Resonance condition second-order effects

The superhyperfine splittings are sufficiently small to ignore second-order effects at X-band, and for adducts of the nitrone compounds splitting from the nitrone-N and the beta-H are the only resolved hyperfine interactions, thus affording the extremely simple resonance condition (cf. Equation 5.10)... 

In going from benzene to 3-carotene (the second structure), the Y value increases by more than three orders of magnitude showing the importance of increase in the effective conjugation length. The third structure exhibits N-phenyl substitution in the benzimidazole type structures to introduce a two dimensional conjugation. The last structure, an organometallic polymer, has also been measured in the solution phase. Because of the resonance condition encountered, the Y value is.complex. 

Fig. 10. Ideal second-order central-transition line shapes for half-integer quadrupolar nuclei in powder samples acquired under static (a) and MAS (h) conditions. The labels on the spectra display the singularities (shoulders S and peaks P) corresponding to the analytical resonance frequencies in Table 4. (c) 2D Al MQMAS spectrum of 9ALO,-2B2O3 on the left and a trace through one of the penta-coordinated Al sites on the right. The simulation labeled Real includes effects of finite pulses, while the Ideal simulation assumes no intensity distortions due to imperfect excitation. Spectra in (c) are reproduced from Ref. 65 with permission.

For a quadrupolar nuclide with a nonintegral spin (/ = 5, " 5, 5, or in high magnetic field, the narrowest static-sample resonance corresponds to the — l/2<- l/2 (or, 1/2) transition. This transition is broadened only in second-order by the quadrupole interaction. The line shapes from the other transitions are typically so broad that they often cannot be effectively excited. Therefore one usually is performing a selective experiment, in the sense that only a particular transition within the allowed manifold of transitions is observed. Under these circumstances the Hartmann-Hahn [11,32,33] match condition becomes... 

The dependence of the second-order quadrupolar shift on the angle 0 means that the peak shape for each resonance position can consist of more than one maximum if quadrupolar effects are significant. This is a major difficulty in the interpretation and quantification of spectra. An additional problem is that peak intensities for sites with different quadrupolar coupling constants are not necessarily quantitative unless very short pulses are used [136]. For example, aluminum in zeolites can be quantitatively monitored by NMR (137-139] provided certain experimental conditions are met when the radiofrequency pulse is short enough, signal intensity is independent of the strength of the quadrupolar interaction. Computation of line intensities for various spin systems has been described in detail [ 140-146]. 

The calculated spectrum for I 3/2 including the effect of second-order dynamic frequency shift leads to the prediction that the two spectrum components (degenerated only for extreme narrowing conditions) are characterized by different decay curves after a simple resonant pulse. The so-called broad component (3/2-1/2,-3/2-(-l/2)) decays exponentially while the narrow component (1/2-(-1/2)) decays nonexponentially. 

In this section the electron-scattering transition probability amplitude through an open QD, t( ), has been studied for a real-space 2D model Hamiltonian. A sharp change of the phase of t E) by tt occurs when t E) intersects the origin. It implies that two conditions should be satisfied in order to observe a sharp drop of the phase by tt in the tail of the resonant peak. One condition is t Eo) = 0, whereas the second condition is dt E)/dE EQ 7 0. We have shown that this phase drop is a resonance interference phenomenon that happens even within the framework of an one electron effective QD potential. The fact that the QD has at least 2D is a crucial point in the mechanism we have presented here. Our explanation of a sharp phase change is based on the destructive interference between neighboring resonances and thus differs from the mechanism based on the Fano resonance (see, for example. Refs [22,25]). 

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