ABC spin system

Five different types of peaks can occur in 3D spectra. These are illustrated in an ABC spin system, in which the Larmor frequencies of the three nuclei are v,, Vg, and v, -, and the coherence transfers are associated with two different mixing processes, M, and Mj ... 

From the foregoing discussion, it is evident that a variety of isomers are possible for unsymmetrically substituted cyclophosphines P NMR spectra are informative for distinguishing between these isomers. For example, two isomers of the cyclic trimers cyclo-(PR)2(PR ) are observed. The symmetrical isomer with identical substituents on the same side of the ring exhibits an A2B spin system, whereas the asymmetric isomer gives rise to an ABC spin system (Figure 11.5) (see Section 3.4.3). 

The 500 MHz H-NMR of the primary organozinc iodides 44a and 44b have been reported . The methylenic protons a to the zinc atom occur as the AB part of an ABC spin system, indicating slow inversion rates. Applying equation 34 (see Appendix, Section IV.A) to the given chemical shifts and coupling constants, a lower limit for the free activation energy can be established as AG > 15 kcalmol" in DMF-rfv or THF-rfg at 25 °C. No further attempts to approach closer to the coalescence temperature were undertaken (equation 26). 

F ure 6.5 (a) Schematic representation of a 3D spectrum of a linear spin syv tern ABC with identical mixing processes Mi and M2. In a linear spin system, the transfer of magnetization between A and C is forbidden for both Mi and M2, (b) Schematic representation of a 3D spectrum of a linear spin system ABC, where transfer via Mi is possible only between A and B and transfer via M2 occurs only between B and C. (Reprinted from J. Mag. Reson. 84, C. Griesinger, et al., 14, copyright (1989), with permission from Academic Press, Inc.)... 

Other programs include EXAN II, a program238 that obtains nonunique sets of chemical shifts and coupling constants by explicit analysis of the experimental line-positions of ABC spectra CHEM 3, a program239 that computes a theoretical spectrum for a three-spin system and NMDRS, a program240 for computation of double-resonance spectra. 

A second variant of the ABC system occurs when the chemical shift of one nucleus differs substantially from that of the other two — an ABX system. The presence of one nucleus only weakly coupled to the others permits factoring of the secular equation so that algebraic solutions are possible. The basis functions for the ABX system are just those shown in Table 6.3 for the general three-spin system. However, because (vA — vx) and (vB — vx) are much larger than Jax and /BX, we can define an Fz for the AB nuclei separately from Fz for the... 

The analysis of the second-order, two-spin (AB) system by inspection is given in Section 4-7 and is explained in Appendix 3. A few other second-order systems may be analyzed without recourse to computer methods. Analyzing a three-spin systems ranges from the trivial (AX2, AMX) to the impossible (many ABC systems). As the AX chemical-shift difference in the AX2 system decreases, degeneracies are lifted, intensities change, and a new peak can appear (Figure A4-1). In the AB2 extreme, a total of nine peaks can be observed. Four of these peaks result from spin flips of A protons, four from spin flips of B protons, and one from simultaneous spin flips of both A and B protons. The ninth peak, called a combination line, is forbidden in the first-order case (AX2) and is rarely observed even in the AB2 extreme. The combination line is seen only in the most closely coupled case at the top, as a very low intensity peak at the far right. 

If spins are strongly coupled, then the convention is to used letters which are close in the alphabet. So, a strongly coupled two-spin system would be denoted AB and a strongly coupled three-spin system ABC. The notation ABX implies that two of the spins (A and B) are strongly coupled but the Larmor frequency of the third spin is widely separated from that of A and B. 

Proton-decoupled P-NMR spectra can also be used for structural elucidation of mixed substituent containing cyclophosphazenes. Different types of three-spin systems such as AB2, AX2, ABC, ABX or AMX can be observed. Similarly, the P H -NMR spectra of cyclotetraphosphazenes can be diagnostic of the structure of the compound. Usually a combination of proton and phosphorus NMR can be quite useful in arriving at the structure of the cyclophosphazene compounds. 

It is obvious that the projection operators for the different species have different numbers of terms in them. The HON species have 12 terms (3 x 2 ) while the A2B-type species have four terms, and the HDT+ isotopomer has only two terms. This results in different sizes of the spin-projected basis sets, and for this reason the properties obtained in this work are not precisely comparable between the A3, A2B, and ABC systems, although a very good idea of the trends may be obtained from the data in Table XVI. While all of the above are given in terms of the original particles, it should be noted that the permutations used in the internal particle basis functions are pseudo -permutations induced by the permutations on real particles. 

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