Line slow exchange

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.

This is most readily studied with cyclohexane- /n in which 11 of the 12 protons are replaced with deuterium. The spectrum of cyclohexane- /n resembles the behavior shown in Fig. 4-8 at about — 100°C (the slow exchange regime) two sharp lines are seen these broaden as the temperature is increased, reaching coalescence at — 61.4°C, and becoming a single sharp line at higher temperatures. (The deuterium nuclei must be decoupled by rf irradiation.) Rate constants t for the conversion were measured over the temperature range — 116.7°C to — 24.0°C by Anet and Bourne. It is probable that the chair-chair inversion takes place via a boat intermediate. 

In the slow exchange limit, where 22 > A2, two Lorentzians, centered at cb + A and bb — A, respectively, are observed with width 2/Tf + 20. The exchange imposed by the molecular motion thus causes an extra broadening of the lines observed in absence of motion. 

Thus a single Lorentzian line is obtained that is centered at a weighted average resonant frequency and has a width proportional to a weighted average T2x plus a term proportional to the average lifetime and the square of the separation of the slow exchange resonances. 

In the so-called intermediate exchange region, eqn (5.18) is not easily tractable and recourse is usually made to computer simulations. Qualitatively, however, it is clear that as the rate increases, the separate resonances of the slow exchange limit broaden, shift together, coalesce and then begin to sharpen into the single line of the fast exchange limit. 

Simpler expressions for the line shape are available for both the fast and slow exchange regimes (see Ref. [9]). The possibility of measuring the dissociation equilibrium constant in each of these three regimes will now be considered. 

The linewidth of the diamagnetic MnOT resonance, fV°, is broadened on the addition of the paramagnetic MnO ", but there is no shift in the signal position, which is proof that we are in the slow-exchange region. The broadened line width is a linear function of added MnOj"... 

Fig. 7. One-dimensional NMR spectra of the designed four-helix bundles SA-42 (lower trace) and GTD-43 (top two traces). The chemical shift dispersion of SA-42 in 90% H2O and 10% D2O at 323 K and pH 4.5 is poor and the resonances are severely broadened due to conformational exchange. The chemical shift dispersion of GTD-43 in the same solvent at 288 K and pH 3.0 is comparable to that of the naturally occurring four-helix bundle IL-4 and the resonances are not significantly affected by conformational exchange. Upon raising the temperature to 298 K line broadening is observed (top trace) which shows that GTD-43 is in slow exchange on the NMR time scale, unlike SA-42 where an increased temperature reduces the line width. These spectra are therefore diagnostic of structures with disordered (SA-42) and ordered (GTD-43) hydrophobic cores...

In aqueous iodide solution to which small amounts of iodine has been added, the I127 resonance for I- is broadened over that for pure iodide solutions. Degree of broadening here is related to the average lifetime of an iodine nucleus as Ir- These experimental conditions then appear to meet the conditions of slow exchange. The frequency separations between the I- and 12 and between the I and I3 resonances are not known, but presumably these are large with respect to the I line width and Eq. (38) is valid for this system. 

McConnell and Weaver (78) have utilized line width measurements of Cu6S and Cu66 resonances in a Cu1—Cu11—HC1 system to estimate the C is a constant evaluated under conditions of slow exchange. 

This is valid, as shown by Alexander, for any spin system in the slow-exchange range provided that the broadened lines do not overlap appreciably with each other. (36) The following three equations can also be useful ... 

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