Pacific Northwest National Laboratory's 800 MHz NMR spectrometer being loaded with sample.

Nuclear magnetic resonance (NMR) is a physical phenomenon involving the interaction of atomic nuclei placed in an external magnetic field with an applied electromagnetic field oscillating at a particular frequency. Magnetic conditions within the material are measured by monitoring the radiation absorbed and emitted by the atomic nuclei.

NMR is used as a spectroscopic technique to obtain physical, chemical, and electronic information about molecules. It is also the underlying principle of magnetic resonance imaging. NMR is one of the techniques that has been used to build quantum computers.

How NMR works

A single atomic nucleus can be thought of as a spinning charged body, which acts as a tiny magnet. An external magnetic field into which the sample material is placed exerts a torque on the nucleus that acts to align the nuclear magnetic field with the external field; however, since the nucleus is spinning, it will precess about the magnetic field instead of aligning with it. The angle of the nucleus' magnetic field is quantized (due to the quantization of angular momentum), often referred to as being 'up' or 'down'.

The effect of the magnetic field is to cause the energies of the spin states to become nonequal, with the difference increasing in a linear fashion in proportion to the strength of the magnetic field. If the spin is aligned with the applied field the state drops in energy and vice versa. The lower energy state becomes more populated than the higher energy state, and when electromagnetic radiation of the correct frequency is applied (where photons have energy equal to the gap between the 'up' and the 'down' states), resonance occurs and nucleii rapidly switch states. This may be detected with sufficiently accurate apparatus.

The frequency of radiation at which resonance occurs is distinct for each nucleus, depending on its gyromagnetic ratio. In addition, nuclei of the same element undergo resonance at slightly different frequencies depending upon the local environment of the nucleus in question. It is possible, therefore, to distinguish between (for example) the carbonyl and the methyl carbon atoms in ethanal (acetaldehyde). In this manner, NMR is an extremely useful analytical tool for chemists, as it allows the chemical structure of an unknown compound to be probed to the degree that the structure may be completely deduced.

Only nuclei with non zero magnetic moment can undergo NMR. Such nuclei must have an odd number of protons or neutrons (e.g. ¹H, ¹³C, ¹⁵N, ³¹P, ¹⁹F).

A technique related to NMR is electron spin resonance that deals with electrons instead of nuclei. The principles are otherwise similar.

Relaxation

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 returns 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. In this state the population difference required to give a net magnetization vector is not at its thermodynamic state. Some of the spins were flipped by the pulse and will remain so until they have undergone population relaxation.

<math>\frac{1}{T_2} = \frac{1}{T_2^*} + \frac{1}{2T_1}<math>.

It is seen that T₁ is larger (slower) than T₂*.

Uses of NMR

Nuclei are surrounded by orbiting electrons, which are also spinning charged particles [i.e. 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 a NMR 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 may 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 NMR timescale is rather slow (compared to other spectroscopic methods), changing the temperature of an T₂* experiment can also give information about fast reactions, such as the Cope reaction or about structural dynamics, such as ring-flipping in cyclohexane.

A relatively recent example of NMR being used in the determination of a structure is that of buckminsterfullerene. This now famous form of carbon has 60 carbon atoms forming a football shaped molecule. (That's a soccer ball, to Americans.) 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 NMR has to be used (a more difficult form of NMR to do). However in 1985 the spectra 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.

NMR is extremely useful for analyzing samples nondestructively. Radio waves and static magnetic fields easily penetrate many types of matter (in practice, anything that is not inherrently ferromagnetic). For example, if one wanted to decisively know whether or not a bottle of wine was 'off', NMR could be used to analyze the wine without ever opening the bottle. This also makes NMR a good choice for analyzing dangerous samples.

History

NMR was 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.

The development of NMR as a technique of analytical chemistry and biochemistry parallels the development of electromagnetic technology and its introduction into civilian use. Purcell had worked on the development and application of RADAR during World War II at MIT's Radiation Lab. 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.

Throughout the next several decades, NMR practice utilized a technique known as continuous-wave, or 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. This technique is limited in that it probes each frequency individually, in succession, which has unfortunate consequences due to the insensitivity of NMR--that is to say, NMR suffers from poor signal-to-noise ratio.

Fortunately for NMR in general, signal-to-noise ratio (S/N) can be improved by signal averaging. Signal averaging increases S/N by the square-root of the number of signals taken. A technique known as Fourier transform NMR spectroscopy (FT-NMR) can speed the time it takes to acquire a scan by allowing a range of frequencies to be probed at once. This technique has been made more practical with the development of 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, FT-NMR works by irradiating the sample (still held in a static, external magnetic field) with a short pulse of radiofrequency energy (RF). According to Fourier theory, the shorter the pulse, the broader the range of frequencies it contains. Detectors record the decay of this excitation as a time-dependent pattern, known as the free induction decay (FID). This time-dependent pattern, when processed through the Fourier transform, reveals the frequency-dependent pattern of nuclear resonances, the NMR spectrum.

The use of pulses of various shapes, frequencies, and durations, in specifically-designed patterns, gives the spectroscopist great flexibility in determining what portions of a molecule, or what intra- and intermolecular dynamic processes, to study. A similar technique used for optical rather than NMR spectroscopy is simply called Fourier transform spectroscopy.

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 time between a pair of pulses is varied. The first dimension is the frequency of the excitation, and the second dimension is based on the time differential between the pair of pulses (because of the properties of the Fourier transform, this second dimension is eventually expressed as a frequency as well). In multidimensional nuclear magnetic resonance, there will be a sequence of pulses, and at least one variable time period (in 3D, two time seqences will be varied. In 4D, three will be varied).

There are many such experiments. In one, these time intervals allow for, among other things, magnetization transfer between nuclei and therefore the detection of the kinds of nuclear-nuclear interactions that allowed for the magnetization transfer. The kinds of interactions that can be detected are classed into two kinds, usually. 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.

Kurt W�thrich, Ad Bax, Vladimir Sklenar and many others, developed 2D 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. W�thrich shared the 2002 Nobel Prize in Chemistry for this work. This technique complements biopolymer X-ray crystallography in that it is most 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 NMR is used to study solids, extensive atomic-level biomolecular structural detail is especially difficult to obtain in the solid state.

Because the intensity of NMR signals, and hence the sensitivity of the technique, depend 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 the audio-visual technology sector have also improved the signal generation and processing capabilities of newer machines.

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

For the latest NMR news (http://www.sciencebase.com/speclines.html), visit the Resonants webzine online

Correlation Spectroscopy; a form of two-dimensional Nuclear Magnetic Resonance

Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy. Other types of two-dimensional NMR include J-spectroscopy, exchange spectroscopy (EXSY), and Nuclear Overhauser effect spectroscopy (NOESY.) Two-dimensional NMR spectra provide more information about a molecule than one-dimensional NMR spectra and are especially useful in determining the structure of a molecule, particularly for molecules that are too complicated to work with using one-dimensional NMR. The first two-dimensional experiment, COSY, was proposed by Jean Jeener, a professor at Universit� Libre de Bruxelles, in 1971. This experiment was later implemented by Walter P. Aue, Enrico Bartholdi and Richard R. Ernst, who published their work in 1976^1.

A two-dimensional NMR experiment involves a series of one-dimensional experiments. Each experiment consists of a sequence of radio frequency pulses with delay periods in between them. It is the timing, frequencies, and intensities of these pulses that distinguish different NMR experiments from one another. During some of the delays, the nuclear spins are allowed to freely precess (rotate) for a determined length of time known as the evolution time. The frequencies of the nuclei are detected after the final pulse. By incrementing the evolution time in successive experiments, a two-dimensional data set is generated from a series of one-dimensional experiments.²

An example of a two-dimension NMR experiment is the homonuclear correlation spectroscopy (COSY) sequence, which consists of a pulse (p1) followed by an evolution time (t1) followed by a second pulse (p2) followed by a measurement time (t2). A computer is used to compile the spectra as a function of the evolution time (t1). Finally, the Fourier transform is used to convert the time-dependent signals into a two-dimensional spectrum.

The two-dimensional spectrum that results from the COSY experiment shows the frequencies for a single isotope (usually hydrogen, ¹H) along both axes. (Techniques have also been devised for generating heteronuclear correlation spectra, in which the two axes correspond to different isotopes, such as ¹³C and ¹H.) The intensities of the peaks in the spectrum can be represented using a third dimension. More commonly, intensity is indicated using contours or different colors. The spectrum is interpreted starting from the diagonal, which consists of a series of peaks. The peaks that appear off of the diagonal are called cross-peaks. The cross-peaks are symmetrical (both above and below) the diagonal and indicate which hydrogen atoms are spin-spin coupled to each other. One can determine which atoms are connected to one another by only a few chemical bonds by matching the center of a cross-peak with the center of each of two corresponding diagonal peaks. The peaks on the diagonal when matched with cross-peaks are coupled to each other.

For example: a CH_{3CH2COCH3 molecule (ethanone) would show three peaks on the diagonal, due to the three distinct hydrogen groups. By drawing a line straight down from a cross-peak to the point on the diagonal directly above or below it, and then drawing a line from the cross-peak directly across to another peak on the diagonal, one can determine which peaks are coupled. This is done in such a way that the lines from the cross-peak form a 90� angle between the two peaks on the diagonal. The matching peaks, as determined by using the cross-peaks, indicate which hydrogen are coupled, giving a clearer understanding of the structure of the molecule under examination.}

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ProgesteroneCOSY.png
image:progesteroneCOSY.png

Above is an example of a COSY NMR spectrum of progesterone in DMSO-d6. The spectrum that appears along both the <math>x<math>- and <math>y<math>-axes is a regular one dimensional ^{1</sub>H NMR spectrum. The COSY is read along the diagonal - where the bulk of the peaks appear. Cross-peaks appear symmetrically above and below the diagonal.}

How COSY NMR works

COSY-90 is the most common COSY experiment. In COSY-90, the sample is irradiated with a radio frequency pulse, p1, which tilts the nuclear spin by 90�. After p1, the sample is allowed to freely precess during an evolution period (t1). A second 90� pulse, p2, is then applied, after which the experimental data are acquired. This is done repeatedly using a series of different evolution periods (t1). At the conclusion of data acquisition the data is Fourier transformed in each dimension to generate the two dimensional spectrum. It is only because the evolution period is varied that cross-peaks appear in the spectrum.

Cross-peaks result from a phenomenon called magnetization transfer. Depending on the experiment, this transfer can be achieved through space or bonds, or even through chemical or physical means. In COSY, magnetization transfer occurs through the bonds.

Another member of the COSY family is COSY-45. In COSY-45 a 45� pulse is used instead of a 90� pulse for the first pulse, p1. The advantage of a COSY-45 is that the diagonal-peaks are less pronounced, making it simpler to match cross-peaks near the diagonal in a large molecule. Additionally, the relative signs of the coupling constants can be elucidated from a COSY-45 spectrum. This is not possible using COSY-90^{3. Overall, the COSY-45 offers a cleaner spectrum while the COSY-90 is more sensitive. Related COSY techniques include double quantum filtered COSY and multiple quantum filtered COSY.}

COSY NMR has useful applications. Organic chemists often use COSY to elucidate structural data on molecules that are not satisfactorily represented in a one-dimensional NMR spectrum. Using cross-peaks, along with the diagonal spectrum, one can often discover much about the structure of an unknown molecule.

Notes

1. Martin, G.E; Zekter, A.S., ��Two-Dimensional NMR Methods for Establishing Molecular Connectivity��; VCH Pusblishers, Inc: New York, 1988 (p.59)
2. Akitt, J.W.; Mann, B.E., ��NMR and Chemistry��; Stanley Thornes: Cheltenham, UK, 2000. (p273)
3. Akitt, J.W.; Mann, B.E., ��NMR and Chemistry��; Stanley Thornes: Cheltenham, UK, 2000. (p287)

References

Hornak, Joseph P. The Basics of NMR (http://www.cis.rit.edu/htbooks/nmr/)

J. Keeler, Understanding NMR Spectroscopy (http://www.spectroscopynow.com/Spy/basehtml/SpyH/1,,5-14-9-0-0-education_dets-0-1839,00.html)

Wuthrich, Kurt NMR of Proteins and Nucleic Acids Wiley-Interscience, New York, NY USA 1986.

See also

• physics
• electromagnetism
• chemistry
• medicine
• materials science
• MRI
• Chemical_shift
• Gyromagnetic_ratio
• Larmor_equation

ca:Reson�ncia Magn�tica Nuclear de:Kernspinresonanz fr:R�sonance magn�tique nucl�aire nl:Kernspinresonantie ru:Ядерный магнитный резонанс sl:Jedrska magnetna resonanca

External Links

The International Society of Magnetic Resonance (http://www.ismar.org)