Temperature Calibration - An Alternative Method

It is well known that the actual temperature of a sample in an NMR probe is not necessarily the same as that read from the variable temperature unit on the spectrometer. This is because the thermocouple used by the variable temperature unit is below the sample tube and not in the center of the rf coil where the NMR measurements are made. One normally must make a calibration plot for the actual temperature vs. the set temperature. For temperatures above room temperature this can be done by employing the known temperature dependent chemical shift difference between the two proton resonances of ethylene glycol (see this link). At temperatures below room temperature, the same measurement can be made for the known temperature dependent chemical shift difference between the two proton resonances of methanol. The actual temperature is determined from the chemical shift difference and plotted against the temperature read from the variable temperature unit. One potential problem with this method is that the resistance of the magnet shim coils change slightly with temperature affecting the shim currents and the NMR line shapes of the resonances. This makes it difficult to measure a precise chemical shift difference. In order to obtain reliable results, the magnet must be reshimmed at each temperature.

I have used is a very simple alternative method for calibrating the temperature of the sample compared to that of the variable temperature unit. This is illustrated in the figure below.A "sample" is prepared by pushing a NONMAGNETIC thermocouple through an NMR tube cap. The depth of the thermocouple is adjusted such that when the cap is put on the NMR tube, the tip of the thermocouple sits in the center of the rf coil. The NMR tube should contain a suitable liquid filled to the correct depth. The tube is placed in the spinner and set to the proper depth with a depth gauge. While holding onto the thermocouple, the sample is lowered into the magnet until it sits correctly in the NMR probe. The thermocouple is connected to a digital thermometer (some of these devices can use a second thermocouple in an ice water bath as a reference). The desired temperature is set on the variable temperature unit. When the temperature on both the variable temperature unit and digital thermometer have stabilized (~ 10 minutes), the values from each are recorded. This is repeated for temperatures over the desired temperature range and a calibration plot is constructed. Shimming is not an issue. Note that no NMR measurements are made and that the sample tube is not spinning.

Solid State NMR of Half Integer Quadrupolar Nuclei

Many students who do liquid state NMR or solid state NMR of spin I=1/2 nuclei have very little appreciation for the information content and complexity of the solid state NMR spectra of spin I = n/2 quadrupolar nuclei (n= 3, 5, 7....). In part, I think this may be due to the mathematics involved with explaining the important effects. With this post, I attempt to describe the NMR spectrum of an I = 5/2 nucleus in the soild state without resorting to mathematics. I hope that this post helps to boost the understanding and appreciation for the NMR spectra of these important nuclei.

When one collects the NMR spectrum a spin I = n/2 nucleus in solution, one normally observes a single NMR resonance line for each species as the (n+1) Zeeman energy levels are equally spaced and the nucleus is undergoing fast isotropic motion. The width of the resonance depends upon the efficiency of the relaxation (usually dominated by the quadrupolar interaction). The more efficient the relaxation, the broader the resonance. In many cases, the width of the resonance may be comparable to the complete chemical shift range for the nucleus and in some cases it may be so broad as to make its observation impractical or impossible. For these reasons I = n/2 quadrupolar nuclei generate less than their share of interest in liquid state NMR compared to spin I = 1/2 nuclei like ¹H, ¹³C, ³¹P ..... etc.

In the solid state, the situation is much different as there is rarely fast isotropic motion. When the quadrupolar interaction is much less than the Zeeman interaction, the Zeeman energy level diagram is affected by both a first order and a second order quadrupolar perturbation as shown in the figure below for an I = 5/2 nucleus. The second order perturbation is much smaller than the first order.The energy levels are no longer equally spaced. Furthermore, the position of the resonances resulting from the transitions depends on the orientation of the nucleus with respect to the magnetic field. Since all orientations are represented equally in a powder sample, each transition gives a powder spectrum. This is illustrated on the right-hand side of the figure. Note that the m = 1/2 and m = -1/2 energy levels are affected equally to first order and that the central (m = 1/2 - m = -1/2) transition is affected only by the second order perturbation. As a result the line width of the resonance from the central transition is much narrower than the other transitions. (In the figure, the central transition is clipped significantly.). Unlike the first order interaction, the second order interaction is field dependent. The width of the central transition depends inversely on the strength of the magnetic field.

Magic angle spinning is a technique used by solid state NMR spectroscopists to obtain high resolution NMR spectra of solids. Magic angle spinning at infinite speed completely averages the first order quadrupolar interaction but only partially averages out the second order interaction. The energy level diagram for a spin I = 5/2 nucleus spinning infinately fast at the magic angle is shown in the figure below along with a simulated spectrum. The spectrum consists of a central transition, CT, and two satellite transitions, ST1 and ST2. Note that along with a lineshape due to the orientational dependence of the nucleus in the magnetic field, there is also an isotropic quadrupolar shift. The central and satallite transitions are not at the same frequency. This effect is completely separate from the chemical shift.
In practice, we cannot spin at infinite speed, however, we can often spin at a rate fast with respect to the width of the central transition. If the quadrupolar coupling constant is small enough, the central transition will be observed and affected only by the second order interaction. The satellite transitions, affected by both the first and second order interaction, are observed as a manifold of spinning sidebands. The intensity of the centerbands for the satellite transitions is greatly attenuated as the overall intensity is spread among all of the sidebands. Often the centerbands for the satellite transitions are so small in comparison to that of the central transition that they are not observed. This is illustrated with simulations in the lower portion of the figure below. For comparison, the upper portion shows similar simulated spectra without magic angle spinning. The spectra highlighted in yellow are expansions of the central portion of the spectrum. These simulations are also supported by observations.

Heat Dissipation in Bruker AVANCE Spectrometers

It is very important that an NMR spectrometer operate within a fixed temperature range. To control the temperature, many units within the console are equipped with cooling fans which must be kept in good working order. Failure to do so will shorten the life of the spectrometer and cause instability or malfunctions. In the Bruker AVANCE series of spectrometers, the SGU (Signal Generation Unit) boards are particularly sensitive to temperature. Each SGU houses a DDS (Direct Digital Synthesizer) containing numerically controlled oscillators which regulate rf frequencies and amplitudes. The DDS is normally temperature regulated at 55° C to insure stability. Both the SGU board temperature and DDS temperature can be measured either with the "UniTool" (AVANCE and AVANCE II) or web based tools (AVANCE III).

After years of service, two of our Bruker AVANCE spectrometers were running very warm. Using "UniTool" to check the temperature of the SGUs revealed that the board temperatures averaged 58° C! The DDS temperatures were all >55° C and not regulated. The air filters in the console doors were removed and cleaned and all eight fans of the AQS unit, housing the SGU's, were replaced on each spectrometer. After a day for the instruments to come to a thermal steady state, the SGU and DDS temperatures were again measured. The SGU board temperatures averaged 49°C. The DDS units in three of the five SGU's were now regulated properly at 55°C. The other two were still > 55°C and unregulated. In an attempt to lower the temperature further, the backs of the spectrometers were removed and again the instruments were allowed to reach a thermal steady state over a 24 hour period. The SGU and DDS temperatures were measured again. This time the SGU board temperatures averaged 38°C and all five DDS units were regulated properly at 55°C. The SGU temperatures in our AVANCE II and III spectrometers (with backs on) did not exceed 40°C and the DDS temperatures were regulated properly.

Although this may not be recommended by Bruker, I now run our AVANCE spectrometers with the back panels removed.

19F - 13C HMQC

If one has an NMR spectrometer with hardware capable of synthesizing and amplifying the frequency of ¹⁹F from the ¹H channel and a broadband NMR probe whose ¹H channel can tune down to ¹⁹F, then one is able to do ¹⁹F - ¹³C HMQC experiments. The figure below shows an example of a ¹⁹F - ¹³C HMQC spectrum collected on a Bruker AVANCE 500 NMR spectrometer using a 5 mm broadband probe. The fluorine spectrum is plotted on the top and the ¹³C[¹⁹F] spectrum is plotted on the side. The panel on the left shows the spectrum optimized for one-bond coupling, while that on the right shows the spectrum optimized for two-bond coupling. Note that the protonated carbons are doublets as proton decoupling is not possible in this configuration. The large signal, off scale in the ¹³C[¹⁹F] spectrum is due to the solvent (benzene-d₆).

E.COSY and the Relative Signs of Coupling Constants

Spin-spin coupling constants can have values greater than or less than zero. The absolute sign of the coupling constants cannot be discerned from the simple examination of a ¹H NMR spectrum. The E.COSY¹ (Exclusive COrrelation SpectroscopY) technique is one method which can be used to determine the relative signs of coupling constants. E.COSY is a phase sensitive COSY variant which produces off-diagonal signals showing only the active coupling (i.e. the coupling directly responsible for the cross-peak) as 2x2 antiphase square tetrads displaced in both the F2 and F1 domains by an amount equal to the passive coupling constants (i.e. the couplings not directly responsible for the cross peak). The slope of a line drawn through the cross-peaks is used to determine the relative signs of the passive coupling constants. The sign of the slope depends on whether the signs of the passive couplings are the same or whether they differ. The figure below shows the gradient E.COSY spectrum² (using the Bruker pulse program,"ecosygpph" ) for the ABX three-spin system in phenylalanine.The cross-peaks highlighted in yellow in the top panel of the figure are expanded in the bottom panel. Black contours are positive and red contours are negative. The panel on the bottom left shows the cross-peaks for AX and BX. In the case of the AX cross-peak, the line drawn through the cross peak has a positive slope indicating that the passive couplings J_AB and J_BX are of opposite sign. The line drawn through the BX cross peak also has a positive slope indicating that the passive couplings J_AB and J_AX are of opposite sign. From this we can deduce that J_AX and J_BX are of the same sign. The panel on the bottom right shows the cross-peak for AB. In this case, the line drawn through the cross peak has a negative slope confirming that the passive couplings J_AX and J_BX are of the same sign. In conclusion, the geminal and vicinal coupling constants are of opposite sign.

1. C. Griesinger, O.W. Sorensen & R.R. Ernst, J. Magn. Reson. 75, ; 474 - 492 (1987).

2. The ecosygpph pulse program produces spectra similar to those described in reference 1 as "complimentary" E.COSY spectra. The slope of the lines through the cross peaks in "complementary" E.COSY spectra are of opposite sign to those obtained from the E.COSY spectra described in reference 1.