Fast exchange limit 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.

In presence of molecular motion the NMR line shape will change. A particularly simple situation arises, if the motion is rapid on timescale defined by the inverse width of the spectrum in absence of motion 6 1. In this fast exchange limit, which in 2H NMR is reached for correlation times tc < 1CT7 s, the motion leads to a partially averaged quadrupole coupling and valuable information about the type of motion can directly be obtained from analysis of the resulting line shapes. The NMR frequency is then given by... 

Let us investigate what happens to the NMR spectrum of DMF as we increase the exchange ratio from the slow-exchange limit to the fast-exchange limit. 

Finally, when R is greater than 50, the system is essentially at the fast-exchange limit, and the spectrum consists of one sharp signal at v v (Figure 10.1,/ = 50). At higher values of R the halfwidth of this signal approaches v j-... 

The methylene protons at position A become non-equivalent in two identical twisted conformations of the aromatic rings. The inversion between the two twisted conformations renders the methylene protons equivalent in the fast-exchange limit. Collapse of the AB spectrum at low temperature to a single line at high temperature yields the following parameters for the activated inversion process,... 

The spectrum of a chemically reacting system is in general a very complicated function of the frequency. In this section we explore two limits in which the form of the spectrum simplifies considerably. These are the slow exchange and fast exchange limits. In the slow exchange limit the rates ka and kb are small compared to the Doppler frequencies cui and 0)2, whereas in the fast exchange limit, the contrary is valid that is, the rates ka and kb are large compared to the Doppler frequencies. We now consider each of these limits. 

In the fast exchange limit ka and kb are large compared to the frequencies co 1 and a>2 and to the diffusion rates q2D and q2D2 The spectrum then simplifies considerably. 

The important conclusion from Figure 14 is that the DISPA plot can readily show whether a system undergoing chemical exchange has reached the "slow" or "fast" exchange limit (i.e., Lorentzian line shape, with DISPA data points on the reference circle) or not, based on data at a single temperature. It is always inconvenient, and not always practical (as with heat-labile compounds) to vary the temperature to discover whether the "slow" or "fast" limit has been reached here the DISPA plot gives an immediate answer from a single spectrum. 

The quantum theory must describe not only the shape of a resolved rotational structure of the Q-branch but its transformation with increase of pressure to a collapsed and well-narrowed spectrum as well. A good example of such a transformation is shown in Fig. 4.6. The limiting cases of very low and very high pressures are relatively easy to treat as they relate to slow modulation and fast modulation limits of frequency exchange. 

At temperatures around 50-60°C the three-site jump model is not a good approximation to the multi-site jump model, because the motion is not sufficiently rapid to be in the fast motion limit. However, the calculated spectra are fairly fitted with the observed ones. This is because the calculated spectrum is a superposition of constituent spectra whose rates are spread over several orders, so that the resultant spectrum is governed by the constituent spectra in the fast and slow motion limits having greater intensity than that in the intermediate exchange regime. 

The bicapped square pyramidal structure of Ni Pbio has two chemically distinct lead environments, but its ° Pb NMR spectrum shows a single, somewhat broad resonance at —996 ppm (25°C, 104.7 MHz) as a result of fast exchange [57]. As the Ni Pbio sample is cooled to —45°C, the signal broadens significantly due to slowing of intramolecular exchange on the NMR time scale, but the limiting spectrum has not been achieved. 

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