Sorting Out NOE's for Exchanging Rotamers

2D NOESY spectra contain cross peaks from both NOE interactions and peaks due to rotamers in slow exchange with one another on the NMR tine scale. For small molecules, the cross peaks resulting from slowly exchanging rotamers are of the same sign as the diagonal peaks. The NOE cross peaks, on the other hand, are of opposite sign compared to the diagonal peaks. When both types of correlations are present there may be more NOE correlations than expected. What follows is an example of this. The figure below shows a color coded chemical structure of a ruthenium complex with a color coded partial ¹H NMR spectrum.It is obvious from the NMR spectrum that all of the signals from the color coded protons are doubled in the spectrum. One possible explanation for this is that there is a slow rotation about the ruthenium carbon bond indicated with the red curly arrow allowing for two possible nonequivalent rotamers. This is confirmed with the 2D ¹H NOESY spectrum shown in the figure below with a 0.9 second mixing time. The spectrum clearly shows exchange peaks between corresponding pairs of ¹H signals from each rotamer.The interesting thing to note from the NOESY spectrum is that each aromatic proton (pink) from a single rotamer shows NOE correlations to the methyl groups (blue and yellow) of both rotamers - not just those from a single rotamer. With this data, it is not possible to assign the subspectrum of a single rotamer. Presumably, the assignment could be made by collecting a 2D NOESY spectrum at low temperature where the rotation was completely frozen out or by collecting a 2D NOESY spectrum with a very short mixing time where the rotation would be limited. The problem with the former approach is that the solvent may freeze at a temperature too high to stop the bond rotation. The problem with the latter approach is that the NOE's would be much reduced due to the short mixing time and collecting a 2D data set with sufficient signal to noise ratio would take a great deal of time. Another approach is to collect selective 1D gradient NOESY spectra with selective excitation of the aromatic proton from each rotamer individually. These data are shown in the figure below for two different mixing times.Each spectrum is displayed in two parts. The left-hand panel is the aromatic region with the selectively excited resonance colored red and the right-hand panel is the aliphatic region showing the NOE correlations to the methyl groups. From the spectra collected with a 2 second mixing time, one can see that the selective excitation is no longer selective due to bond rotation during the long mixing time. One can see inverted peaks for the aromatic protons of both rotamers despite the fact that the ¹H signal of only one rotamer was selectively excited. Furthermore, NOEs to the methyl signals from both rotamers are present. The spectra collected with only a 0.2 second mixing time, on the other hand, show very selective excitation. The time scale of the bond rotation is obviously longer than the 0.2 second mixing time. The spectra show only the NOEs between the selectively excited aromatic proton and the methyl groups from a single rotamer. The NOEs build up fast enough to be observed during the 0.2 second mixing time before rotation occurs. These data allow for the assignment of signals from each of the rotamers.

Thank you to Justin Lummiss of Dr. Fogg's research group for aharing this interesting system.

13C NMR of a Delicious Christmas Treat

As my Santa Claus-like belly may indicate, I love holiday treats. The solid-state ¹³C NMR spectra below were collected from a special sample of a holiday treat prepared by my wife, Patty from her Great Grandma Jennings lab book. The sample was prepared from only four ingredients as follows:

To 227 g of softened butter, 65 g of fructose was added while stirring with a spatula. Slowly, 199 g of flour and 1.26 g of sodium chloride were stirred into the mixture until it became difficult to mix with a spatula. The mixture was kneaded gently until cracks in the surface began to appear after which it was rolled to a thickness of 38 mm and cut into round samples of approximately 51 mm in size. The samples were heated in an oven at 436 K - 450 K for approximately 600 seconds until gold in color.

The bottom trace is a ¹³C CPMAS spectrum and the top trace is a ¹³C MAS spectrum. Both spectra were acquired with high power ¹H decoupling. This pair of spectra serves to illustrate the different types of information available from each of these techniques. The sample is a mixture of rigid and mobile components. The ¹³C CPMAS technique detects mainly the more rigid components as it relies on the dipolar coupling between protons and ¹³C for the cross polarization. The dipolar coupling is averaged to nearly zero for the mobile constituents and therefore they do not appear in the spectrum. The ¹³C CPMAS spectrum therefore, shows primarily all of the rigid constituents (mainly flour and sugar). The ¹³C MAS spectrum with high power ¹H decoupling shows both rigid and mobile constituents. The resonances from the mobile constituents (mainly butter) have sharp lines while the broader lines from the rigid constituents show up at very low intensity as the sensitivity is not enhanced by cross polarization.

Now, you too have enjoyed Patty's delicious shortbread.

Enlightening NMR Videos on YouTube

The Journal of Magnetic Resonance (JMR) has been publishing important contributions from NMR spectroscopists since 1969. Some of these contributions have become "classic papers" and have been sited thousands of times. A play list of videos has been assembled on YouTube highlighting some of the most significant contributions in NMR spectroscopy over the last few decades. The research is described anecdotally (and in some cases very humbly) by the original authors in the videos. I think you will enjoy putting faces to the names of the authors of these highly cited papers.

The Effect of Viscosity on 1H NOESY Spectra

For small molecules, ¹H 2D NOESY spectra exhibit positive NOE's between protons close to one another in space and the off-diagonal correlations are opposite in phase to those of the diagonals. As molecules become larger and larger the motional correlation times become longer and longer. As the correlation times become longer and longer, the NOE's become less positive, cross zero and then become negative. For large molecules, like proteins, the NOE's are negative and the off-diagonal correlations between close protons are of the same phase as the diagonal peaks. When the correlation times are extremely long, for example in rigid macromolecules or solids, the dipolar coupling among all of the protons is inefficiently averaged by molecular motions and spin diffusion becomes efficient. Spin diffusion allows all of the protons in a dipolar coupled network to exhibit correlations with one another. The sign of the correlations is similar to that observed for chemical exchange or negative NOE's. This phenomenon is demonstrated in the figure below. In the figure, positive contours are represented in black and negative contours are represented in red. The NOESY spectrum on the left is that of a solution of menthol in CDCl₃. The off-diagonal correlations between proximate protons is opposite in phase compared to the diagonal responses, typical of small molecules with short correlation times. The NOESY spectrum on the right is that of the same solution of menthol dissolved in a very viscous fluorinated oil. The extreme viscosity of the sample is sufficient to make the correlation time for the molecules very long such that the menthol behaves like a very large macromolecule where spin diffusion is efficient. As a result, off-diagonal responses are of the same phase as those of the diagonal and are observed between all protons in the molecule.This technique has been cleverly applied* to mixtures of molecules immersed in viscous oils where intra-molecular correlations are observed whereas inter-molecular correlations are not observed. The data allow for the observation of the constituent components of complex mixtures.

* Andre J. Simpson, Gwen Woods, and Omid Mehrzad, Anal. Chem, 80, 186-194 (2008).

Resolution During a Liquid Nitrogen Refill

Just as it is not advisable to collect high resolution NMR data during (and shortly after) a liquid helium refill, it is similarly not advisable to collect data during a liquid nitrogen fill. The figure below illustrates this point. A 300 MHz NMR spectrometer was set up to collect an NMR spectrum every minute before, during and after a liquid nitrogen refill. The resolution deteriorates as soon as the one-way valves are removed from the nitrogen cryostat. One can see that the resolution during the fill is much worse than before the fill. Even 60 minutes after the fill, the magnet has not fully recovered the resolution attained before the fill. The last spectrum of the series was collected after re-shimming the magnet and is comparable to the spectrum collected before the fill. The resolution profile during a fill may be different for every magnet. For this particular magnet, it is advisable not to collect high resolution data for at least 90 minutes after a nitrogen refill.

"The Resonance" - A New Web Site from Bruker

Bruker has introduced a new web site called "The Resonance". This well organized site has NMR/MRI news, posts related to specific areas of research, hardware and software information and more. The site is frequently updated and permits posts from users. It will be a great resource for users of Bruker NMR instruments as well as those interested in how magnetic resonance is applied in research.

Probe Tuning and 90 Degree Pulses

In order to get meaningful results from multiple-pulse NMR pulse sequences, it is essential that the 90° and 180° pulses are calibrated at the power levels used in the sequences (see this post for example). The calibrations are usually done on a standard sample in a well tuned and matched probe. The calibrations are typically stored in a file which is called up when setting up particular NMR experiments. It is important to know that these calibrations are correct for the particular sample of interest only when the probe is well tuned and matched. For samples of high ionic strength, it may not be possible to properly tune and match the probe and the 90° and 180° pulses for these samples will be longer than those previously calibrated, resulting in questionable data. In these cases, the pulses must be calibrated on the problematic sample. The figure below addresses the question of how important proper tuning and matching are with respect to the 90° pulse duration. The ¹H 90° pulses for a sample HDO in a 500 MHz broadband probe were measured by the fast nutation method for various states of probe tuning and matching. In the left-hand side of the figure, pulses were calibrated for a perfectly matched probe as a function of tuning frequency. One can see that the 90° pulse is at a minimum when the probe is perfectly tuned and increases as the probe is detuned in either direction. In the right-hand side of the figure, pulses were calibrated for a perfectly tuned probe as a function of probe mismatch. One can see that the 90° pulse is at a minimum in a perfectly matched probe and increases as a function of the degree of mismatch (in units of screen divisions on the spectrometer display). It is interesting to note that the 90° pulse duration is more forgiving to mismatch than to errors in probe tuning.

Resolution During a Liquid Helium Refill

Students sometimes ask whether or not they can collect NMR data during a liquid helium refill. The answer depends on the type of NMR experiment. For most solids experiments, where high resolution ( <~ 100 Hz) is not required, one can often collect data without a problem. In experiments for liquids, where high resolution is almost always required, the quality of data are affected drastically by the disturbance from the liquid helium refill and it is not advisable to collect data during this time. Furthermore, after a liquid helium refill, the magnet must recover in order to obtain the same resolution prior to the fill. The figure below illustrates this point. A 300 MHz NMR spectrometer was set up to collect an NMR spectrum every minute before, during and after a liquid helium refill. One can see that the resolution during the fill is much worse than before the fill. Even 15 minutes after the fill, the magnet has not fully recovered the resolution attained before the fill. The last spectrum of the series was collected after re-shimming the magnet and is comparable to the spectrum collected before the fill.
The resolution profile during a fill will probably be slightly different for every magnet. For this particular magnet, it is advisable not to collect high resolution data for at least 30 minutes after a helium fill.

Nitrogen Pressure and Spectral Resolution

Super-conducting NMR magnets are cooled with liquid helium. The boil off rate of the liquid helium is minimized by surrounding it with a high vacuum and a liquid nitrogen cryostat. The liquid nitrogen cryostat may either be vented directly to the atmosphere or it may be maintained at a pressure slightly above atmospheric pressure with the use of pressure relief valves. NMR users should be aware that the homogeneity of an NMR magnet is affected drastically by the pressure in the liquid nitrogen cryostat. The left-hand panel of the figure below shows a well resolved 400 MHz ¹H NMR spectrum of the methyl triplet of ethylbenzene in a well shimmed magnet where the nitrogen cryostat was maintained slightly above atmospheric pressure with pressure relief valves for several days. The spectrum in the right-hand panel was run under identical conditions after the cap to the nitrogen fill port was removed, relieving the pressure in the nitrogen cryostat.

Virtual Coupling

When the chemical shift difference between two J coupled nuclei is of the same order as the coupling constant, second order spectra are obtained. See this and this. One, often unrecognized, second order effect is virtual coupling which is often misinterpreted as first order weak coupling. In a three-spin system, virtual coupling occurs when the observed nucleus appears to be coupled to both of the other two nuclei even though it is only coupled to one of them. This arises in AA'X and ABX spin systems when X (the observed nucleus) is coupled to only one of the other two strongly coupled spins. This is illustrated in the figure below. The figure consists of simulations of X in an AA'X spin system as a function of J_AA' with J_AX set at 10 Hz and no coupling between A' and X. Clearly, the spectrum of X is affected by the coupling between A and A'. When J_AA' = 0, a first order doublet is observed with a coupling constant of 10 Hz. As J_AA' increases, complicated second order multiplets are observed. When J_AA' = 50 Hz (or more) a "virtual triplet" with a coupling constant of 5 Hz is observed. This appears to be identical to a 1:2:1 triplet in a first order spectrum with a coupling constant of 1/2 J_AX. It is however a second order spectrum and should not be misinterpreted as first order weak coupling. An example of this is illustrated in the figure below. The figure shows the ¹³C NMR signals for the ipso and ortho aromatic carbons of 1,2-bis(diphenylphosphino)ethane (DPPE). These carbon atoms are coupled to the nearest phosphorus but not to the remote phosphorus. The two phosphorus atoms are strongly coupled to one another. The ortho carbons appear as a "virtual triplet" and the ipso carbons, a second order multiplet.

The Bruker Almanac for iPhone / iPod

Over the years, I have made much use of the Bruker Almanac. My bookshelf still holds several copies from the past 20 years or so. For those who have never seen a copy, it contains a great deal of useful information for NMR, EPR, ENDOR, IR and mass spectrometry. The NMR information includes, useful NMR formulas, chemical shift tables for some of the commonly observed isotopes, reference compounds, frequency tables etc... Recently Bruker has released its almanac in an iPod / iPhone app. Not only can you use your iPod / iPhone to take a course on Fourier transforms but you can also use it as an NMR reference book. The Bruker Almanac app is a very useful tool making it convenient to have a great deal of NMR information in your pocket - and at the console where it is most often needed. How often have you awakened at 2:18 am. and wondered what the chemical shift range is for ⁹⁹Ru? Well .... now you can quickly look it up and go back to sleep. Below are three screen shots from the app. Good job Bruker!

In Honor of Rod Wasylishen

Rod Wasylishen is dear to the hearts of the entire Canadian NMR community and to many worldwide. Not only are his scientific achievements stellar, but he has mentored an entire generation of Canadian NMR spectroscopists with his contagious curiosity and positive approach to research. All who have had the privilege of working with Rod speak highly of him. In his honor, his former students and colleagues have contributed to a special issue of the Canadian Journal of Chemistry - a journal Rod has enthusiastically supported throughout his career.

Congratulations Rod!

Saturation Transfer and Exchange

Exchange processes that occur on the NMR time scale affect the NMR line shapes and can be studied by line shape analysis. If the exchange process is slow on the NMR time scale, one can employ EXSY or inversion transfer methods to study the exchange. An alternative to these is the saturation transfer technique. In this method, one of the slowly exchanging resonances (A) is saturated with low power CW irradiation and the effect on the intensity of the resonance of the exchange partner (B) is monitored. If there is exchange between A and B during the period of saturation some of the saturation from A will be transferred to B. The change in the intensity of B will depend on both the rate of exchange, k and the relaxation time of B, T_1B . If there is no nuclear Overhauser effects between A and B, then the rate of exchange is given by: where I_o is the intensity of B with no saturation of A, and I_∞ , is the intensity of B when A is saturated for an infinite time. The saturation transfer effect is useful for situations where the exchange is slow on the NMR time scale but faster than (or of the same order as) T_1B. An example using ³¹P NMR is illustrated in the figure below for a ruthenium phosphine complex which undergoes slow exchange between isomers with different modes of bonding. The ³¹P [¹H] NMR spectrum is shown in the upper right-hand panel of the figure. In this case, the P atoms of isomer A are chemical shift equivalent and give a singlet while those for isomer B are chemical shift nonequivalent and give an AB pattern. The spectrum of isomer B is shown in the lower panel of the figure as a function of saturation time of isomer A.

Many thanks to Carolyn Higman and Prof. Deryn Fogg for kindly allowing their data to be used in this post.

Shaped Pulses

Shaped rf pulses are used frequently in modern NMR experiments for selective excitation and more efficient inversion. The figure below shows some of the pulse shapes in the Bruker shape library measured with an oscilloscope on an AVANCE III console. Each 50.3 MHz rf pulse was 1 msec in duration and was measured at the output of the signal generation unit.

"Absolute" Water Suppression

Collecting ¹H NMR spectra of aqueous samples is complicated by the presence of the enormous, broad water signal which is often many orders of magnitude more intense than the signals from the solute of interest. The water signal can be suppressed by presaturation or multiple pulse techniques employing gradients (such as WATERGATE). These techniques are compared here and do a very good job, but neither is able to completely suppress the water signal in very dilute challenging samples. Recently, a technique introduced by Buuan Lam and Andre Simpson* which uses both presaturation and W5-WATERGATE has been used to suppress the water signal. In this case, the presaturation consists of many low power shaped 180° pulses. The combination of these two techniques provides incredible water suppression. The authors are able to measure the ¹H NMR spectra of dissolved organic matter in natural waters without any preconcentration of the samples. Their spectra are completely free of the water signal! At the 2011 ENC the same group presented a poster** highlighting the water-free ¹H NMR spectrum of the dissolved organic matter in melted glacial ice. The water suppression is so remarkable that this technique should be called "The Simpson Sledgehammer". The figure below illustrates further examples of the implementation of this suppression method. The bottom trace shows the 32 scan ¹H NMR spectrum of a dilute unlabelled protein (which includes the NH resonances, albeit attenuated due to chemical exchange). The middle trace shows the 32 scan ¹H NMR spectrum of supernatant human saliva. The upper trace shows the ¹H NMR spectrum of rain water collected from an asphalt tile roof. The spectrum was collected overnight and shows the presence of long chain hydrocarbons from the asphalt as well as formaldehyde. In all cases the water signal is completely absent in the spectrum.

* Buuan Lam and Andre J. Simpson. Direct ¹H NMR Spectroscopy of Dissolved Organic Matter in Natural Waters. The Analyst 113 263 (2008).

** Brent Pautler, Andre Simpson, Li-Hong Tseng, Manfred Spraul, Ashley Dubnick, Martin Sharp and Myrna Simpson. Trace Level Analysis of Dissolved Organic Matter in Glacial Ice Using SPR-W5-WATERGATE. POSTER 264, ENC (2011).

Heteronuclear Double Quantum Filters

Double quantum filters are used to filter out single quantum magnetization and allow the passage of double quantum magnetization. In the proton observe heteronuclear case, the double quantum filter (like the BIRD filter) allows the selective observation of the weak satellite signals from protons coupled to dilute spin I = 1/2 X nuclei (e.g. X = ¹³C, ¹⁵N, ²⁹Si ....) but rejects the strong singlets from the uncoupled protons in the vicinity of ¹²C, self decoupled ¹⁴N, and ²⁸Si . The figure below illustrates the heteronuclear double quantum filter described by Stefan Berger and Siegmar Braun in 200 and More NMR Experiments applied to the ¹H NMR spectrum of tetramethylsilane. The bottom trace of the figure shows a conventional ¹H NMR spectrum. The middle trace was collected using a ¹H-²⁹Si double quantum filter and shows only the ¹H-²⁹Si doublet. The top trace was collected using a ¹H-¹³C double quantum filter and show only the ¹H-¹³C doublet. In both cases there is excellent suppression of the ¹H singlet signal.

FT NMR Spectra Without Pulses

An FT NMR spectrum is obtained by applying a pulse at the Larmor frequency to a sample in a magnetic field. The precession of the spins induces a voltage in the receiver coil which is recorded as a function of time. The Fourier transform of the time dependent signal is the NMR spectrum. What happens if you do not provide any pulses? You might think that you would not observe a signal - but this is not the case. Even without any pulses there is sufficient noise present to allow incoherent precession of the nuclear spins. This precession can be measured and indeed produce an NMR spectrum. This is demonstrated in the figure below. The bottom trace shows a conventional 300 MHz ¹H NMR spectrum of ethyl acetate collected with one scan using a 30° pulse. The top trace was collected on the same sample by adding 256 single scan magnitude spectra using no pulses whatsoever. Although very weak, one can clearly see the NMR spectrum of ethyl acetate.

QCPMG for 2H NMR

QCPMG has made a tremendous impact on the field of solid state NMR in that it has enabled the collection of data for very broad resonances for unreceptive nuclei. This technique is based on the collection of a train of echoes, the Fourier transform of which produces a "spikelet" spectrum whose intensity envelope mimics the static line shape. The figure below compares the ²H quadrupolar echo spectrum and the QCPMG spectrum of perdeuterated poly-methyl methacrylate. The spectrum contains two overlapping powder patterns; a narrow one from the rotating methyl groups (QCC ~ 56 kHz) and a much less intense broad one from the rigid methlyene deuterons (QCC ~ 170 kHz). It is clear from the figure that the envelope of spikelets in the QCPMG spectrum reproduces quite well the lineshape in the quadrupolar echo spectrum.

MAS Rotor Crashes

There is no sound more pleasing to a solids NMR spectroscopist than that of an MAS rotor spinning stably. What happens though when the spinning is abruptly interrupted? This is called a rotor "crash" and when it occurs not only is the pleasing sound replaced by the horrible sound of rushing air, but one often finds damage to both the MAS rotor and the NMR probe. The picture below shows what used to be the solenoid coil of a 4 mm MAS probe after an unfortunate rotor crash. The rotor and sample were reduced to dust. Fortunately in this case the stator was not destroyed.

Here are a few tips to avoid expensive rotor crashes:

1. Spin only as fast as needed for your experiment. Just because your car can go 200 km/h does not mean that it should be driven at 200 km/h. Likewise, just because your probe is rated to spin samples at 15 kHz does not mean that all samples should be spun at 15 kHz.

2. Check the integrity of the rotor and the cap before use. Damaged rotors are weakened and should NEVER be used. Damaged caps can cause instability which may lead to a rotor crash.

3. Make sure the cap fits snugly on the rotor. A cap that lifts or comes off the rotor while spinning will cause a rotor crash.

4. Be aware of sample heating due to spinning. The rotor and sample heat up during spinning due to friction. If the temperature increases such that your sample melts or emits a gas, the rotor may become unbalanced or the cap may be forced off causing a rotor crash.

5. Make sure the rotor is marked properly so the speed can be monitored and regulated. Failure to do this may result in the spin counter receiving a bogus signal and it is possible that the rotor may spin faster than its rated speed causing a crash.

6. Pack your sample evenly to ensure that the rotor is properly balanced during MAS. Rotors that do not spin smoothly and stably should be repacked until they do.

7. Start and stop the rotor gradually to ensure stability while speeding up or slowing down.

(Photo courtesy of Paul Morris of Morris Instruments Inc., manufacturer of very useful probe tuning devices and provider of magnetic resonance products and services.)

Two New Twitter Feeds to Follow

Two new and very useful Twitter feeds have recently appeared online. The first is by Luke O'Dell called solidstateNMR. It posts links to publications related to solid state NMR as soon as they appear online. The second is by Victor Terskikh called nmr900 which posts news and information from Canada's showpiece high field solids NMR facility, The National Ultrahigh-Field NMR Facility for Solids.

Stay up-to-date and check them out!

Excitation Profiles for Shaped Pulses

Shaped pulses are very commonly used for selective excitation and nonselective inversion in a large number of NMR pulse sequences. The frequency domain excitation profile of a radio frequency pulse is the Fourier transform of the time dependent pulse shape and determines the width, uniformity and phase of the frequency spectrum excited. Since time and frequency are reciprocals of one another, short rf pulses have very wide excitation profiles and long rf pulses have very narrow selective excitation profiles. In a previous BLOG post the excitation profiles of rectangular pulses of varying duration were determined experimentally. The Fourier transform of a rectangular pulse is a sinc function which is observed to be the experimentally determined excitation profile. Short high power rectangular pulses are very desirable for uniform excitation over wide frequency ranges as the entire NMR spectrum of interest usually occupies only a very small central portion of the central lobe of the sinc shaped excitation profile which, to a first approximation, is flat over the observed spectral width. Rectangular pulses are often not desirable when narrow excitation profiles are required as the excitation is not uniform over the desired region and the ripples of the sinc excitation profile cause nodes of excitation and negative peaks.

The Fourier transform of a sinc function is a box function, so if a long low power sinc shaped rf pulse is used one obtains a narrow flat box shaped excitation profile. This is indeed the case as can be seen in the bottom trace of the figure below. The trace is composed of a series of ¹H NMR spectra of H₂O/D₂O where a truncated, 200 msec, 10 cycle sinc shaped monochromatic rf pulse was applied with varying rf frequency offsets. One can see that the excitation profile is, to a good approximation, a narrow flat box function. The deviation from a flat box function is the result of the truncation of the sinc pulse. It should be noted that the phase of the resonances is not constant across the excitation profile. Sinc pulses are not frequently used for selective excitation because of the phase problem and the fact that very long, minimally truncated pulses must be used. A frequently used alternative to the sinc pulse for selective excitation is the Gaussian shaped pulse. The Fourier transform of a Gaussian is a Gaussian and one therefore will obtain a narrow Gaussian shaped excitation profile when a long low power Gaussian shaped pulse is used. This is shown in the top trace of the figure below. This trace is similar to the bottom trace except a 20 msec Gaussian shaped pulse (with truncation at 1 % of the total height) was used rather than a 200 msec sinc pulse. Although the excitation is not flat, the phase is constant across the excitation profile and the total duration of the pulse is 10 times shorter than the sinc pulse.

First-Order Phase Errors

The phase of a signal in an NMR spectrum is described here and is determined by the axis on which the magnetization vector resides after the observe pulse relative to the receiver. The phase of the spectrum is typically corrected such that the peak in the real spectrum is entirely in absorption mode while that in the imaginary spectrum is entirely in dispersion mode. The correction in phase is referred to as the zero-order phase correction. A zero-order phase correction applies to all peaks in the spectrum regardless of their offset, Ω, from resonance. There are also first-order phase errors where the phase error for a resonance is linearly dependant on Ω and the duration of the pulse, t_p. The further a peak is away from the center of the spectrum for a given pulse duration, the larger the first-order phase error. Similarly, the longer the duration of the pulse for a peak of given offset, the larger the first-order phase error. These errors arise from the fact that a 90° pulse of fixed duration is only a true 90° pulse for a peak on-resonance. For off-resonance peaks, the pulse will not only be slightly less than 90° but also produce a small amount of magnetization along the axis of the pulse. For example, a 90°_x pulse applied to an equilibrium magnetization vector will produce only –y magnetization for an on-resonance signal but for an off-resonance signal, it will also leave a small amount of residual z magnetization as well as produce some x magnetization. It is the x magnetization that gives rise to the first order phase error. The effect of the pulse duration for a peak of given offset frequency is demonstrated in the figure below. The sample was a mixture of chloroform and acetone. The transmitter was set such that the chloroform signal was on-resonance. Six 90° pulses were calibrated at different power levels based on the on-resonance chloroform signal, ranging from 10 µsec in the lower trace to 320 µsec in the upper trace. For all spectra, the same zero-order phase correction was applied such that the chloroform signal was in-phase. No first-order phase correction was applied. One can see that the phase error in the off-resonance acetone signal increases as a function of the pulse duration. It should also be noted that the overall intensity of the acetone signal decreases with respect to the chloroform signal as a function of the pulse duration due to the width of the excitation profile decreasing as a function of the pulse duration.

Agilent's MR BLOG - SPINSIGHTS

Recently Agilent Technologies has started a MR BLOG called "SPINSIGHTS". The posts to this BLOG are written by Agilent employees and discuss the advances of Agilent's MR products as well as educational posts on both MRI and NMR spectroscopy. It is a very interesting read and promises to be a very useful resource. Thanks Agilent - keep it up!

"The MRI Photocopier"

A very interesting note* has recently been published in Concepts in Magnetic Resonance Part A by Joseph Hornak (generous provider of the two excellent free online text books, The Basics of NMR and The Basics of MRI ). In this work, it is demonstrated that an MRI scanner can be used to reproduce an image of printed text. The technique is based on the fact that the toner used to print text contains ferromagnetic particles and when placed in the uniform magnetic field of an MRI magnet, the magnetic field near the ferromagnetic toner is distorted. The "sample" is prepared by placing the printed page face up on a polycarbonate plate and covering it with a very thin sheet of polyethylene. The polyethylene is covered with water (doped with CuSO4 as a relaxation agent). The "sample" is placed in the magnet such that the plane of the page is perpendicular to the magnetic field. The text is "scanned" by taking a 2D proton MR image of a slice of the water near the surface of the polyethylene. The distortion in the magnetic field due to the ferromagnetic toner renders the text visible in the 2D magnetic resonance image. This is demonstrated in the figure below (from the reference) where a 2.5 mm thick slice above the polyethylene was imaged. The text was printed in #36 Arial font. The author speculates that this technique may be applied to the analysis of paintings.

* Joseph P. Hornak, "Magnetic Resonance Imaging of Printed Text", Concepts in Magnetic Resonance Part A. 36A, 347 (2010).

Sample Slice Selection in NMR Spectroscopy

In MRI, field gradients are used routinely for slice selection while imaging a sample. Gradients are also finding applications in high resolution NMR spectroscopy employing fast data collection techniques using parallel data acquisition for multiple slices of the same sample. A good example of this can be found in Carlos' BLOG (and the references therein). The slice selection is accomplished by turning on a linear field gradient across the sample while applying an excitation pulse. While the gradient is on, the frequencies of each of the NMR resonances is spread out according to length of the sample and the strength of the field gradient across the sample. A particular individual slice of the sample can be selected by either modifying the strength of the gradient while using a semi-selective pulse of a given excitation frequency or by modifying the offset frequency of the semi-selective pulse for a constant gradient strength. Both the gradient strength and the excitation profile of the pulse determine the thickness of the slice selected. When the gradient is turned off and the receiver turned on, the FID representing only the spectrum of the selected slice of the sample is collected. An educational example is shown in the figure below. A sample of toluene and H₂O/D₂O was prepared. As these two liquids are immiscible, the sample is layered with the less dense toluene on top and the more dense water on the bottom. The bottom trace in the figure shows a conventional ¹H NMR spectrum. Since the pulse used to collect the spectrum was a hard 90° pulse with a wide excitation profile, one can see both the toluene and the water in the spectrum. For the middle and upper traces, a field gradient of 48 G/cm was turned on while a 100 µs 90° Gaussian excitation pulse was applied. The only difference between the middle and upper traces is the offset frequency used in the excitation pulse. The middle trace represents the spectrum of a slice of the water in the bottom layer of the sample and the upper trace represents the spectrum of a slice of the toluene in the top layer of the sample.

NMR and Candy Canes

The Phase of an NMR Spectrum

Most students know that the phase of an NMR spectrum has to do with the degree to which the NMR resonances are above or below the baseline of the spectrum (i.e. the amount of absorption and dispersion character). Most students have also learned that the phase of a periodic time domain function depends only on the value of the function at time zero. Thus, the only difference between a cosine and a sine function is where the function starts at time zero. A sine is said to be 90° out of phase with respect to a cosine. Many students do not understand the connection between the phase of their NMR spectrum and the phase of the periodic time domain function giving rise to their spectrum by way of a Fourier transform. The figure below is an attempt to make the connection. The left-hand portion of the figure shows equilibrium magnetization vectors being rotated by radio frequency pulses. 90° pulses along the x, y, -x and -y axes rotate the z magnetization vector to the -y, x, y and -x axes of the rotating frame, respectively according to the right-hand screw rule. After the pulse, the magnetization vector rotates in the rotating frame of reference at a frequency equal to the difference between the transmitter frequency and the frequency of the NMR resonance. In the figure, the magnetization is assumed to be rotating anti-clockwise representing an NMR resonance with a positive frequency with respect to the transmitter frequency. The NMR spectrometer measures the time dependent voltages on two of the four orthogonal axes of the rotating frame separated by 90° (quadrature detection). The time dependent voltages are proportional to the amount of magnetization on the axis as a function of time. One of the two time dependent voltages is called the "real" signal and the other is called the "imaginary" signal. Together these two signals make up the complex free induction decay (FID) which is Fourier transformed to produce the NMR spectrum. In the figure, the -y(t) voltage is the real FID and the x(t) voltage is the imaginary FID. The figure shows representations of the real and imaginary FIDs after the delivery of pulses along each of the orthogonal axes. Note that the phases of the real and imaginary FIDs depend on the pulse delivered. For example, after a 90°_x pulse, the magnetization resides on the -y axis. The real FID (along the -y axis) starts at a maximum (cosine) and the imaginary FID (along the x axis) starts at zero (sine) and increases as the magnetization vector rotates anti-clockwise. The Fourier transform of the complex FID produces a real spectrum (typically the one displayed to the user) and an imaginary spectrum (typically not displayed to the user). Note that the degree of absorption vs. dispersion character in the spectrum depends on the phase of the FID signals. If an NMR spectrum is not in phase, perhaps due to a receiver dead time problem, it can be corrected after the collection of the data by calculating the phase angles needed to put the real spectrum enitirely in absorption mode and the imaginary spectrum entirely in dispersion mode.

New Bench Top 1H NMR Spectrometer

A very interesting product has just been put on the market from a company called picoSpin. - a 7 lb bench top 45 MHz ¹H NMR spectrometer at a very tempting price. From the information available on their website (including a YouTube video), it looks as if this instrument would be an excellent teaching tool in a university laboratory.








This is not meant as a product endorsement.

NMR and Food Chemistry - Coffee

Many of us enjoy a hot delicious cup of coffee. Many (not including myself) will even spend a great deal of money and a great deal of their time in a long queue to get it! The coffee snobs will preach about the differences between a freshly brewed cup of java and the lowly cup of instant coffee. Is there really a difference? Spectrum A in the figure below shows the ¹³C CPMAS NMR spectrum of ground coffee. Among other things, the spectrum consists of resonances from the woody fibers, polysaccharide gums, tannins, alkaloids and aromatic oils. Spectrum B is the spectrum of used coffee grounds which were subsequently dried. The spectrum is due to the woody fibers and other insoluble material. Spectrum C is the difference between spectrum A and B and represents all the "goodness" of a fresh brewed cup of coffee. Among other things, it represents all of the alkaloids, tannins and aromatic oils. Spectrum D is the ¹³C CPMAS NMR spectrum of instant coffee which is manufactured by freeze drying brewed coffee. The spectrum is very similar to the difference spectrum, C. This indicates either that the difference between a freshly brewed cup of coffee and a cup of instant coffee lies in very low concentration constituents or that the coffee snobs are wasting their money and time in long queues. I think both are true.

13C NMR of "Perdeuterated" Solvents

When one acquires a ¹³C NMR spectrum of a sample, the deuterated solvent is observed with resonances characterized by the J coupling pattern of the deuterons attached to the carbon atoms. (CD = 1:1:1 triplet, CD₂ = 1:2:3:2:1 quintet, CD₃ = 1:3:6:7:6:3:1 septet). Often, however; small peaks are observed near the main solvent resonances. These are due to other isotopomers of the solvent. An example of this is shown in the bottom spectrum of the figure below for the high frequency resonance of "THF-d₈". The spectrum consists mainly of the expected 1:2:3:2:1 quintet however, there is a small peak present on the high frequency side of the quintet marked by the arrow. It is due to one of the components of the C1 resonance from THF-1,2,2,3,3,4,4-d₇. The supplier of the solvent claims that the isotopic purity is 99.5 atom % D. If the deuteration is uniform, approximately 0.5 % of the molecules will contain a single proton. Half of these molecules will be mono-protonated on the high frequency carbons. If a DEPT spectrum is acquired on the same sample, the non-protonated carbons are suppressed leaving only the mono-protonated carbons. This is shown in the top spectrum of the figure, which shows a 1:1:1 triplet from CHD. The isotope shift between CHD and CD₂ is 0.354 ppm. Other examples can be found here and here.