Optimizing the Signal-to-Noise-Ratio with Spin-Noise Probe Tuning

We have all been taught to tune our NMR probes to maximize the pulse power delivered to our sample (or minimize the reflected power back to the amplifier).  This prevents damage to the amplifiers and minimizes the duration of 90° pulses at fixed power levels.  This is typically done with the spectrometer hardware (eg, "atmm" or "wobb" on a Bruker spectrometer). Tuning a probe in this way optimizes the transmission of rf to the sample, however, the NMR probe must also detect signals from the sample to be amplified and sent to the receiver.  The "receive" function uses a different electronic path compared to the "transmit" function.  Since the electronic paths for the "transmit" and "receive" functions are completely different, they are expected to have different tuning characteristics.  A probe optimized to transmit rf to the sample is not necessarily optimized to receive the rf NMR signal from the sample.  As a result, one may not be getting the optimum signal-to-noise-ratio with a probe tuned and matched in the conventional manner.  The question then arises as to how can we tune  an NMR probe optimized to detect and receive the NMR signals from the sample.  This can be done by measuring a spin noise spectrum of the sample - using no rf pulses whatsoever.  It has been shown¹ that a probe is optimized to detect and receive the NMR signals when one observes an inverted spin noise NMR signal from the sample.  Since the spin noise signal is measured without any pulses from the "transmit" function of the spectrometer, it depends only on the electronic path of the "receive" function. To tune a probe for optimum "receive" function, one must adjust the tuning frequency and matching of the probe followed by the measurement of a spin noise spectrum until an inverted spin noise signal is observed.   The figure below illustrates an example of this using a 2 mM sucrose solution in 90% H₂O/10% D₂O.

The proton channel of a 600 MHz cryoprobe on a Bruker AVANCE III HD NMR spectrometer was tuned and matched at 10 different frequencies using the "atmm" function of the spectrometer.  The tuning offset frequencies were measured using the "wobb" display of the spectrometer.  For each tuning offset frequency, a spin noise spectrum of water was measured using 64 power spectra collected in a a pseudo 2D scheme and summed to produce the spin noise spectrum displayed.  The spin noise spectrum for the probe optimized for the "transmit" function is highlighted in pink and the spin noise spectrum for the probe optimized for the "receive" function is highlighted in yellow.  For every tuning offset frequency, the 90° pulse was measured with the "pulsecal" routine of the spectrometer which uses this method.  As expected, the minimum 90° pulse is obtained for the probe tuned to optimize the "transmit" function.  With all pulses optimized, a ¹H spectrum of the sample for each tuning offset frequency was measured using excitation sculpting as a means of solvent suppression (pulprog= zgesgp).  The sucrose signal at ~ 3.9 ppm is displayed in the figure.  The maximum signal intensity (highlighted in yellow) is obtained at a tuning offset frequency of -695 kHz corresponding closely to where the spin noise spectrum is inverted (-895 kHz).  The noise levels in the spectra were found to vary somewhat at higher tuning offset frequencies.  As a result, the maximum signal-to-noise-ratio (highlighted in yellow) was observed at a tuning offset frequency of -488 kHz.  This represents a 21% improvement in the signal-to-noise-ratio compared to that observed for a probe tuned in the conventional manner (highlighted in pink).  The degree of solvent suppression using excitation sculpting was also found to deteriorate at higher tuning offset frequencies.  In conclusion, one can obtain spectra with higher signal-to-noise-ratios by using a tuning offset frequency other than zero.  One expects the specific optimum tuning offset frequency to be probe, instrument and sample dependent.  This phenomenon is described much more elegantly in the reference below.

1.  M. Nausner, J. Schlagnitweit, V. Smrecki, X. Yang, A. Jerschow, N. Müller.  J. Mag. Res. 198, 73 (2009).

Boron Isotope Effects in Fluorine NMR Spectra

In previous posts on this BLOG, examples of  ¹H/²H and ¹²C/¹³C isotope effects were discussed.  The figure below shows an example of a ¹⁰B/¹¹B isotope effect observed in the ¹⁹F NMR spectrum of tetrabutyl ammonium tetrafluorobarate.

The spectrum clearly shows two resonances separated by 0.05 ppm with an intensity ratio of approximately 20:80 corresponding to the natural abundances of  ¹⁰B and ¹¹B, respectively.  The low frequency resonance is due to ¹¹BF₄^-.  Since  ¹¹B is a spin I = 3/2 nuclide we observe a 1:1:1:1 quartet with J = 1.25 Hz corresponding to the one bond ¹⁹F - ¹¹B coupling.  The high frequency resonance is due to ¹⁰BF₄^-.  Since  ¹⁰B is a spin I = 3 nuclide we observe a very poorly resolved 1:1:1:1:1:1:1 septet with J ~ 0.4 Hz corresponding to the one bond ¹⁹F - ¹⁰B coupling.  

Correcting NMR Spectra for Poor Shimming - Reference Deconvolution

The pleasingly symmetric and narrow Lorentzian resonances in a high resolution NMR spectrum are truly things of stunning beauty, appreciated by all NMR spectroscopists. Their majesty depends on the homogeneity of the NMR magnet around the sample. Inhomogeneous fields yield low resolution NMR spectra with broad asymmetric peaks pleasing no one. These repugnant, distasteful spectra are often obtained when automatic shimming routines are used on under-filled samples, samples with solids present (precipitates, floaters of suspended solids), samples with thermal gradients, poorly mixed samples etc…. Have you ever looked at such a spectrum and longed to recover the hidden beauty, resolution and information you know is present in the depths of its repulsive form? In many such cases reference deconvolution is a processing technique able to help. The distortions in a spectrum from an inhomogeneous magnetic field affect all peaks in the spectrum in the same way. The imperfect FID giving rise to the offensive spectrum, FID_exp(t), is essentially a perfect FID, FID(t) multiplied by an error function, E(t), resulting from the inhomogeneous field.

FID_exp(t) = FID(t) * E(t)

If we could find the error function and divide the experimental FID, by it, we could produce a perfect (or at least improved) FID, the Fourier transform of which would be a spectrum corrected from the effects of field inhomogeneity. In the reference deconvolution technique, one selects a high signal-to-noise ratio singlet peak as a reference in the experimental spectrum and sets all other points in the spectrum to zero. This spectrum is inverse Fourier transformed to produce an FID of the distorted singlet, FID^r_exp(t). A synthetic FID, FID^r_syn(t) is constructed for what one would expect the time domain signal to be for a perfect reference peak (e.g. a sharp Lorentzian). The error function for the reference peak E^r(t) is then determined by:

E^r(t) = FID^r_exp(t) / FID^r_syn(t)

Since all peaks in the experimental spectrum are affected equally by the inhomogeneity, E(t) = E^r(t) and we can compute a corrected FID for the entire spectrum,

FID(t) = FID_exp(t) / E^r(t)

The corrected FID is Fourier transformed yielding a much improved spectrum. This technique is available in newer NMR software processing packages and is particularly easy to implement in the MestReNova software package available to NMR users at the University of Ottawa. An example is shown in the figure below for a 300 MHz ¹H NMR spectrum of a mixture of compounds.

The top two traces show portions of the spectrum obtained in a carefully shimmed magnet. The middle traces show the same portions of the spectrum obtained in a poorly shimmed magnet. The bottom traces were obtained by applying reference deconvolution to the spectrum obtained in the poorly shimmed magnet. Clearly, there is much improvement in the reference deconvoluted spectrum, allowing one to obtain much more information and recover some of the lost beauty. In fact, the corrected spectrum is very similar to the one obtained in the homogeneous field of a carefully shimmed magnet. The penalty paid is a lower signal-to-noise ratio, as the noise from the experimental reference signal is convolved into the error function which in turn gets convolved into the corrected spectrum. The loss in signal-to-noise ratio can be minimized by choosing a reference signal with a higher signal-to-noise ratio.

Testing an MAS Spin Detection Device

Recently, I had a problem with an MAS probe which would no longer allow measurement of an MAS spinning frequency.  I thought it might be instructive to describe the device and the steps I took to solve the problem.  An MAS spin detection device includes an IR LED source, an IR detector, a fiber-optic cable (split in two on one end), some electronics and an MAS speed controller.  Everything except the the MAS speed controller is shown in the figure below.

The spin detector is connected through a three-pin cable to the MAS speed controller from which it receives power and to which it sends information about the MAS rotor frequency.  The IR LED emitter inside the spin detector sends IR light through one leg of the split end of the fiber-optic cable.  The IR light passes through the fiber-optic cable where it is directed towards the bottom of the MAS rotor.  The position of the end of the fifer-optic cable with respect to the bottom of the rotor is very critical.  The IR light must strike the bottom to the rotor.  Half of the rotor bottom is marked with a black pen.  When the IR light strikes the dark side of the rotor, there is very little reflected IR light "seen" at the end of the fiber-optic cable near the rotor.  When the IR light strikes the white side of the rotor, most of the IR light is reflected back to the end of the fiber-optic cable and returned to the detector through one of the spit ends.  When the rotor is spinning an "off" - "on" binary pulse equal to the rotor spinning frequency is returned to the detector and sent to the MAS speed controller through the electronic cable.  If the device does not work, one possible problem could be that the fiber-optic cable is broken.  This can happen if the cable is fastened too tightly to a support rod in the probe.  It can be tested as shown in the figure below with a laser pointer or a flashlight.

Almost all of the light should pass through the fiber-optic cable.  Another possible problem could be a failing IR LED emitter.  Unfortunately, the IR light is not visible so you cannot just inspect it visually.  The IR light can however be detected by the front facing camera of an iPhone which does not have a built-in IR filter like the rear-facing camera.  Simply taking a picture with the front facing camera will indicate whether the emitter is working.  This is shown in the figure below, where the emitter is clearly visible when the spin detector receives power from the MAS speed controller but not visible when not connected to the MAS speed controller.

There could also be a problem with the detector.  This can be tested with a stroboscopic LED flashlight as shown in the figure below.

The strobe light is positioned at the end of the fiber-optic cable and one of the split ends is positioned at the detector.  When the spin detector is connected to the MAS speed controller, one should be able to observe the frequency of the strobe light on the rotor frequency display.  Other possible problems could be with the MAS speed controller or with the electronic cable.  I have two MAS probes for this instrument.  In one probe, the MAS spinning frequency could not be counted and in the other probe it could.  In the failing probe, the fiber-optic cable, IR LED emitter  and IR detector were all working properly.  The problem was with the connector on the cable between the spin detector and the MAS speed controller.  The connection was OK for one probe but not the other.  I will be happy if this post helps someone who may run into a similar problem.

The Effect of the 2H Lock on Environmental Instability

The ²H lock of an NMR spectrometer continuously monitors the frequency of the ²H resonance of a deuterated solvent used to prepare the NMR sample.  If the frequency of the ²H resonance changes due to an environmental instability while the lock is engaged, a feedback mechanism is used to correct the magnetic field via a B_o shim coil, returning the ²H resonance to its original position.  It is very effective at reducing (if not eliminating) environmental instability from NMR data collected over periods of time spanning minutes or hours.  The effect of the lock is illustrated in the figure below.

Each panel in the figure represents a contour plot of a pseudo 2D ¹H NMR data set for the residual protons of D₂O on a Bruker Fourier 300 NMR spectrometer.  Each panel represents 2048 single-scan 1D ¹H NMR spectra collected over 1.5 hours.  The data in the left-hand panel were collected during the day without the ²H lock.  The data in the center panel were collected in the middle of the night without the ²H lock.  The data in the right-hand panel were collected during the day using the ²H lock.  The ²H lock clearly compensates for environmental instability.  There was no student traffic in the lab during the collection of any of the data.  Outside of the lab are two construction sites which are busiest during the day and quieter at night.  This is reflected in a comparison between the left-hand and center panels of the figure.  The data collected in the middle of the night without the ²H lock show somewhat less instability compared to similar data collected during the day.      

HMBC vs. H2BC

NMR spectroscopy is an indispensable tool for assigning the structure of organic compounds.  One very useful method in the NMR toolbox is the Heteronuclear Multiple Bond Correlation (HMBC) experiment.  HMBC data are ¹H detected and provide a 2D correlation map between ¹H and ¹³C similar to HMQC or HSQC except that the correlations are between protons and carbons separated by two, three and sometimes even four bonds.  This long range information is very helpful in elucidating chemical structures, especially those with non-protonated carbons.  The problem, however with HMBC data is that the correlations depend only on the magnitude of the long-range ¹H-¹³C coupling constants.  Two- or three- bond coupling constants are very similar in magnitude to one another and therefore it is not possible to distinguish between two- and three- bond correlations.  Also, since many long range ¹H-¹³C coupling constants (including two-bond coupling constants) are near zero, some correlations may be absent.  These problems may make structure elucidation frustrating or impossible.  The Heteronuclear 2 Bond Correlation (H2BC) experiment¹ provides an HMBC-like correlation map with (almost) exclusively two-bond ¹H-¹³C correlations.  Unlike the correlations in the HMBC measurement, which rely exclusively on long range ¹H-¹³C coupling constants, the ¹H-¹³C correlations in the H2BC experiment rely on three-bond ³J_H-H coupling between the protons on adjacent carbons.  It is a combined HMQC-COSY experiment.  The size of the H2BC correlations depends on the magnitude of the ³J_H-H coupling constant.  Three-bond ¹H-¹³C correlations are possible only if four-bond ⁴J_H-H coupling is significant.  One disadvantage to the H2BC experiment is that all correlations between protons and non-protonated carbons are necessarily absent because of the absence of H-H coupling.  In general, two-bond ¹H-¹³C correlations that are weak or absent in HMBC spectra are strong in H2BC spectra and three-bond ¹H-¹³C correlations which are strong in HMBC spectra are absent or very weak in H2BC spectra.  The techniques are very complimentary.  The figure below illustrates  the complimentary nature of the two methods for styrene.

The HMBC spectrum in the left panel was scaled up until some of the HMQC artifacts (color coded in blue) were visible.  The data show only one 2-bond ¹H-¹³C correlation (color coded in pink). The three-bond ¹H-¹³C correlations are color coded in yellow.  In comparison, the H2BC spectrum in the right panel shows exclusively two-bond ¹H-¹³C correlations with the exception of those involving the C1 non-protonated carbon.

1. Nyberg, Duus, Sorensen.  J. Am. Chem. Soc. 127, 6154 (2005).

Improved 1H Resolution with 14N Decoupling

The J coupling between ¹³C and quadrupolar nuclides can be resolved, for example, in the cases of the ¹³C NMR spectra of deuterated compounds, some cobalt complexes and some tetraalkyl ammonium salts.  The ability to resolve the coupling depends on the relaxation rates among the Zeeman levels of the quadrupolar nuclide with respect to the reciprocal coupling constant.  When the relaxation is slow, the J coupling can be resolved and when it is very fast, the ¹³C is a sharp singlet and said to be "self decoupled".  When the relaxation rates among the Zeeman levels of the quadrupolar nuclide are on the same order of the coupling constant, the NMR resonance of the ¹³C will be broadened.  This is a very common observation for the ¹³C resonances of nitrogen bearing carbons.  It is also possible to see broadened ¹H or ¹⁹F resonances due to coupling to ¹⁴N.  Such is the case for the resonances of the proton on C6 and the fluorine on C2 in 2,3-difluoropyridine as can be seen from the figure below which clearly shows these resonances broadened compared to the resonances of ¹H or ¹⁹F further removed from the nitrogen.

The broadening of the resonance of the ¹H on C6 can be reduced by applying ¹⁴N decoupling during the acquisition time, thus providing much improved resolution.  This is  demonstrated in the figure below.

PSYCHE to Evaluate 1H-19F Coupling Constants

Even small molecules can yield very complex ¹H NMR spectra as the result of spin - spin coupling.  This is particularly true for small molecules that contain fluorine.  It can sometimes be challenging to determine which splittings are due to ¹H-¹H coupling and which are due to ¹H-¹⁹F coupling.  One can collect a ¹H spectrum with ¹⁹F decoupling to give a spectrum with only ¹H-¹H coupling present.  Even with this data, it may be difficult to evaluate the ¹H-¹⁹F coupling constants by comparing the ¹H[¹⁹F] spectrum to the ¹H spectrum due to the complexity of the multiplets.  The ¹H-¹⁹F coupling constants can however be read directly from a ¹H PSYCHE spectrum.  The PSYCHE spectrum provides a ¹H decoupled ¹H spectrum, leaving only the ¹H-¹⁹F coupling behind.  The bottom trace of the figure below shows the 300 MHz ¹H NMR spectrum of 2,3-difluoro pyridine.  The spectrum is quite complex, making it difficult to assign ¹H-¹H and ¹H-¹⁹F couplings.  The middle trace shows the ¹H[¹⁹F] spectrum which allows the evaluation of all of the ¹H-¹H coupling constants (³J_H5-H4 = 4.8 Hz, ⁴J_H5-H3 = 1.6 Hz and ³J_H4-H3 = 8.0 Hz.  The top trace shows the ¹H PSYCHE spectrum which allows one to evaluate all of the ¹H-¹⁹F coupling constants.  For this compound, ⁴J_H3-F1 = ³J_H3-F2 = 9.8 Hz, ⁴J_H4-F2 = 3.2 Hz and ⁴J_H5-F1 = 1.8 Hz.

Pure Shift 1H NMR - PSYCHE

Much effort has been directed to obtain broadband ¹H decoupled ¹H NMR spectra.  The subject has been reviewed recently.¹  One technique used to obtain such spectra is the pseudo-2D Zangger - Sterk method^2,3 based on a selective refocusing pulse applied simultaneously with a weak field gradient centered in the t1 evolution period allowing all chemical shifts to be measured at the same time but from different slices of the column of sample in the NMR tube.  For each resonance, the coupling from all of the coupling partners is refocused.  The data are collected in a conventional 2D matrix however, a single FID is constructed by concatenating a chunk from each of the individual 2D time domain signals.  The Fourier transform of the reconstructed FID is a pure shift, ¹H decoupled ¹H NMR spectrum.  The PSYCHE (Pure Shift Yielded by CHirp Excitation) modification⁴ of the Zangger - Sterk method uses a pair of small flip angle, frequency swept chirp pulses rather than a selective 180° pulse applied simultaneously with the weak spatially selective field gradient.  This modification offers improved sensitivity.  The details of implementing this technique are kindly provided on-line by the Manchester NMR Methodology Group.  As an example, the figure below shows the 600 MHz PSYCHE spectrum of sucrose in in DMSO-d6, collected in less than 3 minutes.  One can observe the collapse of all multiplets into singlets.

The PSYCHE technique can dramatically simplify complex ¹H NMR spectra as shown in the figures below. The second figure is an expansion of the low frequency region of the first.

1.  Castañar and Parella. Mag. Res. Chem. 53, 399 (2015).
2.  Zangger and Sterk. J. Mag. Reson. 124, 486 (1997).
3.  Aguilar, Faulkner, Nilsson and Morris. Angew. Chem. Int. Ed. 49, 3901 (2010)
4.  Foroozandeh, Adams, Meharry, Jeannerat, Nilsson, Morris. Angew. Chem. Int. Ed. 53, 6990 (2014).

Exchange Effects in HSQC Spectra

The effects of chemical or dynamic exchange on NMR spectra are very well known.  Exchange is often studied by observing line shape changes as a function of temperature, by 2d EXSY, inversion transfer or saturation transfer methods.  Effects due to exchange can also be observed in ¹H - ¹³C HSQC spectra.  The HSQC method works by transferring ¹H magnetization to ¹³C magnetization via an INEPT transfer through the one-bond J coupling across the ¹H - ¹³C chemical bond.  The ¹³C magnetization evolves during the incremented delay, t1, of the 2D pulse sequence according to its chemical shift.  The ¹³C magnetization is then transferred back to ¹H magnetization where is observed during t2.  HSQC spectra thus exhibit cross peaks between ¹H resonances and the resonances of their attached carbons.  If there is exchange between nonequivalent carbon sites during t1, some ¹H resonances may appear to be correlated to two carbon resonances.  An example of this is shown in the figure below.

The ¹³C spectrum of cannabidiol has equally intense broad, resolved aromatic resonances for non-protonated carbons 2 and 6 (not shown) as well as for the protonated carbons 3 and 5.  The ¹H spectrum has broad resolved resonances for both aromatic protons.  This indicates that either the aromatic ring undergoes 180° flips about the 1 - 4 axis or it has two equally probable rotomers defined by a rotation about the 1 - 4 axis.  In either case, the dynamic exchange is slow enough on the NMR time scale to produce resolved resonances yet fast enough to cause significant line broadening.  For each of the two aromatic protons, the HSQC spectrum shows correlations to both C3 and C5; a strong correlation to the carbon to which it is chemically bonded and a weaker correlation to the carbon site in exchange with its attached carbon.          

NMR and Food Chemistry - Maple Syrup

Maple syrup is arguably one of the tastiest traditional Canadian condiments.  In honor of Canada Day (July 1), it is appropriate to take a look at this delicious golden treat.  The bottom trace of the figure below shows the 600 MHz ¹H NMR spectrum of pure Quebec maple syrup dissolved in D₂O.

The spectrum is overwhelmingly dominated by sucrose.  Clearly, nature gives us the maple flavor with very low concentration components.  The top trace is a similar spectrum of "table" syrup which has a taste somewhat similar to maple syrup.  The spectrum is much more complicated than that of pure maple syrup.  In order to mimic the flavor of pure maple syrup, the food chemists resort to a complex mixture of sugars and artificial flavors.  Canada keeps it simple and of course better!  Happy Canada Day.

Non-uniform Sampling (NUS)

Collecting 2D or 3D NMR data can be very time consuming. The indirect dimension of a 2D experiment is sampled linearly via the t1 increments in the pulse sequence.  An FID must be collected for every single linearly spaced t1 increment. In the interest in collecting 2D or 3D NMR data in a more time efficient manner, a great deal of effort is made towards faster data collection techniques.  While some of these methods are based on spatial selectivity, others are based on sparse sampling techniques in the indirect dimensions of nD NMR sequences.  One such sparse sampling method, given the name non-uniform sampling (NUS), samples a sub-set of the indirect dimension in a random (or weighted random) manner and then predicts the uncollected data based on the data sampled, in much the same way data are predicted in the forward and backward linear prediction methods.  The reconstructed data is then used for the indirect Fourier transforms.  A comparison of the conventional and non-uniform data sampling methods is illustrated in the figure below.

Collecting only a fraction of FID's reduces the experiment time by the same fraction.  The figure below shows a superposition of partial 600MHz ¹H-¹³C HSQC spectra of a D₂O solution of sucrose.

All of the spectra were collected with 2 scans per increment using a 1.5 second recycle time.  The lower spectrum in black was collected conventionally with 256 increments in 15 minutes. The middle spectrum in blue was collected conventionally with 64 increments in 3.75 minutes. The top spectrum in purple was collected using NUS with 25% of 256 increments (i.e. 64 increments) collected in 3.75 minutes.  A comparison of the two conventionally collected data sets shows the expected loss in F1 resolution with the 4-fold reduction in experiment time by reducing the number of increments by a factor of 4. The bottom (black) conventional spectrum and the top (purple) NUS spectrum are however virtually indistinguishable despite the 4-fold reduction in experiment time for the NUS spectrum.  NUS is a very valuable technique for reducing experiment times without sacrificing resolution.

CEST - Chemical Exchange Saturation Transfer

Chemical Exchange Saturation Transfer (CEST) is a technique where one resonance, in slow exchange with a second resonance, is saturated with a selective low power pulse followed by a hard non-selective 90° pulse.  The intensity of the second resonance is then diminished due to the transfer of saturation from the first resonance as the result of  chemical exchange.  The figure below demonstrates this for a 25 mM solution of salicylic acid in H₂O/D₂O buffered at pH 7.

The left-hand panel of the figure is a stacked plot of extracted spectra collected in a pseudo 2D acquisition as a function of saturation frequency.  The saturation frequency was varied from an initial value of 20 ppm to a final value of -20 ppm in steps of 0.2 ppm.  The spectra are plotted such that only the water resonance is on scale.  One can see that the intensity of the water resonance dips when a saturation frequency of ~14 ppm is applied, corresponding to the resonance frequency of the –COOH and –OH protons of the salicylic acid (which appear to be in fast or intermediate exchange with one another).  The water resonance of course also dips to zero when a saturation frequency of ~4.7 ppm is used, corresponding to a simple presaturation of the water.  The right-hand panel of the figure is a plot of the integral of the water resonance as a function of saturation frequency, showing again a dip at ~14 ppm.

CEST is used in MRI to provide image contrast where a chemical exchange agent is introduced and images are collected with and without saturation of the exchange agent.  The difference provides an image enhanced by the presence of the chemical exchange agent.

Thank you to Dr. Mojmir Suchy of Prof. Adam Shuhendler’s group at the University of Ottawa for arousing my interest in the use of CEST for MRI and preparing the sample used in this post. 

INEPT

The sensitivity of a low γ, spin I = ½ nucleus is determined by the difference in populations between the low energy and high energy states, governed by the Boltzmann distribution. If the low γ, spin I = ½ nucleus is coupled to a proton the energy level diagram is more complicated than simply two levels and is shown in the figure below where a ¹³C-¹H spin pair is used as an example.

The populations of the states involved in the ¹³C transitions and hence the sensitivity of the ¹³C signal can be altered by inverting the H1 or H2 ¹H transitions with 180° pulses. This is illustrated in the figure below.

In the left panel, the H1 transition of a ¹³C-¹H spin pair is inverted (i.e. the populations of the two energy levels of the H1 transition are swapped). This also affects the populations of the energy levels involved in the C1 and C2 ¹³C transitions. After inversion of the H1 ¹H transition, the intensities of the C1 and C2 ¹³C transitions have changed from their equilibrium value of 1:1 to an enhanced value of 5:-3. If the H2 transition is inverted (right-hand panel), the C1:C2 intensity ratio is -3:5. In both cases the sensitivity of the ¹³C doublet has been enhanced compared to its equilibrium value. This enhancement is called INEPT (Insensitive Nuclei Enhanced by Polarization Transfer) and is one of the most common sensitivity enhancement techniques used in NMR pulse sequences. The simplest implementation of INEPT is shown in the figure below along with the vector diagrams.

Phase cycling can be employed to obtain a -4:4 anti-symmetric doublet, rather than doublets with components of unequal magnitude. This is represented in the figure below.

A refocusing element can be added to the end of the sequence to refocus the anti-symmetric doublets and data can be collected with proton decoupling.

The result is a singlet with 4 times  (i.e. γ_H/γ_C) the intensity of the singlet one would expect under equilibrium conditions without an NOE.  For ¹⁵N, one obtains a sensitivity gain of ~10. The results of these implementations of INEPT are compared to the equilibrium situation in the figure below.

INEPT has the additional advantage that its repetition rate is determined by the ¹H T₁ rather than the ¹³C T₁.  This is a tremendous additional sensitivity improvement when multiple scans are collected because the ¹H T₁ is often shorter than the ¹³C T₁ by an order of magnitude.  One can collect approximately ten times as many scans per unit time.  This advantage is even more significant for ¹⁵N.  Reverse INEPT is used in the collection of ¹H data for  carbon-proton pairs to suppress the protons bound to ¹²C. 

Solid-State 13C NMR of Chicken Eggshells

¹³C CP/MAS and direct single pulse ¹³C MAS NMR with high power decoupling can give very different results for a wide variety of materials.  ¹³C CP/MAS NMR relies on the transfer of magnetization from protons to ¹³C via the dipolar coupling mechanism whereas the direct single pulse method does not.  An interesting material to demonstrate this principle is the shell of a chicken egg.  Chicken eggshell is a complex bio-mineral consisting largely (~ 95%) of the calcite polymorph of calcium carbonate as well as proteins and lipids.  The ¹³C CP/MAS and ¹³C single pulse MAS NMR spectra of a sample of dry ground eggshell, from which the membranes had been removed, are shown in the lower and upper traces in the figure below, respectively.

The ¹³C CP/MAS spectrum in the lower trace has very broad resonances in the aliphatic region of the spectrum due to the proteins and lipids.  The carbonyl region of the spectrum  consists of two resonances; one at ~173 ppm due to the carbonyl carbons of the amino acid residues of the proteins and a resonance at  ~169 ppm which has been shown^1,2 to originate from bicarbonate ions (HCO₃)^-.  Although ~95% the eggshell consists of CaCO₃, the carbonate resonance is not present in the ¹³C CP/MAS spectrum as there are no proximate protons for cross polarization.  In contrast, the single pulse ¹³C MAS spectrum in the top trace shows only the ¹³C resonance from the carbonate ions which has a coincident chemical shift with that of the bicarbonate ions.  All of the other ¹³C resonances are buried in the noise as they are in much lower concentration. These spectra are an excellent example of how one can obtain different information from ¹³C CP/MAS and single pulse ¹³C MAS spectra.

1. D.M. Pisklak, L. Szcleszczuk, I. Wawer, Journal of Agricultural and Food Chemistry, 60, 12254 (2012).
2. J. Feng, Y.J. Lee, R.J. Reeder, B.L. Phillips, American Mineralogist, 91, 957 (2006).

Ultra-Fast 1H COSY

It cannot be disputed that the introduction of routine 2D NMR spectroscopy in the 1980's revolutionized the way in which NMR measurements are made. Now, with literally thousands of 2D methods available, the quantity of accessible information has dramatically increased. One cannot imagine a modern NMR lab without a 2D NMR toolbox.  One of the main drawbacks to traditional 2D NMR spectroscopy has always been the time required to collect the data.  Data collection can take anywhere from a few minutes to tens of hours.  Many 1D FIDs (typically more than 128) must be acquired as a function of evolution time to construct the 2D data matrix.  The measurement of each of these signals may require multiple scans as a result of necessary phase cycling between which a relaxation delay must be employed.  Once all of the data have been collected, each of the FID's is Fourier transformed followed by a second Fourier transform with respect to the evolution time.  Typical data collection and processing are illustrated here. The introduction of pulsed field gradients for coherence selection has reduced the time required to collect 2D spectra by reducing or  eliminating the need for phase cycling however, one still has to collect many FID's as a function of evolution time.  Even when multiple scans are not required for sensitivity, data collection can take minutes to hours.

Ultra-fast 2D measurements, employing an entirely different method of data collection, were introduced in 2002 and subsequently improved.  In this method, z-field gradients combined with linearly swept chirp pulses are used to phase encode spins linearly along the z axis of the sample according to specific evolution times.  The dephasing depends on both the position along the z axis of the sample and the resonance frequency of each spin.  After this encoding scheme is applied, each slice element of the sample has experienced a different evolution time as a function of its position in the sample.  After a conventional mixing period dictated by the type of 2D measurement, the site specific, spatially phase encoded spins must be read.  This is accomplished by applying a series of bipolar gradient pulse pairs while the receiver is collecting data.  During each gradient pulse (lasting typically 250 μsec) echos are collected.  The position of each echo during a single gradient pulse is related in a one-to-one fashion to the frequency of each of the spins in the sample thus mimicking a mini NMR spectrum whose frequency axis is replaced by a linearly related time axis.  The "spectra" collected during the negative gradient pulses are mirror images to those collected during the positive gradient pulses and must be reversed during data processing.  A series of typically 128 bipolar gradients are applied with the receiver open thus all of the data are acquired in a single scan.  Each "spectrum" collected is a function of the z slice position in the sample, which in turn is linearly related to the evolution time. The collection of "spectra" represent the ultra-fast domain and is Fourier transformed point by point as a function of evolution time (or z position).  The entire data collection sequence takes approximately 100 msec.

The left panel of the figure below shows a conventional 300 MHz gradient enhanced COSY-45 spectrum for a concentrated sample of menthol in CDCl₃ collected in 4.5 minutes.  The panel on the right shows a 300 MHz ultra-fast COSY spectrum of the same sample collected in only 100 msec - a time saving factor of 2700!  Both spectra were collected on a Bruker AVANCE II 300 NMR spectrometer equipped with a standard BBOF probe.  Both data sets were symmetrized.  Although the ultra-fast data set has noticeably lower resolution and sensitivity, one can see that it is very similar to the conventional COSY.

There are, of course, a number of drawbacks to the ultra-fast scheme including low sensitivity, limited resolution and limited accessible spectral widths.  Some of these drawbacks can be overcome  with the use of cryoprobes and strong pulsed field gradients. Molecular diffusion over the course of the measurement may also cause problems.  Despite the drawbacks however, the method is extremely well suited to time studies of chemical reactions where conventional 2D data collection would simply take too long.

The references below are a good place to start in order to find out more about this technique.  There is also a very well documented setup procedure available on the Bruker User Library, provided by Patrick Giraudeau, including pulse sequences and processing scripts.

Annual Rev. Anal. Chem. 7, 129-161 (2014).
Mag. Res. Chem. 53, 986-994 (2015).
J. Am. Chem. Soc. 125, 9204–17 (2003).
J. Am. Chem. Soc. 125, 12345–50 (2003).

NMR of the Christmas Tree

One of my fondest memories as a child is the colorful lights and especially the smell of a decorated Christmas tree.  The hot incandescent lights used years ago would heat up the tree evaporating the fragrant compounds in the needles producing the very memorable and wonderful smell of Christmas.  Although modern artificial Christmas trees and cool LED lights have made the holiday season safer with respect to fires, they have taken much of the magic out of Christmas.  Among many other compounds, it is pinene, bornyl acetate and citronellol that contribute to the Christmas smell of evergreen needles.

We can use NMR spectroscopy to look for these compounds and perhaps recover a bit of the Christmas magic.  The bottom panel of the figure below shows the ¹³C CPMAS spectrum of spruce needles.  One can easily identify the signals from cellulose in the CPMAS spectrum of the needles while some of the smaller peaks can be attributed to fragrant compounds.  Many of the fragrant compounds in the needles are likely to be in a liquid-like state and not cross polarize very well.  These will either be absent or under-represented in the CPMAS spectrum.  The top panel of the figure shows the ¹H - ¹³C HSQC spectrum of a benzene-d₆ extract prepared from crushed spruce needles.  The top and left-side projections are the high resolution ¹H and ¹³C NMR spectra, respectively.  This sample is expected to contain all of the benzene soluble compounds.  The spectrum is free of cellulose resonances and shows a mixture of fragrant compounds.

These data don't recover the childhood magic of Christmas but they do bring a little bit of joy to this NMR spectroscopist.

Merry Christmas  

NMR Signals in Tuning Curves

The quality of the tuning and matching of an NMR probe on a Bruker NMR spectrometer can be monitored by using the wobble (or "wobb") routine in the TOPSPIN software.  This routine sweeps the frequency using low power and displays a plot corresponding roughly to the absorbance vs frequency for the probe electronics.  If the probe has very high sensitivity (eg: a cryoprobe) and contains a sample rich in protons (eg: water) then one is able to observe the proton spectrum in the frequency swept wobble curve.  This is demonstrated in the figure below which shows wobble curves for a 600 MHz cryoprobe containing a sample of water.

The curves show the tuning profile of the probe with an anomaly at the proton frequency.  The anomaly is the proton signal of the water in the NMR probe. The top panel is the wobble curve for the probe in a well-shimmed magnet and the bottom panel is the same curve after the magnet shims had been grossly maladjusted.  One can see that the anomaly is much more broad in the wobble curve collected on a poorly shimmed magnet as one would expect the signal from the water to be much broader in an inhomogeneous magnetic field.



Thank you to Stan Woodman of Bruker Canada for pointing this phenomenon out to me.

Radiation Damping and Pulse Calibration

Radiation damping causes broadening in the NMR resonances of very strong signals (such as the ¹H signal of pure water) as a result of currents induced in the coil from the strong transverse magnetization.  Radiation damping can also produce asymmetry and phase irregularities in the affected resonances.  These problems make pulse calibration by the standard nutation curve problematic when very strong signals are used for the calibration.  The left-hand panel (black) of the figure below shows the standard ¹H nutation curves for 0.1% H₂O in D₂O (bottom) and 80% H₂O in D₂O (top).  In both cases, single-scan spectra with a recycle delay of 30 sec were collected and plotted horizontally.  The pulse was varied from 1 µsec to 24 µsec in steps of 1 µsec.  In the case of 0.1% H₂O in D₂O, the nutation curve is well behaved and one is easily able to read off the 90°, 180°, 270° and 360° pulse durations.  In the case of 80% H₂O in D₂O, where radiation damping is a problem, the nutation curve is not well behaved.  There are asymmetry and phase distortion problems which make it impossible to determine the 90° pulse, based on maximum signal height, with any accuracy.  Nor is it possible to determine a reliable 180° based on the first minimum.  The spectra show very little distortion in the vicinity of the second minimum so the 360° pulse can be used reliably to determine the 90° pulse.  The right-hand panel of the figure (red) shows the integrals of the corresponding nutation spectra.  The integrals for both samples behave similarly.  It is clear that even in the case of severe radiation damping, one is able to determine a well behaved nutation curve from the integrals.

TROSY

The chemical shift resolution and sensitivity of NMR generally benefit from an increase in magnetic field strength.  As a result, large sums of money are spent on magnets with higher and higher fields.  The boost in sensitivity means that smaller and smaller quantities of sample are needed and measurements can be completed in shorter periods of time.  There are particular cases however, where an increase in magnetic field can lead to a loss of sensitivity and resolution.  This is the case for ¹⁵N decoupled ¹H spectra of the ¹H-¹⁵N spin pairs in very large ¹⁵N labelled proteins.  The very long correlation times of the protein combined with the high resonance frequencies associated with high field strength lead to very short T₂ relaxation times and therefore broader lines.  The broad lines account for a significant loss in resolution and sensitivity.  One might then wonder why protein structural chemists spend so much money on very high field magnets.  What follows is one possible answer to this question.

The two main relaxation mechanisms for the ¹H and ¹⁵N in proteins are dipolar coupling and chemical shielding anisotropy.  These two mechanisms are also cross correlated with one another.  The cross correlation term is of different sign for each of the two peaks in a ¹H-¹⁵N doublet resulting in one of the peaks of the doublet having a shorter T₂ (and broader line) than the other one.  If ¹⁵N decoupling is applied, one sees a single resonance with a line width determined by the average of the two components of the doublet.  This is illustrated in the figure below for a ¹H-¹⁵N spin pair in a small and large molecule at high field .  The same is true in the ¹⁵N-¹H doublets in the ¹⁵N spectra of ¹⁵N-¹H spin pairs.

At very high fields, One of the lines in the ¹H-¹⁵N doublet is very sharp and the other very broad.  If, in the ¹H spectrum of a protein, we could eliminate all of the broad doublet components leaving only the sharp ones, we would have a high resolution ¹H spectrum.  Further, if we could combine such a measurement with an HSQC, we would have a high resolution ¹H-¹⁵N HSQC at high field.  The combination of these two measurements is called transverse relaxation optimized spectroscopy (TROSY).  TROSY data collection employs an HSQC measurement with neither ¹H nor ¹⁵N decoupling elements (as described in a previous post) as well as other elements which suppress the broad lines of the doublets and retain the sharp lines.  The results of this are illustrated in the figure below for small and large proteins at high field.

Clearly, it is not advantageous to use the TROSY technique on small proteins rather than the conventional HSQC.  For large proteins at high field however, there is a significant sensitivity and resolution advantage compared to a conventional HSQC.  It should be noted that the TROSY cross peaks are shifted by ½ ¹J_HN in both the F2 and F1 domains.  The figure below shows a superposition of a conventional HSQC (black) and a TROSY (blue) for a protein at 500 MHz.

One can clearly see the ½ ¹J_HN shift in the F2 and F1 domains of the TROSY compared to the HSQC.  In this case, the conventional HSQC gives higher sensitivity than the TROSY.

Thank you to Adam Damry of Professor Roberto Chica’s research group at the University of Ottawa for providing the sample of ¹⁵N labelled protein.

Decoupling in 2D HSQC Spectra

HMQC and HSQC NMR data are commonly used to correlate the chemical shifts of protons and ¹³C (or ¹⁵N) across one chemical bond via the J coupling interaction.  The data are ¹H detected, with the ¹H chemical shift in the horizontal F2 domain and the ¹³C (or ¹⁵N) chemical shift in the vertical F1 domain.  In the case of ¹H and ¹³C, the technique depends on protons bonded to ¹³C.  ¹H–¹²C spin pairs provide no coupling information and are suppressed by the method.  If one is to observe the ¹H signal of a ¹H-¹³C spin pair, one expects to observe a doublet with splitting ¹J_H-C (i.e. the ¹³C satellites).  Likewise, if one is to observe the ¹³C signal of a ¹H-¹³C spin pair, one expects to observe a doublet with the same splitting.  2D HSQC spectra are normally presented with both ¹H and ¹³C decoupling yielding a simplified ¹H-¹³C chemical shift correlation map over one chemical bond.  The figure below shows one of the most commonly used gradient HSQC pulse sequences.  The ¹H and ¹³C decoupling elements of the sequence are highlighted in yellow and pink, respectively.

During the evolution time, t1, the ¹³C chemical shift and ¹H-¹³C coupling evolve.  The ¹H 180° pulse (color coded in yellow) in the center of the evolution time refocuses the coupling and as a result decouples protons in the F1 (¹³C) domain of the spectrum.  ¹³C is broadband decoupled from the F2 (¹H) domain by applying a GARP pulse train (color coded in pink) at the ¹³C frequency during the collection of the FID.  One can turn each of these elements “on” or “off” for data collection.  The figure below shows the ¹H-¹³C gradient HSQC spectrum of benzene with all possible combinations of ¹H and/or ¹³C decoupling.

In the top left panel both ¹H and ¹³C decoupling are turned “on” and one observes a singlet in both the F2 (¹H) and F1 (¹³C) domains.  In the top right panel, the ¹H decoupling element is “on” while the ¹³C decoupling element is “off”.  The result is a ¹H-¹³C doublet in the F2 (¹H) domain and a singlet in the F1 (¹³C) domain.  In the bottom left panel, the ¹H decoupling element is “off” while the ¹³C decoupling element is “on”.  The result is a ¹³C-¹H doublet in the F1 (¹³C) domain and a singlet in the F2 (¹H) domain.  In the bottom right panel, both the ¹H and ¹³C decoupling elements are “off”.  The result is a ¹H-¹³C doublet in both the F2 (¹H) and F1 (¹³C) domains.

Dead Time and Phase

The phase of an NMR peak depends on the sine/cosine character of the free induction decay (FID) when the receiver is turned on.  Positive and negative cosine FIDs will yield positive and negative in-phase peaks, respectively whereas positive or negative sine FIDs will yield peaks 90° out of phase.  FIDs that are neither a pure sine nor pure cosine with yield peaks which are out of phase to an extent dependent on the cosine/sine character of the FID.  In a perfect world, the receiver is gated on immediately after a perfect 90° pulse and all FID’s are cosines producing positive in-phase NMR peaks.  In the real world however, there are problems with acoustic ringing, pulse breakthrough imperfect pulses of finite duration and finite electronic switching times.  These problems produce a dead time between the end of the pulse and time at which the receiver is gated on during which data cannot be collected.  As a result the FID may not be a perfect cosine function and a phase correction will need to be applied after Fourier transform.  The first two figures below illustrate this point for a single off-resonance NMR signal as the dead time is increased.  The first figure shows the FID’s as a function of increasing dead time from bottom to top while the second figure shows the Fourier transformed spectra without phase correction as a function of dead time from left to right.

When there is more than one signal, the FID is an interferogram representing the sum of all time domain signals, each with a different frequency.  Since each component has a different frequency, its phase is affected to a different extent as a result of the dead time.  Higher frequency time domain components  (i.e. those representing peaks further off-resonance) are affected more than lower frequency components (i.e. those representing peaks closer to being on-resonance).  This is illustrated in the figure below for the ¹H NMR data for p-xylene.  The left-hand portion of top panel of the figure shows the FID containing both methyl and aromatic components while the right-hand portion of the top panel shows an expansion of the initial portion of the same FID.  The bottom panel of the figure shows a stacked plot of the NMR spectra collected as a function of dead time.  One can see that the phase of the aromatic peak furthest off-resonance is affected to a greater extent by an increased dead time than the methyl peak closer to resonance.

The last figure also shows a stacked plot of the ¹H NMR spectra of p-xylene as a function of dead time.

In this case, the methyl signal was set on-resonance.  One notices immediately that the phase of the on-resonance methyl peak is unaffected by an increase in the dead time whereas that of the off-resonance aromatic peak is severely affected.  The on-resonance methyl peak is not affected by an increase in dead time as its time domain signal is a simple exponential with no sine/cosine oscillations.  A loss of the beginning of a simple exponential FID due to the dead time still leaves a simple exponential and thus the phase is not affected.

Thank you to Dr. Michael Lumsden of the NMR Facility of Dalhousie University for suggesting the subject of this post.

The Information Content of an FID

The free induction decay (FID) is a function representing the decay of transverse magnetization as a function of time after the application of a pulse (or pulse sequence).  The NMR spectrum is obtained by Fourier transforming the FID.  All of the information in the NMR spectrum (line width, intensity, phase, line shape ....) is contained in the FID.  Knowledge of what part of the FID represents a particular property of an NMR spectrum allows a user to process the raw time domain data in a way that maximizes the quality and information content of the processed frequency domain spectrum.  The figure below shows the real component of the complex FID for a sample in which there is a single resonance.  The FID is labelled in terms of its information content.

The shape of the envelope of the overall decay defines the line shape of the NMR resonance.  Exponential decays yield Lorentzian line shapes.  The frequency in the FID represents the offset of the resonance from the carrier frequency or in other words, how far the resonance is from the center of the spectrum.  The higher the frequency, the further off-resonance the peak.  The FID for an on-resonance peak is a simple decaying exponential with no oscillation frequency present.  The first point of the FID contains the integrated intensity and phase information.  Since time and frequency are reciprocals of one another, the duration of the decay before it disappears into the noise determines the sharpness of the NMR resonances and ultimately the resolution in cases where there is more than one resonance in the spectrum.  The longer the decay - the narrower the lines.  The early portion of the FID (short time) defines the broad features (wide frequency distributions) whereas the the latter portion of the FID (long time) defines the sharp features (narrow frequency distributions).  Also, since the FID is a decaying function, the early portion has a higher signal-to-noise ratio than the latter portion.  With this knowledge its is very easy to understand how best to apply apodization functions to the raw data for the purpose line broadening and resolution enhancement.  Processing techniques such as zero filling, forward linear prediction, backward linear prediction and signal-to-noise optimization as well as spectral artifacts such as truncation errors, baseline roll and receiver saturation errors are easily understood with knowledge of the information content in the FID.   

NMR of Edible Oils

NMR spectroscopy is one of the most informative techniques for the study of structure, composition and dynamics of matter.  One of the many thousands of applications of NMR spectroscopy is in the study of edible oils.  Plant and animal oils are composed of complex mixtures of fatty acid tri-esters of glycerol.  The fatty acid moieties are generally straight chains of 16 - 24 carbons in length with various degrees of unsaturation.  In natural oils the double bonds are all cis-.  Fatty acids with trans- double bonds are usually the result of food processing.  The double bonds in polyunsaturated fatty acids are generally separated by single methylene groups.  The end methyl carbon of each fatty acid chain in the glycerol tri-esters is referred to as the omega position.  Omega-3 fatty acids are those with a double bond on the third carbon from the omega methyl position.  The most common omega-3 fatty acid in plant oils is α-linolenic acid (ALA), a C₁₈ acid with three cis- double bonds in the 9-, 12- and 15- positions.  Two of the most common omega-3 fatty acids in marine oils are eicosapentaenoic acid (EPA), a C₂₀ acid with five cis-double bonds in the 5-, 8-, 11-, 14-, and 17- positions and docosahexaenoic acid (DHA), a C₂₂ acid with six cis- double bonds in the 4-, 7-, 10-, 13-, 16- and 19- positions.  The human body benefits from EPA and DHA which are only inefficiently synthesized from ALA in the human body.  Also, it is recommended that consumption of saturated oils should be limited and that polyunsaturated oils are a better alternative.  With these concerns, the study of edible oils has become important.  One might expect that the complexity of the mixtures constituting the natural edible oils would limit the usefulness of NMR as a method of study however; the spectra contain a great deal of information as can be seen in the figures below.  The ¹³C NMR spectra of 4 plant oils and 1 commercial “wild fish” oil are shown in the first figure.

The olefinic carbons are color-coded in yellow and give an indication of the degree of unsaturation in the oils.  Clearly, the coconut oil is saturated and the fish oil contains the highest degree of unsaturation.  The ¹H NMR spectra of the same oils are shown in the second figure.

The resonances color-coded in yellow are those of the protons on olefinic carbons and are a direct indication of the degree of unsaturation.  The resonances color-coded in pink are methylene protons on carbons adjacent to two olefinic carbons and represent the degree of polyunsaturation.  The resonances color-coded in blue are methylene protons attached to carbons adjacent to both methylene carbons and olefinic carbons.  The methyl resonances are at the lowest chemical shift.  Those color-coded in green are from the omega-3 fatty acid moieties.  Qualitatively, from the data, it is obvious that the coconut oil is saturated and the fish oil contains the most omega-3 polyunsaturated fatty acid moieties.