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.

Deuterium Decoupling

Bruker NMR spectrometers equipped with a ²H TX board and ²H amplifier can be setup to carry out ²H observation and decoupling experiments while still maintaining a ²H lock. Two channel systems can use the ²H transmitter for ²H, ¹H[²H], ²H[¹H] and X[²H] measurements. In addition to these, a three channel system can be set up for X[²H, ¹H] measurements. The first figure below shows the ¹³C and ¹³C[²H] spectra collected for a mixture of deuterated solvents using two channels of an AVANCE spectrometer. The second figure shows the ¹³C, ¹³C[¹H], ¹³C[²H] and ¹³C[¹H, ²H] spectra for the standard ¹³C sensitivity sample (40% para-dioxane and 60% deuterobenzene) collected on a three channel Bruker AVANCE spectrometer.

HSQC - TOCSY

There are many different NMR techniques used to probe molecular structure. Two very useful methods are the HSQC (or HMQC) sequence used to obtain heteronuclear coupling correlations and the TOCSY sequence used to look at extended homonuclear coupling correlations. These are among the most widely used pulse sequences by chemists to help elucidate the molecular structure of organic molecules. The sequences can also be combined into a single HSQC-TOCSY sequence which is simply an HSQC followed by a TOCSY spin lock. For the case of ¹H and ¹³C in organic molecules, the HSQC-TOCSY spectrum provides ¹H TOCSY subspectra of the isolated spin systems in the rows at each of the ¹³C frequencies. Overlap of ¹H resonances which may have appeared in a simple ¹H TOCSY spectrum can be resolved in the HSQC-TOCSY spectrum provided there is enough shift dispersion in the ¹³C spectrum. An example of this is shown in the figure below. The top panel shows the HSQC-TOCSY spectrum for 3-heptanone collected on a 300 MHz instrument. One can see the two spin systems on either side of the carbonyl group, color coded in yellow and pink. The second panel shows an expansion of the region within the red square of the first panel. Here we can separate the overlapping quartet and triplet for the methylene protons on either side of the carbonyl group.

Temperature Calibration - An Alternative Method

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

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

Solid State NMR of Half Integer Quadrupolar Nuclei

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

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

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

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

Heat Dissipation in Bruker AVANCE Spectrometers

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

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

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

19F - 13C HMQC

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

E.COSY and the Relative Signs of Coupling Constants

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

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

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

Job Opening: NMR Technician, University of Ottawa

The Faculty of Science of the University of Ottawa is seeking a technician for its very active Nuclear Magnetic Resonance (NMR) facility. This rapidly growing NMR facility serves more than 25 active research groups and consists of 7 NMR instruments ranging in field from 200 to 500 MHz. The facility conducts a wide range of modern NMR experiments on both solids and liquids as well as MRI. As the NMR technician, you must hold at least a B.Sc. degree in chemistry or a related field (M.Sc. preferred) with at least two years experience in either one or both high resolution or solid state NMR spectroscopy. You must be enthusiastic, highly motivated and work well both independently and in groups. Extensive computer experience is mandatory. As you will be interacting daily with students and faculty, you must have excellent interpersonal skills as well as excellent oral and written communication skills. Reporting to the NMR facility manager, you will collect routine NMR data as a service, assist students and answer questions, train new users of the equipment, help with equipment maintenance (including cryogen fills), maintain a data archive, keep accurate time and usage records, and assist the NMR facility manager in the general operation of the facility. French/ English bilingualism is a definite asset. The position is open for one year starting August 15, 2010 and will be renewable, availability of funds permitting. The annual salary range for this position is $38,862 - $51,504. For consideration, please email your CV and cover letter to the Human Resources Service mycareer@uottawa.ca and refer to competition number TSCI9583NEP. Please also have three letters of recommendation emailed or sent to:

Dr. Glenn A. Facey
NMR Facility Manager,
Department of Chemistry, University of Ottawa
10 Marie Curie, Ottawa, Ontario, K1N 6N5
CANADA
ph. (613) 562-5800 ext 6077
fax. (613) 562-5170
email. gafacey@uottawa.ca

The deadline for applications is Friday June 25 at 5:00 pm.

More information is available at the following web site:

http://www.hr.uottawa.ca/careers/support/competition/cont/sci/TSCI9583NEP.php

Retrieving Empty Spinners From Magnets

Despite my best efforts in teaching students how to properly use NMR spectrometers, invariably a new user will, on occasion, drop a sample spinner into a magnet without a sample. This is usually done in our undergraduate laboratory by inexperienced students who have finished collecting their data and feel a need to return the empty spinner to the magnet. The problem is that ejecting the empty spinner with the eject air is not possible as the air passes through the spinner. In the past I have removed empty rotors from magnets on Varian spectrometers by removing the upper barrel of the magnet. On Bruker spectrometers, I have removed the probe and inserted a semi-rigid NONMAGNETIC plastic hose in the bottom of the magnet and pushed the spinner to the top of the upper barrel where it can be removed by a helper. In either case, the entire operation took between 5 minutes (Varian) and 30 minutes (Bruker) depending on how much reshimming was required. To avoid this tedious chore, I had our machine shop make a plastic tool for empty rotor removal shown below.

This tool consists of a pole with a diameter slightly less than that of the spinner. On the end of the pole is a tapered prong with a diameter of 4 mm at the tip and 6 mm at the base. This tool is inserted in the top of the magnet and gently lowered until the prong gets wedged into the empty spinner. The spinner is removed with the tool. The entire operation takes less than 10 seconds and no reshimming is required.

Gradient Spin Echoes for Selective Excitation

Shaped excitation pulses can replace the non-selective hard pulses typically used in a one-pulse measurement to achieve selective excitation. Another method of achieving selective excitation is the gradient spin echo using a selective 180° pulse. This technique is demonstrated in the figure below. A non-selective hard 90°_x pulse is first given followed by a pair of identical pulsed field gradients sandwiching a soft selective 180° pulse about the y axis. The hard 90° pulse rotates all spin vectors onto the -y axis. During the first gradient pulse the spin vectors dephase and evolve according to their offset frequencies. The soft 180°_y pulse flips a single resonance 180° about the y axis leaving all other resonances untouched. During the second gradient pulse, the "selected" resonance is rephased and its offset frequency evolution is refocused. The unselected resonances dephase more and continue to evolve according to their offset frequencies. The receiver is then turned on to collect the FID of the "selected" resonance, all others are dephased and therefore suppressed. This is demonstrated in the figure below which shows ¹H NMR spectra for a mixture of methylence chloride and acetone. The bottom trace shows a standard one-pulse measurement. The middle and top traces show results from a selective gradient spin echo measurement with the selective 180° pulse set for methylene chloride and acetone, respectively.

Background Suppression in Liquids

High resolution NMR probes for liquids may contain parts near the coil consiting of the nuclei being observed. The parts give rise to background signals which can severely affect the NMR data. When observing¹¹B, there is a background signal from boron containing parts near the coil and also the borosilicate glass in the NMR tube containing the sample.

Cory and Ritchey* introduced a very simple, clever method to suppress background signals in 1988. Their method uses a composite pulse, consisting of a 90° and two 180° pulses with appropriate phase cycling, in place of a conventional 90° pulse. The phase cycled composite pulse is essentially a 90° pulse for all spins inside the coil and 0° for all spins outside of the coil. An example of its implementation is shown in the figure below. The bottom traces show the ¹¹B [¹H] NMR spectra for a dilute sample of NaBH₄ and a "real" synthetic sample on the left and right, respectively. One can see an enormous background signal from both the NMR probe and the NMR tube. In the case of the "real" synthetic sample, the information from the spectrum is difficult or impossible to recover. The top traces show similar spectra acquired using the composite pulse. The only background signal remaining is that from the portion of the NMR tube inside the coil. This pulse sequence (without proton decoupling) is in the Bruker pulse program library called "zgbs". It is not exclusive to ¹¹B.

D.G. Cory and W.M. Ritchey. Journal of Magnetic Resonance, 80, 128 (1988).

Hahn Echo for 11B Background Suppression in Solids

Solids NMR probes often contain boron rich parts near the coil in which the sample resides. Boron nitride, in particular, is a material very commonly used. This can be very problematic if one wishes to collect ¹¹B NMR data, in that a strong background signal may be observed. Even though these parts are not directly inside the coil with the sample, they do experience a small amount of rf from the coil and the coil does detect a ¹¹B NMR signal from them. One simple way to avoid this problem is to use a Hahn echo to observe the ¹¹B spectrum. Unlike the sample inside the coil, which experiences the 90° and 180° pulses required for the Hahn echo, the boron rich parts outside of the coil experience pulses of much smaller flip angles and therefore the echo signal from them is much reduced. This is illustrated in the figure below, which shows ¹¹B NMR spectra collected in a 4 mm MAS probe without magic angle spinning. In the lower trace a simple one-pulse measurement was made with high power ¹H decoupling. The spectrum contains a very large background signal and it is very difficult to extract any useful information from the data. The spectrum in the upper trace was collected with a Hahn echo with high power ¹H decoupling during the acquisition. The background signal is completely removed revealing a beautiful, information-rich line shape for the central transition resulting from the second order quadrupolar and chemical shielding anisotropy interactions.

Thank you to Joseph Weiss of David Bryce's laboratory for providing the sample and collecting the data. See more of Joseph's beautiful ¹¹B spectra here:

Joseph W.E. Weiss and David L. Bryce J. Phys. Chem. 114 (2010) ASAP.
http://dx.doi.org/10.1021/jp101416k

Dummy Scans

Dummy scans (DS, Bruker) or steady state scans (SS, Varian) are scans taken in an NMR acquisition before the receiver is turned on and data are collected. Each dummy scan contains all of the rf pulses, delays and gradients used in the pulse program; the only difference is that the receiver is not turned on to collect data. Dummy scans are typically used to ensure that a spin system is in a steady state before data are collected. For example, One may collect a spectrum using a relaxation delay short with respect to the T₁'s of some of the resonances in the spectrum. The first scan may find the system at equilibrium, as the sample may have sat in the magnet for a few minutes while the probe was being tuned and matched or the magnet was being shimmed. The second and subsequent scans will find the system not at equilibrium, as the system has been perturbed by the rf pulses of the preceding scan(s) and not allowed to fully relax. The data from the first and seccond scan are therefore not the same. After several scans, although not at equilibrium, the system will be in a steady state before each additional scan and therefore each subsequent scan will collect similar data. An example of the use of dummy scans is shown in the figure below. The bottom trace shows a single scan ¹³C NMR spectrum of a concentrated solution of menthol in CDCl3 after the sample had sat in the magnet for a minute or so. The top trace shows a similar single scan acquisition preceded by 16 dummy scans. The relaxation delay was set to 1 second and the acquisition time for the FID was 1 second. 90° pulses were used in both spectra. One can see that some of the resonances in the top spectrum are attenuated in comparison to the bottom spectrum. The ¹³C signal from the CDCl₃ (which has a long T₁) is missing in the spectrum acquired with dummy scans. The dummy scans have selectively presaturated the solvent.

Household Dust (Bunnies)

Many people will be celebrating Easter this coming weekend. Children will be searching for Easter eggs left by the Easter Bunny. A word of caution though: Not all bunnies are cute!

Household dust bunnies seem to magically reproduce and grow. They must be collected regularly either with a broom or a vacuum cleaner and disposed of. What exactly is household dust? A bit of internet searching reveals that household dust is composed largely of fibers from clothing, dead human skin and the bodies of dust mites - a very disgusting mixture indeed. The top trace in the figure below is the ¹³C CPMAS NMR spectrum of a sample of household dust. The middle trace is a similar spectrum of clothing fibers from a sample of dryer lint. The difference spectrum (in the bottom trace) is consistent with a complex mixture of proteins and largely represents the spectrum of dead human skin and the bodies of dust mites.

Free and Inexpensive NMR Processing Software for Students

Processing NMR data has just become more affordable for students. Our friends at Advanced Chemistry Development have recently decided to make their NMR processing software free of charge to academics. As a student, you can put this software on your personal laptop or PC and process your NMR data at home or anywhere your travels take you. You can register and download the software here. They have even started a BLOG dealing with use of the software. I think I speak for all students when I say "Thanks guys!!"

Also, our friends at Bruker Biospin have recently introduced an inexpensive personal student license for their TOPSPIN software which can be purchased online.
There are other excellent NMR processing software options available. I mention specifically those above as the University of Ottawa currently holds network licenses for them and our students are most familiar with them.

Watergate vs Presaturation

Biochemists and protein chemists are often interested in observing the NH protons in their samples. Since the NH protons usually undergo slow chemical exchange with water, it is desirable to run the samples in H₂O rather than D₂O so the NH protons will not exchange with the deuterium in the solvent which would make them invisible in the ¹H NMR spectrum. In practice, a mixture of 10% D₂O and 90% H₂O is used as a solvent so that a deuterium lock can be established and used while running the spectrum. The very high concentration of water compared to the very low concentration of solute necessitates the use of solvent suppression methods.

Both presaturation and WATERGATE are efficient techniques used to suppress strong water signals from proton NMR spectra, however, there are differences between the two methods of which the user must be aware. Presaturation employs a selective, long, low power pulse to saturate the water resonance. This pulse is usually several seconds in duration during which exchange can occur between the unsaturated NH protons and the saturated water protons. If this exchange occurs, the NH protons become partially saturated to an extent related to the rate of chemical exchange between the NH and the water. The intensity of the NH protons in the spectrum is non-quantitative. WATERGATE, on the other hand, uses a pair of gradients surrounding a composite pulse which in effect inverts all but the water signal. The duration of the composite pulse is about 4 orders of magnitude shorter than a presaturation pulse, so exchange between the NH protons and the solvent occurs to a much lesser extent during the WATERGATE sequence compared to presaturation. As a result, the NH region is much less attenuated and more quantitative in a spectrum collected using WATERGATE compared to a similar spectrum run with presaturation. This is illustrated in the figure below which shows the NH region of the ¹H spectrum of a small disaccharide substituted peptide.One can see that some of the NH's are greatly attenuated in the spectrum acquired with presaturation compared to the spectrum run using WATERGATE. The more attenuated the signal, the faster the chemical exchange for that particular NH with water.

The WATERGATE suppression sequence is very similar to the gradient spin echo sequences used to measure diffusion constants and DOSY spectra. As a result, when WATERGATE suppression is used, one expects diffusion losses for small molecules (which diffuse quickly) compared to large molecules (which diffuse slowly). This effect is demonstrated in the figure below which shows the NH/aromatic region of the ¹H spectrum of a partially degraded ¹⁵N labelled 10 kDa protein.Here, one can see the same exchange losses pointed out in the previous figure for the presaturation spectrum compared to the WATERGATE spectrum. In addition, one can see that the intensity of a very sharp peak marked in yellow (likely due to a CH proton from free histidine) is less intense in the WATERGATE spectrum compared to the presaturation spectrum. This loss is due to the fast diffusion of the small free amino acid compared to the very large protein. In conclusion, one must be aware of the differences between the two solvent suppression methods if quantitative results are being sought.

I would like to thank Roger Tam from Robert Ben's Laboratory and Allison Sherratt from Natalie Goto's Laboratory for kindly providing the samples of the peptide and protein, respectively.

Fast 90 Degree Pulse Determination

Almost all NMR measurements rely on the correct calibration of 90° pulses. This is traditionally done by collecting a series of spectra as a function of pulse duration, finding a null for the 180° or 360° pulse and calculating the 90° pulse by simple division by 2 or 4 in the case of the 180° and 360° nulls, respectively. This determination, although trivial, can be very time consuming. Wu and Otting* have presented a much faster method of determining a 90° pulse based on measuring the nutation of a magnetization vector directly. Continuous nutation is depicted in the figure below. Here, the sample is subjected to continuous irradiation about the x axis. While being irradiated, the magnetization vector rotates in the z-y plane at a nutation frequency proportional to the pulse power. The magnetization on the -y axis is defined by a sine function. Fourier transformation of this magnetization gives an antiphase doublet centered at zero whose splitting Δν is twice the nutation frequency. The reciprocal of the nutation frequency is the time it takes the magnetization vector to rotate one complete cycle in the z-y plane and therefore the time it takes to rotate by one quarter of a cycle (i.e. the 90° pulse duration) is defined as 1/(2 Δν). The problem with continuous irradiation is that the sample must be irradiated at the same time magnetization is being detected. To eliminate this problem, a scheme similar to homonuclear decoupling is used where the radiation is turned off long enough to sample a data point. This is depicted in the figure below.Here each dwell period is divided up into a period for irradiation and a period for detection. The duty cycle for the irradiation is the fraction of time for which the sample is being irradiated. The magnetization is sampled when the power is off. As in the case for continuous irradiation, the magnetization vector still rotates in the z-y plane however, the rotation is slower as it is scaled according to the duty cycle. The duration of the 90° pulse is d/(2 Δν), where d is the duty cycle for irradiation. An example of this is shown in the figure below. The nutation spectrum was measured for HDO using a duty cycle, d = 0.10 and a power level of 12 dB (Bruker). Since the response of the amplifiers is linear, the 90° pulses at higher power levels can be calculated. Each decrease by 6 dB cuts the duration of the 90° pulse in half. In this case the 90° pulse at 0 dB was calculated to be 10.93 µsec at 0 dB based on the measured 90° pulse of 43.71 µsec at 12 dB. This pulse agrees to within a couple of percent of that measured by the more traditional method however, the measurement took only a few seconds. You can use a program called "pulsecal" on newer Bruker spectrometers to do this in complete automation.

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* Peter S.C. Wu and Gottfried Otting J. Mag. Res. 176, 115 (2005).

Faster Relaxation Time Measurements in Solids

T₁ relaxation times are typically measured with the inversion recovery technique. In this method the magnetization is inverted and its recovery is monitored as a function of time. For nuclei with long T₁'s, the measurements are very time consuming as a recycle delay of at least five times T₁ must be used between scans. Typical T₁'s for ¹³C in the solid state range from several seconds to tens of minutes, so their direct measurement via the inversion recovery method could be prohibitively long.

High resolution ¹³C solid state NMR spectra of solids are routinely measured with cross polarization and magic angle spinning (CPMAS) in order to take advantage of the signal enhancement due to magnetization transfer between the abundant protons and isotopically dilute ¹³C nuclei. Additionally, the recycle delay needed for this measurement depends on the T_1ρ of the protons rather than the T₁ of the ¹³C. Proton T_1ρ's are typically shorter than ¹³C T₁'s by at least an order of magnitude, so many more scans can be collected per unit data collection time compared to a direct one-pulse measurement.

One might think that ¹³C T₁'s can simply be measured with cross polarization using a simple inversion recovery scheme by applying a 90° pulse to the ¹³C spins immediately following the contact pulse and then following their recovery over time. This method would have both the advantages of signal enhancement due to CP and more scans per unit time. The problem however, is that the enhanced magnetization of the inverted spins relaxes back to its unenhanced Boltzmann value and not its enhanced value. So, in order to measure the T₁, the direct ¹³C magnetization would have to be measured first (without CP) which would be very time consuming. This difficulty can be eliminated with the pulse sequence introduced by Torchia in 1978^* shown in the figure below.
This sequence uses a simple two step phase cycle to subtract out the effect of the direct ¹³C Boltzmann magnetization. The first part of the sequence uses a (90°_-y) pulse to return the CP enhanced magnetization to the z axis. The decay of the enhanced magnetization down to its Boltzmann value is followed using a (90°_x) pulse with detection of signals on the -y axis. The second part of the sequence uses a (90°_y) pulse to put the CP enhanced magnetization on the -z axis. The recovery of the enhanced inverted magnetization back to its equilibrium Boltzmann value is followed using a (90°_x) pulse with detection of signals on the y axis. The addition of the first and second parts of the experiment by way of the phase cycle allows for a simple calculation of the ¹³C T₁ with both the advantages of CP enhancement and the ability to collect more scans per unit time. An illustration of this method is shown in the figure below where the ¹³C T₁'s of glycine were measured. (The small peak in the spectrum is a spinning sideband of the carbonyl carbon)

* D.A. Torchia, J. Mag. Res. 30, 613, (1978).

NMR WIKI

An excellent resource for NMR users has been gaining more and more popularity on the web over the last few years. The brainchild of Evgeny Fadeev (Director of the Biomolecular Spectroscopy Facility at the University of California Irvine), NMR Wiki is an information sharing site offering a question and answer forum, job postings, a pulse sequence library, course material, history, information on meetings etc.... I think this is a fantastic place to learn more about NMR and Evgeny is to be commended for his efforts.

The Scale on an NMR Spectrum

Some people new to NMR spectroscopy have trouble with the meaning on the scales of their NMR spectra. Usually the data are plotted with a chemical shift scale (δ). This scale increases to the left and is usually reported in units of parts per million (ppm). The chemical shift of a resonance in a sample, δ_sample , in ppm is defined as follows:where ν_sample is the absolute frequency of the sample resonance and ν_reference is the absolute frequency of an agreed upon reference compound. For ¹H, ¹³C and ²⁹Si NMR, tetramethylsilane (TMS) is the agreed upon reference standard. When the scale is plotted in this manner, the peak positions are relative to that of the standard compound. This scale is particularly useful, as it independent of a single absolute frequency and therefore does not depend on the magnetic field strength, which varies from laboratory to laboratory. Spectra recorded using magnets of unequal field strength can be compared more easily.

Scales are also plotted in frequency units (Hz), usually with the reference compound assigned a value of 0 Hz. This scale also increases to the left and is usually of use when coupling constants (which are independent of field) are being measured.

Although absolute electronic shielding values are inconvenient to measure, one may hear people refer to one resonance being "more shielded" or "less shielded" than another, The shielding constant, σ, for a particular nucleus in a particular environment can be expressed by rearranging the Larmor equation.The shielding scale increases to the right.

In the age of continuous wave NMR spectrometers, NMR spectra were measured by irradiating the sample with continuous wave radiation and sweeping the magnetic field from a low value (on the left) to a high value (on the right). The scales were sometimes plotted in magnetic field units and one still hears about one peak being described as "upfield" or "downfield" from another. These terms have little relevance in FT NMR and should be avoided.

Some of the older literature reported ¹H NMR peak positions on a τ scale. Here, τ was equal to (10 ppm - δ ) and the scale increased to the right. This is no longer in use and has caused considerable confusion. It should be avoided.

The Dephasing Power of Pulsed Field Gradients

Pulsed field gradients are used in many modern NMR measurements to select specific coherence pathways and eliminate (or at least minimize) the need for time consuming pulse and receiver phase cycles. The gradients are most often used in conjunction with spin echos such that unwanted coherences can be dephased and the desired coherences can be rephased. They are also used to measure diffusion constants or collect DOSY data. It is instructive to examine the magnetization vectors in the active volume of an NMR tube as a function of the gradient strength after the delivery of a 90° pulse. While a gradient is applied, the magnetization vectors precess at frequencies in the rotating frame which depend on their position in the NMR tube along the axis of the gradient. When the gradient is turned off, all of the magnetization vectors again precess at the same frequency however the phases of the vectors remain as they were at the end of the gradient. The top part of the first figure shows a series of 6 cases where z gradients of increasing strength are delivered after a 90°_-x pulse. Each case shows 8 equally spaced slices of the NMR tube on the z axis (the center of the sample is between the 4th and 5th slices). The stronger the gradient the larger the dephasing angle between slices. In this figure, the receiver is assumed to be on the y axis. From left to right, the number of degrees of dephasing between slices are 0° (no gradient), 22.5°, 45°, 67.5°, 90° and 112.5°. The y components of all the vectors are added and the sum is shown in blue below. One can see the the y magnetization decreases and oscillates about zero as a function of the gradient strength. This is illustrated more clearly in the bottom part of the figure which shows a plot of y magnetization as a function of gradient strength for a numerical calculation done using 50 slices. The second figure demonstrates this experimentally. It shows the 500 MHz ¹H NMR spectrum of HDO using the pulse sequence shown in the figure as a function of the % gradient strength (100% ~ 0.5 T/m). The gradient pulses were 1 msec in duration and rectangular in shape. One can see that the intensity profile matches closely to that predicted in the bottom of the first figure. The sample is almost entirely dephased using only 2% of the maximum gradient strength.

iPods and Fourier Transforms

The way people collect and listen to music has changed drastically over the last several years. One's entire music collection, which once occupied several shelves in the living room, can now fit in the palm of one's hand and can be listened to virtually anywhere. The iPod / mp3 technology is also being used to change the way we can learn. Many, if not all of us, have spent tens of thousands of dollars to educate ourselves. If you are like me, there were courses in university you would have liked to take but did not have the time. Now, many universities have made their courses available free of charge online through iTunes University. Now, one can audit all of those expensive university courses for free through their iPod Touch or iPhone on the bus or train on the way to work. One excellent course I have been auditing is one called The Fourier Transform and its Applications, given by Brad Osgood of Stanford University's School of Engineering. As NMR spectroscopists, we use the Fourier Transform daily. This course covers many of the mathematical details not learned in NMR courses and explores many applications (other than NMR spectroscopy) where Fourier Transforms are useful. I highly recommend it and I hope that many more universities make their course material public.I regret to say that Bob Dylan is temporarily taking a back seat on my daily commute to work. Sorry Bob!

Presaturation

One of the simplest and widely used ways to eliminate a strong water signal is to use presaturation. In this technique, the transmitter is set to the water resonance. a very long (seconds) low power (mW) pulse is given. The excitation profile of this pulse is very narrow due to its length and it saturates the water resonance at the transmitter frequency. A non-selective hard 90° pulse (with a wide excitation profile) is then given to place all remaining spins in the transverse plane for detection. An example of this is shown in the figure below. The top trace is a standard 500 MHz ¹H NMR spectrum of phenylalanine in 90% H₂O / 10% D₂O. The resonance due to the water is huge and off-scale in the figure. The bottom trace is the same sample run with presatutation.

WATERGATE

WATER suppression by GrAdient Tailored Excitation (WATERGATE) is a clever technique used to suppress the water signal in an aqueous sample. It is widely used in many complicated pulse sequences. Unlike presaturation which irradiates the water resonance with a long low power pulse, this method is based on the gradient spin echo technique used also to measure diffusion constants and DOSY spectra. The pulse sequence is shown here:The transmitter frequency is set on the water resonance. A non-selective hard 90° pulse is applied followed by a 1 -2 msec gradient pulse. The gradient pulse dephases all of the resonances. A composite pulse (consisting of 6 hard pulses seperated by a delay, τ) is then applied which acts as a 180° pulse for everything except peaks on resonance (i.e. water) and any peaks at frequencies n/τ away from the transmitter, where n is an integer. τ is chosen such that 1/τ lies outside of the spectral width (typically several hundred µsec). The second gradient pulse (equal in magnitude, duration and sign, to the first) further dephases the water resonance at the center of the spectrum which was unaffected by the composite pulse but rephases everything else which was inverted by the composite pulse. The gradients and composite pulse act as a gradient spin echo for all but the water. The FID is then collected with the water resonance suppressed by the two dephasing gradients. An example of the application of WATERGATE is shown in the figure below. The top trace shows a standard 500 MHz ¹H NMR spectrum of phenylalanine in H₂O / D₂O scaled to the water peak. The resonances of the phenylalanine are not visible on this scale. The middle trace is the same spectrum as the top trace with the phenylalanine resonances on scale. The huge water resonance is truncated. The bottom trace shows the WATERGATE spectrum. The water signal is greatly suppressed.

CPMG to Enhance Sharp Lines

The Carr - Purcell - Meiboom - Gill (CPMG) sequence is used to measure T₂ relaxation times and more recently has made an impact in measuring the line shapes of very broad solid lines by breaking them up into spikelet patterns which mimic the static line shape. The very simple pulse sequence is shown here:During the (D2 - π -D2)_n period the intensity of lines with short T₂ (broad lines) diminishes much more quickly than that for lines with long T₂ (sharp lines). The CPMG sequence is therefore useful for enhancing the sharp features in a spectrum by suppressing the broad features. This is demonstrated in the figure below. The top panel of the figure shows a portion of a conventional 500 MHz ¹H NMR spectrum of a polymer sample contaminated with small amounts of smaller molecules. The broad lines (truncated in the figure) are due to the polymer whereas the much smaller sharp lines are due to the impurities. The bottom panel of the figure shows the CPMG spectrum of the same sample with D2 = 4 msec and n = 32. One can see that the broad polymer lines are greatly suppressed and the smaller sharp lines are much more obvious.

Pulse Power Expressed in Hz

On several occasions I have been asked what it means when a power level for a pulse is expressed in frequency units (e.g. "The proton decoupling power was 75 kHz"). The frequency here is the precession frequency about the magnetic field due to the pulse in the rotating frame of reference and NOT the frequency within the pulse itself. The power level expressed in Hz is simply the reciprocal of the time required for a magnetization vector to travel 360° (one cycle) under the influence of the pulse (i.e. the reciprocal of the 360° pulse duration). The algebra is as follows where the power level in Hz is expressed with respect to the 90° pulse rather than the 360° pulse.

Field Homogeneity and VT Gas

In order to obtain optimum resolution, NMR spectroscopists always correct the inhomogeneity of the magnetic field around the sample by adjusting the current in the the room temperature shim coils. The magnetic field homogeneity around the sample depends not only on the quality of the superconducting magnet but also on the magnetic susceptibility of the materials in the vicinity of the coil and the sample. The careful selection of materials in probe manufacturing and their use around the coil are essential for being able to produce a homogeneous field in the vicinity of the sample using the shim coils. This is one of the reasons why high resolution NMR probes are very expensive. One "material" near the coil which is often overlooked by the NMR user is the VT (variable temperature) gas being passed over the sample. The two most common VT gasses are air and nitrogen. One might think that these are very similar to one another as dry air is approximately 80% nitrogen. The magnetic susceptibility between the two however, is quite large and they will distort the magnetic field around the sample to differing extents. This is demonstrated in the figure below. A sample of CHCl₃ in acetone-d₆ was placed in a 500 MHz magnet equipped with a probe using air as the VT gas. The magnet was shimmed and the spectrum acquired is shown in the top trace. The air source was then replaced by a source of nitrogen gas at the same flow rate. The spectrum was measured again without re-shimming the magnet and is displayed in the lower trace. The difference in line shape and width is due to the difference in magnetic susceptibilities between the two gases. It should be noted that a spectrum of similar quality to the one obtained using air can be obtained after re-shimming the magnet to correct for the susceptibility difference.

Measuring Power

Anyone who takes care of NMR equipment knows that visits from service engineers are very expensive. These visits can often be avoided by becoming familiar with the components of the NMR spectrometer and learning how to make simple diagnostic measurements. These measurements can be sent to service engineers who can provide advice on replacement parts. One such measurement is the determination of the output power from the amplifiers of the spectrometer. This measurement requires an oscilloscope with a band width greater than the output frequency from the amplifier. Since properly functioning amplifiers put out tens to hundreds of watts, the output must be attenuated in order to prevent damage to the oscilloscope. An attenuator of 30 or 40 dB (rated for at least 10 watts of CW power) is suitable. Also, the measurement must be made at 50 Ω impedance. The spectrometer must be set up to take pulses at regular intervals (e.g. 10 µsec pulses every second). For oscilloscopes with only a 1 MΩ input impedance setting, the measurement can be made according to the following figure using a "T" connector and a low power 50 Ω terminator to match the impedance. The "T" connector and 50 Ω terminator are not required if the oscilloscope has in input impedance setting of 50 Ω. In this case, the connections can be made according to the following figure. The output power (in Watts) is determined by the peak to peak voltage, V_pp , of the pulse as follows.