Homonuclear spins

A homonuclear spin-system may be excited with radiofrequency (r.f.) pulses that are so Intense (in the order of p.s), compared to the frequency width of the spectrum, that all resonances are excited essentially uniformly. This is a nonselective excitation. A homonuclear spin-system may also be excited with a relatively weak, r.f. pulse (in the order of ms), in the sense that all components of a given multiplet are inverted at time zero, whereas the other resonances in the spectrum remain essentially unperturbed this is a selective excitation. The r.f. pulse may be single-selective, that is, there is an inversion of one multiplet in the spectrum, or double-selective, triple-selective, and so on, where two, three, or more separate multiplets in the spectrum are inverted simultaneously while the remaining resonances remain unperturbed. 

No. Since the direction of precession of the vectors is reversed during the second half of the sequence, they continue to diverge from each other. The effect of a spin-echo experiment on spin-spin coupling in a first-order homonuclear spin system is shown in the following vector representation ... 

One-dimensional double-resonance or homonuclear spin-spin decoupling experiments can be used to furnish information about the spin network. However, we have to irradiate each proton signal sequentially and to record a larger number of ID H-NMR spectra if we wish to determine all the coupling interactions. Selective irradiation (saturation) of an individual proton signal is often difficult if there are protons with close chemical shifts. Such information, however, is readily obtainable through a single COSY experiment. 

Figure 17. Contour plot of the 360MHz homonuclear spin correlation mpa of 10 (2 mg, CDCL, high-field expansion) with no delay inserted in the pulse sequence shown at the top of the figure. Assignments of cross peaks indicating coupled spins in the E-ring are shown with tljie dotted lines. The corresponding region of the one-dimensional H NMR spectra is provided on the abscissa. The 2-D correlation map is composed of 128 x 512 data point spectra, each composed of 16 transients. A 4-s delay was allowed between each pulse sequence (T ) and t was incremented by 554s. Data was acquired with quadrature phase detection in both dimensions, zero filled in the t dimension, and the final 256 x 256 data was symmetrized. Total time of the experiment was 2.31 h (17).

The so-called HORROR experiment by Nielsen and coworkers [26] introduced continuous rf irradiation recoupling to homonuclear spin-pairs and initiated the later very widely used concept of /-encoded recoupling. Using a irreducible spherical approach as described above, the HORROR experiment (Fig. 2d) is readily described as starting out with the dipolar coupling Hamiltonian in (10) and x-phase rf irradiation in the form Hrf = ncor(Ix +SX), also here without initial constraint on n. The dipolar coupling Hamiltonian transforms into tilted frame (rotation n/2 around Iy + Sy)... 

Total correlation spectroscopy (TOCSY) is similar to the COSY sequence in that it allows observation of contiguous spin systems [35]. However, the TOCSY experiment additionally will allow observation of up to about six coupled spins simultaneously (contiguous spin system). The basic sequence is similar to the COSY sequence with the exception of the last pulse, which is a spin-lock pulse train. The spin lock can be thought of as a number of homonuclear spin echoes placed very close to one another. The number of spin echoes is dependent on the amount of time one wants to apply the spin lock (typically 60 msec for small molecules). This sequence is extremely useful in the identification of spin systems. The TOCSY sequence can also be coupled to a hetero-nuclear correlation experiment as described later in this chapter. 

Fig. 11.7 a Pulse sequence for rotational-resonance recoupling of homonuclear spin pairs, b The spinning frequency is matched to the isotropic chemical-shift difference, and one of the resonances is selectively inverted and the polarization exchange measured as a function of the mixing time, c The difference polarization as a function of the mixing can be evaluated to give the dipolar coupling constant. 

As previously observed, the dominant terms in the Hamiltonian which describe a spin system in the solid state are the dipolar and quadrupolar terms. In the case of nuclei with 1 = 1/2 (such as H, 13C, 19F and 29Si) the quadrupolar interaction is zero. The dipolar Hamiltonian HD (for a homonuclear spin system) has the general form ... 

Undesired homonuclear spin interactions can be also suppressed using suitable multiple-pulse sequences while still exploiting the information content provided by interactions that are not affected. Using a combination of MAS and pulse decoupling it is even possible to reintroduce parts of an interaction that would be averaged out by one of the manipulation techniques alone ( recoupling ) [11]. This high flexibility of solid-state NMR enables one to fully exploit the rich information content provided by the spin interactions. It becomes particularly powerful if such experiments are combined to multidimensional NMR techniques as discussed in Section 14.3. 

However, in all the papers mentioned above the authors analyzed only three-dimensional (3D) systems, while a two-dimensional (2D) case is also experimentally observed surfaces of various absorbers, heterogeneous catalysts, photocatalysts, etc. In [137], Fel dman and Lacelle examined the quenched disorder average of nonequilibrium magnetization, i.e., a free induction decay G(t) and its relative fluctuations for dipolar coupled homonuclear spins in dilute substitutionally disordered lattices. The studies of NMR free induction decays and their relative fluctuations revealed that the functional form of the disorder average (G(t))c depends on the space-filling dimentionality D of the lattice. Explicit evaluations of these averages for dilute spin networks with D = 1, 2, 3 were presented in [137] ... 

Many of the individual lines observed in spectra such as those shown in Figure 1 can be assigned to specific silicate structures based on spectra of well defined silicate sparies and detailed NMR studies of the homonuclear spin-spin coupling of 2 Si nuclei in Z Si-enriched silicate solutions r6-81. Such studies have revealed that the chemical shift of a given silicon atom depends on its connectivity, the length of the Si-O bonds, and the angle of Si-O-Si bonds, as well as the pH of the medium and the cation type. 

Values of the spin-spin relaxation-time (Tz) for individual spectral lines may be measured by Fourier transformation of the echoes produced by a Carr-Purcell-Meiboom-Gill type of pulse sequence,174 but only in a simple manner, if there is no homonuclear spin-coupling present.175 Refocusing of the dispersing magnetization-vector by... 

Use the dipolar Hamiltonian for a homonuclear spin system, Eq. 7.6, together with symmetrized wave functions from Chapter 6, to compute the energy levels and spectrum for a single H20 molecule in a solid. 

By substituting the expressions for spectral densities in Eq. 8.11, we obtain an equation that is algebraically cumbersone in general but that can be simplified in either of two regimes (1) homonuclear spins (I = S) or (2) rapid tumbling (extreme narrowing limit). 

As a second example, we look at echoes. We saw in Chapter 9 that a 180° pulse refocuses not only chemical shifts and the effects of magnetic field inhomogeneity but also spin coupling provided that the pulse does not also disturb the spin state of the coupled nucleus (see Fig. 9.2) However, in a homonuclear spin system a nonselective pulse does effect spin states. We found in Chapter 7 that dipolar interactions have the same mathematical from as indirect spin coupling, and it is known that a 180° pulse does not produce an echo in a solid because spin states are disturbed. However, it is possible to obtain a solid echo or dipolar echo by applying the pulse sequence 90, T, 90r It is very difficult to rationalize an echo from... 

FIG. 10. Amplitude modulation of spectra obtained by Fourier transformation of the last half of a spin-echo when there is a small unresolved homonuclear spin-spin coupling constant. The spectra are from the protons in 2,4,5- trichloronitrobenzene which has a para coupling of 0-4 FIz. From ref 145. 

An early report (560) mentions the use of homonuclear spin tickling to aid the assignment of the lines of an AB spectrum from an oriented molecule. The method has been applied to the 4-proton spectrum from ethylene oxide in EBBA (561) and to the detection and assignment of weak transitions in the proton spectrum of oriented o-dichlorobenzene. (562)... 

Although in general, only one multiple-pulse sequence is applied to homonuclear spin systems, it can be useful to apply different multiple-pulse sequences to several nuclear species at the same time by using separate rf channels. In heteronuclear Hartmann-Hahn experiments, the same multiple-pulse sequence is usually applied simultaneously to two or more nuclear species. However, some selective homonuclear Hartmann-Hahn experiments are also based on the simultaneous irradiation of a multiple-pulse sequence at two or more different frequencies (see Section X). If only a single homonuclear rf channel is used, this can be achieved experimentally by adding an amplitude or phase modulation to the sequence, in order to create appropriate irradiation sidebands (Konrat... 

Hence, in a homonuclear spin system, an effective isotropic mbdng... 

In general, the full isotropic coupling tensor between two homonuclear spins i and j can only be preserved by a multiple-pulse sequence if Ui (t) Uj U) [i.e., if fl j (t) = ap(t)] for 0 < / < Tj,. For multiple-pulse sequences with constant rf amplitude this is only possible for spin pairs with small offset differences p - Vj v, that is, for small angles 0-j. In general, the average coupling tensors are nonisotropic. Even if isotropic effective coupling tensors (with c J = c Jy = c 0 and c Jp = 0 for a = p)... 

For a given spin system, it is often possible to create different effective coupling topologies. For example, consider a homonuclear spin system that... 

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