Tuning Problems for Samples of High Ionic Strength

Tuning and matching an NMR probe are essential in getting optimum NMR results (also, see this link). The pulse widths and power levels called up by the spectrometer for use with parameter sets are based on the NMR probe being optimally tuned and matched. When the probe is not optimally tuned and matched, the pulse widths and power levels stored in the parameter files of the spectrometer are no longer calibrated correctly (eg. what the spectrometer calls a 90 degree or 180 degree pulse may actually be an 80 degree or 160 degree pulse). The tuning and matching of the NMR probe are affected by the sample inside the coil. It is therefore good practice to tune and match the NMR probe for each sample to insure that the pulses will be correctly calibrated for your NMR measurement. Problems may arise with samples of high ionic strength. These samples very strongly affect the tuning and matching of a probe especially at higher frequencies. The effect can be so large that the probe cannot be tuned and matched optimally. In fact, several times per year, NMR users will report to me that they are unable to tune the NMR probe on their sample. In such cases the pulses should be recalibrated for the specific sample or (if this is not possible) on a sample of similar ionic strength. This effect is illustrated at 300 MHz in the figure below. The top panel is a tuning curve for the probe containing a sample of water after the the tuning and matching were optimized. The middle panel shows the tuning curve for the probe after the water sample was replaced with a concentrated solution of NaCl. Note the gross mismatching. The bottom panel shows the tuning curve for the concentrated NaCl solution after the probe was retuned and rematched. It should be noted that the matching is not as good as that for the water sample and therefore the pulses stored in the spectrometer parameter files will not be correctly calibrated for this sample. Again note, that this problem is more pronounced at highr frequencies.

Resolution of Overlapping Signals Based on T1's

When students are asked what defines an NMR signal, they will most often say: the chemical shift, the coupling pattern, and the line width. One parameter which is often overlooked is the T₁ relaxation time. The T₁ is the time constant for the build up of magnetization along the magnetic field direction (z axis) when a sample is first placed in a strong magnetic field or after a pulse has been applied. It governs how long a spin system takes to come to equilibrium. T₁'s are measured with a 180-tau-90 inversion recovery sequence as a function of tau. For each resonance in an inversion recovery spectrum, there is a value of tau for which the signal will be nulled. If two signals with different relaxation properties overlap one another, tau values can be found which will null each of the signals individually and thus reveal the other signal. An example of this is shown in the figure below where the overlapping ¹H signals of the methylene protons one either side of the carbonyl group of 3-heptanone are examined (i.e. those in the 2 and 4 positions). The black trace in the bottom panel is the ¹H spectrum of the overlapping signals. The blue trace in the middle panel is an inversion recovery spectrum (phase corrected by 180 degrees) where a 4.1 second delay was employed. This delay nulls the protons on the 4 position revealing the quartet in the 2 position. The red trace in the top panel is an inversion recovery spectrum where a 5.5 second delay was employed. This delay nulls the protons on the 2 position revealing the triplet in the 4 position.

T2 vs T2*

The T₂ relaxation time is the exponential decay constant for transverse magnetization (i.e. magnetization in the xy plane). In principle, one should be able to measure the T₂ relaxation time by applying a 90 degree pulse to create transverse magnetization and measuring the decay constant of the FID. In reality however, the decay rate of the FID is also affected by such things as magnetic field homogeneity, unresolved coupling, temperature gradients.....etc. Because of these effects, the decay constant of the FID is called T₂* rather than T₂. T₂* is an instrumentally dependant parameter and it determines the line width of an NMR resonance. T₂, on the other hand, is a physically meaningful parameter independent of field inhomogeneity, J coupling and other factors. It is measured with a 90-tau-180-tau-FID pulse sequence as a function of tau. T₂ is always greater than or equal to T₂*. The figure below compares T₂ to T₂* for the proton resonance of CHCl₃ for the lineshape sample in a reasonably well shimmed 300 MHz magnet. The line shape specifications were 0.3 Hz (at 50%), 2.9 Hz (at 0.55 %) and 6.2 Hz (at 0.11%). Even in a well shimmed magnet, the T₂ for CHCl₃ is nearly 19 times longer than the T₂*.

Magnitude COSY-90 vs. Phase Sensitive COSY-90

Most commonly, chemists run simple COSY spectra in magnitude mode. A magnitude COSY provides positive peaks for both the diagonal and off-diagonal responses due to the magnitude calculation. The responses in a standard COSY-90 sequence have lines with a phase twist shape. The magnitude calculation is necessary to provide positive responses and the time domain data are usually treated with a sine bell weighting function (or something similar) to enhance the resolution lost in the phase twist lineshape. There are however, several versions of the COSY experiment. One such version is a phase sensitive COSY-90. This version provides off-diagonal responses that can be phased. Furthermore, the coupling giving rise to the cross peak (the active coupling) will be antiphase. The disadvantage to this method is that the diagonal responses are 90 degrees out of phase and can obscure off-diagonal responses close to the diagonal. The figure below compares a magnitude COSY-90 to a phase sensitive COSY-90 for ethyl acetate. In the figure, black is positive and red is negative.

What are Those Positive Peaks in My NOESY Spectrum?

Students will sometimes ask me, "What are those positive off-diagonal peaks in my NOESY spectrum?". Since the NOESY pulse sequence is exactly the same as the EXSY sequence, a NOESY spectrum will show all possible correlations due to cross relaxation. These correlations include those from NOE's, chemical exchange and conformational (or rotational) exchange. For small molecules, if one phases the diagonal responses such that they are positive, the NOE's correlations will be negative and the exchange correlations will be positive. The answer to the question is therefore that the positive peaks are due to exchange. The figure below shows an example where three different types of cross peaks are visible. The molecule in the figure has two distinct rotational conformations in slow exchange with one another and gives a proton spectrum with every resonance doubled. Each resonance for one rotational conformation gives a positive (black) cross peak correlating it to the corresponding resonance of the other conformation. There is also a positive cross peak correlating the -NH- proton in the molecule to the residual water in the DMSO-d6 solvent. These protons exchange chemically with one another. Finally, the negative (red) correlations in the figure are due to NOE's.
Thank you to Jean-Gregoire Roveda of Dr. Beauchemin's group for giving me permission to use his spectrum as an example.

2D EXSY

The 2D EXchange SpectroscopY (EXSY) technique is exactly the same as the same as the 2D NOESY technique. The pulse sequences are identical. The method provides off-diagonal responses for spins which exchange slowly with one another (either conformationally or chemically) and also between spins with NOE's. The EXSY method is useful for showing exchange when the rate of the exchange is greater than or of the same order as the T₁ relaxation rate (1/T₁) but less than the frequency difference between the two spins (in the absence of exchange). Depending on the experimental conditions, the responses due to exchange are often much more intense than those due to NOE's. The figure below shows the 300 MHz 2D ¹H EXSY spectrum of N,N-dimethylacetamide at room temperature. At this temperature, the molecule exhibits slow rotation about the (CH₃)₂N - C bond such that both methyl groups exchange with one another rotationally yet are distinct in the spectrum. This is evident by the cross peaks in the spectrum between the two methyl groups on the nitrogen. Note that the off diagonal peaks are of the same phase as the diagonal peaks.

1D Selective Gradient TOCSY as a Function of Mixing Time

Total Correlation SpectroscopY , TOCSY (see links here, here and here) is a technique that employs a spin lock during the mixing time of the sequence for which chemical shifts are invariant but J couplings evolve. The technique is used to correlate spins in the same J coupled spin system. The 1D selective TOCSY uses a shaped pulses to select a single spin and one gets a convenient 1D spectrum with all spins in the same spin system as the selected spin. The intensity of the coupled resonances depends on the duration of the mixing time as well as the magnitude of the coupling between spins. For short mixing times, one can often trace out the spin system by running a series of spectra as a function of the mixing time. The figure below shows a series of 1D selective gradient TOCSY spectra for 3-heptanone (selectively irradiated at the 6 position) collected as a function of mixing time. This molecule has two spin systems, separated by the carbonyl group, namely the protons in positions 6, 5, 4 and 3 and those in positions 1 and 2. With a short 10 msec mixing time, one observes the nearest protons at position 5. For 20 msec, one observes the protons at positions 5 and 4. For 30 msec and 50 msec mixing times, one observes all of the protons in the same spin system as the protons in the 6 position. Furthermore, one is able to observe the protons in the 3 position independent of the overlapping protons in position 2 which are not in the same spin system.

Second Order 1H NMR Spectra of Isopropyl Groups

One of the first things a chemistry student learns about NMR is how to interpret the coupling patterns in first order NMR spectra. With the high magnetic fields available for NMR today, this really goes a long way in interpreting spectra. Chemistry students also learn that when the chemical shift difference between two spins is comparable to their coupling constant that second order NMR spectra are observed and furthermore, that these second order spectra are "very complicated". Many do not bother to understand the line shapes. Sadly, many students carry around laptops with software packages capable of simulating these spectra and do not even know it. Several years ago, a student came to me with a proton NMR spectrum of an isopropylsilyl compound and asked why he could not see the typical septet - doublet isopropyl pattern in the spectrum. He was very concerned that he did not have the right compound. I told him he had a second order spectrum and that it was just as "beautiful" as any first order spectrum.

The first figure below shows simulations (carried out in TOPSPIN) for an isopropyl group as a function of the C-H chemical shift. One can see the typical septet -doublet pattern when the chemical shift difference between the methyl and CH protons is much greater than the coupling constant. When the shift difference is comparable to the coupling constant, complicated second order spectra are obtained. When the shift difference is zero one obtains a singlet.

The left panel of the second figure shows the isopropyl region of the experimental NMR spectrum of (triisopropylsilyl)acetylene. The complicated second order spectrum is simulated in the right hand panel.

Thank you to Mattieu Leclere for providing the sample used in the figure above.

New Data Processing Option at the U of O

University of Ottawa students now have another option for processing their NMR data. The University of Ottawa has just purchased a university-wide site license for ACD's NMR processing software package. This software will run on WINDOWS 2000, XP and VISTA computers. It is currently installed on the workstation in D'Iorio room 430. Please try it out and visit the NMR lab to arrange to have it installed on your PC.

Apodization of 2D Data

In the interest of data collection time and disk storage space, 2D data sets are often collected with short t2 acquisition times and as few as possible t1 slices. In such cases, the FID's in the t2 domain do not decay into the noise and the interferograms in the t1 domain do not decay completely. Applying a 2D Fourier transform to such truncated data will cause ripples in the 2D frequency domain spectrum analogous to those observed in 1D spectra where the acquisition time is too short. The application of an appropriate apodization function (and/or forward linear prediction) to the t2 and t1 domains is important to produce high quality spectra. The figure below illustrates the effect of the more common apodization functions on the cross peak in the phase sensitive COSY spectrum of ethyl acetate. The panel on the upper left shows the appearance of the cross peak when no apodization is applied. One can easily see the ripples in both the F2 and F1 frequency domains. The panel on the upper right shows the effect of applying a 2 Hz exponential line broadening function to each domain. The data are improved but the ripples are still visible. The panel on the lower left shows the effect of applying a sine bell weighting function with the maximum at the midpoint of each of the t2 and t1 domains. This apodization function is suitable for magnitude mode data where the phase is irrelevant. In this example of a phase sensitive data set, one can see a major distortion in the cross peak. The panel on the lower right shows the effect of using a sine squared weighting function with the maximum at the beginning of the t2 and t1 signals. The spectrum is free of ripples and clearly shows the phase information.