General Information

A fluxional molecule is one that undergoes a dynamic molecular process that interchanges two or more chemically and/or magnetically different groups a molecule. If the rate of this exchange is faster than the time scale of our spectroscopic observation, these two different groups can appear to be identical. We also use the term, dynamic exchange process, to express a molecular motion that interchanges the positions of the inequivalent groups.

Multinuclear NMR spectroscopy, one of the favorite tools of the organometallic chemist, is one of the most common ways of observing dynamic behavior.

Dynamic Exchange Processes

Classical kinetics can often be used to determine the rate constant and activation energy of a chemical reaction. In a typical study, changes in concentration of products and/or reactants versus time are monitored using any number of experimental techniques (IR, NMR and UV-VIS are the most common). This method works well for reactions that take place on the laboratory time scale (minutes to hours) where the rate constants for the reactions are typically 10^-6 to 10^-3 s^-1.

This analysis becomes more complicated when we have to consider reversible reactions or systems that are at equilibrium. For example:

1. If we are interested in the energy barrier to interconversion between two isomers but the two isomers can not be resolved or separated, then we can't use this approach (since their concentrations would be constant with time).
2. If the rate of the reaction is very fast, we'd have an equilibrium mixture before we could even obtain the first measurement.

The prototypical example of such a system is the axial-equatorial interconversion of the chair form of cyclohexane. At room temperature the axial and equatorial protons are interchanged by a dynamic (fluxional) process in which the ring undergoes a "chair-chair" conformation change. As shown here, H_a and H_b are interchanged between axial and equatorial positions:

To understand why this complicates our analysis remember that in the ¹H NMR experiment we irradiate the protons to flip their nuclear spins and then wait as they give off this excess energy. The energy (frequency) of this relaxation is what we more commonly call the chemical shift of our proton. It takes time for our protons to relax to their nuclear ground states and this relaxation is governed by both the spin-lattice, T₁, and spin-spin, T₂, relaxation time.

Imagine that we irradiate a proton while it is in the equatorial position. Under normal circumstances, the proton would relax and we would detect it at a chemical shift characteristic of equatorial protons. However, if the molecule rearranges so that this proton is in the axial position when it relaxes, the chemical shift would be consistent with an axial proton.

To prevent exchange from occurring, all we have to do is cool the sample to a sufficiently low temperature. At -90 degrees C, the axial and equatorial protons of cyclohexane no longer interchange and are resolved as two separate resonances. But as we raise the temperature, the two peaks move together and broaden, indicating that there is some exchange, a regime we call slow exchange.

When the two peaks merge such that there is no distinguishable valley between them we say that the peaks have coalesced. As we raise the temperature even more, the merged broad peak sharpens again. At this point, the lifetime of a species as axial or equatorial is much shorter than the time scale of the experiment (flipping the nuclear spin and observing the relaxation). We call such a system fast on the NMR timescale or denote it as being at the high temperature limit.

Figure 1. VT-NMR spectrum of cyclohexane-d₁₁ (See Kegley, page 21). Note: All peaks are singlets instead of doublets because J_H-D is small and 11 of the 12 protons are deuterated. In a non-deuterated sample, each peak would be a doublet with a J_ax-eq of approximately 13 Hz.

An organometallic system that undergoes a similar interconversion, but at higher temperature is the bent metallocene complex, Cp₂TiS₅. In the structures below, notice that S_a and S_e of the pentasulfide unit are closer to one cyclopentadienyl ring than the other. This creates two chemically and magnetically inequivalent Cp rings which appear as separate signals in the ¹H or ¹³C NMR spectrum.

Above room temperature, Cp₂TiS₅ undergoes a chair-chair rearrangement which effectively switches the polysulfide ligand from one side of the molecule to the other. As far as our NMR spectrometer is concerned, the two Cp rings (conveniently marked in blue and red) appear to have exchanged positions even though they did not actually move. The sulfurs have been marked to show you that this process is not merely rotation of the entire molecule by 180 degrees, but an inversion of the ring:

Note: The Cp rings themselves freely rotate about the Ti-ring centroid with an exceedingly low energy barrier. Therefore, all five protons on the same ring act chemically equivalent at all temperatures and appear as a singlet even though some may be closer to the S5 ring in the static picture shown above.

This chair-chair inversion exchange process is slow at room temperature, but can be conveniently studied over the range 20-120 degrees C using variable temperature ¹H NMR. This makes a good advanced undergraduate laboratory experiment which you can get at http://www.chem.uky.edu/courses/che450g/handouts/cp2tis5.html if they are still using the experiment in the lab course I used to teach.

Quantitative Aspects of Dynamic NMR

Using methods described in the references below, an Arrhenius and Eyring plot can be obtained from variable temperature NMR data. This permits one to calculate the activation energy, E_a, as well as the G, H and S of activation for the dynamic process. This, in turn, can give you valuable information that you can use to support or rule out certain mechanisms. We hope to include this information in this document in the near future.

Spin Saturation Transfer

This is another useful technique; watch for a separate entry sometime in the near future.

How to Interpret Dynamic NMR Data

1. Start at the low-T limit. It is usually easiest to start here because (presumably) there is no fluxionality. Thus, your task is simply finding static structures that are consistent with the available data. Use your knowledge of the system, integrals, multiplicities, coupling constants, decoupling data, and chemical shifts as you would in any other system.
2. Look at the high-T limit. Having assigned your spectrum at low T, it is now easy to understand which groups are interconverting on the NMR time scale.
3. Find a chemically reasonable pathway for the interconversion. Possibilities to look for include:
   
   
   1. Dissociation and recoordination of a ligand. To probe for such behavior, add some of the free ligand to the solution. If the fluxional process involves dissociation of that species, the chemical shift of the free ligand and bound species will come at the weighted average of the individual species. One can also try adding an isotopically-labeled version of the free ligand and see if the label is incorporated into the complex.
   2. Rotation about a hindered bond. We can typically ignore rotation about simple bonds such as a metal-alkyl, metal-Cp and metal-alkoxide because these are so facile that they are almost impossible to freeze out. However, large groups, or phenyl rings with ortho substituents can display hindered rotation. Alkenes and other pi-bonding ligands sometimes have a preferred orientation for coordination; an fragment MO approach can help us assess this (more on that in a future chapter).
   3. Opening/closing of bridges. In dinuclear systems, it is not uncommon for a carbonyl or alkoxide ligand to switch between a bridging and terminal position.
   4. Monomer-dimer or dimer-tetramer equilibrium. Dimers (or dimers of dimers) held together only by weakly bridging ligands often undergo dissociation. Note: This is unlikely in a case where a metal-metal bond exists. To probe such equilibria, try decreasing the concentration, which should give more of the lower nuclearity species at a given temperature, as well as increasing the concentration, which should favor the higher nuclearity species. Likewise, high T should favor the dissociated form and low T the more associated form.
   5. Structural or skeletal rearrangements. Two examples are cyclohexane and Cp₂TiS₅ as discussed above. 5-coordinate systems are quite notorious for fluxional behavior as the energy barrier between trigonal bipyramid (TBP) and square pyramidal (SP) geometries is often quite low. Such interconversions can occur through a Berry pseudorotation or turnstile mechanism. Watch for an entry on the these two mechanisms at a later date.
4. Remember to consider other possibilities. Remember that you can never prove a mechanism, only disprove one. For example, perhaps there are two processes being observed, not just one!

Self-Test

The following problems involve examples of dynamic behavior. These problems are mechanistic in nature so you will not be presented with multiple choice answers here. Instead, print the problem out, find a solution that fits the data and then come back to this page.

When you hit the "Start Solving" button, you will be presented with a series of questions that will probe your assessment. Each will either allow you to proceed or point out an error in your reasoning. If you do not get a correct answer along the way then stop, examine the feedback and think about the problem some more before continuing. Remember, these problems are not meant to be solved in five minutes.

THESE EXERCISES ARE NOT CURRENTLY WORKING - We moved to a new server platform in March 2023 and I have to go back and redo the coding that drives the grading. Stay tuned...

Question 1. On the right are 1H NMR spectra of (tetramethylallene)Fe(CO)4 (1) at -60 oC and 30 oC (tetramethylallene is Me2C=C=CMe2). In the low temperature spectrum, the integrated ratios of the peaks are 1:1:2. When tetramethylallene is combined with 1, the 30 oC 1H NMR spectrum of the mixture "consists of two singlets" (the spectrum is not shown here). Explain these spectra. Be sure to draw careful and complete structures in your answer. Assign the peaks at high and low temperature and be certain to explain whatever processes are occurring.

Question 2. Consider this pseudo-octahedral ethylene complex of osmium. At +80 oC, the 31P-decoupled 1H NMR of this complex in solution with an equimolar amount of added ethylene shows a single sharp line at 6.0 ppm (ignoring the PMe3 and PPh3 resonances). Cooling this solution to 0 oC results in the splitting of this resonance into a single line at 4.9 ppm (about where free ethylene is observed) and two doublets at 7.5 (J = 2 Hz) and 6.7 (J = 2 Hz) ppm. Upon cooling to -80 oC, the two doublets split further into a complex multiplet. Explain these observations. Careful and complete drawings will help you assign equivalent protons and be a large help in solving this problem.

Question 3. The compound shown on the right exhibits fluxional behavior in the proton-decoupled 31P NMR. As the sample is cooled, the singlet resonance broadens and decoalesces between -80 and -100 oC (the T depends on the nature of group X). Below the coalescence point a pattern that appears to be a quartet is observed. Addition of excess PEt3 to this reaction mixture has no effect on the observed NMR behavior. Using clear drawings, explain what is being observed and show how this is consistent with the NMR observations.

Suggested Reading

1. Kegley, S.E.; Pinhas, A. R. Problems and Solutions in Organometallic Chemistry, University Science Books: Mill Valley, California, 1986, pp 20-26.
2. Gasparro, F. P.; Kolodny, N. H. J. Chem. Ed. 1977, 4, 258-261.