Nuclear magnetic resonance spectroscopy
Synonyms and keywords: NMR spectroscopy

# Overview
Nuclear magnetic resonance spectroscopy most commonly known as NMR spectroscopy is the name given to the technique which exploits the magnetic properties of certain nuclei. The most important applications for the organic chemist are proton NMR and carbon-13 NMR spectroscopy.  In principle, NMR is applicable to any nucleus possessing spin.
Many types of information can be obtained from an NMR spectrum. Much like using infrared spectroscopy to identify functional groups, analysis of a 1D NMR spectrum provides information on the number and type of chemical entities in a molecule.
The impact of NMR spectroscopy on the natural sciences has been substantial. It can, amongst other things, be used to study mixtures of analytes, to understand dynamic effects such as change in temperature and reaction mechanisms, and is an invaluable tool in understanding protein and nucleic acid structure and function. It can be applied to a wide variety of samples, both in the solution and the solid state.

# Basic NMR Techniques
When placed in a magnetic field, NMR active nuclei (such as 1H or 13C) absorb at a frequency characteristic of the isotope.  The resonant frequency, energy of the absorption and the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21 teslamagnetic field, protons resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900 MHz magnet, although different nuclei resonate at a different frequency at this field strength.
In the Earth's magnetic field the same nuclei resonate at audio frequencies. This effect is used in Earth's field NMR spectrometers and other instruments. Because these instruments are portable and inexpensive, they are often used for teaching and field work.

## Chemical Shift
Depending on the local chemical environment, different protons in a molecule resonate at slightly different frequencies. Since this frequency shift is proportional to the strength of the magnetic field, it is converted into a field-independent dimensionless value known as the chemical shift.  The chemical shift is reported as a relative measure from some reference resonance frequency. (For the nuclei1H, 13C, and 29Si, TMS (tetramethylsilane) is commonly used as a reference.)  This difference between the frequency of the signal and the frequency of the reference is divided by frequency of the reference signal to give the chemical shift.  The frequency shifts are extremely small in comparison to the fundamental NMR frequency.  A typical frequency shift might be 100 Hz, compared to a fundamental NMR frequency of 100 MHz, so the chemical shift is generally expressed in parts per million (ppm).
By understanding different chemical environments, the chemical shift can be used to obtain some structural information about the molecule in a sample.   The conversion of the raw data to this information is called assigning the spectrum.  For example, for 1H-NMR spectrum for ethanol (CH3CH2OH) one would expect three specific signals at three specific chemical shifts. One for the CH3 group, one for the CH2 group and one for the OH. A typical CH3 group has a shift around 1 ppm, the CH2 attached to a OH has a shift of around 4 ppm and the OH has a shift around 23 ppm depending on the solvent used.
Because of molecular motion at room temperature, the three methyl protons average out during the course of the NMR experiment (which typically requires a fewms). These protons become degenerate and form a peak at the same chemical shift.
The shape and size of peaks are indicators of chemical structure too. In the example abovethe proton spectrum of ethanolthe CH3 peak would be three times as large as the OH. Similarly the CH2 peak would be twice the size of the OH peak but only 2/3 the size of the CH3 peak.
Modern analysis software allows analysis of the size of peaks to understand how many protons give rise to the peak. This is known as integrationa mathematical process which calculates the area under a graph (essentially what a spectrum is). The analyst must integrate the peak and not measure its height because the peaks also have widthand thus its size is dependent on its area not its height. However, it should be mentioned that the number of protons, or any other observed nucleus, is only proportional to the intensity, or the integral, of the NMR signal, in the very simplest one-dimensional NMR experiments. In more elaborate experiments, for instance, experiments typically used to obtain carbon-13 NMR spectra, the integral of the signals depends on the relaxation rate of the nucleus, and its scalar and dipolar coupling constants. Very often these factors are poorly understood - therefore, the integral of the NMR signal is very difficult to interpret in more complicated NMR experiments.

## J-coupling
Some of the most useful information for structure determination in a one-dimensional NMR spectrum comes from J-coupling or scalar coupling (a special case ofspin-spin coupling) between NMR active nuclei.  This coupling arises from the interaction of different spin states through the chemical bonds of a molecule and results in the splitting of NMR signals.  These splitting patterns can be complex or simple and, likewise, can be straightforwardly interpretable or deceptive.  This coupling provides detailed insight into the connectivity of atoms in a molecule.
Coupling to n equivalent (spin 12) nuclei splits the signal into a n+1 multiplet with intensity ratios following Pascal's triangle as described on the right.  Coupling to additional spins will lead to further splittings of each component of the multiplet e.g. coupling to two different spin 12 nuclei with significantly different coupling constants will lead to a doublet of doublets (abbreviation: dd).   Note that coupling between nuclei that are chemically equivalent (that is, have the same chemical shift) has no effect of the NMR spectra and couplings between nuclei that are distant (usually more than 3 bonds apart for protons in flexible molecules) are usually too small to cause observable splittings.  Long-range couplings over more than three bonds can often be observed in cyclicand aromatic compounds, leading to more complex splitting patterns.
For example, in the proton spectrum for ethanol described above, the CH3 group is split into a triplet with an intensity ratio of 1:2:1 by the two neighboring CH2 protons.  Similarly, the CH2 is split into a quartet with an intensity ratio of 1:3:3:1 by the three neighboring CH3protons.  In principle, the two CH2 protons would also be split again into a doublet to form a doublet of quartets by the hydroxyl proton, but intermolecular exchange of the acidic hydroxyl proton often results in a loss of coupling information.
Coupling to any spin 12 nuclei such as phosphorus-31 or fluorine-19 works in this fashion (although the magnitudes of the coupling constants may be very different). But the splitting patterns differ from those described above for nuclei with spin greater than 12 because the spin quantum number has more than two possible values.  For instance, coupling to deuterium (a spin 1 nucleus) splits the signal into a 1:1:1 triplet because the spin 1 has three spin states.  Similarly, a spin 3/2 nucleus splits a signal into a 1:1:1:1 quartet and so on.
Coupling combined with the chemical shift (and the integration for protons) tells us not only about the chemical environment of the nuclei, but also the number ofneighboring NMR active nuclei within the molecule.  In more complex spectra with multiple peaks at similar chemical shifts or in spectra of nuclei other than hydrogen, coupling is often the only way to distinguish different nuclei.

### Second-order (or strong) coupling
The above description assumes that the coupling constant is small in comparison with the difference in NMR frequencies between the inequivalent spins.  If the shift separation decreases (or the coupling strength increases), the multiplet intensity patterns are first distorted, and then become more complex and less easily analyzed (especially if more than two spins are involved).  Intensification of some peaks in a multiplet is achieved at the expense of the remainder, which sometimes almost disappear in the background noise, 
although the integrated area under the peaks remains constant.
In most high-field NMR, however, the distortions are usually modest and the characteristic distortions (roofing) can in fact help to identify related peaks.
Second-order effects decrease as the frequency difference between multiplets increases, so that high-field (i.e. high-frequency) NMR spectra display less distortion than lower frequency spectra.  Early spectra at 60 MHz were more prone to distortion than spectra from later machines typically operating at frequencies at 200 MHz or above.

### Magnetic inequivalence
More subtle effects can occur if chemically equivalent spins (i.e. nuclei related by symmetry and so having the same NMR frequency) have different coupling relationships to external spins.  Spins that are chemically equivalent but are not indistinguishable (based on their coupling relationships) are termed magnetically inequivalent.  
For example, the 4 H sites of 1,2-dichlorobenzene divide into two chemically equivalent pairs by symmetry, but an individual member of one of the pairs has different couplings to the spins making up the other pair.
Magnetic inequivalence leads to highly complex spectra which can only be analyzed by computational modeling.  Such effects are more common in NMR spectra of aromatic and other non-flexible systems, while rapid rotation about C-C bonds in flexible molecules ensures that the couplings between protons on adjacent carbons are identical, avoiding problems with magnetic inequivalence.

# Correlation spectroscopy
Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy. This type of NMR experiment is best known by itsacronym, COSY.  Other types of two-dimensional NMR include J-spectroscopy, exchange spectroscopy (EXSY), Nuclear Overhauser effect spectroscopy (NOESY), total correlation spectroscopy (TOCSY) and heteronuclear correlation experiments, such as HSQC, HMQC, and HMBC.  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 Universite 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.

# Solid-State nuclear magnetic resonance
A variety of physical circumstances does not allow molecules to be studied in solution, and at the same time not by other spectroscopic techniques to an atomic level, either. In solid-phase media, such as crystals, microcrystalline powders, gels, anisotropic solutions, etc., it is in particular the dipolar coupling and chemical shift anisotropy that become dominant to the behaviour of the nuclear spin systems. In conventional solution-state NMR spectroscopy, these additional interactions would lead to a significant broadening of spectral lines. A variety of techniques allows to establish high-resolution conditions, that can, at least for 13C spectra, be comparable to solution-state NMR spectra.
Two important concepts for high-resolution solid-state NMR spectroscopy are the limitation of possible molecular orientation by sample orientation, and the reduction of anisotropic nuclear magnetic interactions by sample spinning. Of the latter approach, fast spinning around the magic angle is a very prominent method, when the system comprises spin 1/2 nuclei. A number of intermediate techniques, with samples of partial alignment or reduced mobility, is currently being used in NMR spectroscopy.
Applications in which solid-state NMR effects occur are often related to structure investigations on membrane proteins, protein fibrils or all kinds of polymers, and chemical analysis in inorganic chemistry, but also include "exotic" applications like the plant leaves and fuel cells.

# NMR spectroscopy applied to proteins
Much of the recent innovation within NMR spectroscopy has been within the field of protein NMR, which has become a very important technique instructural biology. One common goal of these investigations is to obtain high resolution 3-dimensional structures of the protein, similar to what can be achieved byX-ray crystallography. In contrast to X-ray crystallography, NMR is primarily limited to relatively small proteins, usually smaller than 35 kDa, though technical advances allow ever larger structures to be solved. NMR spectroscopy is often the only way to obtain high resolution information on partially or wholly intrinsically unstructured proteins.
Proteins are orders of magnitude larger than the small organic molecules discussed earlier in this article, but the same NMR theory applies. Because of the increased number of each element present in the molecule, the basic 1D spectra become crowded with overlapping signals to an extent where analysis is impossible. Therefore, multidimensional (2, 3 or 4D) experiments have been devised to deal with this problem. To facilitate these experiments, it is desirable toisotopically label the protein with 13C and 15N because the predominant naturally-occurring isotope 12C is not NMR-active, whereas the nuclear quadrupole moment of the predominant naturally-occurring 14N isotope prevents high resolution information to be obtained from this nitrogen isotope. The most important method used for structure determination of proteins utilizes NOE experiments to measure distances between pairs of atoms within the molecule. Subsequently, the obtained distances are used to generate a 3D structure of the molecule using a computer program.