The Selective 1D Gradient NOESY

Many students run very long 2D NMR experiments to find one particular piece of information. This is especially true for 2D NOESY experiments where perhaps only a single NOE correlation is sought. Depending on the amount of compound available, 2D NOESY measurements often take hours or tens of hours to acquire and can cost alot of money in instrument user fees. Many people do not realize that there are selective 1D analogs to the non selective 2D experiments. These 1D experiments rely on shaped pulses for selective excitation and take only a small fraction of the time required to run the comparable non selective 2D experiment. Previously I have posted entries in this BLOG on the very useful 1D selective gradient TOCSY experiment. The figure below demonstrates the use of the 1D selective gradient NOESY experiment for bis(phenylthio)methane compared to the standard proton NMR spectrum. In this case, the methylene protons were selectively irradiated and the NOE's were observed on the phenyl rings. The experiment took less than 5 minutes to acquire.

The Background from a Dirty NMR Probe

Have you ever wondered why the manager of your NMR equipment gets on your case about wiping down NMR tubes before putting them in the NMR probe? The figure below should answer your question. It shows the ¹H NMR spectrum of a clean empty NMR tube inside an NMR probe before and after the NMR probe has been cleaned.

Over time, the "stuff" from your hands and residue on the outside of your NMR tubes builds up on the inside of the inserts inside the coil of the NMR probe. This "stuff" contains protons and results in a background signal in all subsequent NMR spectra. I have seen inserts of NMR probes so dirty that samples have "stuck" inside the probe. The offending gunk resembles grey-black bubble gum or perhaps dirty dried nasal effluent. Periodically NMR probes must be cleaned to remove this offensive residue. This can usually be accomplished by gently inserting and removing a cotton swab soaked in alcohol inside the coil insert. For the particular case in the figure above, the NMR probe could not be cleaned in this way and had to be disassembled by a service engineer and cleaned in an ultrasonic bath.

WIPE YOUR NMR TUBES BEFORE PUTTING THEM IN AN NMR PROBE !!

Thank you to Dr. Michael Lumsden who manages the NMR Facility at Dallousie University for suggesting this post, kindly sharing his tale and providing the figure.

Spin Echos for Uncoupled Spins

The spin echo is one of the most fundamental building blocks for NMR pulse sequences. Its main purpose is to refocus chemical shifts. The simplest spin echo is that for uncoupled spins where only the offset, Ω (i.e. the frequency difference between the carrier and the resonance) need be considered. The pulse sequence is represented in the upper portion of the figure with the vector and product operator representations below. A 90_x pulse is first given to create magnetization along the -y axis of the rotating frame. During the first delay period, τ, the magnetization rotates in the x-y plane at a rate, Ω. The 180_x pulse rotates the magnetization 180 degrees about the x axis. During the second delay period, the magnetization again rotates in the x-y plane at a rate, Ω in the same direction as during the first delay. At the end of the second delay, the magnetization is on the y axis and the collection of the FID is started. It is important to note that the echo will always have its maximum at 2τ after the 90 degree pulse regardless of its offset, Ω or the duration of τ. The value of τ however is limited by the T₂.

What is T1ρ and How is it Measured?

The time constant for the build up of magnetization along the direction of the main magnetic field, B_o, (the z axis) either after a pulse or upon initially exposing a sample to the magnetic field is called the T₁ relaxation time or spin-lattice relaxation time. It is this relaxation time which determines the rate at which a pulse sequence can be repeated. The time constant for the decay of magnetization in the x-y plane of the rotating frame of reference after a pulse is called the T₂ relaxation time, the spin-spin relaxation time or the transverse relaxation time. It is this relaxation time which determines the natural line width of a particular resonance. There is another relaxation time constant of interest to NMR spectroscopists - T₁ρ. T₁ρ is the time constant for the decay of magnetization along the radio frequency field, B₁, of an applied spin locking pulse in the rotating frame of reference. It is analogous to T₁ except it describes relaxation along the radio frequency field of the pulse (which is static in the rotating frame) rather than relaxation along B_o. T₁ρ's are of interest in ROESY, TOCSY and cross polarization experiments. The T₁ρ is measured by first applying a 90 degree pulse to an equilibrium magnetization vector. A spin locking pulse is then applied. The phase of this pulse is shifted 90 degrees with respect to the excitation pulse such that the field of the spin locking pulse is coincident with the spin vector in the rotating frame of reference. During the spin locking pulse, the large magnetization vector (which was initially polarized in B_o) decays to its equilibrium value in the much smaller field, B₁, with time constant, T₁ρ. The T₁ρ is measured by analysing the intensity of the NMR signal in spectra collected as a function of the duration of the spin locking pulse. This is illustrated in the figure below.

Ottawa U Takes Delivery of a Bruker AVANCE III 400

The Bruker AVANCE III 400 NMR spectrometer for solids was delivered to Ottawa U last week and is currently being installed. It will be available for use in February. With the addition of this instrument, the Ottawa U campus boasts 7 NMR instruments (8, including the Bruker AVANCE II 900 on the NRC campus ). For some photos of the installation, follow this link.

Weak One-bond or Multiple Bond Correlations in 1H / 13C HMQC / HSQC Spectra

Many people are quite surprised to see either unusually weak one-bond correlations or weak multiple bond correlations in their ¹H / ¹³C HMQC / HSQC spectra. These people must be reminded that there is nothing "magic" about these experiments - the responses are based solely on an assigned delay proportional a reciprocal coupling constant. The large scale success of the ¹H / ¹³C HMQC / HSQC techniques can be attributed to the fact that most one-bond ¹H - ¹³C coupling constants are very similar ( ~ 145 Hz). The pulse sequences are therefore run with a delay based on a 145 Hz coupling constant. When one-bond coupling constants are significantly different than 145 Hz then the correlation will be either very weak or absent in the spectrum. Also, if multiple bond couplings are unusually large then those multiple bond correlations may be present in the spectrum. The figure below is an example. In the 500 MHz HMQC spectrum of an alkyne (optimized for 145 Hz coupling), one can see an unusually small one-bond correlation between the terminal alkyne proton and its attached carbon. There is also a weak two-bond correlation between the terminal alkyne proton and the other alkyne carbon.

The Effect of Magic Angle Spinning and High Power 1H Decoupling on 13C Cross Polarization NMR Experiments

Cross polarization (CP), magic angle spinning (MAS) and high power ¹H decoupling are all routine methods used in solid state NMR experiments. It is useful to see the effect of each of these techniques on a solid sample. The figure below shows ¹³C cross polarization NMR spectra of glycine at 4.7 Tesla collected with various combinations of magic angle spinning and high power ¹H decoupling.The bottom spectrum was collected with neither MAS nor high power ¹H decoupling. One can see two very broad overlapping lines due to the carbonyl and methylene carbons. The broadening is due to chemical shielding anisotropy and heteronuclear dipolar coupling between the ¹³C and both ¹H and ¹⁴N. The second trace from the bottom was collected with high power ¹H decoupling but no magic angle spinning. The spectrum contains two broad resonances with very informative line shapes. The high power ¹H decoupling effectively removes the ¹³C - ¹H heteronuclear dipolar interaction. The line shapes are determined from the chemical shielding anisotropy and ¹³C - ¹⁴N dipolar coupling interactions. The second trace from the top was collected with magic angle spinning at 4.5 kHz but no high power ¹H decoupling. The spectrum apparently contains only one broad resonance with spinning sidebands. The magic angle spinning effectively removes the ¹³C chemical shielding anisotropy interaction. Although MAS does help average the ¹³C - ¹H heteronuclear dipolar interaction, the averaging is not very effective at a speed of 4.5 kHz. Also, MAS only partially averages the ¹³C - ¹⁴N heteronuclear dipolar interaction. The resonances are therefore broadened out by residual heteronuclear dipolar coupling. The methylene resonance is broadened to such an extent that it does not show up in the spectrum at all. The top spectrum was collected with both MAS and high power ¹H decoupling. One can see two very sharp resonances due to the carbonyl and methylene carbons. The ¹³C chemical shielding anisotropy and ¹³C - ¹H heteronuclear dipolar coupling interactions are effectively removed by the MAS and high power ¹H decoupling, respectively. Since MAS does not average J coupling and only partially averages dipolar coupling between a spin I = 1/2 and quadrupolar nucleus, the methylene carbon shows fine structure due to both J coupling and residual ¹³C - ¹⁴N dipolar coupling (see inset in yellow).

The BIRD Filter

Many modern NMR experiments exploit coupling interactions between protons and heteronuclei (eg. ¹³C). In such sequences the goal is to selectively observe the protons bound to ¹³C and suppress those bound to ¹²C. Since ¹³C is only 1 % naturally abundant, this means that 99% of the signal must be suppressed. One particularly simple scheme to accomplish this is the BIRD (BIlinear Rotation Decoupling) filter. The BIRD filter uses a heteroneuclear spin echo with delays equal to 1/(2¹J_CH) to align the ¹H(¹²C) and ¹H(¹³C) spin vectors along the -y and y axes of the rotating frame of reference, respectively. The 180 degree phase difference between the ¹H(¹²C) and ¹H(¹³C) spin vectors allows a 90 degree pulse to align the these vectors on the -z and z axes, respectively. At this point the ¹H(¹²C) spins are allowed to relax according to their T₁ to the null point. A final 90 degree read pulse puts the ¹H(¹³C) spins in the transverse plane for observation. The first of the two figures below demonstrates the use of the BIRD filter on the lineshape sample. The second figure shows a vector diagram explaining the sequence.

 

HMQC vs HSQC

Proton detected Heteronuclear Multiple Quantum Coherence (HMQC) and Heteronuclear Single Quantum Coherence (HSQC) are both NMR techniques used to correlate the chemical shift of the protons in a sample to a heteronucleus such as ¹³C or ¹⁵N via the J coupling interaction between the nuclei. Since both techniques essentially provide the same information - a correlation map between the coupled spins - students sometimes ask which of these two methods is better and which should they use routinely. The difference between the two techniques is that during the evolution time of an HMQC both proton and X magnetization (eg: X = ¹³C ) are allowed to evolve whereas in an HSQC only X magnetization is allowed to evolve. This means that an HMQC is affected by homonuclear proton J coupling during the evolution period while an HSQC is not affected as there is no proton magnetization during the evolution time. The homonuclear proton J coupling manifests itself as broadening in the X dimension. The top panel of the figure below shows the 7.05 T ¹H /¹³C HMQC and HSQC spectra of menthol with an expansion of one of the resonances highlighted in yellow. One can see that the expanded cross peak of the HMQC is broader in the ¹³C dimension than that of the HSQC. The bottom panel of the figure shows the corresponding ¹³C projection spectra. One can see that the resolution is better in the projection of the HSQC compared to the HMQC. One might conclude that, due to the higher ¹³C resolution, it is always better to run an HSQC rather than an HMQC. This is definitely the case if all of the pulses are calibrated well, however since there are many more pulses in an HSQC compared to an HMQC, it is more susceptible to losses in signal-to-noise-ratio due to poor probe tuning or poor pulse calibration. My advice to students is that, if high ¹³C resolution is required, then make sure the pulses are calibrated well on a well tuned and matched probe and run an HSQC. If high ¹³C resolution is not critical then run an HMQC.

Bloch-Siegert Shifts

Bloch Siegert shifts are frequency differences between NMR signals observed in the presence and absence an rf field applied during the acquisition time. The shifts arise because the applied rf field changes the effective magnetic field experienced by nearby resonances. The resonances are always displaced away from the frequency of the irradiating field. The shift is inversely related to the difference in frequency between the irradiation and the resonance and therefore is generally not observed when heteronuclear decoupling is applied. When homonuclear decoupling is employed these shifts can become significant and are typically used to calibrate the strength of the homonuclear decoupling field. One must be aware of these effects when reporting chemical shifts in homonuclear decoupling experiments. The figure below shows the effect of applying homonuclear decoupling fields of varying strength in the 300 MHz ¹H NMR spectrum of dimethyl acetamide. One can see that the displacement of the resonances is away from the decoupling frequency and that the magnitude of the shift is inversely related to the frequency difference between the resonance and the irradiation frequency.

1H / 27Al TRAPDOR NMR of Kaolinite

TRAPDOR (TRAnsfer of Populations in DOuble Resonance) NMR (Grey and Vega, JACS 117, 8232 (1995)) is a solid state NMR technique where the effects of dioplar coupling between a quadrupolar nucleus and a spin I = 1/2 nucleus can be observed in the spectrum of the spin I = 1/2 nucleus. The technique relies on a rotor synchronized spin echo of the spin I = 1/2 nucleus with CW irradiation of the quadrupolar nucleus during the first echo delay period. The CW irradiation during a single rotor cycle behaves like an adiabatic frequency sweep as the quadrupolar frequencies vary over the course of the rotor cycle. The effects of dipolar coupling between the quadrupolar nucleus and the spin I = 1/2 nuclei, which are normally averaged by MAS, are reintroduced in the TRAPDOR measurement and the complete refocusing of the spin I = 1/2 NMR signal is prevented. The technique therefore can be used to determine whether or not a spin I = 1/2 nucleus is close in proximity to a quadrupolar nucleus. The figure below shows the ¹H / ²⁷Al TRAPDOR NMR spectrum of kaolinite at 11.7 Tesla. The top two traces are conventional rotor synchronized ¹H Hahn echo spectra acquired with MAS rates of 12 kHz and 2.8 kHz, respectively. The bottom trace was acquired at the same spinning speed as the middle trace with CW irradiation of the ²⁷Al during the first echo delay. One can see a very much reduced ¹H echo indicating the presence of heteronuclear ¹H - ²⁷Al dipolar coupling.
This technique can be used to "find" quadrupolar neuclei which are "invisible" by direct detection due to their very large quadrupolar coupling constants.

Merry Christmas

The Importance of Mixing Your NMR Samples

It is very important that your NMR samples are mixed well before NMR data are acquired. If the sample has a concentration gradient (i.e. more concentrated at one end of the sample column compared to the other) it will be very difficult to shim the magnet over the entire volume of the sample as the magnetic susceptibility is not constant over the sample volume. As a result the NMR lines may be skewed and will be much broader than necessary. This will lead to a much lower signal-to-noise ratio based on signal heights. The figure below shows partial 300 MHz ¹H NMR spectra for 2-bromobutane in CDCL₃. The spectrum on the left was acquired on a sample where 1 drop of 2-bromobutane was added to CDCL₃ in an NMR tube. The tube was gently swirled but not shaken. The magnet was shimmed using a gradient shimming routine and the data collected. The spectrum on the right was acquired on the same sample except the tube was removed from the magnet, shaken and reinserted. The magnet was reshimmed with the same gradient shimming routine and the same number of scans were collected. The difference in the quality of the NMR data is obvious.

Optimizing Decoupler Pulses for CP/MAS NMR

The ¹³C line width of protonated carbons, the signal-to-noise ratio and often the resolution in a CPMAS spectrum depends on effective high power proton decoupling during the acquisition time. A convenient sample to optimize the decoupling power or pulses for ¹³C CPMAS NMR is glycine, as the line width of the methylene carbon is very sensitive to the quality of the decoupling. The figure below shows such an optimization of the pulse widths used in TPPM (Two Pulse Phase Modulation) decouipling. The data were collected at 11.7 T.

QCPMG

The quadrupolar Carr-Purcell-Meiboom-Gill (QCPMG) sequence can be used to measure the NMR spectra quadrupolar I = n/2 nuclei in the solid state. This technique is essentially a T₂ sequence where a series of echos are collected. The entire echo train represents the time domain data and is Fourier transformed to produce a frequency domain spectrum. The QCPMG spectrum consists of spikelets separated in frequency by the reciprocal of the time separation between the echos in the echo train. The intensity envelope of the spikelets mimics the static line shape. This is analogous to the rotational echoes in the FID's of MAS data and the associated spinning sidebands in the frequency domain MAS spectra. The QCPMG technique represents an improvement in sensitivity compared to a single conventional Hahn echo as the intensity is concentrated in the spikelets rather than spread across the entire frequency span of the spectrum. The figure below shows the pulse sequence, an echo train and a QCPMG ²³Na spectrum of solid sodium sulfate at 4.7 Tesla. The ²³Na Hahn echo spectrum is also ahown as a comparison to the QCPMG spectrum. The spectrum represents the central transition only. The satallite transitions are not visible.

90 Degree Pulses for I = n/2 Quadrupolar Nuclei in the Solid State

The 90 degree pulse for an I = n/2 quadrupolar nucleus in the solid state depends on the strength of the rf pulse with respect to the quadrupolar frequency. If the strength of the pulse is much greater than the quadrupolar frequency, the pulse is non-selective and excites all transitions equally. If however it is much less than the quadrupolar frequency, then the pulse is selective to the central (m = 1/2 - m = -1/2) transition. The duration of the pulse producing a maximum signal is shorter for selective vs. non-selective pulses at a similar power level. In solution, where the quadrupolar interactions is averaged by random isotropic molecular motion or in the solid state, if the symmetry around the I = n/2 nucleus is cubic, the quadrupolar frequency is small with respect to the strength of the rf pulses and the pulses are non-selective. When the symmetry around the I = n/2 nucleus in the solid state is non-cubic, the quadrupolar frequency is significant and the pulses are very often selective to the central transition. This is illustrated in the figures below for the ²³Na MAS spectrum of a mixture of NaCl (cubic) and Na₂SO₄ (non-cubic). The first figure shows the ²³Na MAS spectrum labelling each component of the mixture. The second figure shows the effect of increasing the pulse duration. One can clearly see that the 90 degree pulse for NaCl is close to twice that of Na₂SO₄.

Before You Leave .....

This may seem to be a strange post .... a rant really...... but very important.

Over the years I have seen many students start a long acquisition (or series of acquisitions) on spectrometers and then immediately leave the lab. After a long lunch, an afternoon of playing billiards, a good night sleep or perhaps a weekend of skiing, they return to the lab and find no useful data waiting for them.

Why? ......

Well ....... perhaps the spectrometer was set up to run 4 rather than 20,000 scans, perhaps the receiver was saturated, perhaps the recycle delay was set to 1000 seconds rather than 2 seconds, perhaps the pulses were not set correctly, perhaps the spectral width was set too small, perhaps the probe was not tuned and matched, perhaps a delay was set to 10 seconds rather than 10 milliseconds. perhaps a typing error was made in the command to start the acquisition..... etc.

The NMR lab charges you for your time whether you get useful data or not, so it is important to be careful.

Before you leave the lab......

1. Double check the parameters in your experiment and for all queued experiments.
2. Query the spectrometer as to how long the experiment will take ("expt" (Bruker), "time" (Varian)) and ask yourself if the response makes sense.
3. Check the probe tuning and matching.
4. Make sure the receiver gain has been set correctly.
5. Look at the first few scans to make sure you have a signal.

The Importance of Grinding Solid Samples

When the heteronuclear dipolar coupling interaction has been removed by high power decoupling, the NMR spectra of dilute spin I = 1/2 nuclei in a single crystal give rise to relatively sharp lines. The frequencies of the lines depend on the chemical shift tensor and the orientation of the single crystal with respect to the magnetic field. Finely powdered samples have many thousands of crystallites and all orientations of the crystallites with respect to the magnetic field are represented equally. As a result, for powders, one obtains a broad powder pattern. Samples that are not ground into a powder contain many fewer crystals than crystallites in a powder and will yield spectra with partially resolved lines. The envelope of lines for all of the crystals will approximate the true powder spectrum. An example of this is shown in the figure below.

Thank you to Victor Terskikh of the National Ultrahigh Field NMR Facility for Solids. for suggesting this post and kindly providing the data for the figure.

Complexed Solvents

I was once asked by an inorganic chemist: why do I have two THF signals in the spectrum of my compound dissolved in THF-d8? Many inorganic compounds crystallize with complexed solvent molecules as a fundamental component of their structure. This is particularly true of tetrahydrofuran (THF). The complexed solvent molecules are released when the solid compound is re-dissolved in solution and can easily be detected by high resolution NMR. The figure below shows the 500 MHz ¹H NMR spectrum of an inorganic compound containing complexed THF which was re-dissolved in THF-d8. One can see the spectrum of the residual protons of the THF-d8 solvent and the spectrum of the complexed THF that was released when the solid was dissolved. The signals are separated due the isotope effect.

The Effect of the Contact Time on CP/MAS NMR Spectra

One parameter for CP / MAS data collection that must be set by the user is the contact time during which magnetization is transferred from the abundant nucleus (usually ¹H) to the dilute nucleus (e.g. ¹³C). In the case of the ¹³C nuclei in organic samples, the build up of magnetization for each type of carbon depends on the extent of the dipolar coupling to the proton network. The extent of ¹³C - ¹H dipolar coupling depends on both the degree of protonation for each type of carbon and any molecular motion (such as methyl group rotation) which may average the dipolar coupling. At longer contact times, the magnetization decays as a function of the T₁(rho) of the protons. It should be noted that cross polarization is also affected by MAS. The length of the contact time should be chosen such that all types of carbons have had sufficient time to polarize yet not so long as to loose significant magnetization due to the proton T₁(rho). For ¹³C CP/MAS an appropriate choice is usually between 1 and 10 ms. The figure below shows the effect of the duration of the contact time for the two ¹³C resonances of glycine. The 50 MHz ¹³C CP/MAS spectra were run as a function of contact time and plotted side by side. The intensities of each resonance are marked with color coded points. One can see that the carbonyl carbon builds up more slowly than the protonated carbon. An appropriate choice of contact time for glycine is 2 -3 msec.

Kinetic Experiments on Bruker Spectrometers

Students often have to monitor the progress of a chemical reaction as a function of time using NMR spectroscopy. I have written three simple programs for XWINNMR (which should work with little or no modification for TOPSPIN). Each program uses a different method to control the time allowed between collecting spectra. All are very simple and easily implemented. They should be added to the Bruker/XWINNMR/exp/stan/au/src directory. The first two programs, kinetic_ds and kinetic_t, are suitible for slow reactions where precise timing is not critical as they do not take into account the time required to initialize each acquisition. The third program, kinetic_2d avoids the problem by using a pseudo 2d approach and is suitible for faster reactions.

1. kinetic_ds
This program uses dummy scans to control the time allowed between spectra. (A dummy scan is a scan taken without turning on the receiver.) The more dummy scans, the longer the time between experiments. The user should set up the appropriate parameters and then run the program (by typing xau kinetic_ds). You will be asked for the total number of spectra to be collected, the number of scans to be collected for each spectrum and the number of dummy scans to be used in all but the first spectrum. The first spectrum will be collected in the current experiment and the others in subsequent experiments.

/* kinetic_ds */
/* written by Glenn Facey, August 24, 2005 */
/* This program will set up a kinetic run based on the use of dummy scans */
/* The user is asked for the number of spectra, the number of scans for */
/* each spectrum and the number of dummy scans for all but the first spectrum */
/* the first spectrum uses no dummy scans. */
GETCURDATA
GETINT("Enter total number of spectra",i1)
GETINT("Enter the number of scans for each spectrum",i2)
GETINT("Enter the number of dummy scans for all but the first spectrum", i3)
STOREPAR("ns",i2)
STOREPAR("ds",0)
Proc_err(0,"Kinetic Run in Progress");
RGA
ZG
TIMES(i1-1)
IEXPNO
SETCURDATA
STOREPAR("ds",i3)
STOREPAR("ns",i2)
ZG
END
QUITMSG("Data Collection Complete!")

2. kinetic_t
In this program, the user should set up the appropriate parameters and then run the program (by typing xau kinetic_t). You will be asked for the total number of spectra to be collected, the number of scans to be collected for each spectrum and the time in seconds allowed between the end of one acquisition and the beginning of the next acquisition. The first spectrum will collected in the current experiment and the others in subsequent experiments.

/* kinetic_t */
/* written by Glenn Facey, August 24, 2005 */
/* This program sets up and runs a kinetic experiment */
/* The user is asked to input the number of spectra, */
/* the number of scans for each spectrum and the time in */
/* seconds between the end of an acquisition and the */
/* beginning of the next. The program will measure the */
/* receiver gain and start the acquisitions. */
GETCURDATA
GETINT("Enter total number of spectra",i1)
GETINT("Enter the number of scans for each spectrum",i2)
GETINT("Enter the time interval (in seconds)", i3)
STOREPAR("ns",i2)
Proc_err(0,"Kinetic Run in Progress");
RGA
ZG
TIMES(i1-1)
IEXPNO
SETCURDATA
STOREPAR("ns",i2)
ssleep(i3);
ZG
END
QUITMSG("Data Collection Finished")

3. kinetic_2d
This program avoids initialization delays by collecting the data in a pseudo 2D format where each slice of the experiment is a spectrum. The program uses a pulse program called zg30kin.gf (see below) which should be put in the directory Bruker/XWINNMR/exp/stan/lists/pp (This pulse program program should be modified to suit the needs of the user). A variable delay list called kinetic must also be set up. This list contains the same number of lines as the number of spectra to be collected. Each line in the variable delay list defines the time interval (in seconds) to be allowed before each acquistion. The user must set up the appropriate parameters (including the number of scans to be collected for each spectrum) and then run the program (by typing xau kinetic_2d). You will be asked only for the total number of spectra to be collected. The program will set up a pseudo 2d acquisition. Data collection is started with the zg command. The data are processed with the xf2 command.

/* kinetic_2d */
/* written by Glenn Facey, August 24, 2005 */
/* This program sets up a pseudo 2D kinetic run */
/* using the pulse program zg30kin.gf with a Variable */
/* delay list called "kinetic". */
GETCURDATA
GETINT("How many spectra do you want to acquire?", i1)
FETCHPAR("SFO1",&d1)
FETCHPAR("DW",&f2)
FETCHPAR("SW",&d2)
FETCHPAR("SF",&d3)
XCMD("parmode 2D")
XCMD("pulprog zg30kin.gf")
XCMD("vdlist kinetic")
STOREPAR("SFO1",d1)
STOREPAR("DW",f2)
STOREPAR("SW",d2)
STOREPAR("SF",d3)
STOREPAR1("TD",i1)
STOREPAR1("SI",i1)
QUITMSG("Setup Complete!\n1. Define 'VD' List called 'kinetic'.\n2. Run the experiment with 'zg'.\n3. Process data with the 'xf2' command.")

Pulse program zg30kin.gf

;zg30kin.gf
;zg30 modified to run kinetic experiment in pseudo 2D mode
;using VD list
;avance-version (00/02/07)
;1D sequence
;using 30 degree flip angle

#include
"d11=30m"
1 vd
ze
2 d1
p1*0.33 ph1
go=2 ph31
d11 wr #0 if #0 ivd
lo to 1 times td1
exit

ph1=0 2 2 0 1 3 3 1
ph31=0 2 2 0 1 3 3 1

;pl1 : f1 channel - power level for pulse (default)
;p1 : f1 channel - 90 degree high power pulse
;d1 : relaxation delay; 1-5 * T1
;d11 : short delay for I/O

Proton Spin Pairs

In the solid state, in the absence of very fast magic angle spinning or homonuclear multiple pulse decoupling schemes, the ¹H NMR spectrum of a typical solid is a broad featureless line greater than 50 kHz in width. This is due to the homonuclear dipolar coupling interactions between the many protons present in the system. The situation is different for an isolated pair of protons. For an isolated pair of protons, there is only one dipolar interaction between the protons and the energy level diagram for the system has only three levels corresponding the combination of spin states among the two protons and the dipolar coupling between them. There are two transitions and therefore two resonances. The separation between the resonances depends on the magnitude of the dipolar coupling constant, R, and the orientation of the internuclear vector with respect to the applied magnetic field. For powdered samples where all orientations with respect to the applied magnetic field are represented, one observes a "Pake" doublet. This situation is very similar to the solid state NMR of ²H where, in that case, the three energy levels arise from the Zeeman states of a single ²H nucleus and their coupling to an electric field gradient.

Isolated proton pairs occur naturally in the waters of hydration of inorganic salts and the solid state ¹H NMR spectrum is a Pake doublet. The separation between the inner peaks of the Pake doublet is 3/2 R and between the two shoulders is 3R, where R is the dipolar coupling constant. The dipolar coupling constant is directly proportional to the inverse cube of the distance between the protons. Therefore from a single spectrum, one can measure the internuclear separation, r. For the case of the waters of hydration, one can measure the H-O bond length with knowledge of the H-O-H bond angle. The figure below illustrates the Pake doublet spectrum obtained for CaSO₄^. 2 H₂O. The asymmetry in the spectrum is the result of chemical shielding anisotropy and the broadening is the result of dipolar coupling to distant protons.

Positive NOE's and the Decision on Which Decoupling Mode to Use

Nuclei with positive gyromagnetic ratios, such as ¹³C, exhibit positive NOE's with nearby protons. When observing ¹³C directly with proton decoupling, the intensity of the resonances will be increased to an extent dependant on the magnitude of the NOE's and the amount of time over which they are allowed to build up. When quantitative results are not sought after, it is always best to collect the NMR data with decoupling during both the acquisition time and the relaxation delay so that the effect of the NOE's on the intensity of the lines is maximized. The figure below compares the ¹³C NMR spectra for formamide collected with inverse gated decoupling (left) and full decoupling (right).
The above spectra were collected at 11.7 tesla with 4 scans, using a recycle delay of 30 seconds and an acquisition time of 2.3 seconds. This effect of positive NOE's on the resonance intensity should be compared to that for negative NOE's.

Negative NOE's and the Decision on Which Decoupling Mode to Use

Nuclei with negative gyromagnetic ratios, such as ¹⁵N and ²⁹Si, exhibit negative NOE's with nearby protons. When observing these nuclei directly with proton decoupling, the intensity of the resonances will be decreased to an extent dependant on the magnitude of the NOE's. Usually it is best to collect the NMR data for these nuclei with inverse gated decoupling so that the effect of the NOE's on the intensity of the lines is minimized. There are cases however where the magnitude of the NOE is so large that the intensity of the resonance collected with full decoupling becomes negative and even stronger than that observed with inverse gated decoupling. In such cases it is advantageous to leave the decoupler on 100 % of the time. As the figure below shows, this is indeed the situation with the ¹⁵N resonance of formamide where the magnitude of the signal is smaller when inverse gated decoupling decoupling is used.
The above spectra were collected at 11.7 tesla with 4 scans, using a recycle delay of 120 seconds and an acquisition time of 2.3 seconds.

Dilute "D2O" in Benzene-d6

The ¹H NMR spectrum of a mixture of H₂O and D₂O is a single line at about 4.8 ppm. The H₂O and HDO resonances are unresolved in the spectrum due to fast chemical exchange between the isotopomers and possibly line broadening due to radiation damping. When traces of D₂O are added to benzene-d₆, which already contains traces of H₂O, the situation is different. The resonance is shifted by more than 4 ppm to lower frequency compared to the bulk and since the water is now dilute and in small quantities, chemical exchange is slow on the NMR time scale and radiation damping is no longer a problem. The figure below shows the 500 MHz ¹H NMR spectrum of dilute D₂O in benzene-d₆. The isotope shift between H₂O and HDO and the HD coupling constant can easily be measured from the spectrum.

T1 Anisotropy

In the solid state, in the absence of magic angle spinning, the frequency of NMR lines depends on the orientation of the molecules with respect to the static magnetic field. For powdered samples, all orientations are represented in the sample and one obtains a broad envelope of peaks resulting from all possible orientations. Such broad resonance are called powder patterns and are said to be anisotropic. The frequency is not necessarily the only orientation dependant parameter. In some cases, the T₁ relaxation time also depends on the orientation of the molecules with respect to the magnetic field. In such cases the T₁ is said to be anisotropic. In contrast to the NMR resonances in solution which are characterized with a single T₁, the powder pattern can be characterized with many different T₁ relaxation times. Furthermore, the presence or absence of anisotropy in the T₁ can help discriminate between certain types of molecular motion. An example of an anisotropic T₁ is illustrated in the figure below for the wide line ²H inversion recovery spectra of acetone-d6 trapped in an organic inclusion compound. The line shape indicates that the acetone molecules undergo both fast methyl group rotation and fast two-fold flips about he carbonyl bond. One can see that the entire powder pattern does not have the same T₁ as the line shapes are a function of the inversion recovery delay, tau. The T₁ depends on the frequency within the powder pattern which in turn depends on the orientation of the molecules with respect to the magnetic field.

The Effect of Dissolved Oxygen on Relaxation Times

Proton T₁ relaxation occurs, to a very large extent, due to inter-proton dipole-dipole interactions and their time dependence as a result of molecular motion. Potentially, there is also dipole-dipole interactions between protons and unpaired electrons which also contribute greatly to proton relaxation. In fact, for ¹³C NMR, paramagnetic materials are sometimes added to the sample to make relaxation more efficient. Dissolved molecular oxygen from air is a paramagnetic material that is often overlooked. Like other paramagnetic materials it contributes significantly to the relaxation rate of protons. It can be eliminated from NMR samples by simply bubbling nitrogen through the sample for a few minutes or freeze-pump-thawing the sample a few times. The following data show the effect of dissolved oxygen on the proton relaxation times of ethyl acetate in acetone-d6.

T₁'s for sample under air 
quartet = 8.7 seconds
singlet = 7.7 seconds
triplet = 6.9 seconds
T₁'s for sample under nitrogen
quartet = 17.7 seconds
singlet = 13.2 seconds
triplet = 12.5 seconds

One can see that the relaxation times are nearly 100% longer when oxygen is eliminated from the sample. The figure below shows the proton T₁ inversion recovery measurement for the acetate methyl singlet of ethyl acetate for the same sample before and after nitrogen was bubbled through the solution.

Fast Molecular Motions and Solid State Wide Line 2H NMR

On occasion, I have been asked why people make such a big deal about solid state wide line ²H NMR. After all, ²H has a low natural abundance and isotopic labelling is necessary to collect the data. The answer is that the ²H line shapes depend on the interaction between the ²H quadrupole moment and the electric field gradient tensor surrounding the ²H nucleus. The electric field gradient tensor is dramatically affected by the averaging of different types of molecular motions and this effect is readily observed in the NMR line shapes. The line shapes are sensitive to the rates, order and axes defining the motion. For molecular motions occurring at rates fast with respect to the width of the static ²H NMR spectrum, one can determine the type of molecular motion by doing reasonably straight forward calculations or often simply by inspecting the motionally averaged spectrum. The figure below shows the effects that some common fast molecular motions have on ²H NMR line shapes. The same static quadrupolar coupling constant of 160 kHz was used in the calculation of all of the spectra in the figure.

The line shapes observed for molecules undergoing motions at rates comparable to the width of the static ²H NMR spectrum can also be calculated however, the calculations are a bit more involved.

Baseline Correction in 2D NMR Spectra

Sometimes a 1D NMR spectrum will have a baseline roll. One way of correcting this is to fit the baseline of the spectrum (between two limits) to a polynomial and then subtract the polynomial from the spectrum to produce a flat baseline. Baseline roll is not an exclusive problem to 1D data. It can also be present in each domain of a 2D data set. Baseline orrection can be applied to each of the dimensions. The figure below shows a proton NOESY spectrum which is uncorrected (top left), baseline corrected in the rows (top right), baseline corrected in the columns (bottom left) and baseline corrected in both domains (bottom right).

Output Power Expressed in decibels (dB)

It is often very confusing for students to know exactly how much RF power (in Watts) they are using in their NMR experiments, especially since the two major instrument manufacturers express the output power differently. It is very expensive to use a power level too high as NMR probes can be damaged if proper safety measures are not taken. Both Varian and Bruker express the output power of their instruments in decibels (dB). The maximum power level (pl1, pl2, pl3 .... etc) on a Bruker spectrometer is -6 dB and the minimum power is 120 dB. On Varian spectrometers (at least our INOVA), the maximum power (tpwr, dpwr etc) is 63 dB and the minimum power is 0 dB. Because of amplifier non-linearity, one may get maximum power below 63 dB on a Varian instrument (perhaps 55 dB to 60 dB) with no further gain at higher settings. On Bruker instruments, the non-linearity can be taken into account by calibrating with known attenuators and creating a correction table (CORTAB). If one is using an amplifier with a maximum output power of 100 Watts and the effects of amplifier non-linearity are neglected, the output power will be approximately:

100 W @ 63 dB (Varian) and -6 dB (Bruker)
1 W @ 43 dB (Varian) and 14 dB (Bruker)
1 mW @ 13 dB (Varian) and 44 dB (Bruker)

The figure below shows a plot of the power level in dB vs. the fraction of total amplifier power. The expressions in the figure do not take into account amplifier saturation.

CAUTION : Exact output power on any particular instrument must always be measured and calibrated.

Thank you to Victor Terskikh of the National Ultra-high Field NMR Facility for Solids for suggesting this post.