What is nuclear spin? All nuclei carry a charge. In some nuclei this charge "spins", causing the nucleus to behave like a tiny bar magnet. This is why it aligns with or against the magnetic field of an NMR spectrometer. However unlike a bar magnet, the low energy state is aligned with the field and the high energy state is aligned against the field. Up to now we have been talking about nuclei with a uniform spherical charge distribution. These nuclei are said to have a spin of ½. Protons, ^{13}C and ^{31}P are all spin half nuclei. Note that the most common isotope of carbon, ^{12}C, has no spin and can therefore not be observed using NMR. Nuclei with a non-spherical charge distribution have a spin number I of 1, 3/2 or higher (in steps of ½ ), and are referred to as quadrupolar nuclei. Spin ½ nuclei have two orientations (with or against the field). Spin 1 nuclei have three orientations, spin 3/2 nuclei have 4 orientations, etc. Deuterium is an example of a spin 1 nucleus. Although deuterium is chemically the same as hydrogen, for the purposes of NMR it is completely different. For example a carbon spectrum of CDCl_{3} is a 1:1:1 triplet regardless of whether you turn on the proton decoupler. This is because the deuterium attached to the carbon can have three orientations, and occurs at a different frequency to protons.

What is a double quantum coherence? When you put your sample in the magnet, all the spin half nuclei align either with or against the magnetic field. The population difference between these two orientations (known as the Boltzman distribution) is field dependent, and is determined by their energy difference. An NMR signal is observed when nuclei flip from one orientation to the other. This is a single quantum coherence. When two nuclei are coupled, they can flip together as though they were a single unit. If they flip in opposite directions, the flips "cancel each other out" (sort of) resulting in a zero quantum coherence. If they both flip the same way, you get a double quantum coherence. The frequency of a zero quantum coherence is between zero and a few kilohertz, so it is not directly observed. Similarly the frequency of a double quantum coherence is roughly twice the normal observe frequency, so that is not observed directly either. You can also have triple quantum coherences from groups of three coupled nuclei. The effect of double and triple quantum coherences can only be observed by inserting pulses or delays into a pulse sequence to convert them to single quantum coherences before acquisition of the NMR signal. Do not confuse double quantum coherences with coupling in a normal spectrum. A doublet for example, arises when there are two coupled spins, but only one of these spins flips.

What are pulsed field gradients? Imagine if you could really mess up the Z1 resolution for a few milliseconds then restore it to its proper value during the course of the pulse sequence. This is an oversimplification, since pulsed field gradients do not use the normal shim circuits. A special PFG probe, and a PFG amplifier are necessary. By applying a gradient to the magnetic field, the top of the sample experiences a slightly different magnetic field to the bottom of the sample. Since magnetisation precesses at different rates in different fields, it is possible after a 90 degree pulse and a PFG of a few milliseconds to have the magnetisation vectors along the length of the tube pointing in all directions instead of nicely aligned along one axis of the rotating frame. Obviously if the magnetisation vectors are pointing in all directions, there is no net signal. The vectors are said to be dephased. If you now apply a PFG of opposite sign for the same time, you will rephase the magnetisation, and get your signal back. You could achieve the same thing by giving the dephased vectors a 180 degree pulse, then applying a PFG of the same sign. The other thing to be aware of is that double quantum coherences dephase at twice the rate of normal single quantum coherences, so by adjusting the strength or duration of pulsed field gradients, you can select single, double or triple quantum coherences. The "old fashioned" way of selecting certain types of coherences is to use elaborate phase cycles which cause the unwanted signals to cancel out on successive scans. The PFG method acquires only the desired signal on each scan, resulting in fewer artifacts and allowing fewer scans. The old method can be thought of as "cancellation of unwanted signals over time" whereas the PFG method can be thought of as "cancellation of unwanted signals over space" where "time" refers to successive scans, and "space" refers to the physical length of the sample in an NMR tube.

What is the Nuclear Overhauser Effect? Glad you asked. Have a look at our NOE guide.

How do I run a quantitative spectrum? A quantitative spectrum is simply a spectrum where you can trust the integral ratios. In other words, if the integral of resonance A is twice the height of the integral of resonance B, you can say with certainty that resonance A is due to twice the number of nuclei as resonance B. Why do we use integrals? Because it is the area of the resonances that is proportional to the number nuclei. The height of a broad line may be less than that of a sharp line, but its area may be greater. How do we get accurate integrals? By ensuring that all resonances are equally excited, well digitised, and properly relaxed.

Equally excited : if the pulse power is not high enough, some resonances far from the observe frequency may experience a reduced flip angle, resulting in a smaller observed signal.

Well digitised : if the number of data points in the spectrum is too low, there will not be enough points to accurately define each resonance, resulting in inaccurate integrals (and peak heights).

Properly relaxed : resonances that are not fully relaxed give a weaker signal than fully relaxed resonances. The nuclei in your compound will not all relax at the same rate, so if you pulse too rapidly the quickly relaxing resonances will appear stronger than the slowly relaxing ones. To be sure of obtaining accurate integrals, you need to measure the relaxation times of your compound, and set a delay equal to 5 times the longest relaxation time. Fortunately it is easy to run an inversion - recovery experiment to measure relaxation times.

It is harder to obtain quantitative carbon spectra, because carbon relaxes more slowly than protons, is less intense, and steps have to be taken to eliminate the Nuclear Overhauser Effect which builds up when protons are decoupled.

What is digital resolution? Digital resolution is simply the separation in hertz between each data point in your spectrum. It has nothing to do with shimming! Say, for example, you set the number of points np to 32,768 and acquire a normal 1 dimensional FID. The number of points in the spectrum you see will be 16384, since half the data points are imaginary. Now if the spectral width (sw) is 6000, the digital resolution will be 6000/16384, or 0.366 hz per point. (Before you grab your calculator to measure your own digital resolution, note that the number of points in the spectrum is not always simply np/2. See the section below on the Fourier number). The Vnmr command to display the digital resolution is dres. If you place the cursor on a peak and type dres, two values will be displayed:

the linewidth which is the width of the peak at half-height, and depends on shimming, weighting functions and the natural width of the line. Also the

digital resolution, which is what this section is all about.

The dres command may give a different linewidth value for every peak you put the cursor on, but the digital resolution value will always be the same, unless you change the Fourier number fn and do another Fourier transform. If the natural linewidth of a resonance is comparable to the digital resolution, the resonance may only be defined by one or two data points. If you expand a line like this, it will look more like a spike than a proper Lorentzian line. Consequently the height of the line may appear less then it really is, the integral will be inaccurate, and even the chemical shift value will be less accurate than it should be. Also, if the separation between two resonances is comparable to the digital resolution, they may appear as a single resonance in the spectrum, because no data point falls in the space between the tops of the two peaks.

What is the fourier number? Mathematicians can do a Fourier transform of any number of points. NMR spectrometers speed things up by using the Cooley-Tukey fast fourier transform algorithm. As implemented on NMR spectrometers, this requires the number of points to be a power of two. So what happens if the number of points np is not a power of two? On Varian spectrometers this can be controlled by the Fourier number (fn) parameter. If it is used, fn can only be set to powers of 2, and the value of fn is the number of points that are actually used in the Fourier transform. If fn is less than np, some points on the end of the FID are not used in the Fourier transform. If fn is greater than np, the end of the FID is padded with zeros to increase the number of points. This is referred to as zero filling. Zero filling does not write extra zeros on to the end of the FID file on the disk where the FID is stored, it merely adds the zeros in memory just before doing the transform. It is also possible to set the Fourier number to n (not used). In this case, the spectrometer uses the first power of 2 which is higher than np when doing the Fourier transform. So for example if np was 16385 (that is, 2^{14} + 1) it would use 32768 (i.e. 2^{15}) points for the Fourier transform.

What is the relaxation time? It would be an oversimplification to say that the relaxation time is the time taken for a nucleus to relax to equilibrium. After a pulse, a nucleus relaxes toward its equilibrium value at an exponential rate. The value quoted as the relaxation time is actually the time constant of this exponential curve. It takes five time constants for the magnetisation to relax to 95% of its equilibrium value. There are two basic types of relaxation, T_{1} and T_{2}. In the T_{1} process, the magnetization remaining along the z-axis relaxes back to its equilibrium value. This is also known as spin-lattice relaxation because relaxation occurs by the loss of energy from the excited nuclear spins to the surrounding molecular lattice. In the T_{2} process, the magnetization in the x-y plane fans out out until the net magnetization is zero. This is also known as spin-spin relaxation because it is due to the excited spins exchanging energy with each other.

What NMR Simulation Programs are Available?

To simulate a normal (non-exchanging) spin system, you can perform the simulation using the same Vnmr program that you use for data processing. There are instructions in the folders. The first step is to decide what sort of spin system you have - AB, A2X, ABCXY etc. The letters are not important to Vnmr, so it doesn't matter whether you tell it that you have an ABC or an AMX system. Vnmr only needs to know the values of the chemical shifts and coupling constants.

To simulate a dynamic (exchanging) spin system, the program you use depends on the type of experiment you ran. If you ran a series of normal spectra at different temperatures, then you need to simulate the lineshape. This is done using the DNMR5 program. There is another program, dnmr5input, to help you create the input file for DNMR5. Instructions are in the folders by the Sun computers.
If you ran a series of
selective inversion pulse -- delay -- hard pulse -- acquire
experiments to use magnetization transfer information to determine rate constants, we have a program provided by Prof. Brian Mann of Sheffield University that you can use to analyse your data.