Spin-12 Nuclei

Since phosphorus and protons are both abundant spin-1/ nuclei, it is simple to design an experiment in which we correlate protons and phosphorus rather than protons with themselves. The result of this experiment, a P,H correlation, is shown in Fig. 26. Again we have the 2D spectrum in the form of a central rectangle and two (previously recorded) ID spectra parallel to the axes. One is the proton spectrum, the other the phosphorus spectrum. The latter of course consists of a single line, and in the 2D spectrum we do not need to look for a diagonal as there cannot be one. 

B) How many lines are expected from this model The total number of nuclear spin states is (2 f + 1) x (2I2 + 1) x (2/3 + 1). Thus, if the model structure has six protons (I = 1/2), there should be (2 x 1/2 + l)6 = 26 = 64 nuclear spin states. If some of the nuclei are expected to be equivalent, then the number of lines will be less than the number of spin states, i.e., some of the spin states will be degenerate (to first-order in perturbation theory). Thus, if the six protons are in three groups of two, it is as if you had three spin-1 nuclei and you expect (2 x 1 + l)3 = 33 = 27 distinct lines. If there is one group of four equivalent protons and another group of two, then it is as if you had one spin-2 nucleus and one spin-1 nucleus and you expect (2x2+ 1)(2 x 1+1) =15 lines. 

For higher spin nuclei, one can construct a splitting diagram. For example, for two spin-1 nuclei ... 

This procedure can be extended to three spin-1 nuclei by thinking of each line of a 1 1 1 triplet split into a 1 2 3 2 1 quintet ... 

Now consider a concrete example. Suppose we have a nitroxide biradical with aN = 13 G. In the strong exchange limit, we expect a five-line spectrum with a spacing of 6.5 G and the usual 1 2 3 2 1 intensity ratios for two equivalent spin-1 nuclei. In the weak exchange limit, we expect a three-line spectrum with a spacing of 13 G and intensity ratios 1 1 1. In intermediate cases, up to 15 lines are expected, as shown in Figure 6.1. 

RDCs belong to the so-called anisotropic NMR parameters which cannot be observed in isotropically averaged samples as, for example, is the case in liquids. Besides RDCs, a number of other anisotropic parameters can be used for structure elucidation, like residual chemical shift anisotropy, residual quad-rupolar couplings for spin-1 nuclei, or pseudo-contact shifts in paramagnetic samples. Here, we will focus on RDCs where we give a brief introduction into the dipolar interaction, then into the averaging effects with the description by the alignment tensor and concepts to deal with the flexibility of molecules. For the other anisotropic NMR parameters, we refer the reader to ref 19 for an introduction and to refs. 6-8 for a detailed description. 

It was shown that REDOR or its variants can be used when one coupling partner is a quadrupolar spin.113,114 However, there are some limitations, such as the fact that only a fraction of the spin-1, nuclei are involved in the dephasing.115 Accordingly, more specific dephasing methods have been proposed for this type of system. One is TRAPDOR (transfer of population in double resonance), which uses continuous irradiation.116 The other is REAPDOR (rotational-echo, adiabatic passage, double resonance),117,118 which is a more straightforward extension of REDOR. 

Contents 1. Introduction 104 2. Theory 106 2.1. Specifically for spin-1 nuclei 112 2.2. Two-axis jump processes 114 2.3. 2-by-2-site jump 114 2.4. 2-by-3-site jump 115 3. Numerical Simulations 117 3.1. Spin-1 nuclei 118 3.2. Half-integer quadrupolar nuclei 118 4. Results and Discussion 119 4.1. Spin-1 nuclei 119 4.2. Dynamic effects in 14N MAS spectra by SQ or DQ coherences 123 4.3. Multi-axis jump processes 124 4.4. Half-integer quadrupolar nuclei 129 5. Conclusions 134 Acknowledgements 135 References 135... 

For spin-1 nuclei, both QCPMG and single-pulse MAS experiments were suitable for dynamics studies of nuclei having CqS typical for 2H or 6Li. In case of 14N, the single-pulse MAS experiment was the method of choice for investigation of dynamics for CqS larger than 750 kHz at 14.1 T. 

In principle, all of the experiments mentioned above would be applicable for the other two NMR active spin-1 nuclei 6Li and 14N. Solid-state 6Li NMR have so far been utilized in materials research39-42 and even exchange experiments on 6Li enriched Li2Si04 have been performed.42... 

In the case of spin-1 nuclei, an extra term is added to the Hamiltonian the third-order quadrupolar term, Hq-3 ... 

The spatial part of this will be added to c in Equation (17). For spin-1 nuclei, it is noted that dim = 8 and that the Av matrix during an x-pulse (6 = 0) is given as... 

For half-integer nuclei, MAS experiments have also been explored focussing on the effect of the spinning sideband manifold. Similar to what is observed for spin-1 nuclei, significant line broadening of the spinning sidebands was observed in a regime that depends on Cq, I and the Larmor frequency. 

The frequency shift can cause the non-central transitions (i.e. m 2) to be shifted sufficiently far from the Larmor frequency that these transitions become difficult to observe with conventional pulse techniques. Equation 2.116 also shows that there is an orientational dependence of the frequency so that very broad lines occur in a powder. This is important for spin-1 nuclei as there is no central transition and all transitions are broadened to first-order. For the satellite transitions the shape extent will depend on Xq and the shape will depend on -q (Figure 2.9A). It should be noted that for m — m transitions there is no first-order effect. 

Vaara and Pyykko presented a theory for the magnetic-field-dependent quadrupole splitting in the Xe NMR spectra in isotropic media and tested it by ab initio electronic structure calculations. Evidence exists only for even-power magnetic field dependence. The dominant mechanism is verified to be the electric field gradient caused by the diamagnetic distortion of the atomic electron cloud, quadratic in the magnetic field. NQCC for diatomic molecules were calculated by Bryce and Wasylishen. Turner et al performed a systematic computational study of the geometrical dependence of the deuteron quadrupole interaction parameters (DQCC and asymmetry parameter) for the water-formaldehyde model system. Bematowicz and Szymanski studied NMR spectra of a spin nucleus scalar coupled to two equivalent spin-1 nuclei... 

Fig. 3.2.6 P ilse sequences for magnetization echoes of spin-1 nuclei in the solid state.

Fig. 4. Special pulse schemes for 2D- X, "Y H) correlations. The same notation as before is used A denotes a fixed delay of length ( /( H,Y(X)) l (a) HMQC sequence for indirect detection of spin-1 nuclei. (b) INEPT-HMQC. (c) INEPT-HETCOR. (d) HMQC-TOCSY si denotes an MLEV spinlock sequence of duration t which is framed by trim pulses. ...

Fig. 13. Pulse sequences for indirect pulse calibration (a) 90° pulses, (b) 180° pulses, (c) modified sequence for indirect calibration of 90° pulses on spin-1 nuclei."...

Let us consider a monocrystalline sample that contains chemically identical spin-1 nuclei. In our physical model it will be assumed that the quadrupole principal axes for each of the spins have the same orientation. The quadrupole Hamiltonian in the quadrupole principal axes frame is given as... 

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