Dynamic Processes and Chemical Exchange in NMR

If the average lifetime in one state (rex) is longer than the shutter speed, we will see two distinct peaks in the spectrum. If the average lifetime is shorter than the shutter time we will only see one averaged peak. This shutter time is formally called the coalescence time, rc, for the exchange process, or simply the NMR timescale . 

The DMF bond rotation can be considered as a dynamic equilibrium with equilibrium constant of 1 (k = k- )  

If the nucleus is farther away in the molecule from the site of chemical change, its chemical shift may be affected less so that Av is small or even zero. We can have as many NMR timescales as there are distinct nuclei within a molecule. Thus, the NMR timescale is not an absolute time, but rather it depends on field strength and on the significance of the chemical exchange in terms of its effects on the chemical shift of a particular nucleus. 

Even with slow exchange it is possible to detect the exchange by an NOE experiment. During the mixing time of the NOE, the perturbed z magnetization on Ha becomes perturbed z magnetization on Hb in an exchange event  

The spin state has not changed we just changed the label on the proton when it passed into a new chemical environment with a different Larmor frequency. 

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Beeause NMR is capable of distinguishing minute changes in the geometric and stereoisomeric properties of a structure and is also capable of obtaining qualitative as well as quantitative information, which includes information on dynamic processes of chemical exchange within the molecule or with other molecules, it is an essential, invaluable, technique for the study of aggregation phenomena, of self-assemblies, and of supramolecular structures. both in solution and in the solid state. 

These exchanges often occur while the system is in macroscopic equilibrium—the sample itself remains the same and the dynamics may be invisible to other teclmiques. It is merely the enviromnent of a given nucleus that changes. Since NMR follows an individual nucleus, it can easily follow these dynamic processes. This is just one of several reasons that the study of chemical exchange by NMR is important. 

The averaging effects of exchange apply to any dynamic process that takes place in a molecule (or between molecules). However, many processes occur at rates that are too fast or too slow to give rise to visible broadening of NMR spectra. The NMR time-scale happens to coincide with the rates of a number of common chemical processes that give rise to variation of the appearance of NMR spectra with temperature and these include ... 

Multidimensional and heteronuclear NMR techniques have revolutionised the use of NMR spectroscopy for the structure determination of organic molecules from small to complex. Multidimensional NMR also allows observation of forbidden multiple-quantum transitions and probing of slow dynamic processes, such as chemical exchange, cross-relaxation, transient Over-hauser effects, and spin-diffusion in solids. 

Molecular Motions and Dynamic Structures. Molecular motions are of quite general occurrence in the solid state for molecules of high symmetry (22,23). If the motion does not introduce disorder into the crystal lattice (as, for example, the in-plane reorientation of benzene which occurs by 60° jumps between equivalent sites) it is not detected by diffraction measurements which will find a seemingly static lattice. Such molecular motions may be detected by wide-line proton NMR spectroscopy and quantified by relaxation-time measurements which yield activation barriers for the reorientation process. In addition, in some cases, the molecular reorientation may be coupled with a chemical exchange process as, for example, in the case of many fluxional organometallic molecules. ... 

It is obvious that independently of the rate of exchange the NMR spectrum of a system subject to a dynamic equilibrium depends on the relative concentrations of the components present. These may be expressed as mole fractions or, in the case of intramolecular exchange, as conformer populations. Sometimes the populations are governed by symmetry effects alone and are independent of the experimental conditions. This is always the case for mutual exchange when the process does not alter the chemical identity of a molecule. Examples of such exchange may be drawn from rotations of the t-butyl group in (CH3)3C-C(R1)(R2)(R3), and those about the CO-N bond in N,N-dimethyl-substituted amides (CH3)2N-C(=0)R. Other examples include ring inversions such as those in 1,2-ds-dimethylcyclohexane, 1,3-trans-... 

In the earlier discussion of the effects of dynamic processes on NMR spectra of small molecules (Chapter 10), the NMR time scale for the exchange process was determined by the relationship between the preexchange lifetimes (or the inverse rate constants) and the chemical shift difference between the two states (or sites). This is also true for many systems of biological importance when the line widths of the resonances... 

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