Dynamic Processes And Chemical Exchange In

So far we have assumed that a nucleus exists in a stable chemical environment; that is, that its chemical shift does not change with time. The chemical shift is a result of the effective field at the nucleus, and this is sensitive to inductive effects (electron withdrawal or donation through bonds), through-space effects (magnetic anisotropy due to nearby n-bonds), and steric effects. A nucleus can change its chemical environment, and therefore its chemical shift, by a chemical reaction (bond breaking and bond breaking) or by a conformational change (bond rotation). The effect this has on the NMR spectrum depends on the rate of the exchange process, compared to a time commonly referred to as the NMR timescale. There are actually a number of different timescales that can be studied using NMR, but the commonly used NMR timescale is that of direct observation of chemical shifts—the timescale of recording an NMR spectrum. The NMR timescale is essentially the "shutter speed" of taking an NMR picture of the molecule, and is of the order of magnitude of

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Figure 10.4

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Figure 10.4

milliseconds. This is a very slow timescale compared to optical spectroscopies, which operate on a nanosecond to picosecond or faster timescale. In fact, most molecular motions (molecular tumbling, bond rotation of methyl groups, etc.) and many chemical reactions (e.g., acid-base reactions) are much faster than the NMR "shutter" and we see only a single chemical shift that is the time average of the chemical shifts of the individual environments that the nucleus visits.

The simplest effect occurs when a given nucleus in a molecule changes its magnetic environment, and thus its chemical shift, as a result of a simple molecular motion. For example, the methyl groups in N,N-dimethylformamide (DMF) change places as a result of the relatively slow rotation about the amide bond (Fig. 10.4). The protons of the methyl group closer to the carbonyl oxygen have a larger chemical shift (2.94 ppm) than the other site (2.79 ppm) so that the resonant frequency of a given nucleus is bouncing back and forth between these two chemical shifts as the bond rotates. A "shutter time" can be defined for the NMR experiment, which is inversely proportional to the difference in chemical shift (in Hz!) between the two environments. On a 200-MHz instrument:

"shutter time ' = V2/(nAv) = 1/(2.22Av) = 1/(2.22 x 0.15 ppm x 200 Hz/ppm) = 1 /(2.22 x 30 Hz) = 0.015 s = 15 ms

If the average lifetime in one state (tex) 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, tc, for the exchange process, or simply the "NMR timescale".

Slow exchange (tex » Tc) means that each nucleus is, on average, entirely in one environment during the shutter time, so that the motion is "frozen" and two sharp peaks are observed for different nuclei in the two environments (Fig. 10.5, top). Heating the sample speeds up the exchange so that a blur is observed (Fig. 10.5, center) as nuclei move back and forth between chemical environments during the shutter time (tex ~ Tc). At even higher temperature, the average nucleus moves back and forth so many times during the shutter time that a single sharp peak is observed (Fig. 10.5, bottom) at the average of the two chemical shifts (fast exchange, tex ^ tc). Study of this behavior as a function of temperature allows determination of the rate constant and the energy barrier for the bond rotation.

"Shutter time" =

T — Average time spent in one state

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