Second-order effects spectra

Figure 6. Channel spectram and related spectral phase shifts. Top compensated dispersion the phase is constant over the spectrum. Middle and bottom Second order effect with or without first order. The spectral phase variation induces channel in the spectrum.

Nuclear hyperfine coupling results in a multi-line ESR spectrum, analogous to the spin-spin coupling multiplets of NMR spectra. ESR spectra are simpler to understand than NMR spectra in that second-order effects normally do not alter the intensities of components on the other hand, ESR multiplets can be much more complex when the electron interacts with several high-spin nuclei, and, as we will see in Chapter 3, there can also be considerable variation in line width within a spectrum. 

Here, A is the nearly isotropic nuclear coupling constant, I is the nuclear spin (Iun = I), and m is the particular nuclear spin state. It may be observed that the zero field splitting term D has a second-order effect which must be considered at magnetic fields near 3,000 G (X-band). In addition to this complication nuclear transitions for which Am = 1 and 2 must also be considered. The analysis by Barry and Lay (171) of the Mn2+ spectrum in a CsX zeolite is shown in Fig. 35. From such spectra these authors have proposed that manganese is found in five different sites, depending upon the type of zeolite, the primary cation, and the extent of dehydration. 

FIGURE 5.1 Isotropic hyperfine pattern for 51VIV in S-band. The spectrum is from V0S04 in aqueous solution. Use of the low frequency enhances the second-order effect of unequal splitting between the eight hyperfine lines. 

Al MAS NMR has been demonstrated to be an invaluable tool for the zeoHte sdentist It provides a simple and direct way to quantify the proportions of A1 in four [Al(4)j, five [Al(5)j and six [Al(6)j coordinations. Quantitative determination of these species is an important issue in catalysis, and major effort is devoted on this topic. As mentioned already, for A1 only the central transition (-i-half to —half selective exdtation ) is detected. The central transition is unaffected by first order quadmpolar interaction, but the presence of second order effects causes broadening and complicates the quantitation of the A1 species. Usually hydrated samples and short radiofrequency pulses are employed for quantitative determination of framework and extra framework aluminum species. It is uncertain whether hydration changes the coordination of A1 species. Certain extra framework A1 can have very large quadmpolar interactions resulting in very broad lines ( NMR invisible ) [155, 202]. Unlike Si NMR, Al has a short relaxation time due to its quadmpolar nature, and the Al NMR spectrum with good signal to noise can be obtained in a relatively short time. 

Often the proton NMR spectra in cyclophosphazenes is complicated by the presence of second order effects in the form virtual coupling [3, 82]. This is manifested in the form of a broad hump that often is seen between the normal fine structure due to the first order spectrum. The criterion for the observation of... 

Strongly overlapping multiplets may be resolved by two-dimensional J,<5-spectros-copy2" 11G 118, where the first frequency domain (F,) contains coupling and the second frequency domain (F2) chemical shift information. The spectrum in Figure 2 (homonuclear [JH H, 6 ( H)]) demonstrates the use of this technique by showing unperturbed multiplets for ll signals. Second-order effects are principally not eliminated. Heteronuclear experiments [7uc,<5(13C)] are also common. 

Frozen-solution ESR spectra of Tc2G in mixed aqueous hydrochloric acid and ethanol provided data consistent with equal coupling of the unpaired electron to both technetium nuclei (101). IsotopicaUy pure "Tc (/ = 9/2) in 99Tc2Cl leads to a large number of lines in the X-band spectrum owing to second-order effects, in addition to the hyperfine lines presence for this dimeric axially symmetric system. The Q-band spectrum obtained at 77°K with a microwave frequency of 35.56 GHz exhibited fewer lines, and computer-simulated spectra were generated to correspond to the experimental spectrum withgit = 1.912, gi = 2.096, An = 166 x 10 4 cm"1, IAL = 67.2 x 10 4 cm 1, and gav = 2.035. 

Exercise 9-31 Sketch the proton nmr spectrum and integral expected at 60 MHz, with TMS as standard, for the following substances. Show the line positions in Hz neglect spin-spin couplings smaller than 1 to 2 Hz and all second-order effects. Remember that chlorine, bromine, and iodine (but not fluorine) act as nonmagnetic nuclei. 

The value of P—H coupling constant determined from the spectrum is slightly different from the true value of V(P H) because of second-order effects (see later) and, hence, is designated as the apparent P - H coupling constant, iJ (P—H). 

Figure 9.10. Predicted and observed 60-MHz H ABC spectra of compound 9-3. (a) Predicted first order spectrum (b)-(d) multiplet slanting due to second-order effects (e) observed spectrum [From Prediction of the Appearance of Non-First-Order Proton NMR Spectra, by R. S. Macomber, Journal of Chemical Education, 60, 525 (1983). Reprinted by permission.

A graphical representation of the general solution for the AB system is shown in Figure 9.14b. The most significant features to remember are (1) the AB spectrum is symmetrical around its midpoint (vav), with the inner lines larger and the outer lines smaller (2) the doublets are centered not at SA and SvB but rather at vav C. The latter feature is what makes the measurement of exact chemical shifts difficult in spectra that show second-order effects. 

Before we leave the topic of second-order effects, we revisit the three-spin system previously introduced in Example 9.15. There we established that if the chemical shifts of the three nuclei in a structure such as 9-3 are sufficiently different (i.e., an AMX system), the spectrum will consist of 12 lines 3 (first-order) doublets of doublets, each one centered at the appropriate chemical shift and exhibiting line spacings equal to the appropriate coupling constants. 

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. 

A further study of these second-order effects has been made by Dingle and Dixon (133) who had earlier found that the F NMR spectrum of [PtF(PPh3)3] could not be interpreted using a simple first-order analysis procedure (134). Their conclusions on the hydro. complexes (133) were essentially the same as those proposed earlier (279) however, they extended the study to cations [PtH(PEt3)3]and... 

T = 50 K, alignment parallel to c-axis. Lower Central transition, alignment perpendicular to c-axis, showing similar second-order effects in the distribution of the EFGs as in the satellite transition spectrum. From Takigawa et al. (1991). B. Relationship between the O relaxation rate and the Cu relaxation rate for the planar sites of YBa2Cu30v with temperature as an implicit parameter. The solid line of unity slope indicates the relationship Cu V O T = 19.3. The data deviate from this relationship above 110 K. From Hammel et al. (1989). Both figures used by permission of the... 

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