Coupling between spins

The relaxation theory used in the Appendix to describe the principle of TROSY clearly tells us what to expect, but it is always a little more satisfying if one can obtain a simple physical picture of what is happening. We consider a system of two isolated scalar coupled spins of magnitude %, 1H (I) and 15N (S), with a scalar coupling constant JHN. Transverse relaxation of this spin system is dominated by the DD coupling between spins XH and 15N and by the CSA of each individual spin. The relaxation rates of the individual multiplet components of spin 15N are now discussed assuming an axially symmetric 15N CSA tensor with the axial principal component parallel to the 15N-XH vector as shown in Fig. 10.2. 

Here, Ttfs describes the isotropic and anisotropic chemical shift of spin k describes the anisotropic dipolar coupling between spins k and j is the anisotropic quadru-polar coupling of spin k and H[. describes the isotropic and anisotropic J-coupling be-... 

The heteronuclear dipolar coupling between spin species I and S is given in Eq. (2) and rewritten below in different form ... 

The susceptibility should also increase if the coupling between spin polarons is ferromagnetic—or in other words because of the Zener coupling. The condition for ferromagnetism is that... 

These are derived frum a. lensui force resulting from a coupling between individual pairs of nucleons and from the coupling between spin and orbital angular moments of the individual nucleus, as described by the shell model of the nucleus. 

The coupling between spin centers (in the case of molecule-based compounds, it is helpful to distinguish between intra- and intermolecular coupling), that is, the interaction energies. 

It must be stressed that the above examples serve only to illustrate the way in which the Hund rules are applied. When ions are in crystal lattices the basic coupling between spin momenta and orbital momenta differs from what has been assumed above, and under certain conditions the rules are not obeyed. For instance six-coordinated Fe2+ and Co3+ ions contain six d electrons which most commonly have one pair with opposed spins and four with parallel spins but, in exceptional circumstances, have three pairs with opposed spins and two unfilled states. These differences have a marked effect on their magnetic properties (cf. Section 9.1) and also alter their ionic radii (Table 2.2). The possibility of similar behaviour exists for six-coordinated Cr2+, Mn3+, Mn2+ and Co2+ ions but occurs only rarely [1]. 

The origin of these interactions, called exchange, was first realized by Heisenberg and Dirac in 1926. The interpretation of the exchange effect as formally equivalent to the coupling between spins permits the use of a vector-coupling scheme to model the quantitative behavior of coupled spins with the... 

Use HSQC if passive coupling between / spins is present. 

Fig. 12.6 A three-level system used in the text to demonstrate the promotion of effective coupling between spin levels 1 and 2 via their mutual coupling with level 3.

Dipolar coupling—coupling between spins that occurs through space the strength of the interaction is dependent on the distance between the nuclei, theb gyromagnetic ratios, and the molecular dynamics of the coupled pab. 

JoQ,eff is the sum of the couplings between spin i and all other spins plus the sum of the couplings between spin j and all other spins.. /ZQeffis the sum of the couplings between spin i and all other spins minus the sum of the couplings between spin j and all other spins. 

Period B is a spin echo in which a 180° pulse is applied only to spin 1. Thus, the offset of spin 1 is refocused, as is the coupling between spins 1 and 2 only the offset of spin 2 affects the evolution. 

The starting point will be equilibrium magnetization on spin 1, 7lz after the spin echo the magnetization has evolved due to the coupling between spin 1 and spin 2, and the coupling between spin 1 and spin 3 (the 180° pulse causes an overall sign change (see section 6.4.1) but this has no real effect here so it will... 

As is also shown in section 6.9, DQ 13J and DQic13) do not evolve under the coupling between spins 1 and 3, but they do evolve under the sum of the couplings between these two and all other spins in this case this is simply (Ju+J2t)- Taking each term in turn... 

In words, what has been generated in double-quantum between spins 2 and 3, anti-phase with respect to spin 1. The key thing is that no coupling between spins 2 and 3 is required for the generation of this term - the intensity just depends on Jl2 and Jl3 all that is required is that both spins 2 and 3 have a coupling to the third spin, spin 1. 

The second and third terms are anti-phase with respect to the coupling between spins 2 and 3, and if this coupling is zero there will be cancellation within the multiplet and no signals will be observed. This is despite the fact that multiple-quantum coherence between these two spins has been generated. 

We shall assume that spin 1 is proton, and spin 2 is carbon-13. During period A, tv the offset of spin 1 evolves but the coupling between spins 1 and 2 is refocused by the centrally placed 180° pulse. During period B the coupling evolves, but the offset is refocused. The optimum value for the time A is 1/(2J12), as this leads to complete conversion into anti-phase. The two 90° pulses transfer the anti-phase magnetization to spin 2. 

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