Spin-coupling equivalence

In addition to the above requirements for a first-order spin system, we now consider the concept of magnetic equivalence (or spin-coupling equivalence) by comparison with the concept of chemical-shift equivalence. 

The discussion of rotamers is taken in part from Silverstein, R.M., and LaLonde, R.T. (1980)./. Chem. Educ., 57,343 t For excellent introductions to stereoisomeric relationships of groups in molecules, see Mislow, K., and Raban, M. (1967). In Topics in Stereochemistry, Vol. I. page 1 Jennings, W.B. (1975) Chem. Rev., 75, 307. These authors prefer the term spin-coupling equivalence. ... 

Key Words NMR, EPR, Spin-spin coupling, Equivalent nuclides, Spin-Hamiltonian energies and eigenstates, Exchange degeneracy. 

A further refinement involves the concept of magnetic-equivalent nuclei, also termed spin-coupling equivalent nuclei . If nuclei in the same set (i.e., chemical-shift equivalent nuclei) couple equally to any nucleus (probe nucleus) in the same spin system, they are magnetic equivalent, and the designations A2, X2, and so on apply. However, if the nuclei are not magnetic equivalent, the designations A A XX are used. The designation AA BB is used if AiVJ < 8. 

See references to Mislow and Raban, and to Jennings (this Section). Those authors object to the term magnetic equivalence because it has been used ambiguously in the literature they prefer the term spin-coupling equivalence." However magnetic equivalence is widely used in the literature and will be retained here. 

The role of coordinated ethylene is evidenced by the recent ab initio calculation performed by Espelid and Borve [121-123], who have shown that ethylene may coordinate in two different ways to the reduced Cr(II) species, either as a molecular complex or covalently bound to chromium. At longer Cr-C distances (2.36-2.38 A) an ethylene-chromium zr-complex forms, in which the four d electrons of chromium remain high-spin coupled and the coordination interaction is characterized by donation from ethylene to chromium. Cr(II) species in a pseudo-tetrahedral geometry may adsorb up to two equivalents of ethylene. In the case of a pseudo-octahedral Cr(II) site a third ethylene molecule can also be present. The monoethylene complex on the pseudo-tetrahedral Cr(II) site was also found to undergo a transformation to covalently bound complex, characterized by shorter Cr-C distances (about... 

There are two other important consequences of spin-spin coupling. First, n equivalent protons will split another signal into n + 1 lines (hence three methyl protons split a methylene CH2 into 3 + 1 = 4 lines). Second, the relative sizes of peaks of a coupled multiplet can be calculated from Pascal s triangle (Figure 1.5). 

The ESR spectra of the radical anions of the ladder polysilanes show a relatively broad signal with satellites (Fig. 16). From the intensity, the satellites are attributed to the 13C nuclei at the -positions of the isopropyl groups rather than the 29Si nuclei. The number of spin couplings is equal to the number of equivalent carbon atoms at the a-positions, indicating that the spin is highly delocalized. These results resemble those of the radical anions of other cyclopolysilanes observed by ESR57 and can be explained by... 

So the NMR spectrum shows a doublet for the methylene protons due to one adjacent non equivalent CH proton. There is a triplet for CH proton due to spin-spin coupling of two adjacent non equivalent CH2 protons. 

This is due to spin-spin coupling. It should be noted that chemically equivalent protons do not show spin-spin coupling due to interactions among themselves. 

Magnetic equivalence. A group of protons is magnetically equivalent when they not only have the same chemical shift (chemical equivalence) but also have identical spin-spin coupling to each individual nucleus outside the group. 

The 7hh spin coupling constants (Table 7) also provide valuable insight into the structure of aUyhnagnesium compounds. Assuming the Karplus relationship holds, the magnitude of the coupling between the unique hydrogen, H, and the two equivalent... 

Spin-spin coupling usually, but not always, occurs between nonequivalent H s on adjacent atoms. In general, if n equivalent H s are affecting the peak of H s on an adjacent C, the peak is split into n -t- 1 peaks. A symmetrical multiplet is an ideal condition and not always observed in practice. 

In this method we take advantage of the fact that each spin % nucleus will split the peak due to its non-equivalent neighbour into a doublet of separation J (Hz). Interacting nuclei are represented by letters of the alphabet, with the gap between the letters in the alphabet indicating the separation between the nuclei in chemical shift. For example, in the description of the origin of spin-spin coupling, we used a two-nuclei system this would be termed... 

FeMoco, both as a constituent of the FeMo protein and an isolated entity, has been the subject of detailed spectroscopic examination. 57Fe Mossbauer and EPR studies of the cofactor have been interpreted in terms of an S = centre that contains one molybdenum and ca. six irons in a spin-coupled structure. The EPR signal serves as a valuable fingerprint of FeMoco furthermore, release of FeMoco from the FeMo protein produces an EPR spectrum with broader features, but the same profile, thereby indicating that the core of this cluster is little changed by the extraction procedure. Treatment of FeMoco with ca. one equivalent of... 

Finally, bisgalvinoxyl, 11, is a stable triplet.89 Its triplet ESR spectrum displays no appreciable hyperfine splittings, in contrast to the monoradical spectrum which is a quintet due to splitting by four equivalent meta protons. Therefore this biradical is a true triplet with reasonably strong spin coupling. 

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