The NMR Time Scale

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

What is Quadrature Detection?

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

Establishing the Lock with Varian's VNMR

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

Happy Birthday !

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

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

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

The Fourier Transform of a Single Rotational Echo

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

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

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

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

Measuring Parameters from Solid State 2H NMR Spectra

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

Pulse Sequences to Minimize Acoustic Ringing

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

MOOT NMR Minisymposium

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

Setting the Magic Angle with Glycine

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

Chemical and Magnetic Equivalence

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

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

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

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

What Does an RF Pulse Actually Look Like?

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