Nuclear magnetic resonance
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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.
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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's magnetic field is quantized (due to the quantization of angular momentum). However, when the angles are randomly oriented, in net, they will align with the magnetic field slightly.
The sample to be tested is placed in a static external magnetic field. The nuclei (on a quantum mechanical level) are all precessing at approximately the same rate, and more precessing with net magnetic field aligned with the magnet. Then 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 align. so that they all precess in phase with each other, yielding a new changing magnetic field with a characteristic frequency. This field can be detected and its frequencies quantified via Fourier transform.
This can also be though of in the classical sense where the net magnetization vector of the sample is tilted and then begins to precess at its characteristic frequency.
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 Wüthrich, 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. Wüthrich 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 sinal 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.
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Correlation Spectroscopy; a form of two-dimensional Nuclear Magnetic Resonance
Correlation spectroscopy (COSY) is one of several types of two-dimensional nuclear magnetic resonance (NMR) spectroscopy. Other types of two-dimensional NMR include J-spectrum, exchange spectroscopy (EXSY), and nuclear Overhouser effect spectroscopy (NOESY.) Two-dimensional NMR spectra give more information about a molecule than a one-dimensional NMR and are especially useful in determining the structure of a molecule, particularly molecules too complex to determine the structure completely by one-dimensional NMR. The first two-dimensional correlation spectroscopy NMR was proposed by Jean Jeener, a professor at Université Libre de Bruxelles, in 1971. COSY is the original two-dimension NRM technique. The technology to perform a two-dimensional NMR did not come about until Aue, Bartholdi and Ernst published their paper in 19761.
A two-dimensional NMR spectrum is a compiled from of a series of radio frequency pulses spaced over a number of periods of time where the molecules are allowed to freely precess (or rotate) for a determined length of time. The data detection or acquisition period is after the final pulse. Each specific type of two-dimension NMR uses a different set of parameters in timing of pulses, delays, and acquisition times. However, all two dimensional NMR have similarities in how they function. The name two-dimensional is based on how the free induction decay (FID) readings are taken. The first dimension is like the one-dimension NMR regular FID reading, and involves time and intensity. The second dimension is based on the systematically varying time period between the second pulse (perturbation or disturbance) and the collection of the first FID reading2. A general example of a two-dimension NRM is a pulse, (p1) followed by a time of precession (t1) followed by a second pulse (p2) followed by a measurement or acquisition of the FID time (t2). A computer compiles the spectra. Fourier transform is used to convert signal into spectrum peaks, which are plotted on the x-axis and y-axis.
A homonuclear COSY spectrum is a hydrogen (proton) NMR is graphed such that one NMR data set is plotted along the x-axis and another NMR data set is plotted along the y-axis. (A heteronuclear COSY spectrum is one where carbon-hydrogen are decoupled through more complicated pulse-evolution sequences.) The spectrum is interpreted by reading the diagonal of the graph, which appears as a series of points or peaks. Off the diagonal are additional points that are called cross-peaks. The cross-peaks are always symmetrical, both above and below, the diagonal spectrum and are indicative of which hydrogen atoms are spin-spin coupled to each other. One can determine which atoms are near each other 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 (near each other on the molecule.) For example: a CH3CH2COCH3 molecule would show three points on the diagonal. By drawing a line straight down from a cross-peak to the point on the diagonal directly beneath it, and then drawing a line from the cross-peak directly across to the point on the diagonal one can determine which points 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 points, as determined by cross-peaks, indicate which hydrogen are coupled, giving a clearer understanding of the structure of the molecule under examination.
Above is an example of a COSY NMR spectrum of progesterone in DMSO-d6. Notice the spectrum appears along both x-axis and y-axis. 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 NMR is the most common in COSY NMR family. In COSY-90, the sample is hit with a radio frequency (or pulse), p1, which tilts the nuclear spin to 90°. After p1, the sample is allowed to freely precess, (or spin,) over an evolution period called t1. The evolution period, t1, varies for each pulse. A second 90° pulse, p2, is applied to the sample, after which the spectrum is acquired. This is done repeatedly, and a series of FID data are collected for different evolution periods (t1). At the conclusion of data acquisition the FID data is Fourier transformed into spectra – the second dimension. It is only because the evolution period t1 is varied that cross-peaks appear in the spectrum.
Preparation is known as d1. The first pulse is p1, and is generally 90 ° in a COSY, and is fixed throughout a specific experiment. The evolution period (t1) is the time between the two pulses. The evolution period is a variable time frame; indeed, it is varied in a systematic and incremental way in order to create the second dimension in the NMR spectrum. The two pulses separated by changing evolution time effect the changes or perturbations (disturbances) in the precession. The second pulse is p2, and is delivered at varying times, according to t1, the variable delay. The effect of the second pulse, p2, is that it perturbs (or disturbs) the FID and creates additional points, or cross-peaks, off the diagonal for nuclei, which are coupled.
Cross-peaks are a result of a phenomenon called coherence transfer. Coherence transfer in NMR is the exchanging of alignments of spins, and can be achieved in various experiments through space or bonds or even through chemical or physical means. Coherence transfer can occur between same or different spins. In COSY NMR coherence transfer occurs through the bonds. The effect of coherence transfer is that the spin of a precessing nuclei changes alignment, for example from along the z-axis to along the y-axis. It is this change that results in the signals that are plotted as cross-peaks. The equations that represent the coherence transfer in I S two-spin homonuclear COSY are: 3
<math> -I_y cos ({ \Omega_I t1}) cos ({ \pi J_{t1} }) \longrightarrow -I_z cos ({ \Omega_1 t1}) cos ({ \pi J_{t1} })<math>
<math> +2I_x S_z cos ({ \Omega_I t1}) sin ({ \pi J_{t1} }) \longrightarrow -2I_x S_y cos ({ \Omega_1 t1}) Sin ({ \pi J_{t1} })<math>
<math> +I_x sin ({ \Omega_I t1}) cos ({ \pi J_{t1} }) \longrightarrow +I_x cos ({ \Omega_1 t1}) cos ({ \pi J_{t1} })<math>
<math> +2I_y S_z sin ({ \Omega_I t1}) sin ({ \pi J_{t1} }) \longrightarrow -2I_z S_y sin ({ \Omega_1 t1}) Sin ({ \pi J_{t1} })<math>
Where the arrow indicates a 90° pulse, I and S represent the two spins. Subscripts x and y represent the spin axis and 90° pulse aligned with the x-axis.
Another member of the COSY family is the COSY-45. The COSY 45 is similar to the COSY-90, except 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 or points are less pronounced, making it simpler to match cross-peaks near the diagonal in a large molecule. Additionally, the coupling constants relative signs can be elucidated from a COSY-45 whereas this is not possible from COSY-904. Overall, the COSY-45 offers a cleaner spectrum of narrower peaks while the COSY-90 is more sensitive. Other members of the COSY NMR family include Phase Sensitive COSY, Long Range COSY, Broadband Proton Decoupled COSY, Super COSY, Spin-Echo Correlated Spectroscopy, Multiple Quantum filtration, Double Quantum Filtered COSY, and the list continues.
COSY NMR has useful applications. Organic chemists often use COSY NMR to elucidate structural data on molecules that are not satisfactorily represented in a one-dimension NMR. Using cross-peaks, along with the diagonal spectrum, one can often discover much about the structure of an unknown molecule.
Notes
- Martin, G.E; Zekter, A.S., ‘’Two-Dimensional NMR Methods for Establishing Molecular Connectivity’’; VCH Pusblishers, Inc: New York, 1988 (p.59)
- Akitt, J.W.; Mann, B.E., ‘’NMR and Chemistry’’; Stanley Thornes: Cheltenham, UK, 2000. (p273)
- http://bouman.chem.georgetown.edu/nmr/cohtra/cohtra.htm (accessed 12/5/04, slides 1 and 5)
- Akitt, J.W.; Mann, B.E., ‘’NMR and Chemistry’’; Stanley Thornes: Cheltenham, UK, 2000. (p287)
References
Hornak, Joseph P. The Basics of NMR
J. Keeler, Understanding NMR Spectroscopy
Wuthrich, Kurt NMR of Proteins and Nucleic Acids Wiley-Interscience, New York, NY USA 1986.
See also
ca:Resonància Magnètica Nuclear de:Kernspinresonanz fr:Résonance magnétique nucléaire nl:Kernspinresonantie ru:Ядерный магнитный резонанс sl:Jedrska magnetna resonanca
