The NMR Time Scale

Many people use statements like, "It is fast on the NMR time scale" without really having an understanding of what the "NMR time scale" means. Assume we have a compound with two inter-convertible conformations, A and B, each of which gives a different NMR spectrum. If the interconversion between A and B is very slow then we expect to get a spectrum with both conformations A and B resolved. If the interconversion is very fast then we would get an unresolved spectrum which represents the average conformation of A and B. The interconversion between A and B is fast on the NMR time scale if it occurs at a rate much greater than the difference in frequency between A and B. Since the difference in frequency between A and B depends on the Larmor frequency of the nucleus being observed and the strength of the magnetic field, the "NMR time scale" depends on the particular experiment and the field strength. Therefore, when one uses the expression, "NMR time scale" one must qualify it with details of the measurement. An example of different NMR time scales is shown in the figure below. Here the ¹H (300 MHz) and ¹³C (75 MHz) NMR spectra of the N-methyl groups of N,N-dimethylacetamide are shown at various temperatures. The spectra were plotted on the same scale in Hz. In this molecule there is a hindered rotation about the central C-N bond. One can see that the rotation is fast on the ¹H NMR time scale before it is fast on the ¹³C NMR time scale because the difference in frequency between the methyl groups is smaller in the ¹H spectrum compared to the ¹³C spectrum.

What is Quadrature Detection?

In order to distinguish between negative and positive frequencies relative to the carrier frequency (i.e. the frequency at the center of the spectrum), quadrature detection must be employed. Quadrature detection involves the collection of time domain NMR data on both the x and y axes of the rotating frame of reference. One of these FIDs is called "real" and the other one is called "imaginary". The assignment of the labels "real" and "imaginary" stems from the mathematics of a Fourier transform, which requires a complex input. The Fourier transform in turn produces a "real" spectrum and an "imaginary" spectrum". Having these two signals allows us to phase one of the NMR spectra (eg. the "real" one) entirely in absorption mode after the data have been collected. In an ideal world, it would be nice to have the two FID's collected via separate receiver coils. In this case, with a bit of manipulation, we could improve our signal-to-noise ratio by a factor of the square root of 2 by adding the real and imaginary spectra together. A very nice discussion of this has been presented by Carlos Cobas. In the real world we do not have two receiver coils in quadrature and we must rely on electronic "tricks" to achieve quadrature detection. These "tricks" do not allow us to gain a signal-to-noise advantage by combining the real and imaginary spectra. A simple block diagram of how a spectrometer collects data in quadrature is shown in the figure below. The yellow signal is the intermediate frequency (IF) of the spectrometer. The purple signal is the intermediate frequency of the spectrometer modulated with the NMR spectrum information (IF plus or minus delta nu). Two phase sensitive detectors (PSDs) are used. These devices produce a difference signal between two inputs. The inputs to the first PSD are the IF and the IF plus or minus delta nu. The output is therefore plus or minus delta nu (i.e. the information content of the NMR spectrum). The inputs of the second PSD are identical to the first except the phase of the IF is shifted by 90 degrees. The output is therefore similar to the first PSD except that it has a 90 degree phase difference. The two outputs are the "real" and "imaginary" FID's which provide the input for the Fourier transform.

Establishing the Lock with Varian's VNMR

Many students have problems establishing the deuterium lock on a spectrometer manually. There is an excellent description of how to do so on a Varian spectrometer running VNMR here. The procedure however is always the same.
1. Turn the lock off.
2. Adjust the lock power and lock gain until you see a signal.
3. Adjust the field (Z0) until the signal is as flat as possible.
4. Adjust the lock power and lock gain to get a stable signal on scale.
5. Adjust the lock phase to maximize the lock signal.
6. Turn the lock on.

Happy Birthday !

The University of Ottawa NMR Facility BLOG is one year old today!

I am surprised at the interest shown for this BLOG over the last year. Since March of 2007 the number of readers has steadily increased (even over the summer months).

There are now more than 65 people who receive the posts via email. What started as a way for me to answer the questions and problems posed by the University of Ottawa NMR users has turned out to be useful for a larger audience. 92% of the readers are outside of the University of Ottawa. There are now 188 posts and they are searchable. I'm glad that you have found the contents of this BLOG to be useful.

The Fourier Transform of a Single Rotational Echo

The spinning sidebands in MAS NMR spectra are the result of rotational echos in the free induction decay. These echos show up as spikes in the free induction decay (and can be used conveniently to set the magic angle). The intensity envelope of the spinning sideband manifold in the NMR spectrum mimics the static wideline spectrum. One can obtain an NMR spectrum similar to the wideline spectrum from MAS data by Fourier transforming a single rotational echo rather than the entire FID. This is illustrated in the figure below for the ²⁷Al MAS data for kaolinite at 21.1 Tesla.

Measuring Chemical Shift Parameters for Spin I=1/2 Nuclei in the Solid State

The observed frequency of a spin I = 1/2 nucleus in a molecule depends on the orientation of the molecule with respect to the magnetic field. For powdered solid samples, all possible orientations of the molecules are present in the magnetic field and one obtains an envelope of peaks called a powder pattern. If one can neglect all other interactions (such as dipolar coupling), the powder line shapes are dominated by the chemical shielding interaction. These line shapes provide valuable electronic, geometrical and dynamic information about the molecule. The chemical shift parameters can be read directly or calculated trivially from the spectrum. These parameters are indicated in the figure below.

The parameters shown in the figure are those recommended by IUPAC. There are other conventions used in the older literature and at times it can be confusing. The other conventions are described here by Klaus Eichele. The site also contains a very useful tool to convert the parameters from one convention to another. Thank you Klaus!

Measuring Parameters from Solid State 2H NMR Spectra

Solid State ²H NMR spectra of rigid molecules or molecules moving fast with respect to the overall line width of the static spectrum are characterized by two parameters: the quadrupolar coupling constant and the asymmetry parameter. These parameters are easily measured directly from the NMR spectrum as shown in the figure below.

Pulse Sequences to Minimize Acoustic Ringing

Acoustic ringing can be a real problem at low frequencies. Its effects can be minimized in a simple one-pulse spectrum by either throwing away the initial bad data and applying a large phase correction or by using backward linear prediction to calculate the lost data. There are a number of pulse techniques one can use when collecting the data to cancel out the ringing. Two such examples are shown in the figure below. The bottom spectrum is the result of a simple one pulse experiment. The middle spectrum was collected using Bruker's "aring" pulse program and the top spectrum was acquired using Bruker's "aring2" pulse program. In all three cases a simple Fourier transform was applied with exponential line broadening. The spectra were collected with the same number of scans on a 300 MHz instrument.

MOOT NMR Minisymposium

For more than 20 years I have enjoyed attending the MOOT NMR Minisymposium. This is a regional (but growing) NMR meeting held over a weekend usually in late September or early October. It is a friendly forum for students and researchers to present NMR results and a great way to socialize with old friends or meet new contacts. I have attended all but 3 of the 20 meetings held thus far and even had the privilege of hosting MOOT VIII in 1995. MOOT XXI will be held on October 4 -5 this year, hosted by Robert Schurko at the University of Windsor. This year, for the first time, there are scheduled a number of tutorial talks. You can register on line and find all of the information here. I highly recommend this meeting for all those interested in NMR spectroscopy.

Setting the Magic Angle with Glycine

One of the most precise ways of setting the magic angle is to maximize the number of rotational echos in the FID of a suitable spin I = n/2 quadrupolar nucleus (n =3, 5, 7 ....). When setting up for ¹³C CPMAS, one usually uses the ⁷⁹Br resonance of KBr as the resonance frequency of ⁷⁹Br is very close to that of ¹³C. An alternative method of setting the magic angle is to use the ¹³C carbonyl resonance of glycine. This has the advantage in that the glycine can also be used to set the Hartman Hahn matching condition and to check the decoupling power. The width of the carbonyl resonance is very sensitive to the setting of the magic angle. The angle can easily be adjusted and set properly while maximizing the duration of the signal in the FID interactively. The figure below shows the ¹³C CPMAS FID and spectrum for glycine on- and off-angle with digital filtering such that the methylene resonance is outside of the spectral width. The spectra were collected at 11.7 Tesla using a spinning speed of 12 kHz. When the angle is mis-set, one can see that the line shape for the resonance is a miniature version of the powder pattern observed in the absence of magic angle spinning.

Chemical and Magnetic Equivalence

Many students are unclear about the difference between chemical equivalence and magnetic equivalence. The clearest explanation I have seen on this is in Robin Harris' book, "Nuclear Magnetic Resonance Spectroscopy" (1983). Chemically equivalent nuclei behave the same as one another chemically but do not have the same NMR properties as one another, whereas magnetically equivalent nuclei are chemically equivalent and they have the same NMR properties. One can determine whether two nuclei are chemically or magnetically equivalent by considering the following:

If the nuclei under consideration are not isochronous (i.e. they do not have the same chemical shift) then they are neither chemically nor magnetically equivalent. All chemically or magnetically equivalent nuclei are isochronous however, isochronous nuclei need not be chemically or magnetically equivalent as their chemical shifts may be fortuitously identical.

If the two nuclei being considered are isochronous, one should consider how they couple to a third magnetic nucleus in the molecule which is not equivalent to them. If the coupling to the third magnetic nucleus is different for each of the nuclei being considered, then the nuclei are chemically but not magnetically equivalent to one another. If the coupling to the third magnetic nucleus is identical (and this is true for every magnetic nucleus other than those being considered) then the two nuclei are both magnetically and chemically equivalent.

This is illustrated in the figure below. (The examples from Harris' book were used here.) In the molecule on the left, the two protons are both chemically and magnetically equivalent as they both have the same coupling with the fluorine. In the molecule on the right, the two protons are chemically equivalent but not magnetically equivalent as they do not have the same coupling to each of the fluorines. Similarly, the two fluorines are chemically equivalent but not magnetically equivalent as they do not have the same coupling to each of the protons.

What Does an RF Pulse Actually Look Like?

NMR books and papers always show pulse sequences where the pulses are represented by perfect rectangles indicating perfect rectangular manifolds of monochromatic radiation. This is not the case in the real world. Despite the very impressive timing specifications given by instrument companies which greatly simplify the designing of pulse programs, the pulses at the output of the amplifiers are subject to the imperfect response of electronic components in the console. This manifests itself as pulses with imperfect edges (i.e. measurable rise and decay times). The figure below illustrates this point. The top two panels show 5 microsecond and 1 microsecond pulses measured with a 1 GHz digital oscilloscope at the output of the amplifier of a very modern NMR spectrometer. One can see that to a good approximation, the 5 microsecond pulse is rectangular whereas the 1 microsecond pulse shows an obvious rise and decay.The bottom panel shows an expansion of the beginning and end of the 5 microsecond pulse. The pulses seen by the sample will be even worse due to the response of the capacitors in the tank circuit of the probe.

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.

Glenn is on Vacation!

The U of O NMR Facility BLOG will be quiet for a couple of weeks while I am on vacation. If you leave comments on any post, they will not appear until I return.

This photo was taken by my wife, Patty (I don't paint my nails or wear an ankle bracelet), however it reflects an activity I hope to enjoy in the next couple of weeks.

Artifacts Due To Setting the Receiver Gain Too High in 2D Homonuclear Experiments

Setting the receiver gain too high leads to very characteristic artifacts in 1D NMR spectra. If the receiver gain is set too high in 2D experiments, one can also expect artifacts in the 2D Fourier transformed data. In homonuclear experiments, setting the receiver gain too high will lead to parallel diagonal signals. This is illustrated in the COSY data in the figure below. In the left hand panel, the receiver was set correctly while in the right hand panel it was set too high. Dotted lines were drawn through the artifacts.

Spin-Spin Coupling Between Equivalent Nuclei

When many chemists are asked what is the ²J_H-H coupling for compounds like methane, acetone, methylene chloride, dimethyl ether or DMSO, they will often return a look of confusion. "There is no coupling," they will say, "the proton spectrum is a singlet". Indeed the proton spectrum is a singlet for these compounds but ²J_H-H is not equal to zero. The only reason that the coupling is not observed in the spectrum is because the chemical shifts of each proton are identical. The coupling can easily be measured by observing the spectrum of a partially deuterated isotopomer. The ²J_H-H coupling constant is equal to ²J_H-D multiplied by the ratio of the gyromagnetic ratios of ¹H to ²H. This is illustrated in the figure below for methylene chloride.In fact, ²J_H-H is -7.192 Hz not +7.192 Hz however, this cannot be determined simply by observing the spectrum. Both spectra were measured for dilute solutions with CDCl₃ as solvent. The residual protons of CDCl₃ were used as the chemical shift reference (7.26 ppm). The chemical shift difference between CH₂Cl₂ and CHDCl₂ is due to an isotope effect.

COSY- 90 vs COSY- 45

Aside from the standard ¹H and ¹³C NMR 1D experiments, ¹H COSY experiments are among the most commonly used NMR techniques by organic chemists. There are many different modifications to the standard two pulse COSY experiment and often the organic chemist does not even know which one they are using. Two of the most common experiments for routine work are the gradient magnitude COSY- 90 and COSY- 45 experiments. The only difference between the two methods is the flip angle of the second pulse (90 degrees for the COSY- 90 and 45 degrees for the COSY- 45). For a concentrated sample, these experiments can be acquired in a matter of minutes. Although the signal to noise ratio is higher for a COSY- 90, the COSY- 45 is usually the preferred experiment because the diagonal signals are smaller and less intense allowing correlations between close resonances to be resolved more easily. The figure below shows magnitude gradient COSY- 90 and COSY- 45 spectra for 3-heptanone. Note the smaller diagonal responses in the COSY- 45.

APT vs DEPT-135

Both the APT (Attached Proton Test) and DEPT (Distortionless Enhancement by Polarization Transfer) sequences are very commonly used to help assign ¹³C NMR spectra. Both experiments yield ¹³C NMR spectra where the number of attached protons (the multiplicity) is encoded in the phase of the ¹³C NMR signals. APT spectra have quaternary carbons, and methylene carbons phased negative and methine and methyl carbons phased positive. DEPT-135 spectra show no quaternary carbons and have methylene carbons phased negative and methine and methyl carbons phased positive. A modification to the DEPT-135 method (the DEPTQ-135) will also show quaternary carbons phased negative. Although the APT and DEPT methods provide similar information, the mechanism for multiplicity selection is different for each method. The multiplicity selection in APT experiments is based on ¹³C magnetization dephasing during a delay equal to the reciprocal of the average one-bond ¹³C - ¹H coupling constant. Although DEPT experiments also employ a delay related to the average one-bond ¹³C - ¹H coupling constant, the multiplicity selection is accomplished by adjusting the final ¹H pulse (a DEPT-135 uses a 135 degree ¹H pulse). Another major difference between the two techniques is that the DEPT technique transfers proton magnetization to carbon giving it a sensitivity advantage over the APT method. This is illustrated in the figure below which compares the ¹³C APT and DEPT-135 spectra of menthol. The signal-to-noise ratio is higher in the DEPT 135 spectrum.

11B Background Signals

Unfortunately NMR probes and NMR tubes cannot be "transparent" for all of the isotopes one may want to observe. Depending on the NMR probe, it is very common to have background signals for ¹⁹F, ²³Na, ²⁷Al, ²⁹Si, ⁶⁵Cu, ¹⁰B and ¹¹B. These background signals must be taken into account when interpreting NMR spectra. The background signal for ¹¹B on a Bruker AVANCE 300 with a 5 mm broadband probe is shown in the figure below with several different types of NMR tubes commonly used for routine work in our laboratory. The probe was tuned before running each spectrum and the spectra were collected with proton decoupling. The left hand panel shows the background signal for the NMR probe and the other spectra show the combined background of the probe and the indicated NMR tubes. It is obvious that the magnitude and shape of the ¹¹B background depends on the type of NMR tube used. It should be noted that all of the major NMR tube manufactures offer quartz NMR tubes which have little (if any) ¹¹B background signal.

The Available RF Field for MAS NMR Probes

In order to rotate an equilibrium magnetization vector from the z axis into the transverse plane, one must provide a pulse with an oscillating magnetic field transverse the static field, B_o, at the Larmor frequency of the nucleus being observed. This is usually provided with a vertically oriented Helmholtz coil for liquids and a horizontal solenoid coil for solids. In both cases the coils provide radio frequency fields transverse to the static magnetic field. MAS coils are solenoids oriented at 54.7 degrees from the static magnetic field. They produce an oscillating radio frequency field at the magic angle. It is only the horizontal component of this field which is capable of rotating magnetization vectors. The available radio frequency field is therefore only 82% of that compared to an identical horizontal solenoid coil.

The Effect of Molecular Alignment in a Magnetic Field

Molecules in solution tumble isotropically. The fast random motion averages out the chemical shielding and quadrupolar interactions to their isotropic scalar values. As a result, for solutions, one observes peaks at the isotropic chemical shift values. The quadrupoar interaction averages to zero and is not normally observed directly in solution (except perhaps as broad lines due to short T₂ relaxation times). When molecules are fixed in a particular orientation with respect to the magnetic field, as they are for example in rigid single crystals, one observes NMR lines whose positions (frequencies) depend on the orientation of the single crystal in the magnet. In the case of a quadrupolar nucleus, the observed quadrupolar splitting will depend on the orientation of the crystal in the magnet. Like molecules in single rigid solid crystals, molecules dissolved in liquid crystalline solvents can also have a preferred orientation in a magnetic field. In this case, one is able to observe a quadrupolar splitting which is unobservable in isotropic solution. This is illustrated in the figure below for the ²H NMR spectrum of water in a liquid crystalline solvent. The solvent was prepared according to M. Ruckert and G. Otting, JACS, 122, 7793-7797 (2000). In the bottom trace, the sample is liquid crystalline and one sees a quadrupolar doublet for the spin I = 1 ²H. In the upper trace at higher temperature, the system becomes isotropic and one observes a sharp singlet for the ²H resonance. Thank you to Melanie Mastronardi from David Bryce's lab for kindly providing the sample used in the figure.