Solid-state nuclear magnetic resonance

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Solid-state_nuclear_magnetic_resonance

Solid-state 900 MHz (21.1 T) NMR spectrometer at the Canadian National Ultrahigh-field NMR Facility for Solids

Solid-state NMR (ssNMR) spectroscopy is a technique for characterizing atomic level structure in solid materials e.g. powders, single crystals and amorphous samples and tissues using nuclear magnetic resonance (NMR) spectroscopy. The anisotropic part of many spin interactions are present in solid-state NMR, unlike in solution-state NMR where rapid tumbling motion averages out many of the spin interactions. As a result, solid-state NMR spectra are characterised by larger linewidths than in solution state NMR, which can be utilized to give quantitative information on the molecular structure, conformation and dynamics of the material. Solid-state NMR is often combined with magic angle spinning to remove anisotropic interactions and improve the resolution as well as the sensitivity of the technique.

Bruker MAS rotors. From left to right: 1.3 mm (up to 67 kHz), 2.5 mm (up to 35 kHz), 3.2 mm (up to 24 kHz), 4 mm (up to 15 kHz), 7 mm (up to 7 kHz)

Nuclear spin interactions

The resonance frequency of a nuclear spin depends on the strength of the magnetic field at the nucleus, which can be modified by isotropic (e.g. chemical shift, isotropic J-coupling) and anisotropic interactions (e.g. chemical shift anisotropy, dipolar interactions). In a classical liquid-state NMR experiment, molecular tumbling coming from Brownian motion averages anisotropic interactions to zero and they are therefore not reflected in the NMR spectrum. However, in media with no or little mobility (e.g. crystalline powders, glasses, large membrane vesicles, molecular aggregates), anisotropic local fields or interactions have substantial influence on the behaviour of nuclear spins, which results in the line broadening of the NMR spectra.

Chemical shielding

Main article: Chemical shift

Chemical shielding is a local property of each nuclear site in a molecule or compound, and is proportional to the applied external magnetic field. The external magnetic field induces currents of the electrons in molecular orbitals. These induced currents create local magnetic fields that lead to characteristic changes in resonance frequency. These changes can be predicted from molecular structure using empirical rules or quantum-chemical calculations.

In general, the chemical shielding is anisotropic because of the anisotropic distribution of molecular orbitals around the nuclear sites. Under sufficiently fast magic angle spinning, or under the effect of molecular tumbling in solution-state NMR, the anisotropic dependence of the chemical shielding is time-averaged to zero, leaving only the isotropic chemical shift.

Dipolar coupling

Main article: Magnetic dipole-dipole interaction

Vectors important for dipolar coupling between nuclear spins I₁ and I₂. θ is the angle between the vector connecting I₁ and I₂, and the magnetic field B.

Nuclear spins exhibit a magnetic dipole moment, which generates a magnetic field that interacts with the dipole moments of other nuclei (dipolar coupling). The magnitude of the interaction is dependent on the gyromagnetic ratio of the spin species, the internuclear distance r, and the orientation, with respect to the external magnetic field B, of the vector connecting the two nuclear spins (see figure). The maximum dipolar coupling is given by the dipolar coupling constant d,

${\displaystyle d=\hslash \left(\frac{{\mu }_0}{4\pi }\right)\frac{1}{r^3}{\gamma }_1{\gamma }_2}$,

where γ₁ and γ₂ are the gyromagnetic ratios of the nuclei, ${\displaystyle \hslash }$ is the reduced Planck's constant, and ${\displaystyle {\mu }_0}$ is the vacuum permeability. In a strong magnetic field, the dipolar coupling depends on the angle θ between the internuclear vector and the external magnetic field B (figure) according to

${\displaystyle D\propto 3{\cos }^2\theta -1}$.

D becomes zero for ${\displaystyle {\theta }_m=\arccos \sqrt{1/3}=\arctan \sqrt{2}\simeq {54.7}^{\circ }}$. Consequently, two nuclei with a dipolar coupling vector at an angle of θ_m = 54.7° to a strong external magnetic field have zero dipolar coupling. θ_m is called the magic angle. Magic angle spinning is typically used to remove dipolar couplings weaker than the spinning rate.

Quadrupolar interaction

Nuclei with a spin quantum number >1/2 have a non-spherical charge distribution and an associated electric quadrupole moment tensor. The nuclear electric quadrupole moment couples with surrounding electric field gradients. The nuclear quadrupole coupling is one of the largest interactions in NMR spectroscopy, often comparable in size to the Zeeman coupling. When the nuclear quadrupole coupling is not negligible relative to the Zeeman coupling, higher order corrections are needed to describe the NMR spectrum correctly. In such cases, the first-order correction to the NMR transition frequency leads to a strong anisotropic line broadening of the NMR spectrum. However, all symmetric transitions, between ${\displaystyle m_I}$ and ${\displaystyle -m_I}$ levels are unaffected by the first-order frequency contribution. The second-order frequency contribution depends on the P₄ Legendre polynomial, which has zero points at 30.6° and 70.1°. These anisotropic broadenings can be removed using DOR (DOuble angle Rotation) where you spin at two angles at the same time, or DAS (Double Angle Spinning) where you switch quickly between the two angles. Both techniques were developed in the late 1980s, and require specialized hardware (probe). Multiple quantum magic angle spinning (MQMAS) NMR was developed in 1995 and has become a routine method for obtaining high resolution solid-state NMR spectra of quadrupolar nuclei. A similar method to MQMAS is satellite transition magic angle spinning (STMAS) NMR developed in 2000.

J-coupling

The J-coupling or indirect nuclear spin-spin coupling (sometimes also called "scalar" coupling despite the fact that J is a tensor quantity) describes the interaction of nuclear spins through chemical bonds. J-couplings are not always resolved in solids owing to the typically large linewdiths observed in solid state NMR.

Other interactions

Paramagnetic substances are subject to the Knight shift.

Solid-state NMR line shapes

Powder pattern

Simulations of the shape of different powder patterns for different asymmetry ${\displaystyle \eta }$ and chemical shift anisotropy ${\displaystyle {\mathrm{\Delta }}_{CS}}$parameters.

A powder pattern arises in powdered samples where crystallites are randomly oriented relative to the magnetic field so that all molecular orientations are present. In presence of a chemical shift anisotropy interaction, each orientation with respect to the magnetic field gives a different resonance frequency. If enough crystallites are present, all the different contributions overlap continuously and lead to a smooth spectrum.

Fitting of the pattern in a static ssNMR experiment gives information about the shielding tensor, which are often described by the isotropic chemical shift ${\displaystyle {\delta }_{iso}}$, the chemical shift anisotropy parameter ${\displaystyle {\mathrm{\Delta }}_{CS}}$, and the asymmetry parameter ${\displaystyle \eta }$.

Dipolar pattern

Further information: Pake doublet

Dipolar powder pattern (Pake pattern)

The dipolar powder pattern (also Pake pattern) has a very characteristic shape that arises when two nuclear spins are coupled together within a crystallite. The splitting between the maxima (the "horns") of the pattern is equal to the dipolar coupling constant ${\displaystyle d}$.:

${\displaystyle d=\hslash \left(\frac{{\mu }_0}{4\pi }\right)\frac{1}{r^3}{\gamma }_1{\gamma }_2}$

where γ₁ and γ₂ are the gyromagnetic ratios of the dipolar-coupled nuclei, ${\displaystyle r}$ is the internuclear distance, ${\displaystyle \hslash }$ is the reduced Planck's constant, and ${\displaystyle {\mu }_0}$ is the vacuum permeability.

Essential solid-state techniques

Magic angle spinning

Main article: Magic angle spinning

Magic angle spinning (MAS) is a technique routinely used in solid-state NMR to produce narrower NMR and more intense NMR lines. This is achieved by rotating the sample at the magic angle θ_m (ca. 54.74°, where cos²θ_m=1/3) with respect to the direction of the magnetic field, which has the effect to cancel, at least partially, anisotropic nuclear interactions such as dipolar, chemical shift anisotropy, and quadrupolar interactions. To achieve the complete averaging of these interactions, the sample needs to be spun at a rate that is at least higher than the greater that the largest anisotropy.

Spinning a powder sample at a slower rate than the largest component of the chemical shift anisotropy results in an incomplete averaging of the interaction, and produces a set of spinning sidebands in addition to the isotropic line, centred at the isotropic chemical shift. Spinning sidebands are sharp lines separated from the isotropic frequency by a multiple of the spinning rate. Although spinning sidebands can be used to measure anisotropic interactions, they are often undesirable and removed by spinning the sample faster or by recording the data points synchronously with the rotor period.

Cross-polarisation

The CP pulse sequence. The sequence starts with a 90º pulse on the abundant channel (typically H). Then CP contact pulses matching the Hartmann-Hahn condition are applied to transfer the magnetisation from H to X. Finally, the free induction decay (FID) of the X nuclei is detected, typically with ¹H decoupling.

Cross-polarization (CP) if a fundamental RF pulse sequence and a building-block in many solid-state NMR. It is typically used to enhance the signal of a dilute nuclei with a low gyromagnetic ratio (e.g. ¹³
C, ¹⁵
N) by magnetization transfer from an abundant nuclei with a high gyromagnetic ratio (e.g. ¹
H), or as a spectral editing method to get through space information (e.g. directed ¹⁵
N→¹³
C CP in protein spectroscopy).

To establish magnetization transfer, RF pulses ("contact pulses") are simultaneously applied on both frequency channels to produce ${\displaystyle B_1}$ fields whose strength fulfil the Hartmann–Hahn condition:

${\displaystyle {\gamma }_H{B}_1{(}^1\text{H})={\gamma }_X{B}_1(\text{X})\pm n{\omega }_R}$

where ${\displaystyle \gamma }$ are the gyromagnetic ratios, ${\displaystyle {\omega }_R}$ is the spinning rate, and ${\displaystyle n}$ is an integer. In practice, the pulse power, as well as the length of the contact pulse are experimentally optimised. The power of one contact pulse is typically ramped to achieve a more broadband and efficient magnetisation transfer.

Decoupling

Spin interactions can be removed (decoupled) to increase the resolution of NMR spectra during the detection, or to extend the lifetime of the nuclear magnetization.

Heteronuclear decoupling is achieved by radio-frequency irradiation on at the frequency of the nucleus to be decoupled, which is often ¹H. The irradiation can be continuous (continuous wave decoupling), or a series of pulses that extend the performance and the bandwidth of the decoupling (TPPM, SPINAL-64, SWf-TPPM)

Homonuclear decoupling is achieved with multiple-pulse sequences (WAHUHA, MREV-8, BR-24, BLEW-12, FSLG), or continuous wave modulation (DUMBO, eDUMBO). Dipolar interactions can also be removed with magic angle spinning. Ultra fast MAS (from 60 kHz up to above 111 kHz) is an efficient way to average all dipolar interactions, including ¹H-¹H homonuclear dipolar interactions, which extends the resolution of ¹H spectra and enables the usage of pulse sequences used in solution state NMR.

Advanced solid-state NMR spectroscopy

Rotational Echo DOuble Resonance (REDOR)

Rotational Echo DOuble Resonance (REDOR) pulse sequence. The first excitation step (90º pulse or CP step) puts the magnetisation in the transverse plane. Then two trains of 180º pulses synchronised with the rotor half period are applied on the Y channel to reintroduce X-Y heteronuclear dipolar interactions. The trains of pulses are interrupted by a 180º pulse on the X channel that allows the refocussing of the X magnetisation for the X-detection (spin echo). The delay between the 90º pulse and the beginning of the acquisition is referred to as the "rephrasing time".

Rotational Echo DOuble Resonance (REDOR) experiment, are a type of heteronuclear dipolar recoupling experiment which enable one to re-introduce heteronuclear dipolar couplings averaged by MAS. The reintroduction of such dipolar coupling reduce the intensity of the NMR signal intensity compared to a reference spectrum where no dephasing pulse is used. REDOR can be used to measure heteronuclear distances, and are the basis of NMR crystallographic studies.

Ultra Fast MAS for ¹H NMR

The strong ¹H-¹H homonuclear dipolar interactions associated with broad NMR lines and short T₂ relaxation time effectively relegate proton for bimolecular NMR. Recent developments of faster MAS, and reduction of dipolar interactions by deuteration have made proton ssNMR as versatile as in solution. This includes spectral dispersion in multi-dimensional experiments as well as structurally valuable restraints and parameters important for studying material dynamics.

Ultra-fast NMR and the associated sharpening of the NMR lines enables NMR pulse sequences to capitalize on proton-detection to improve the sensitivity of the experiments compared to the direct detection of a spin-1/2 system (X). Such enhancement factor ${\displaystyle \xi }$ is given by:

${\displaystyle \xi \propto {\left(\frac{{\gamma }_H}{{\gamma }_X}\right)}^{3/2}{\left(\frac{W_X}{W_H}\right)}^{1/2}{\left(\frac{Q_H}{Q_X}\right)}^{1/2}}$

where ${\displaystyle \gamma }$ are the gyromagnetic ratios, ${\displaystyle W}$ represent the NMR line widths, and ${\displaystyle Q}$ represent the quality factor of the probe resonances.

MAS-Dynamic Nuclear Polarisation (MAS-DNP)

Further information: Dynamic nuclear polarization

Magic angle spinning Dynamic Nuclear Polarization (MAS-DNP) is a technique that increases the sensitivity of NMR experiments by several orders of magnitude. It involves the transfer of the very high electron polarisation from unpaired electrons to nearby nuclei. This is achieved at cryogenic temperatures by the means of a continuous microwave irradiation coming from a klystron or a Gyrotron, with a frequency close to the corresponding electron paramagnetic resonance (EPR) frequency.

The development in the MAS-DNP instrumentation, as well as the improvement of polarising agents (TOTAPOL, AMUPOL, TEKPOL, etc.) to achieve a more efficient transfer of polarisation has dramatically reduced experiments times which enabled the observation of surfaces, insensitive isotopes, and multidimensional experiments on low natural abundance nuclei, and diluted species.

Applications

Biology

Solid-state NMR is used to study insoluble proteins and proteins very sensitive to their environment such as membrane proteins and amyloid fibrils,. The latter topic relates to protein aggregation diseases such as Alzheimer's disease and Parkinson's disease. Solid-state NMR spectroscopy complements solution-state NMR spectroscopy and beam diffraction methods (e.g. X-ray crystallography, electron microscopy). Despite often requiring isotopic enrichment, ssNMR has the advantage that little sample preparation is required and can be used on not just dry or frozen samples, but also fully hydrated samples or native non-crystalline tissues. Solid-state NMR structure elucidation of proteins has traditionally been based on secondary chemical shifts and spatial contacts between nuclei.

Solid-state NMR has also been successfully used to study biomaterials such as bone, teeth, hair, silk, wood, as well as viruses, plants, cells, biopsies, and even live animals.

Materials science

Solid-state NMR spectroscopy serves as an analysis tool in organic and inorganic chemistry, where it is used to characterize chemical composition, supramolecular structure, local motions, kinetics, and thermodynamics, with the special ability to assign the observed behavior to specific sites in a molecule.

Solid-state NMR has been successfully used to study metal organic frameworks (MOFS), batteries, surfaces of nanoporous materials, polymers.

Art conservation

NMR can also be applied to art conservation. Different salts and moisture levels can be detected through the use of solid state NMR. However, sampling sizes retrieved from works of art in order to run through these large conducting magnets typically exceed levels deemed acceptable. Unilateral NMR techniques use portable magnets that are applied to the object of interest, bypassing the need for sampling.

Nuclear magnetic resonance spectroscopy

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance_spectroscopy

A 900 MHz NMR instrument with a 21.1 T magnet at HWB-NMR, Birmingham, UK

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy (MRS), is a spectroscopic technique to observe local magnetic fields around atomic nuclei. This spectroscopy is based on the measurement of absorption of electromagnetic radiations in the radio frequency region from roughly 4 to 900 MHz. Absorption of radio waves in the presence of magnetic field is accompanied by a special type of nuclear transition, and for this reason, such type of spectroscopy is known as Nuclear Magnetic Resonance Spectroscopy. The sample is placed in a magnetic field and the NMR signal is produced by excitation of the nuclei sample with radio waves into nuclear magnetic resonance, which is detected with sensitive radio receivers. The intramolecular magnetic field around an atom in a molecule changes the resonance frequency, thus giving access to details of the electronic structure of a molecule and its individual functional groups. As the fields are unique or highly characteristic to individual compounds, in modern organic chemistry practice, NMR spectroscopy is the definitive method to identify monomolecular organic compounds.

The principle of NMR usually involves three sequential steps:

1. The alignment (polarization) of the magnetic nuclear spins in an applied, constant magnetic field B₀.
2. The perturbation of this alignment of the nuclear spins by a weak oscillating magnetic field, usually referred to as a radio-frequency (RF) pulse.
3. Detection and analysis of the electromagnetic waves emitted by the nuclei of the sample as a result of this perturbation.

Similarly, biochemists use NMR to identify proteins and other complex molecules. Besides identification, NMR spectroscopy provides detailed information about the structure, dynamics, reaction state, and chemical environment of molecules. The most common types of NMR are proton and carbon-13 NMR spectroscopy, but it is applicable to any kind of sample that contains nuclei possessing spin.

NMR spectra are unique, well-resolved, analytically tractable and often highly predictable for small molecules. Different functional groups are obviously distinguishable, and identical functional groups with differing neighboring substituents still give distinguishable signals. NMR has largely replaced traditional wet chemistry tests such as color reagents or typical chromatography for identification. A disadvantage is that a relatively large amount, 2–50 mg, of a purified substance is required, although it may be recovered through a workup. Preferably, the sample should be dissolved in a solvent, because NMR analysis of solids requires a dedicated magic angle spinning machine and may not give equally well-resolved spectra. The timescale of NMR is relatively long, and thus it is not suitable for observing fast phenomena, producing only an averaged spectrum. Although large amounts of impurities do show on an NMR spectrum, better methods exist for detecting impurities, as NMR is inherently not very sensitive - though at higher frequencies, sensitivity is higher.

Correlation spectroscopy is a development of ordinary NMR. In two-dimensional NMR, the emission is centered around a single frequency, and correlated resonances are observed. This allows identifying the neighboring substituents of the observed functional group, allowing unambiguous identification of the resonances. There are also more complex 3D and 4D methods and a variety of methods designed to suppress or amplify particular types of resonances. In nuclear Overhauser effect (NOE) spectroscopy, the relaxation of the resonances is observed. As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows for construction of a three-dimensional model of the molecule.

Cutaway of an NMR magnet that shows its structure: radiation shield, vacuum chamber, liquid nitrogen vessel, liquid helium vessel, and cryogenic shims.

NMR spectrometers are relatively expensive; universities usually have them, but they are less common in private companies. Between 2000 and 2015, an NMR spectrometer cost around 500,000 - 5 million USD. Modern NMR spectrometers have a very strong, large and expensive liquid helium-cooled superconducting magnet, because resolution directly depends on magnetic field strength. Less expensive machines using permanent magnets and lower resolution are also available, which still give sufficient performance for certain applications such as reaction monitoring and quick checking of samples. There are even benchtop nuclear magnetic resonance spectrometers. NMR can be observed in magnetic fields less than a millitesla. Low-resolution NMR produces broader peaks which can easily overlap one another causing issues in resolving complex structures. The use of higher strength magnetic fields result in clear resolution of the peaks and is the standard in industry.

History

Credit for the discovery of NMR goes to Isidor Isaac Rabi, who received the Nobel Prize in Physics in 1944. The Purcell group at Harvard University and the Bloch group at Stanford University independently developed NMR spectroscopy in the late 1940s and early 1950s. Edward Mills Purcell and Felix Bloch shared the 1952 Nobel Prize in Physics for their discoveries.

Basic NMR techniques

The NMR sample is prepared in a thin-walled glass tube - an NMR tube.

Resonant frequency

When placed in a magnetic field, NMR active nuclei (such as ¹H or ¹³C) absorb electromagnetic radiation at a frequency characteristic of the isotope. The resonant frequency, energy of the radiation absorbed, and the intensity of the signal are proportional to the strength of the magnetic field. For example, in a 21 Tesla magnetic field, hydrogen nuclei (commonly referred to as protons) resonate at 900 MHz. It is common to refer to a 21 T magnet as a 900 MHz magnet since hydrogen is the most common nucleus detected. However, different nuclei will resonate at different frequencies at this field strength in proportion to their nuclear magnetic moments.

Sample handling

An NMR spectrometer typically consists of a spinning sample-holder inside a very strong magnet, a radio-frequency emitter, and a receiver with a probe (an antenna assembly) that goes inside the magnet to surround the sample, optionally gradient coils for diffusion measurements, and electronics to control the system. Spinning the sample is usually necessary to average out diffusional motion, however some experiments call for a stationary sample when solution movement is an important variable. For instance, measurements of diffusion constants (diffusion ordered spectroscopy or DOSY) are done using a stationary sample with spinning off, and flow cells can be used for online analysis of process flows.

Deuterated solvents

The vast majority of molecules in a solution are solvent molecules, and most regular solvents are hydrocarbons and so contain NMR-active hydrogen-1 nuclei. In order to avoid having the signals from solvent hydrogen atoms overwhelm the experiment and interfere in analysis of the dissolved analyte, deuterated solvents are used where 99+% of the protons are replaced with deuterium (hydrogen-2). The most widely used deuterated solvent is deuterochloroform (CDCl₃), although other solvents may be used for various reasons, such as solubility of a sample, desire to control hydrogen bonding, or melting or boiling points. The chemical shifts of a molecule will change slightly between solvents, and therefore the solvent used will almost always be reported with chemical shifts. Proton NMR spectra are often calibrated against the known solvent residual proton peak as a secondary standard instead of adding tetramethylsilane (defined as a chemical shift of zero).

Shim and lock

To detect the very small frequency shifts due to nuclear magnetic resonance, the applied magnetic field must be constant throughout the sample volume. High resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion (ppb) in a volume of a few cubic centimeters. In order to detect and compensate for inhomogeneity and drift in the magnetic field, the spectrometer maintains a "lock" on the solvent deuterium frequency with a separate lock unit, which is essentially an additional transmitter and RF processor tuned to the lock nucleus (deuterium) rather than the nuclei of the sample of interest. In modern NMR spectrometers shimming is adjusted automatically, though in some cases the operator has to optimize the shim parameters manually to obtain the best possible resolution.

Acquisition of spectra

Upon excitation of the sample with a radio frequency (60–1000 MHz) pulse, a nuclear magnetic resonance response - a free induction decay (FID) - is obtained. It is a very weak signal, and requires sensitive radio receivers to pick up. A Fourier transform is carried out to extract the frequency-domain spectrum from the raw time-domain FID. A spectrum from a single FID has a low signal-to-noise ratio, but it improves readily with averaging of repeated acquisitions. Good ¹H NMR spectra can be acquired with 16 repeats, which takes only minutes. However, for elements heavier than hydrogen, the relaxation time is rather long, e.g. around 8 seconds for ¹³C. Thus, acquisition of quantitative heavy-element spectra can be time-consuming, taking tens of minutes to hours.

Following the pulse, the nuclei are, on average, excited to a certain angle vs. the spectrometer magnetic field. The extent of excitation can be controlled with the pulse width, typically ca. 3-8 µs for the optimal 90° pulse. The pulse width can be determined by plotting the (signed) intensity as a function of pulse width. It follows a sine curve, and accordingly, changes sign at pulse widths corresponding to 180° and 360° pulses.

Decay times of the excitation, typically measured in seconds, depend on the effectiveness of relaxation, which is faster for lighter nuclei and in solids, and slower for heavier nuclei and in solutions, and they can be very long in gases. If the second excitation pulse is sent prematurely before the relaxation is complete, the average magnetization vector has not decayed to ground state, which affects the strength of the signal in an unpredictable manner. In practice, the peak areas are then not proportional to the stoichiometry; only the presence, but not the amount of functional groups is possible to discern. An inversion recovery experiment can be done to determine the relaxation time and thus the required delay between pulses. A 180° pulse, an adjustable delay, and a 90° pulse is transmitted. When the 90° pulse exactly cancels out the signal, the delay corresponds to the time needed for 90° of relaxation. Inversion recovery is worthwhile for quantitative ¹³C, 2D and other time-consuming experiments.

Spectral interpretation

NMR signals are ordinarily characterized by three variables: chemical shift, spin-spin coupling, and relaxation time.

Chemical shift

Main article: Chemical shift

The energy difference, ΔE, between nuclear spin states is proportional to the magnetic field (Zeeman effect). ΔE is also sensitive to electronic environment of the nucleus giving rise to what is known as the chemical shift, δ. The value of δ is often expressed in terms of "shielding": shielded nuclei have higher ΔE. The range of δ values is called the dispersion. For ¹H signals, the dispersion is rather small, but for other nuclei, the dispersion is much larger. NMR signals are reported relative to a reference signal, usually that of TMS (tetramethylsilane). Additionally, since the distribution of NMR signals is field dependent, these frequencies are divided by the spectrometer frequency. However, since we are dividing Hz by MHz, the resulting number would be too small, and thus it is multiplied by a million. This operation therefore gives a locator number called the "chemical shift" with units of parts per million. The chemical shift provides structural information.

The conversion of chemical shifts (and J's, see below) is called assigning the spectrum. For diamagnetic organic compounds, assignments of 1H and 13C NMR spectra are extremely sophisticated because of the large databases and easy computational tools. In general, chemical shifts for protons are highly predictable since the shifts are primarily determined by shielding effects (electron density). The chemical shifts for many heavier nuclei are more strongly influenced by other factors including excited states ("paramagnetic" contribution to shielding tensor). This paramagnetic contribution, which is unrelated to paramagnetism) not only disrupts trends in chemical shifts, which complicates assignments, but it also gives rise to very large chemical shift ranges. For example, most ¹H NMR signals for most organic compounds are within 15 ppm. For ³¹P NMR, the range is hundreds of ppm.

Example of the chemical shift: NMR spectrum of hexaborane B₆H₁₀ showing peaks shifted in frequency, which give clues as to the molecular structure. (click to read interpretation details)

In paramagnetic NMR spectroscopy, the samples are paramagnetic, i.e. they contain unpaired electrons. The paramagnetism gives rise to very diverse chemical shifts. In ¹H NMR spectroscopy, the chemical shift range can span up to thousands of ppm.

J-coupling

Main article: J-coupling

 

Multiplicity	Intensity ratio
Singlet (s)	1
Doublet (d)	1:1
Triplet (t)	1:2:1
Quartet (q)	1:3:3:1
Quintet	1:4:6:4:1
Sextet	1:5:10:10:5:1
Septet	1:6:15:20:15:6:1

Example ¹H NMR spectrum (1-dimensional) of ethanol plotted as signal intensity vs. chemical shift. There are three different types of H atoms in ethanol regarding NMR. The hydrogen (H) on the −OH group is not coupling with the other H atoms and appears as a singlet, but the CH₃− and the −CH₂− hydrogens are coupling with each other, resulting in a triplet and quartet respectively.

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 of spin–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. For a proton, the local magnetic field is slightly different depending on whether an adjacent nucleus points towards or against the spectrometer magnetic field, which gives rise to two signals per proton instead of one. 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 ½) 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 ½ 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 on 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 cyclic and 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 CH₃ protons. 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-1/2 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 ½ 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 such as ³⁵Cl 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 of neighboring 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.

¹H NMR spectrum of menthol with chemical shift in ppm on the horizontal axis. Each magnetically inequivalent proton has a characteristic shift, and couplings to other protons appear as splitting of the peaks into multiplets: e.g. peak a, because of the three magnetically equivalent protons in methyl group a, couple to one adjacent proton (e) and thus appears as a doublet.

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.

Some of these patterns can be analyzed with the method published by John Pople, though it has limited scope.

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.

Furthermore, as in the figure to the right, J-coupling can be used to identify ortho-meta-para substitution of a ring. Ortho coupling is the strongest at 15 Hz, Meta follows with an average of 2 Hz, and finally para coupling is usually insignificant for studies.

Magnetic inequivalence

Further information: 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 can lead 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 conformational averaging about C−C bonds in flexible molecules tends to equalize the couplings between protons on adjacent carbons, reducing problems with magnetic inequivalence.

Correlation spectroscopy

Further information: 2D-NMR

Correlation spectroscopy is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy or 2D-NMR. This type of NMR experiment is best known by its acronym, 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. In correlation spectroscopy, emission is centered on the peak of an individual nucleus; if its magnetic field is correlated with another nucleus by through-bond (COSY, HSQC, etc.) or through-space (NOE) coupling, a response can also be detected on the frequency of the correlated nucleus. 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 Université 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

Solid-state 900 MHz (21.1 T) NMR spectrometer at the Canadian National Ultrahigh-field NMR Facility for Solids

Further information: Solid-state NMR

A variety of physical circumstances do 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 establishing 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. Spinning rates of ca. 20 kHz are used, which demands special equipment. 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. For example, Rahmani et al. studied the effect of pressure and temperature on the bicellar structures' self-assembly using deuterium NMR spectroscopy.

Biomolecular NMR spectroscopy

Proteins

Main article: Nuclear magnetic resonance spectroscopy of proteins

Much of the innovation within NMR spectroscopy has been within the field of protein NMR spectroscopy, an important technique in structural biology. A common goal of these investigations is to obtain high resolution 3-dimensional structures of the protein, similar to what can be achieved by X-ray crystallography. In contrast to X-ray crystallography, NMR spectroscopy is usually limited to proteins smaller than 35 kDa, although larger structures have been solved. NMR spectroscopy is often the only way to obtain high resolution information on partially or wholly intrinsically unstructured proteins. It is now a common tool for the determination of Conformation Activity Relationships where the structure before and after interaction with, for example, a drug candidate is compared to its known biochemical activity. Proteins are orders of magnitude larger than the small organic molecules discussed earlier in this article, but the basic NMR techniques and some NMR theory also applies. Because of the much higher number of atoms present in a protein molecule in comparison with a small organic compound, the basic 1D spectra become crowded with overlapping signals to an extent where direct spectral analysis becomes untenable. Therefore, multidimensional (2, 3 or 4D) experiments have been devised to deal with this problem. To facilitate these experiments, it is desirable to isotopically label the protein with ¹³C and ¹⁵N because the predominant naturally occurring isotope ¹²C is not NMR-active and the nuclear quadrupole moment of the predominant naturally occurring ¹⁴N isotope prevents high resolution information from being obtained from this nitrogen isotope. The most important method used for structure determination of proteins utilizes NOE experiments to measure distances between atoms within the molecule. Subsequently, the distances obtained are used to generate a 3D structure of the molecule by solving a distance geometry problem. NMR can also be used to obtain information on the dynamics and conformational flexibility of different regions of a protein.

Nucleic acids

Main article: Nuclear magnetic resonance spectroscopy of nucleic acids

Nucleic acid NMR is the use of NMR spectroscopy to obtain information about the structure and dynamics of polynucleic acids, such as DNA or RNA. As of 2003, nearly half of all known RNA structures had been determined by NMR spectroscopy.

Nucleic acid and protein NMR spectroscopy are similar but differences exist. Nucleic acids have a smaller percentage of hydrogen atoms, which are the atoms usually observed in NMR spectroscopy, and because nucleic acid double helices are stiff and roughly linear, they do not fold back on themselves to give "long-range" correlations. The types of NMR usually done with nucleic acids are ¹H or proton NMR, ¹³C NMR, ¹⁵N NMR, and ³¹P NMR. Two-dimensional NMR methods are almost always used, such as correlation spectroscopy (COSY) and total coherence transfer spectroscopy (TOCSY) to detect through-bond nuclear couplings, and nuclear Overhauser effect spectroscopy (NOESY) to detect couplings between nuclei that are close to each other in space.

Parameters taken from the spectrum, mainly NOESY cross-peaks and coupling constants, can be used to determine local structural features such as glycosidic bond angles, dihedral angles (using the Karplus equation), and sugar pucker conformations. For large-scale structure, these local parameters must be supplemented with other structural assumptions or models, because errors add up as the double helix is traversed, and unlike with proteins, the double helix does not have a compact interior and does not fold back upon itself. NMR is also useful for investigating nonstandard geometries such as bent helices, non-Watson–Crick basepairing, and coaxial stacking. It has been especially useful in probing the structure of natural RNA oligonucleotides, which tend to adopt complex conformations such as stem-loops and pseudoknots. NMR is also useful for probing the binding of nucleic acid molecules to other molecules, such as proteins or drugs, by seeing which resonances are shifted upon binding of the other molecule.

Carbohydrates

Main article: Nuclear magnetic resonance spectroscopy of carbohydrates

Carbohydrate NMR spectroscopy addresses questions on the structure and conformation of carbohydrates. The analysis of carbohydrates by 1H NMR is challenging due to the limited variation in functional groups, which leads to 1H resonances concentrated in narrow bands of the NMR spectrum. In other words, there is poor spectral dispersion. The anomeric proton resonances are segregated from the others due to fact that the anomeric carbons bear two oxygen atoms. For smaller carbohydrates, the dispersion of the anomeric proton resonances facilitates the use of 1D TOCSY experiments to investigate the entire spin systems of individual carbohydrate residues.

Drug Discovery

Knowledge of energy minima and rotational energy barriers of small molecules in solution can be found using NMR, e.g. looking at free ligand conformational preferences and conformational dynamics, respectively. This can be used to guide drug design hypotheses, since experimental and calculated values are comparable. For example, AstraZeneca uses NMR for its oncology research & development.