∆G, ∆G†† and All That: Implications for NMR

Since we were on the subject of NMR and determining conformations, I think it would be pertinent to briefly discuss one of the more slippery basic concepts that I have seen a lot of chemistry students (naturally including myself) get plagued with; the difference between thermodynamics and kinetics. I find myself often besieged by a distinction between these two important ideas that encompass all of chemistry. Simply saying that thermodynamics is "where you go" and kinetics is "how you get there" is not enough of a light to always assuredly guide students through the sometimes dark corridors of structure and conformation.

Going beyond the fact that thermodynamics is defined by the equilibrium free energy difference (∆G) between reactants and products and that kinetics relates to the activation barrier (∆G^††) for getting from one to the other, I want to particularly discuss the importance of both these concepts for determining conformation by NMR spectroscopy.

There are two reasons why determining conformations in solution can become a particularly challenging endeavor. The first reason is thermodynamics. Again consider the all-important relation ∆G = -RTlnK which makes the equilibrium constant exquisitely sensitive to small changes in free energy (∆G). As mentioned before, an energy difference of only 1.8 kcal/mol between two conformations means that the more stable one exists to the extent of 96% while the minor one exists to the extent of only 4%. In practice such energy differences between conformers are seen all the time. A typical scenario for a flexible molecule in solution will posit a complex distribution of conformers being separated from each other by tiny energy differences ranging from say 0.5-3 kcal/mol. Again, the above exponential dependence of equilibrium constant K on ∆G means that the concentration of minor conformers which are higher in energy than the more stable ones by only 3 kcal/mol will be so tiny (~0.04%) as to be virtually non-existent. NMR typically cannot detect conformers which are less than 2-3% percent in solution (and it's too much to ask of NMR to do this), but such populations exist all the time.

Thus, thermodynamics is often the bane of NMR; in this case the technique is plagued by its low sensitivity

If thermodynamics is the bane, kinetics may be the nemesis. Rotational barriers between conformations (∆G^††) can be even tinier compared to thermal energy available to jostle molecules around at room temperature. For example, the classic rotational barrier for interconversion in ethane (whose origins are still debated by the way) is only 3 kcal/mol. Energy available at room temperature is about 20 kcal/mol which will make the ethane conformations interconvert like crazy. So even for energy barriers that are several kcal/mol, conformational interconversion is usually more than adequate to observe averaging of conformations and consequently all associated parameters- most importantly chemicals shifts and coupling constants- in NMR. The resolution time of NMR is on the order of tens of milliseconds, while conformational interconversion is on the order of tens of microseconds or less. Now in theory one can go to lower temperatures and 'freeze out' such motions. In many such experiments, line broadening at lower temperatures is observed, followed by separation of peaks at the relevant temperature. But consider that even for a barrier as high as 8-10 kcal/mol, NMR usually gives distinct, separate signals for the different conformers only at -100 degrees celsius. For barriers like those in ethane, the situation would be hopelessly challenging. As an aside, that means that sharp, well-defined resonances at room temperature do not indicate lack of conformational interconversion but can simply mean that conformational interconversion is fast compared to the NMR time scale.

Thus, kinetics is also often the bane of NMR; in this case the technique is plagued by low resolution time

Now there may be situations in which either thermodynamics or kinetics is favourable for carrying out an NMR conformational study. But for the typical flexible organic molecule, both these factors are usually pitted against the technique; rapid interconversion because of low rotational barriers, and low thermodynamic energy differences between conformers. Given this fact, it probably should not sound surprising to say that NMR is not that great a technique. However, as is well known to every chemist, its advantages far outweigh its drawbacks. Conformational studies comprise but one important aspect of countless NMR applications.

Nonetheless, when conformational studies are attempted, it should always be kept in mind that thermodynamics and kinetics have both conspired to make NMR an unattractive method for our purposes. Thermodynamics leads to low populations. Kinetics leads to averaging of populations. And yet the average information gained from NMR is invaluable and can shed light on individual solution conformations when combined with a deconvolution technique like NAMFIS or molecular dynamics. On the other hand, fitting the average data to a single conformation for a flexible molecule is inherently flawed and unrealistic. No one who has tried to take pictures of a horse race with a low-shutter speed camera should believe that NMR by itself is capable of teasing apart individual conformations in solution.

For determining conformations then, NMR alone does provide a wealth of data locked inside a safe. Peepholes in the door may illuminate some aspects of the system. But you need a key, best obtained from other sources, that will allow you to open the door and savor the treasures unearthed by NMR in their full glory.