Variable Temperature DNMR Experiments

Dynamic NMR spectroscopy is the observation of a chemical exchange process in order to obtain first-order or pseudo first-order rate constants.

1. Acquire NMR spectra of all important nuclei (1H, 6Li, 7Li, 13C, 15N, 29Si, 31P, 77Se, 119Sn, etc...) at several temperature intervals before coalescence begins, during coalescence, and after coalescence. Intervals of 10 degrees are OK for most purposes, but smaller intervals (5 degrees) are often helpful in the temperature region around coalescence (±15 deg C). Smaller temperature intervals are also advisable at very low temperatures (<-80 C), since the change in rate per degree is proportional to the absolute temperature.

2. During these acquisitions, measure each temperature either externally by ejecting your sample and inserting a thermocouple in the probe (it takes about 15 minutes for temperatures in the sample to equilibrate) or internally with the 13C chemical shift thermometer (preferred, see Sikorski, W. H.; Sanders, A. W.; Reich, H. J. J. Magn. Res. 1998, 36, S118-S124).

3. Acquire at least one other NMR spectrum of your sample at temperatures below coalescence to insure that you are studying a reversible phenomenon and that your sample did not decompose.

4. Work-up your data, including converting your spectra into NUTS (http://www.acornnmr.com/) or Lybrics (Bemis, J. M. “PCNMR for Windows,” J. Chem. Ed.: Software, 1994, Special Issue 7) file format. It is especially important to phase the peaks of interest accurately and preferable to use minimal or no line broadening. Although it is tempting to use DEPT spectra for 13C DNMR studies because of the much higher signal to noise, such spectra will usually not give satisfactory line shapes.

5. Determine the natural line width for each spectrum by measuring the width of a reference peak, such as a non-exchanging peak of the molecule you are studying (preferred), the peak of a spectator compound present in similar concentration (which may be specifically added for this purpose), or a solvent peak, and set this value for the width of the peaks (WA, WB in WinDNMR). If the peaks you are simulating are broadened by small unresolved long-range couplings (for example, benzyl protons), the natural line width must includes these. In this case a reference signal like SiMe4 will not adequately represent the natural line width of the simulated signals. If you are simulating 13C NMR spectra, try to use signals with the same CH connectivity so that line broadening from residual coupling is similar for the model peak and the exchanging signals. Errors in natural line width cause especially large errors in rate constants at the low and high temperature extremes of the experiment, where the extent of exchange line-broadening is small. See Simulation Tutorial.

6. Make a plot of VA-VB (in Hz) vs. T of the spectra well below coalescence to determine the temperature dependence of the chemical shifts of the NMR peaks of interest. These shifts can then be extrapolated into the temperature region close to and above coalescence where the spectra themselves do not define the chemical shifts (i.e., chemical shifts and rates become highly interdependent). The chemical shifts can be obtained by direct measurement from the spectra or by simulation with WinDNMR. A plot of log (VA-VB) vs 1/T is less convenient but more correct, and is mandatory if the VA-VB vs. T plot shows any curvature.

7. Use WinDNMR to simulate your NMR spectra: select the appropriate simulation, load the spectrum (File menu) and select the spectral region of interest (use a round number of Hz for the spectrum width, and select a width and offset such that the peaks of interest at all temperatures will fall in the spectral window).

8. Determine VA-VB for each temperature from your plot of VA-VB vs. T and use this value for the difference between VA and VB. You may change their actual positions to get a best fit provided you keep VA-VB constant. You must use calculated shifts, or leave the shifts unchanged, for spectra above coalescence, since the spectra do not define the shifts.

9. Adjust the simulation (the position of VA-VB and the rate constant k) until you get a best fit. If there is more than one rate constant, then it is usually convenient to set the fastest of the relative rates, for example kAB/k, to 1.0, and the others to suitable values. Change rate constant k as needed. The other relative rates (kAC/k, kAD/k, etc) may also require tweaking, but leave kAB/k at 1.0).

10. Start a new SIM file (Group-Sim menu in WINDNMR)

11. Save the simulation to this file (use the SimSave menu).

12. Load a new spectrum into WinDNMR and repeat steps 5, 7, 8, 9 and 11.

13. A good overall strategy is to first do a trial simulation of the set of spectra (saving each spectrum and simulation in a WINDNMR SIM file) which serves to establish the spectrum window needed to adequately show all of the peaks of interest, the chemical shifts of the various species, the populations of various species (it not defined my molecular symmetry), the natural line width and approximate rate constants. Then temperature dependencies of chemical shifts can be determined (step 6) and applied to the simulation using the Simulation Editor (Sim-Group menu) in WINDNMR. You should also enter the temperature of each spectrum. Similarly, other values such as the relative rates (kAB/k), natural line widths and relative populations may show a systematic temperature dependence. These can also be regularized using the Simulation Editor in conjunction with an Excel spreadsheet, if needed, since the data in a SIM file can be copied to a spreadsheet, and then back to WINDNMR after modification using the calculation capabilities of the spreadsheet. Now one or more rounds of more careful simulations can be done, loading each spectrum/simulation in turn (SimRestore menu) the parameters. However, tweaking the relative chemical shifts above coalescence is likely to lead to errors, as these interact strongly with the rate constants. Inspect the difference spectra to check the quality of each simulation.

11. Determine the rates for each process (kab, kba). DNMR gives pseudo first-order rate constants. If your process is not first-order, then you must account for this in your kinetic rate equations. In the Simulation Editor there are facilities for creating tables of all of the data (including rate constant and delta G# values). These data can be pasted into PLT or an Excel spreadsheet for further manipulation, presentation or record keeping.

12. WINDNMR can calculate rate constants and Delta G‡ values for all rate constants using (use the Simulation Editor. Activation energies and enthalpies can then be determined by an Eyring plot (Delta G‡ vs. T).

References

“Dynamic NMR Spectroscopy,” Sandström, J., Academic Press, New York, 1982.

Reich, H. J. “WinDNMR: Dynamic NMR Spectra for Windows,” J. Chem. Ed.: Software, Series D., 1996, Vol. 3D, No. 2.

Bemis, J. M. “PCNMR for Windows,” J. Chem. Ed.: Software, 1994, Special Issue 7.