For homonuclear spin-system

The secular contributions for these interactions are valid for heteronuclear spin systems. For homonuclear spin systems, the flip-flop term containing (/+S- + /-S+) is also secular. 

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 ... 

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. 

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

In this Appendix the expressions for the terms of the interaction Hamiltonian of a homonuclear spin system in the on-resonance rotating frame are given. 

Static spin echo decay spectroscopy also forms the basis for the measurement of magnetic dipole-dipole interactions between two unlike nuclei I and S. While this interaction is refocused by the Hahn spin echo, it can be recoupled by applying a 7i-pulse to the S-spins during the dipolar evolution period [12]. This manipulation inverts the sign of the heterodipolar Hamiltonian, and thereby interferes with the ability of the Hahn spin echo technique to refocus this interaction. The corresponding pulse sequence, termed SEDOR spin echo double resonance) shown in Fig. 4, compares the I-spin echo intensity as a function of dipolar evolution time (a) in the absence and (b) in the presence of the ti(S) pulses. Experiment (a) produces a decay F(2ti)/Fo, which is dominated by homonuclear dipole-dipole interactions, while experiment (b) results in an accelerated decay, reflecting the contribution from the heteronuclear I-S dipole-dipole interaction, which is now re-introduced into the spin Hamiltonian. For multi-spin systems, a Gaussian decay is expected ... 

A new heteronuclear dipolar interaction recoupling scheme suitable for the characterization of heteronuclear dipolar couplings for multiple-spin systems under very fast MAS condition has been proposed The new technique has been shown to be superior to the rotational echo double resonance method and other recoupling schemes as far as the interference of homonuclear dipolar interaction is concerned. The potential of the technique is illustrated for fluorapatite sample at a spinning frequency of 25 kHz. 

This general process is illustrated for a homonuclear spin system in the scheme of Fig. 5.37 in which only double-quantum coherence existing prior to the pulse is to be retained. Thus, prior to the rf pulse p = 2 coherence exists which experiences a gradient of strength Bgi and duration Ti and thus obtains a spatially dependent phase ... 

Fig. 2.6 Energy levels, drawn approximately to scale, for two spin systems. On the left is shown a homonuclear system (two protons) on this scale the a/3 and f)u states have the same energy. On the right is the case for a carbon-13 - proton pair. The Larmor frequency of proton is about four times that of carbon-13, and this is clear reflected in the diagram. The atf and fia states now have substantially different energies.

HMQC experiment. To simulate an experiment it is necessary to select not only, the spin system and pulse sequence, but also the experimental parameter relating to the simulation. The configuration file and job file features in NMR-SIM enables tested simulation parameters to be edited and stored for use in later sessions. Configuration files have been used extensively in the previous sections in this chapter and are used extensively throughout this text. The NMR Wizard can also be used to set up the necessary simulation parameters this is achieved by searching the spin system and the pulse sequence and, provided that the pulse sequence has been written following the rules in section 4.1.2, the parameters relevant to the simulation are extracted automatically. In the current version the NMR Wizard is restricted to homonuclear spin systems and to the following types of experiments ... 

Relayed COSY experiments are used to establish a link between separate homonuclear spin systems either via a heteronuclear relay step (left side of Fig. 5.24) or in H, H spin systems a homonuclear relay step (right side of Fig. 5.24). In the latter case correlation peaks are generated for protons which are not directly coupled together but form part of the same spin systems. Correlation s can arise using the small value long-range coupling constants " J(H, H) and J(H, H). 

We can consider a CH group with one remote proton H coupled to the CH proton. During the INEPT period this homonuclear coupling evolves, and a part of the polarization from the CH group proton ends up to the H through a COSY-type transfer. Therefore, the density function for this spin system is... 

For the following section, dealing with dipolar recoupling experiments on homonuclear spin systems, we will use an isolated pair of 1 /2 spins ( i, 2), for general purposes of illustration. The Hamiltonian of such a spin pair is derived from Eq. (1) as... 

Homonuclear 2D J spectroscopy was first proposed in a succinct communication by Aue, Karhan and Ernst,followed by two further notesl5,16 on the application of the technique to the proton spectra of biomolecules. Several theoretical analyses of the effects of strong proton-proton coupling on 2D J spectra have been produced,17-19 reference 19 including some experimental data for simple spin systems. Such spectra can be analyzed iteratively if necessary, in order to extract accurate values for coupling constants.l9 20 Homo-... 

The methods for QST of spin 3/2 systems as well as for coupled homonuclear spin 1/2 describe above can, in principle, be adapted for higher spin systems. However, this will certainly imply in the use of more selective pulses. 

Figure 5.10. Echo modulation effects on the spectrum of the A nucleus for (a) an AX and (b) an AX2 homonuclear spin system following a spin-echo pulse sequence, 90°-t-...

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