Simple Two-Site Intramolecular Exchange

Just as we can calculate the appearance of an NMR spectrum if all the chemical shifts and coupling constants are known (Section 9.10), we can accurately predict the appearance of a spectrum of a molecule undergoing dynamic reversible exchange if we know the following  

the chemical shifts and coupling constants for each of the exchanging structures at the slow-exchange limit and, from this, the difference in resonance frequency (AVo = Va - Vb) of the exchanging signals  

the populations (relative amounts) of the exchanging structures (or sites) and 

As the temperature of a collection of molecules increases, the molecules acquire more thermal energy, and the rates of physical processes such as translation, rotation, and torsion increase. At sufficiently high temperature, the rate of rotation of the C-N bond in DMF becomes significant, bringing about reversible exchange of the two methyl groups The cis methyl exchanges position with the trans  

For exchange between two equally populated sites (as with the methyl groups in DMF Section 10.2), the lineshape equation [Eq. (10.1)] that describes NMR signal intensity [/(v)l at each point along the frequency (v) axis is  

If the two sites are equally populated, both individual rate constants are equal, as are both lifetimes, and the total lifetime 

At this point we can be more explicit about what we mean by NMR time scale. We will define the dimensionless exchange ratio (R) as the total rate constant k, in reciprocal seconds) divided by the difference in frequency between two exchanging signals (Avq, in hertz)  

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Although exchange reactions, where bonds are broken and formed, are fundamentally different from a chemical point of view to the intramolecular dynamic phenomena that we have discussed so far, in principle they are the same in terms of observation by NMR spectroscopy. Consider a very simple chemical process, the exchange of protons between HCl and HBr. NMR spectroscopy shows exchange between two sites with resonant frequencies Va and Vb and mean lifetimes Ta and Tb- The lifetimes are equal if the two... 

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