Strongly coupled spectra

As Av/J decreases, the simple multiplets observed in weakly coupled spectra become increasingly distorted new lines can appear and others merge or disappear. Such spectra are termed second-order or strongly coupled spectra. In these cases the chemical shift does not lie in the center of the multiplet and coupling constants are not always obvious. A simple example of such a change is seen... 

Chapter 2 considers how we can understand the form of the NMR spectrum in terms of the underlying nuclear spin energy levels. Although this approach is more complex than the familiar successive splitting method for constructing multiplets it does help us understand how to think about multi-plets in terms of active and passive spins. This approach also makes it possible to understand the form of multiple quantum spectra, which will be useful to us later on in the course. The chapter closes with a discussion of strongly coupled spectra and how they can be analysed. 

Finally, we will look at strongly coupled spectra. These are spectra in which the simple rules used to construct multiplets no longer apply because the shift differences between the spins have become small compared to the couplings. The most familiar effect of strong coupling is the roofing or tilting of multiplets. We will see how such spectra can be analysed in some simple cases. 

There are three more transitions which we have not yet described. For these, M changes by 1 but all three spins flip they are called combination lines. Such lines are not seen in normal spectra but, like multiple quantum transitions, they can be detected indirectly using two-dimensional spectra. We will also see in section 2.6 that these lines may be observable in strongly coupled spectra. The table gives the frequencies of these three lines ... 

The take home message is that from such strongly coupled spectra we can easily measure the coupling, but the Larmor frequencies (the shifts) are no longer mid-way between the two lines of the doublet. In fact it is easy... 

Fig. 2.15 The intensity distributions in multiplets from strongly-coupled spectra are such that the multiplets tilt towards one another this is called the roof effect.

In this way we can extract the Larmor frequencies of the two spins (the shifts) and the coupling from the strongly coupled spectrum. 

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

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. 

In the case of oxidized Fe2S2 the two ions are equal, so there is no valence trapping. The same holds, in principle, for [Fe3S4l". However, here the three ions are always nonequivalent, i.e., two are more strongly coupled together than the third, or all three have different coupling values (42, 83, 84). The spectrum is reported in Fig. 2C. The nonequivalence of the three Fe atoms may lead to their identification within the protein frame. In the case of [Fe4S4p all the irons are equivalent with oxidation state 2.5+ (85, 86). 

Figure 5.22 Artifact signals appear due to strongly coupled nuclei, as shown by the vertical lines of contours at about 6 7.16 in the spectrum.

Anti-Stokes picosecond TR spectra were also obtained with pump-probe time delays over the 0 to 10 ps range and selected spectra are shown in Figure 3.33. The anti-Stokes Raman spectrum at Ops indicates that hot, unrelaxed, species are produced. The approximately 1521 cm ethylenic stretch Raman band vibrational frequency also suggests that most of the Ops anti-Stokes TR spectrum is mostly due to the J intermediate. The 1521 cm Raman band s intensity and its bandwidth decrease with a decay time of about 2.5 ps, and this can be attributed the vibrational cooling and conformational relaxation of the chromophore as the J intermediate relaxes to produce the K intermediate.This very fast relaxation of the initially hot J intermediate is believed to be due to strong coupling between the chromophore the protein bath that can enable better energy transfer compared to typical solute-solvent interactions. ... 

A number of poorly resolved proton ENDOR peaks have been observed between 10-20 MHz269-271. Only small changes of the overall shape of the ENDOR spectrum were detected when the sample was freeze-dried and redissolved in D20, i.e. no strongly coupled exchangeable protons were present. From comparison with the proton ENDOR spectrum in an anhydrous powder, it was assumed that the signals arose from the methylene protons of the cysteine ligands and that the iron-sulfur chromophore was not exposed to solvent water270/. 

The spectra Fo(v) and Ca(v) are represented on the wavenumber scale and the fluorescence spectrum (F(v)) of the donor is normalized on this scale n is the refractive index, e iv) is the molar decadic extinction coefficient of the acceptor and To is the radiative lifetime (s) and R(nm) is the D-A center to center distant. For very strong coupling the rate is given by... 

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