s) conduction electron density of states, background intensity of which was not considered in the calculated spectrum In the calculations, furthermore, in order to account for the excitation of electron-hole pairs, and in order to simulate instrumental resolution, the multiplet lines were broadened by a convolution with Doniach-Sunjic line shapes (for the first effect) and Gaussian profiles (for the second effect). The same parameters as in the case of the calculations for lanthanide metals were used for the asymmetry and the halfwidths ... 

To decide whether a surface effect is present and, if so which, the experimental spectra shown in Fig. 16 have been corrected for the spectrometer transmission. The secondary electron contribution and the emission from conduction band states have also been subtracted. Comparing this spectrum with calculated multiplet intensities it seems that a contribution from a divalent Am surface resulting in a broad structureless 5f 5f line at 1.8 eV is the most suitable explanation of the measured intensity distribution. Theory also supports this interpretation, since the empty 5f level of bulk Am lies only 0.7 eV above Ep within the unoccupied part of the 6d conduction band (as calculated from the difference of the Coulomb energy Uh and the 5 f -> 5 f excitation energy Any perturbation inducing an increase of Ep by that amount will... 

However, this is not the only factor influencing the emission intensities. In fact, already PUO2 shows a smaller 5 f emission intensity than Np02 (Fig. 26). This can only be explained by different final state multiplet intensity distributions for Np02 and PUO2. This kind of considerations makes a more quantitative analysis of the experimental results difficult. 

In Section 9.9 we discussed how the appearance of a spin-coupled NMR spectrum is determined by the ratio of Av (the difference in chemical shifts between the coupling nuclei) to J (the coupling constant they share). For the spectrum to exhibit first-order multiplet intensities (Pascal s triangle Section 8.5), the value of Av//has to be at least 10. Smaller values of Av/J lead to progressively greater complications due to second-order effects. 

Figure 4.20. Selective population transfer (SPT) distorts proton multiplet intensities when the resonance of a coupled partner is unevenly saturated (b). These perturbations are more apparent in the difference spectrum (c), when the unperturbed spectrum (a) is subtracted.

Figure 4.26. Relative multiplet line Intensities in coupled INEPT spectra, (a) conventional multiplet intensities and those from INEPT (b) without and (c) with suppression of natural magnetisation.

In practice, the appearance of decoupled INEPT and DEPT 29Si-NMR spectra are usually the same. However, coupled INEPT and DEPT spectra differ dramatically. Coupled DEPT spectra essentially appear as greatly enhanced standard acquisition spectra the multiplicity, phase, and relative intensities of multiplets using DEPT are the same as those obtained from normal FT-NMR techniques. In contrast, coupled INEPT spectra contain several distinctive distortions (1) the outer lines of multiplets in INEPT spectra are much enhanced compared to relative multiplet intensities obtained using standard acquisition or DEPT-NMR techniques (2) the central line of odd line multiplets in INEPT has zero intensity and (3) the two halves of a multiplet in INEPT are 180° out of phase. Thus, a triplet and a quartet in INEPT would appear as 1 0 —1 and 1 1 —1 patterns, respectively, instead of the normal 1 2 1 and 1 3 3 1 patterns seen with DEPT (see Section IV,A). 

As shown for dodecamethylcyclohexasilane (Section III,A), long-range couplings (provided they are resolvable) can be used for polarization transfer. From (MeO)4Si, for example, one can obtain well-resolved proton coupled spectra (Fig. 6) and decoupled spectra (Fig. 7). The coupled spectra vividly show the alteration of the relative intensities of the (MeO)4Si multi-plet in comparing the standard acquisition spectrum or DEPT spectrum to the INEPT spectrum. The relatively greater enhancement of the outer lines in coupled INEPT spectra is shown by the observation of 11 lines (including the zero-intensity central line) in the INEPT spectrum (Fig. 6a), compared to nine lines seen in the DEPT and standard acquisition spectra (Figs. 6b and c). Multiplet intensities in the DEPT and standard acquisition spectra are nearly identical, as expected. 

The more complex spin systems, IH , n > 1, follow the same logic as above 4) although the equations describing the spin states are correspondingly more complex. In each case, the maximal enhancement is yH/Vi > with a sinusoidal 9 dependence, which varies with n. It can also be shown (4) that decoupled DEPT spectra give normal multiplet intensities, i.e., for n = 2 the intensities are 1 2 1. 

Ti values. Again if the pulse delay is not long enough, the intensity of the center band will be underestimated due to overpulsing. Another related potential source of error in the analysis of multiplet intensities of quaternary carbon atoms is a reduction in the NOE due to dipolar interactions and which leads to a... 

Finally, the spectrum of the Cladophora cellulose which survived the strong acid hydrolysis closely resembled the cotton hydrocellulose spectrum except that the resolution was much better in the former spectrum. A contrast in resolution is consistent with a difference in the average lateral dimensions for the crystallites this difference is corroborated by electron microscopy. The close similarity of multiplet relative intensities in these two samples, in spite of their different crystallite surface-to-volume ratios verifies that surface resoncinces cire not determining the apparent multiplet intensities, particularly, for the 88-92 ppm region of the C l resonance. 

At the heart of the interpretation of the spectra is the postulate that sharper multiplet features associated with chemically equilvalent carbon atoms in the cellulose spectra are expressions of magnetically inequivalent sites within the unit cells. If this "fine structure" were due to some other cause, then the conclusion of multiple crystalline forms would be called into serious question. The fact that the ratios of multiplet intensities for given resonances, such as that of C4 or Cl, vary from sample to sample and rarely have ratios of small whole numbers, reinforces the crystalline composite hypothesis. 

The spectra of Figure 4 are quite similar, although variations in the heights of the central Cl peaks and the upfield and downfield shoulders of the C4 resonance are outside of experimental error. If the multiplet intensities arise from unit oell inequivalence alone, then these variations support the hypothesis of multiple crystalline forms in the algal and bacterial celluloses. 

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