In strongly coupled spin-systems

Homonuclear Hartmann-Hahn transfer functions for off-resonant CW irradiation have been derived for two coupled spins 1 /2 (Bazzo and Boyd, 1987 Bothner-By and Shukla, 1988 Elbayed and Canet, 1990) and for the AX 2 spin system (Chandrakumar et al., 1990). In the multitilted frame, Hartmann-Hahn transfer functions under mismatched effective fields are related to polarization- and coherence-transfer functions in strongly coupled spin systems (Kay and McClung, 1988 McClung and Nakashima, 1988 Nakai and McDowell, 1993). Numerical simulations of homonuclear... 

Gerwick and co-workers have applied the BIRD sandwich sequence for a rapid and accurate determination of Vhh couplings in higher order spin systems present in the spectra of unsaturated fatty adds. Furihata and Seto have proposed new pulse sequences, /hr- and /cR-resolved-HMQC for determination of the Vrr coupling in strongly coupled spin systems. The authors have increased the accuracy of information on H-H /-splittings... 

McClung RED and Aarts G H M 1995 Multisite magnetization transfer in strongly coupled spin systems J. Magn. Reson. A 115 145-54... 

In the TPPI method a single data set with 512 increments is collected. In each successive increment the phase of the 90° pulse at the end of the period is incremented by 90° with respect to the phase of the corresponding pulse in the previous increment. (An equivalent experiment can be performed in which the phases of the pulses before the ti period are shifted by 90°). This is equivalent to changing the reference frame in so that the transmitter in the dimension appears to be shifted to one edge of the spectrum. After performing a real Fourier transformation, all peaks will appear to be shifted to one side of the transmitter in /. The main disadvantage of this technique is that phase distortions can appear for resonances in strongly coupled spin systems. 

The xy magnetizations can also be complicated. Eor n weakly coupled spins, there can be n 2" lines in the spectrum and a strongly coupled spin system can have up to (2n )/((n-l) (n+l) ) transitions. Because of small couplings, and because some lines are weak combination lines, it is rare to be able to observe all possible lines. It is important to maintain the distinction between mathematical and practical relationships for the density matrix elements. 

The experiment is used to separate chemical shifts and J-couplings for homo- and heteronudear systems. In simple cases the chemical shifts and J-couplings may be directly obtained from the 2D spectrum by inspection. For severely overlapped first-order spectra or strongly coupled spin systems the estimated parameters obtained from the spectrum may be used as starting values in a computer assisted spectral analysis as outlined in Modern Spectral Analysis (Volume 3). 

The vector model of a single spin is the vector representation of the complex number in the individual density matrix of a single nucleus. This density matrix consists of only one complex number thus there is only one vector in the model. In the case of more than one nuclei, the density matrix is larger, there are more single quantum coherences and more vectors belong to one spin set in the model. Moreover, in case of a strongly coupled spin system, the density matrix has different numerical form for different basis sets of the vector space of the simulation (the basis can be one of the ) and

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With realistic spectrometer parameters Up = 0.7 /is, t = 2,- ,3 /is) it must be possible with the BR-24 sequence to push the residual dipolar linewidths down to the 0.5 ppm and perhaps to the 0.3-ppm limit even for strongly coupled spin systems. We believe that the full line-narrowing capacity of this sequence probably has never been exhausted in actual experiments. In Section IV we will learn why this is true. 

We can think of the spectrum of spin 1 and 2 as being composed of two subspectra, each from a two spin system but in which the Larmor frequencies are effectively shifted one way of the other by half the coupling to the third spin. This kind of approach is particularly useful when it comes to dealing with strongly coupled spin systems, section 2.6... 

Figure 14 demonstrates the sensitivity improvement that is obtained by the described co-addition in the spin system, and shows that the method is applicable without distortions to strongly coupled spin systems and to CIDNP multiplet effects. 

In any strongly coupled spin system, each line in the spectrum is a mixture of transitions of various nuclei, which depends on the chemical shifts and coupling constants. When a chemical exchange happens, all the spectral parameters change with it. Therefore, a magnetization (or a coherence) that was associated with a single spectral line in one site may be spread among several lines in the other site. In order to deal with these complexities, we must use the density matrix. 

The calculation method presented here also provides a possible extension of the single spin vector model. This extension is performed in two steps first to weakly coupled spin systems, then to strongly coupled ones. In the first case, the introduction of the well-known product basis functions and their coherences is sufficient while in the latter one the solution is not so trivial. The crucial point is the interpretation of the linear transformation between the basis functions and the eigenfunctions (or coherences) during the detection and exchange processes. These two processes can be described by the population changes of single quantum... 

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