Nuclear magnetic resonance

Nuclear magnetic resonance (NMR) is a physical phenomenon 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. It involves 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 spectroscopy technique to obtain physical, chemical, and electronic properties of molecules. It is also the underlying principle of Magnetic Resonance Imaging. NMR is one of the techniques used to build quantum computers.

How NMR works

In NMR, the sample to be tested is placed in a static external magnetic field. An antenna (usually a coil-shaped inductor with the sample inside) is used to irradiate the sample with radio waves. At certain frequencies, atomic nuclei within the sample will absorb the radiation and enter an excited state. After a time, the nuclei will re-emit the radiation, which can be detected by the antenna. Finally, a measurement is taken of how much radiation is re-emitted, and when.

Only nuclei with non zero magnetic moment can undergo NMR. Such nuclei must have an odd number of protons or neutrons (ex. ¹ H, ² H, ¹³ C, ¹⁵ N, ³¹ P, ¹⁹ F).

A description of the interaction of atomic nuclei with the magnetic field involves both quantum and classical effects, and this gives rise to two different interpretations of some parts of the process. Both interpretations are discussed in the sections that follow.

Nuclear precession

An atomic nucleus can be thought of as a spinning charged body, which acts as a tiny magnet. The 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's magnetic field is quantized (due to the quantization of angular momentum). In the case of the ¹H hydrogen nucleus, which has spin 1/2, the magnetic field can either be oriented with the field or against it. The energy difference between the two different orientations is 2μH where μ is the magnetic moment of the nucleus. When no radiation is applied to the sample, the nuclei are distributed between the two orientations with a small excess in the direction of the magnetic field.

Although each nucleus can only be magnetized in a fixed number of directions, the total magnetization of all nuclei in the sample acts like a spinning magnet with arbitrary magnetization. In other words, the individual nuclei act like quantum mechanical objects, but the combination of all nuclei acts like a classical object. The classical magnetization aligns with the external magnetic field, and has magnitude proportional to the field.

Excitation

When radio power is sent to the antenna, it generates an oscillating magnetic field H₁ (not to be confused with the external magnetic field). Quantum mechanically, this magnetic field is composed of an equal mixture of right-handed and left-handed photons, with an energy proportional to their frequency. If the photons' energy is exactly the same as the energy difference between the two orientations of a nucleus, and the photon has the proper handedness, then the nucleus can flip its orientation by absorbing the photon.

Classically, H₁ can be decomposed into a superposition of two magnetic fields, one rotating clockwise about the external field, the other rotating counterclockwise. If the frequency of the rotating magnetic field is equal to the frequency at which the nuclei precess, then the magnetic field that is rotating in the same direction as the nuclear magnetization exerts a torque on the nuclear magnetization, changing its angle with respect to the external field H.

Relaxation

The sample is left in an excited state after the radiation is applied. The nuclei will emit radiation as they return to their equilibrium state, a process called relaxation. The mechanism of emission is exactly the reverse of the absorption described above. The radiation is of the same frequency as the excitation frequency, and can be picked up by an antenna and measured.

The classical and quantum descriptions are equivalent in most respects: the classical rotation frequency is the quantum photon frequency, and in both cases the result is that the magnetization of the sample has moved away from equilibrium. In practice, some effects (e.g. faster relaxation in liquids than in solids) are better explained by classical mechanics, while other effects (e.g. spin exchange between nuclei and electrons) are only explained quantum mechanically.

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.

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 Buckminster Fullerene contains no hydrogen and so ¹³C NMR has to be used [a more difficult form of NMR to do. However in [date here please] the spectra was obtained and sure enough it did contain just the one single spike, confirming the unusual structure of C₆₀.

History

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 phenonmena.

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. The pulse perturbs the equilibrium energy states of the nuclei under study (¹H for instance). At the end of the pulse, the nuclei relax back to their equilibrium state, emitting the energy absorbed by the system again in the radiofrequency range. 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.

Two 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).

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. Note also that experiments of the nuclear Overhauser variety allow you to 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 a part of 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.

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.

References

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