Information about Variable Temperature DNMR Experiments
There are a number of issues that affect the accuracy of a DNMR simulation. Consider each of these points before embarking on DNMR experiments if you wish to achieve reasonably accurate rates and activation parameters.
Sample Temperature
NMR spectrometers have no precise way of measuring the temperature of your sample - the spectrometer can only measure the temperature of the cooling or heating gas stream, and that is what the dial reading reports. It is important to recognize that there may be from a few to over 20 degrees C difference between the dial reading and the actual temperature, and the error is a sensitive function of the gas flow rate, the temperature and operating parameters such as the decoupler power, nature of the sample, and others. Thus the temperature needs to be measured for every experiment at each temperature if reasonable accuracy is expected. There are three main techniques for temperature measurement:
Sample substitution by a chemical shift thermomer. The spectrometer temperature is set and allowed to equilibrate with a sample containing pure methanol, ethylene glycol or similar solvent where the difference between the OH and CH signals is temperature dependent. The proton NMR spectrum is measured, and the temperature is determined. The thermometer sample is removed, the actual sample is inserted, allowed to equilibrate 10-20 min, and the DNMR spectra are measured. The thermometer sample is inserted again, and the temperature measured again after an equilibration period. If both readings are within 1 degree, then the the temperature can be changed, and another experiment performed.
Sample Substitution using a thermocouple or RTD device. Instead of the sealed methanol sample above, place an open tube containing the same solvent as in the actual sample into the probe. The sample is allowed to equilibrate and a thermocouple or RTD device is lowered into the sample, and the temperature measured. The sample is removed, and the actual sample is inserted, allowed to equilibrate, and the spectra measured. The open tube is then placed in the probe again, and the temperature measured again to check for drift. This technique has the advantage that the nuclei need not be switched (if a non-proton sample is being studied), the solvent is the same as in the actual sample, the sample can be pulsed and the decoupler can be on (although it is wise to turn both off immediately before inserting the probe to avoid arcing).
Internal chemical shift thermometer. In this technique a chemical shift thermometer compound is added to the sample, and used to report the actual sample temperature during the experiment. This technique requires no sample substitution or multiple temperature equilibrations, and thus is both more accurate and much faster than the methods above. The most generally useful compound of this type is tris(trimethylsilyl)methane, for which the C-13 shift difference between the CH3 and CH carbons is strongly temperature dependent (over 1 Hz/degree on 400 or higher MHz spectrometers), and in a region (2-5 ppm) where interference from other signals is rare (Sikorski, W. H.; Sanders, A. W.; Reich, H. J. Magn. Reson. Chem. 1998, 36, S118-S124). The compound can be used at natural abundance, but most effective is a ca 10% C-13 enriched sample, where the two signals are almost equal in size. The compound is relatively inert, and 2-4 microliters added to the sample is adequate to quickly get enough signal-to-noise to measure the shift and thus the temperature. Of course, this technique works best when the DNMR experiment is performed using C-13 NMR spectra, since here no additional experimental work is needed to obtain accurate time-averaged sample temperature during the actual DNMR spectrum measurement. But even for other nuclei, all that is required is a nucleus switch to and from C-13 at each temperature.
Temperature Range
It is desirable to measure DNMR rates over the widest temperature range possible in order to get reasonably accurate DH# and DS# values. In a DNMR experiment the rates are usually most accurate around coalescence, and become progressively less accurate as one goes to either lower or higher temperatures. Since it is the rate constants at low and high temperatures that most affect DH# and DS# values, it is important not to "push" the range too far in either direction. In the low temperature region the excess broadening of the NMR signals is directly proportional to the rate of exchange. There must be a significant amount of broadening due to exchange (at least several Hz) before simulations can provide rate constants with an error of less than 20%. From this point to 5-10 degrees above coalescence is is usually possible to obtain optimally accurate rate constants.
Above coalescence the measured rate constants become progressively less accurate as the averaged signal narrows at higher temperature, The line shape becomes increasingly insensitive to the rate constant. Thus line-shape simulations should not be attempted unless the averaged signal is significantly broadened (at least several Hz, more is better) by the exchange process. In addition, well above coalescence the simulation rate constants are very sensitive to the chemical shift between the exchanging signals (broadening is proportional to the square of the chemical shift) but the chemical shifts are not accurately known, and must be extrapolated from lower temperatures as described below.
Temperature Dependence of Chemical Shifts
At temperatures below coalescence, the line shape fitting process usually defines the chemical shifts of the individual exchanging species. However, at temperatures close to and above coalescence, the chemical shifts are no longer well defined, and become strongly interactive with other adjustable parameters. To perform high quality simulations in this region it is necessary to extrapolate chemical shifts from the low teperature region where they can be accurately defined. A plot of d or Dd vs 1/T will usually be linear over the 20-40 degree temperature range of interest.
Spectrum Reference
WINDNMR internally operates on NMR spectra without referencing, and this is the most trouble-free mode of operation. When you begin a simulation, you also have to decide whether to use the reference positon of your spectra or not.
Operating Unreferenced: This is the default. In the Options menu make sure the item Disable Spectrum Reference is checked, and begin the simulation. All frequencies will be measured from the right end of the spectrum at 0 Hz/ppm. The disadvantage of this mode is that the printed or exported spectra and simulations will not be propely referenced.
Operating Referenced: In the Options menu make sure the item Disable Spectrum Reference is unchecked before starting the simulation by loading the first spectrum. It is important that all spectra in the series be referenced the same way, or else the simulation frequencies and spectrum position will move around in an inconvenient way.
Accuracy of )H* and )S* in a DNMR Experiment
The accuracy of a determination of activation parameters by DNMR is determined by a number of factors. One problem is temperature control, since only under special circumstances can the temperature inside the sample be measured during the actual experiment (see above). The second is signal to noise in the NMR spectra - the errors will be much larger for typical C-13 spectra than for H-1 or F-19 spectra. A third is the chemical shift: a larger chemical shift between the coalescing nuclei will give a larger range of temperatures where accurate rate constants can be measured. Finally there is the problem of fitting the line shapes: the rates are most accurate near coalescence (often +-5%), and become progressively less accurate (+-20% or worse) at lower temperatures, and even more so at temperatures higher than coalescence. It is exactly these high and low temperature rates that most affect Delta H* and Delta S* To get some idea of fitting error, it is instructive to have a different researcher repeat the simulations of a set of spectra and compare the values. The standard deviation of the slope and intercept of the plot used to obtain Delta H* and Delta S* (it is most convenient to use a Delta G vs. T plot) will give you some idea, but this will usually underestimate the errors. We find that for a good experiment these can be +/- 0.2 kcal for Delta H* and +/- 2 eu for Delta S*, or better. We have found that a careful complete redo (new samples, new spectra and simulation) by a different researcher of a variable temperature NMR experiment (these are low temperature C-13 experiments under somewhat difficult conditions) we can reproduce Delta H* to better than 1 kcal and Delta S* to 2 or 3 eu, but one can probably do better with a favorable proton or fluorine experiment because of higher signal to noise.
Here is what I consider a good experiment for estimation of Delta H* and DeltaS*:
1. Measure sample temperature for each spectrum of the experiment, before and after (or better, during) the acquisition.
2. Obtain adequate signal to noise (>20:1)
3. Determine the temperature dependence of the chemical shifts (and/or coupling constants) below coalescence for extrapolation into the region of coalescence and higher where these values cannot be defined by the NMR spectra.
4. During the simulation be very careful with interactive parameters - particularly above coalescence chemical shifts and rates become highly interactive, hence item 3.
5. Careful attention to line width in the absence of exchange. This is especially important for those spectra (high and low temperature region) where the amount of broadening due to exchange is small. In fact, don't attempt to simulate spectra that are broadened by only a few Hz - this cannot be done accurately.
6. Accurate rate data over at least a 30 degree temperature range.