# Nuclear magnetic resonance

Image:Pacific Northwest National Laboratory 800 MHz NMR Spectrometer.jpg
Pacific Northwest National Laboratory's high magnetic field (800 MHz, 18.8 T) NMR spectrometer being loaded with a sample.
Image:HWB-NMRv900.jpg
[900MHz, 21.2 T NMR Magnet at HWB-NMR, Birmingham, UK being loaded with a sample

Nuclear magnetic resonance (NMR) is a physical phenomenon based upon the magnetic properties of an atom's nucleus. All nuclei that contain odd numbers of nucleons and some that contain even numbers of nucleons have an intrinsic magnetic moment. The most commonly used nuclei are hydrogen-1 and carbon-13, although certain isotopes of many other elements nuclei can also be observed. NMR studies a magnetic nucleus, like that of a hydrogen atom (protium being the most receptive isotope at natural abundance) by aligning it with a very powerful external magnetic field and perturbing this alignment using an electromagnetic field. The response to the field by perturbing is what is exploited in nuclear magnetic resonance spectroscopy and magnetic resonance imaging.

NMR spectroscopy is one of the principal techniques used to obtain physical, chemical, electronic and structural information about a molecule. It is the most powerful technique that can provide detailed information on the three-dimensional structure of biological molecules in solution. Also, nuclear magnetic resonance is one of the techniques that has been used to build elementary quantum computers.

##  History

###  Discovery

Nuclear magnetic resonance was first described independently by Felix Bloch and Edward Mills Purcell, in 1946, both of whom shared the Nobel Prize in physics in 1952 for their discovery.

Purcell had worked on the development and application of RADAR during World War II at Massachusetts Institute of Technology's Radiation Laboratory. His work during that project on the production and detection of radiofrequency energy, and on the absorption of such energy by matter, preceded his discovery of NMR and probably contributed to his understanding of it and related phenomena.

They noticed that magnetic nuclei, like 1H and 31P, could absorb RF energy when placed in a magnetic field of a specific strength. When this absorption occurs the nucleus is described as being in resonance. Interestingly, for analytical scientists, different atoms within a molecule resonate at different frequencies at a given field strength. The observation of the resonance frequencies of a molecule allows a user to discover structural information about the molecule.

The development of nuclear magnetic resonance as a technique of analytical chemistry and biochemistry parallels the development of electromagnetic technology and its introduction into civilian use. Major NMR makers include Bruker, Varian and JEOL.

###  Continuous wave (CW) spectroscopy

Throughout its first few decades, nuclear magnetic resonance practice utilized a technique known as continuous-wave (CW) spectroscopy in which either the magnetic field was kept constant and the oscillating field was swept in frequency to chart the on-resonance portions of the spectrum or, more frequently, the oscillating field was held at a fixed frequency and the magnetic field was swept through the transitions.

CW spectroscopy technique is limited in that it probes each frequency individually, in succession, which has unfortunate consequences due to the insensitivity of nuclear magnetic resonance—that is to say, nuclear magnetic resonance suffers from poor signal-to-noise ratio. Fortunately for nuclear magnetic resonance in general, signal-to-noise ratio (S/N) can be improved by signal averaging. Signal averaging is an algorithm where the signals from many successive runs of an experiment are added together. The noise, which is random in character, tends to cancel itself out while the actual signal is constant and additive. Signal averaging increases S/N by the square-root of the number of signals taken. This is a general principle and not unique to NMR.

###  Fourier spectroscopy

The technique known as Fourier transform nuclear magnetic resonance spectroscopy (FT-NMR) decreases the time required for a scan by allowing a range of frequencies to be probed at once. This technique has been made more practical with two technologies: the knowledge of how to create an array of frequencies at once and computers capable of performing the computationally-intensive mathematical transformation of the data from the time domain to the frequency domain to produce a spectrum.

Pioneered by Richard R. Ernst, who won a Nobel Prize in chemistry in 1991, FT-NMR works by irradiating the sample, held in a static external magnetic field, with a short square pulse of radiofrequency energy containing all the frequencies in the range of interest because the fourier decomposition of an approximate square wave contains contributions from all the frequencies in the neighborhood of the principle frequency.

The polarized nuclear magnets of the nuclei begin to spin together, creating a radio frequency signal that is observable. However, they ultimately lose alignment and simultaniously decay to the equilibrium state in the magnet of having a net polarization vector that aligns with the field. This decay is known as the free induction decay (FID). This time-dependent pattern can be converted into a frequency-dependent pattern of nuclear resonances using a mathematical function known as a Fourier transformation, revealing the nuclear magnetic resonance spectrum.

###  Multi-dimensional

The use of pulses of different shapes, frequencies and durations in specifically-designed patterns or pulse sequences allows the spectroscopist to extract many different types of information about the molecule.

Multi-dimensional nuclear magnetic resonance spectroscopy is a kind of FT-NMR in which there are at least two pulses and, as the experiment is repeated, the pulse sequence is varied. In multidimensional nuclear magnetic resonance there will be a sequence of pulses and, at least, one variable time period. In three dimensions, two time sequences will be varied. In four dimensions, three will be varied.

There are many such experiments. In one, these time intervals allow—among other things—magnetization transfer between nuclei and, therefore, the detection of the kinds of nuclear-nuclear interactions that allowed for the magnetization transfer. Interactions that can be detected are usually classified into two kinds. There are through-bond interactions and through-space interactions. The latter usually being a consequence of the nuclear Overhauser effect. Experiments of the nuclear-Overhauser variety may establish distances between atoms.

Richard Ernst and Kurt Wüthrich—in addition to many others—developed 2-dimensional and multidimensional FT-NMR into a powerful technique for studying biochemistry, in particular for the determination of the structure of biopolymers such as proteins or even small nucleic acids.

This is used in protein nuclear magnetic resonance spectroscopy. Wüthrich shared the 2002 Nobel Prize in Chemistry for this work.

###  Solids

This technique complements biopolymer X-ray crystallography in that it is frequently applicable to biomolecules in a liquid or liquid crystal phase, whereas crystallography, as the name implies, is performed on molecules in a solid phase. Though nuclear magnetic resonance is used to study solids, extensive atomic-level biomolecular structural detail is especially challenging to obtain in the solid state. There is no signal averaging by thermal motion in the solid state, where molecules are held still, each in a slightly different electronic environment, giving a different signal. This variation in electronic environment lowers resolution greatly and makes interpretation more difficult. Raymond Andrew was a pioneer in the development of high-resolution solid-state nuclear magnetic resonance. He introduced the magic angle spinning (MAS) technique and allowed for an increase in resolution by several orders of magnitude. In MAS, the sample is averaged by spinning it at several kilohertz.

Alex Pines together with John Waugh revolutionized the area with the introduction of the cross-polarization technique in order to enhance low abundance and sensitivity nuclei.

###  Sensitivity

Because the intensity of nuclear magnetic resonance signals and, hence, the sensitivity of the technique depends on the strength of the magnetic field the technique has also advanced over the decades with the development of more powerful magnets. Advances made in audio-visual technology have also improved the signal-generation and processing capabilities of newer machines.

The sensitivity of nuclear magnetic resonance signals is also dependent—as noted above—on the presence of a magnetically-susceptible nuclide and, therefore, either on the natural abundance of such nuclides or on the ability of the experimentalist to artificially enrich the molecules, under study, with such nuclides. The most abundant naturally-occurring isotopes of hydrogen and phosphorus—for instance—are both magnetically susceptible and readily useful for nuclear magnetic resonance spectroscopy. In contrast, carbon and nitrogen have useful isotopes but which occur only in very low natural abundance.

##  Uses of nuclear magnetic resonance

The most obvious use of nuclear magnetic resonance is in magnetic resonance imaging for medical diagnosis, however, it is also widely used in chemical studies, notably in NMR spectroscopy such as proton NMR and carbon-13 NMR.

These studies are possible because nuclei are surrounded by orbiting electrons, which are also spinning charged particles such as magnets and, so, will partially shield the nuclei. The amount of shielding depends on the exact local environment. For example, a hydrogen bonded to an oxygen will be shielded differently than a hydrogen bonded to a carbon atom. In addition, two hydrogen nuclei can interact via a process known as spin-spin coupling, if they are on the same molecule, which will split the lines of the spectra in a recognisable way.

By studying the peaks of nuclear magnetic resonance spectra, skilled chemists can determine the structure of many compounds. It can be a very selective technique, distinguishing among many atoms within a molecule or collection of molecules of the same type but which differ only in terms of their local chemical environment.

By studying T2* information a chemist can determine the identity of a compound by comparing the observed nuclear precession frequencies to known frequencies. Further structural data can be elucidated by observing spin-spin coupling, a process by which the precession frequency of a nucleus can be influenced by the magnetization transfer from nearby nuclei.

T2 information can give information about dynamics and molecular motion.

Because the nuclear magnetic resonance timescale is rather slow, compared to other spectroscopic methods, changing the temperature of a T2* experiment can also give information about fast reactions, such as the Cope rearrangement or about structural dynamics, such as ring-flipping in cyclohexane.

A relatively recent example of nuclear magnetic resonance being used in the determination of a structure is that of buckminsterfullerene. This now famous form of carbon has 60 carbon atoms forming a sphere. The carbon atoms are all in identical environments and so should see the same internal H field. Unfortunately, buckminsterfullerene contains no hydrogen and so 13C nuclear magnetic resonance has to be used, and is a more difficult form of nuclear magnetic resonance to do. However in 1985 the spectrum was obtained by R. Curl and R. Smalley of Rice University and sure enough it did contain just the one single spike, confirming the unusual structure of C60.

Nuclear magnetic resonance is extremely useful for analyzing samples non-destructively. Radio waves and static magnetic fields easily penetrate many types of matter and anything that is not inherently ferromagnetic. For example, various expensive biological samples, such as nucleic acids, including RNA and DNA, or proteins, can be studied using nuclear magnetic resonance for weeks or months before using destructive biochemical experiments. This also makes nuclear magnetic resonance a good choice for analyzing dangerous samples.

Another use for nuclear magnetic resonance is data acquisition in the petroleum industry for petroleum and natural gas exploration and recovery. A borehole is drilled into rock and sedimentary strata into which nuclear magnetic resonance logging equipment is lowered. Nuclear magnetic resonance analysis of these boreholes is used to measure rock porosity, estimate permeability from pore size distribution and identify pore fluids (water, oil and gas).

NMR has now entered the arena of real-time process control and process optimization in oil refineries and petrochemical plants. Two different types of NMR analysis are utilized to provide real time analysis of feeds and products in order to control and optimize unit operations. Time-domain NMR (TD-NMR) spectrometers operating at low field (2-20 MHz for 1H) yield free induction decay data that can be used to determine absolute hydrogen content values, rheological information, and component composition. These spectrometers are used in mining, polymer production, cosmetics and food manufacturing as well as coal analysis. High resolution FT-NMR spectrometers operating in the 60 MHz range with shielded permanent magnet systems yield high resolution 1H NMR spectra of refinery and petrochemical streams. The variation observed in these spectra with changing physical and chemical properties is modelled utilizing chemometrics to yield predictions on unknown samples. The prediction results are provided to control systems via analogue or digital outputs from the spectrometer.

##  Theory of nuclear magnetic resonance

###  Nuclear spin and magnets

Electrons, neutrons and protons, the three particles which constitute an atom, have an intrinsic property called spin. This spin is defined by the fourth quantum number for any given wave function obtained by solving the relativistic form of the Schrödinger equation (SE). It represents a general property of particles which scientists often describe using the language of electron quantum mechanics. Electrons flowing around a coil generate a magnetic field in a given direction; this property is what makes electric motors work. In much the same way atomic electrons circulate around the nucleus, generating a magnetic field. This generated field has an angular momentum associated with it, in addition to the angular momentum associated with electron particles themselves. This internal angular momentum is denoted 'spin' and gives rise to the spin quantum number, ms.

Spin angular momentum is quantized and can take different integer or half-integer values for a given system. Single electrons can have spin values of +½ or -½. Since the Pauli principle states that no two fermions can have the same quantum number, only two electrons - with their spins aligned antiparallel - can appear in a single atomic orbital.

Similarly, protons and neutrons have a spin angular momentum which can take values of + ½ and –½. In the atomic nucleus, protons can pair with other antiparallel protons much in the same way that electrons pair in a chemical bond. Neutrons do the same. Paired particles have a net spin of zero "0" but a nucleus with unpaired protons and neutrons will have a non-zero overall spin, with the number unpaired contributing ½ to the overall nuclear spin quantum number, I. When this is nonzero, a nucleus will have a spin angular momentum and an associated magnetic moment, μ, dependent on the direction of the spin. It is this magnetic moment that we manipulate in modern NMR experiments.

It is worth noting here that nuclei can have more than one unpaired proton and one unpaired neutron, much in the same way that electronic structures in transition metals can have many unpaired spins. For example 27Al has an overall spin I = 5/2.

A technique related to nuclear magnetic resonance is electron spin resonance that exploits the spin of electrons instead of nuclei. The principles are otherwise similar.

####  Values of spin angular momentum

The spin angular momentum of a nucleus can take ranges from +I to –I in integral steps. This value is known as the magnetic quantum number, m. For any given nucleus, there is a total (2I+1) angular momentum states. Spin angular momentum is a vector quantity. The z component of which, denoted Iz, is quantized:

$I_z = \frac{mh}{2\pi}$

where h is Planck's constant and π is pi.

The resultant magnetic moment of this nucleus is intrinsically connected with its spin angular momentum. In the absence of any external effects the magnetic moment of a spin ½ nucleus lies approximately 52.3° from the angular momentum axis or 127.7° for the opposing spin. This magnetic moment is intrinsically related to I with a proportionality constant γ, called the gyromagnetic ratio:

$\ \mu = \gamma I$

####  Spin behaviour in a magnetic field

Consider nuclei which have a spin of one-half, like 1H, 13C or 19F. The nucleus has two possible magnetic moments it could take: +1/2 or -1/2 (also referred to as up and down or α and β, respectively). The energies of each state are degenerate—that is to say that they are the same. The effect is that the number of atoms, their population, in the up or α state is the same as the number of atoms in the β state.

If a nucleus is placed in a magnetic field, the angular momentum axis coincides with the field direction. The resultant magnetic momenta, space quantised from the angular momentum axis, no longer have the same energy since one state has a z-component aligned with an external field and are lower in energy (positive I values) and the other opposes the external field and is higher in energy. This causes a population bias toward the lower energy states.

The energy of a magnetic moment μ when in a magnetic field B0, the zero subscript is used to distinguish this magnetic field from any other applied field, is the negative scalar product of the vectors:

$\ E = - \mu_z B_0$

We've already defined μz=γIz. So placing this in the above equation we get:

$\ E = - \frac{mh\gamma B_0}{2\pi}$

Where γ is the gyromagnetic ratio of the nucleus being scanned.

####  Resonance

The energy gap between our α and β states is (hγB0)/2π. We get resonance between the states, therefore equalizing populations, if a radiofrequency is applied with the same energy as the energy difference ΔE between the spin states. The energy of a photon is E = , where ν is its frequency.

$\ \Delta E = \frac{h\gamma B_0}{2\pi}$

Thus, the frequency of electromagnetic radiation required to produce resonance of a specific nucleus in a field B is:

$\ \nu = \frac{\gamma B_0}{2\pi}$

It is this frequency that we are concerned with, and detect in NMR. It is this frequency which describes the sample we are observing. But most importantly, it is this resonance which gives rise to the nuclear magnetic resonance spectrum.

####  Nuclear shielding

It would appear from the above equation that all nuclei of the same nuclide, which have same the gyromagnetic ratio (γ), resonate at the same frequency. This is not the case. Since the gyromagnetic ratio of a given nuclide does not change, we conclude that the effect of the external magnetic field is different for different nuclei. Local effects of other nuclei, especially spin-active nuclei, and local electron effects shield each nucleus differently from the main external field.

It was stated that the energy of a spin state is defined by E= zB0. It can be seen that by shielding the strength of the magnetic field, the experienced effect, or effective magnetic field at the nucleus is lower:

$\ B_{effective} < B_0$

Thus the energy gap is different, and hence the frequency required to achieve resonance deviates from the expected value.

These differences due to nuclear shielding give rise to many peak frequencies in a nuclear magnetic resonance spectrum. It can be seen why nuclear magnetic resonance is a direct probe of chemical structure.

It is possible for the shielding to change as the orientation of the molecule, this is called chemical shift anisotropy, and can even be used in some types of experiment. Especially if the sample is solid, the external fields of the crystal structure interfere with the nuclear field too much for the spectrum to be of any use. Anisotropy is usually averaged out by spinning the sample. For liquids, anisotropy is often relatively small, but the accuracy is increased by using a pneumatic spinner to rotate the sample. For solids, magic angle spinning at very high angular velocities (20 kHz) is used, since the anisotropy is often very large.

###  Relaxation

For more details on this topic, see Relaxation (NMR).

The process called population relaxation refers to nuclei that return to the thermodynamic state in the magnet. This process is also called T1 relaxation, where T1 refers to the mean time for an individual nucleus to return to its equilibrium state. Once the population is relaxed, it can be probed again, since it is in the initial state.

The precessing nuclei can also fall out of alignment with each other (returning the net magnetization vector to a nonprecessing field) and stop producing a signal. This is called T2 relaxation. It is possible to be in this state and not have the population difference required to give a net magnetization vector at its thermodynamic state. Because of this, T1 is always larger (slower) than T2. This happens because some of the spins were flipped by the pulse and will remain so until they have undergone population relaxation. In practice, the T2 time is the life time of the observed NMR signal, the free induction decay. In the NMR spectrum, meaning the Fourier transform of the free induction decay, the T2 time defines the width of the nmr signal. Thus, a nucleus having a large T2 time gives rise to a sharp signal, whereas nuclei with shorter T2 times give rise to more broad signals. The length of T1 and T2 is closely related to molecular motion.

##  References

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