Nuclear Magnetic Resonance Spectroscopy

Type of physical science: Chemistry

Field of study: Chemistry of molecules: structure

Many nuclei are intrinsically magnetic, and the magnetic properties of these nuclei depend on their chemical environment. Measurements of nuclei in a strong applied magnetic field are used to determine the structure and concentration of molecules and to produce three-dimensional images of plants and animals.

Overview

Nuclear magnetic resonance (NMR) is a powerful spectroscopic technique routinely used by chemists, solid-state physicists, biochemists, and radiologists to determine the structure, concentration, and properties of molecules and to produce three-dimensional images. The technique was developed shortly after World War II by the 1952 winners of the Nobel Prize in Physics, Felix Bloch and Edward Mills Purcell. In an NMR experiment, the sample is placed in a strong magnetic field and is irradiated with radio waves. The irradiation induces a very weak alternating current, which is measured. The intensity and frequency of the induced signal yield information about the number and type of molecules in the sample.

NMR depends on the magnetic properties of nuclei. Any particle that has a nonzero value of spin is a magnetic dipole; that is, it is a microscopic "bar magnet" with a north and a south pole. Spin is a quantum mechanical quantity that was proposed by Wolfgang Pauli in 1925 to explain the statistical properties of elementary particles. The value of a particle's spin may be a positive integer such as 0 or 2 or a positive half-integer such as 1/2 or 7/2. The spin of the proton, the nucleus of the hydrogen atom, is 1/2. Since the proton is the elementary particle most commonly used in NMR, the theory of NMR will be illustrated using it.

When a particle with nonzero spin is placed in an applied magnetic field, the energy of the particle depends on its orientation. This interaction is exhibited by macroscopic objects as well. If a bar magnet is placed near another magnet, a force is required to rotate it. At the level of extremely light particles, where the rules of quantum mechanics apply, only certain orientations of the microscopic dipole are possible. The number of allowed orientations in an applied magnetic field is given by one plus twice the spin. Hence, in the case of the proton, only two orientations are possible: one in which the north pole of the dipole is pointing up (the spin-up state), and one in which the north pole of the dipole is pointing down (the spin-down state). Since each orientation of the proton's dipole has a different energy, a single proton in a magnetic field possesses only two energy states.

The existence of two discrete energy states for a single proton in an applied magnetic field provides the basis for NMR spectroscopy. If a proton in the more stable spin-up state is irradiated with electromagnetic radiation at the resonant frequency, it absorbs a photon, a light particle, and is excited to the more energetic spin-down state. The change in the state of the proton has a simple physical basis. James Clerk Maxwell showed in the nineteenth century that light has an oscillating electric field and an oscillating magnetic field. The magnetic field component of the radiation exerts torque on the proton and flips it from one spin state to the other. The resonant condition is established by conservation of energy; the energy difference between the two states of the proton must match the energy of the photon, which equals Planck's constant, h, times the frequency of the radiation. If the frequency of the radiation does not exactly match the resonance condition, the amount of power absorbed does not drop immediately to zero.

The NMR spectrum, a plot of power absorbed versus frequency, can be compared with the radio tuning curve. At the resonant frequency, at which energy is conserved, the response is a maximum; at either side of the resonant frequency, the response drops down to zero in a symmetric manner. The comparison with radio technology is appropriate, for with the magnets that are commercially available, the resonant frequency lies in the radio-frequency region of the electromagnetic spectrum. Three pieces of information are obtained from the spectrum: the frequency at the peak response, which is indicative of the characteristics of the proton; the area of the peak, which is directly proportional to the number of protons in the sample; and the width of the peak, which is indicative of the rate at which the protons transfer energy when excited.

The chemist working on a molecular structure is particularly interested in the resonant frequencies in an NMR spectrum. A resonant frequency is directly related to the difference in proton energies. This energy difference depends on a number of factors: the strength of the applied magnetic field, the nature of the proton, and the electronic environment surrounding the proton. The magnetic field strength is fixed in a given instrument but may vary from instrument to instrument. It is important that the magnetic field have the same value throughout the sample; this is referred to as spatial homogeneity. Otherwise, molecules in one portion of the sample would absorb at a different frequency than molecules elsewhere, and the line in the spectrum would be broadened or smeared out. The physical properties of an elementary particle are fundamental constants, but they vary from particle to particle. For example, in an instrument with a seven-tesla magnet, protons absorb radio-frequency radiation at three hundred megahertz, whereas carbon-13 nuclei absorb at seventy-five megahertz. Finally, the motion of the negatively charged electrons surrounding a proton generates, according to Faraday's law, a local magnetic field, which cancels out a small portion of the applied magnetic field. Therefore, the magnetic field seen at the nucleus is less than the applied field; consequently, the NMR frequency is also less. The decrease in the absorption frequency is referred to as the chemical shift and depends on the density of the electrons surrounding the proton.

An NMR spectrometer draws heavily on radio technology and has the following components: a radio-frequency transmitter, an antenna, and a magnet. Since variations in the chemical shift are very small, the components must be very stable. For example, frequency fluctuations in a 300-megahertz transmitter must be less than 0.1 hertz. The antenna component, which NMR spectroscopists call the probe, has at its heart a coil of wire wrapped around a glass tube containing the sample. The signals that must be detected in an NMR experiment are very weak, and special care must be taken in the design of the probe.

The first commercially available NMR spectrometers, which were marketed by Varian Associates in 1950, operated in continuous-wave mode. This approach, which is still a feature of many NMR spectrometers, is used in all areas of spectroscopy and is comparable to tuning a radio. The source of radiation is kept on continuously, but the frequency of the radiation is varied. The response of the instrument, in this case the absorption of radiation, is measured as a function of the transmitter frequency. Whenever the resonant condition is satisfied, the absorption of power reaches a maximum. A plot of the response versus frequency is called a spectrum. The plot has one frequency axis and is called a one-dimensional spectrum. Since the NMR resonant frequency depends on the magnetic field strength as well as on the characteristics of the nuclei, two options exist: varying the transmitter frequency of a fixed magnetic field or varying the magnetic field at a fixed frequency. The latter option is more common in continuous-wave NMR spectrometers.

Special characteristics of the source of radiation permit a second approach, the pulsed Fourier transform mode. Modern NMR spectroscopy draws heavily on advances in radio-frequency technology. In contrast to the output from a light bulb, the radiation from a radio-frequency transmitter is intense (high power), monochromatic (single frequency), and coherent (in phase). These are exactly the characteristics of laser radiation that make lasers so powerful; NMR and laser spectroscopy share much in common. Controlling the source is much easier in NMR spectroscopy, however; one can easily vary the frequency, power, and phase of the radiation and turn the radiation on and off in a systematic way.

In the simplest Fourier transform experiment, the transmitter is turned on for a few microseconds and then turned off. The sample is excited by the pulse of radiation, and its response is sampled as a function of time. The elementary experiment therefore consists of a preparation period followed by a detection period. The NMR spectrum is then calculated from the data via a function called a Fourier transform, requiring a computer for control of the hardware and computation. The Fourier transform approach is analogous to determining the frequency of the tone of a bell. First, the bell is struck with a hammer that is capable of exciting all vibrational modes. The ear detects the ringing and transmits the information to the brain, a sophisticated general-purpose computer, where it is processed.

Fourier transform spectrometers are more expensive and much more powerful than the continuous-wire versions. Since the spectrometer is controlled by a computer, the experiment can be repeated many times, and the average signal can be calculated. This results in a marked increase in the signal-to-noise ratio, as the random error of an average of N measurements equals the random error of a single measurement divided by the square root of N. The Fourier transform approach provides an elegant solution to an old problem in NMR: the weakness of the signal. A sequence of pulses rather than a single pulse can also be used, so a wide range of experiments can be designed.

Another way to boost the signal in an NMR experiment is with dynamic nuclear polarization (DNP), in which spin polarization is transferred from the electrons in a polarizing agent to the nuclei being studied, thus increasing the difference in energy between the two spin orientations. This increases the number of nuclei in the lower energy state compared to those in the higher state, which in turn increases the sensitivity of the experiment. DNP is accomplished by exciting the electrons in the polarizing agent with microwave irradiation. The polarization is then transferred from the electrons to the nuclei either directly or as a result of the relaxation that follows the initial excitation, depending on the state of the sample and the specific mechanism used. Although the theory behind DNP was developed in the 1950s by Albert Overhauser, it did not become practical for use in NMR until over half a century later, when instruments capable of producing microwaves in the terahertz range were developed.

Applications

Two major pieces of information are usually obtained from the positions of the peaks in the NMR spectrum: chemical shifts and scalar coupling constants. The energy of a single proton has a small dependence on the density of the surrounding electrons. Quantitatively, the resonant frequency is directly proportional to a dimensionless parameter called the chemical shift. The value of the chemical shift is a direct measure of electron density and is independent of the magnetic field strength. Absolute chemical shifts, which can be calculated from quantum mechanics and from changes in chemical shift from compound to compound, are of the order of magnitude 10^-6. Hence, spectroscopists speak of parts per million. A chemical shift of 2.0 x 10^-6 is reported as 2.0 parts per million. Because of their small magnitude, chemical shifts are measured with respect to a reference compound. A value reported in the literature is a difference between the compound's absolute value and the absolute value of a reference species. Water and tetramethyl silane are commonly used as reference compounds.

Chemical shifts are extremely useful to the organic chemist, as they indicate what types of hydrogen atoms are present in a compound. In the case of acetaldehyde (CH₃CHO), the chemical shift (relative to tetramethyl silane) of the identical protons on the methyl (CH₃) group is 2.20 parts per million, and the chemical shift of the aldehyde proton is 9.80 parts per million.

The chemical-shift scale is designed so that a high value indicates lower electron density. The decrease in the electron density around the aldehyde proton as indicated by the high chemical shift is a consequence of the electron-withdrawing power of the nearby oxygen atom. Proton chemical shifts are well understood, so this type of interpretation yields direct information on the covalent structure of the molecule—that is, which atoms are present and how they are connected, but not the quantitative distances between them.

Most organic compounds contain more than one hydrogen atom, so the interactions between the protons must be considered. Just as two bar magnets can exert a force on one another, the nuclear dipoles also interact. The NMR spectra are normally run on samples dissolved in a solvent such as chloroform or water. In this case, only one type of interaction between the spins, scalar spin-spin coupling, makes a contribution to the positions of the peaks in the spectrum. This coupling is mediated through chemical bonds, and the coupling is strong enough to be easily observed when the interacting spins are separated by one to three bonds. The effect of scalar coupling is to split the peaks in the spectrum into a group of peaks called a multiplet, the exact pattern of which depends on the strength of the coupling and the chemical shifts of the coupled nuclei. The coupling between identical nuclei does not lead to splitting. In the case of acetic acid, the signal for the single aldehyde proton is split into a quartet, an equally spaced group of four peaks, by the coupling between the methyl and aldehyde protons. The signal for the methyl proton is split into a doublet, an equally spaced group of two peaks. The spacing in each multiplet, seven hertz, yields the spin-spin coupling constant, which is a measure of the strength of the coupling. There is an angular dependence on the coupling constant, so in favorable cases coupling data can yield geometrical information.

A direct interaction between the nuclear dipoles, called dipole-dipole coupling, also exists. The mechanism for this interaction is the same as for the classical coupling between two bar magnets. Dipole-dipole coupling does not affect the positions of the peaks when the sample is dissolved in a liquid, as the interaction is averaged out by the rapid rotation of the molecules. The interaction does make an important contribution to the width and intensity of the lines and provides the basis for an important structural tool, the nuclear Overhauser effect (NOE). In an NOE experiment, one proton is selectively excited by irradiation at its resonance frequency. The "hot" proton transfers energy to other protons. The intensity of a peak depends on the temperature of the corresponding nucleus, so the energy transfer affects the intensities in the spectrum. The principal mechanism for the energy transfer is the dipole-dipole coupling, and the rate of energy transfer depends on the inverse of the sixth power of the distance between the protons. An analysis of peak heights or areas in an NOE experiment yields distances between atoms.

Chemists routinely use proton NMR spectroscopy to characterize compounds. The peak areas and chemical shifts yield the relative amounts and types of hydrogen atoms in the sample. Multiplet patterns indicating coupling between protons show which hydrogen atoms are in close proximity. This combination of information is so useful that the covalent structure of simple compounds can be determined on the basis of the proton NMR spectrum alone.

Although NMR spectroscopy with protons has been used to illustrate the technique, magnetic resonance spectroscopy can be done with any particle possessing spin. Other commonly used nuclei are carbon 13, fluorine 19, sodium 23, and phosphorus 31; the number indicates the total number of particles, protons plus neutrons, in the nucleus. Each nucleus will absorb radio-frequency radiation in a separate region of the spectrum. The resonance frequency depends inversely on the mass of the particle and also on the quantum-mechanical Landé g-factor. Carbon 13 absorbs at seventy-five megahertz on an instrument with a seven-tesla magnet.

Organic chemists make heavy use of carbon-13 spectroscopy to obtain information about the number, type, and local geometry of carbon atoms, the same type of information obtained from proton NMR or hydrogen. This form of spectroscopy presents a special challenge. Carbon 13 is a rare isotope of carbon; only 1 percent of carbon is carbon 13. The most abundant isotope of carbon, carbon 12, has a spin of zero and does not yield an NMR spectrum. Because the size of the signal is proportional to the number of absorbers in the sample, carbon-13 spectra using samples with the natural abundance of carbon 13 are very weak, and a Fourier transform instrument is necessary to build up a spectrum with satisfactory signal-to-noise.

Phosphorus NMR is particularly useful to the biochemist and the medical clinician, as many important metabolites contain phosphorus. Phosphorus NMR has many advantages. Phosphorus has only one naturally occurring isotope, phosphorus 31, so signal-to-noise is not a problem. Although the concentration of metabolites is low, their phosphorus signal is not masked by that of more abundant compounds. This is the case with proton NMR when the most abundant hydrogen-containing molecule is water.

Finally, NMR can be used to determine the type and concentration of metabolites in intact living organisms; no surgery is required. Many hospitals have NMR spectrometers with very large magnets. The patient is placed inside the magnet, and the antenna is placed on the portion of the anatomy to be studied. Careful design of the antenna, called a surface coil, and of the excitation pulse from the transmitter allow only a portion of the tissue to be excited, and only that portion yields an NMR spectrum. This technique is very useful for monitoring the status of premature infants who must breathe an atmosphere of pure oxygen.

The electron, which has a spin of 1/2, is a special case, as it is lighter than the proton by a multiplicative factor of 1,838. Because of the inverse dependence on mass, an electron absorbs in the higher-frequency microwave region. Magnetic resonance spectroscopy of electrons is referred to as electron spin resonance (ESR) spectroscopy or electron paramagnetic resonance (EPR) spectroscopy. The latter name comes from the requirement that electrons be unpaired, as materials with weakly coupled unpaired electrons are termed paramagnetic. They yield an ESR spectrum and are moderately attracted to a magnetic field. If the electrons are paired up, the magnetic properties of the individual electrons cancel, and the result has zero spin. Such a substance is called diamagnetic. It does not have an ESR spectrum, and it is very weakly repelled by a magnetic field.

ESR spectroscopy also yields chemical shifts and coupling constants and is used primarily as a research tool to study the properties of electrons and paramagnetic substances. As a rule, paramagnetic organic compounds are highly reactive and have a fleeting existence, so ESR is used mainly in organic chemistry to study exotic species and to determine the pathways of chemical reactions. ESR sees greater use in transition-metal chemistry, in which it is straightforward to prepare stable paramagnetic compounds.

Advances have opened the application of NMR spectroscopy to the study of solids containing carbon. Normally, solids yield extremely broad spectra, because the molecules in the solid do not rotate and the strong dipole-dipole interactions between the protons and the carbon-13 spins do not average out to zero. The dipole-dipole interaction can be suppressed, however, by irradiating the protons with a high-power transmitter tuned to the proton resonant frequency. If the power, the phase, and the timing of the transmitter are properly selected, the signal is also enhanced. A second mechanism that contributes to line broadening is suppressed by rapidly spinning the sample about an axis that makes an angle of fifty-four degrees, forty-four minutes with respect to the applied field. This angle is called the magic angle. The combination of irradiation of the protons and magic-angle spinning yields carbon-13 spectra of solids that have lines nearly as sharp as those obtained with liquids. The application of this technique is very useful in the characterization of polymers such as polyethylene.

Conventional NMR spectroscopy in which there is single frequency axis is referred to as one-dimensional spectroscopy. One-dimensional NMR, as powerful as it is, has its limitations. The spectrum of a complex molecule such as a protein is a superposition of many overlapping components. The result is a broad profile in which the individual components cannot be identified clearly. In addition, it is very difficult, if not impossible, in a one-dimensional experiment to sort out the various interactions, that is, which hydrogen couples with which.

Two-dimensional NMR spectroscopy deals with the limitations discussed above. In a two-dimensional experiment, there are two frequency axes rather than one. As a result, the components of the spectrum are distributed over a plane rather than along a line, and the possibility of overlap is greatly reduced. In addition, the features in a two-dimensional spectrum directly map out the interactions. Various two-dimensional methods exist, and the type of interaction revealed by the two-dimensional spectrum is determined by the design of the experiment. For example, if the goal is to determine all scalar couplings between spins, correlation spectroscopy is ideal, while nuclear Overhauser effect spectroscopy is best used to determine the relative orientations of all atoms in a molecule.

A two-dimensional experiment is an extension of the one-dimensional methodology and requires a Fourier transform spectrometer. The two-dimensional experiment consists of four steps or periods: preparation, evolution, mixing, and detection. During the preparation period, the sample is excited by a pulse of radio-frequency radiation or a sequence of pulses. The system is allowed to oscillate, or ring, for t₁ seconds during the evolution period. A sequence of pulses is then applied during the mixing period. The sequence of pulses is determined by the type of information desired in the final spectrum and is designed to transfer information from one set of nuclei to another. Finally, the signal is measured during the detection period. The entire experiment is repeated many times, with each pass run for a different length of the evolution period. As a result, the accumulated data depend on two independent time scales: the times during the evolution period and the times during the detection period. A Fourier transform is taken for each time scale, and two independent frequency axes are obtained.

Two-dimensional NMR spectroscopy also plays a key role in magnetic resonance imaging, an important medical application. X-rays have been used to obtain pictures of the body since their discovery by Wilhelm Conrad Rontgen in the nineteenth century, and modern methods can yield three-dimensional images. X-rays are used because they penetrate deeply, but medical imaging with x-rays has a number of disadvantages. X-ray radiation is highly energetic and can induce cancer. Soft tissue does not absorb x-rays as much as bone, so it is difficult to obtain good pictures of organs such as the brain or the heart. In contrast, the low-frequency radio-frequency radiation used in NMR penetrates deeply but does not alter or destroy molecules. Proton NMR is ideally suited for the imaging of soft tissue, as it has a high concentration of hydrogen-containing substances such as water.

A conventional NMR spectrometer must be modified in several respects for imaging. First, the bore in the magnet where the sample is inserted must be enlarged to accommodate a patient. A trick is used to measure the density of hydrogen versus distance. Normally, the magnetic field is kept as homogeneous as possible, but in imaging, a magnetic field gradient is applied, meaning that the magnetic field varies linearly through the sample. Since the NMR frequency depends linearly on the strength of the magnetic field, there is a direct relationship between the NMR frequency in the spectrum and its position. In other words, the frequency axis in the spectrum can be replaced with a distance axis so that the spectrum gives the amount of hydrogen versus location.

Three-dimensional NMR is required to obtain a three-dimensional image. In one implementation of medical imaging, three separate gradients are applied along the x, y, and z axes. Two evolution periods are used, so with the detection period there are three time scales. A separate gradient is applied during each time period, and a triple Fourier transform is applied to the data, resulting in three frequencies. Because the gradients are applied separately, each frequency is directly related to the position along one of the three axes, and the spectrum gives exactly what is required: a plot of hydrogen density versus location. Once the data have been acquired and processed, obtaining a picture of a particular slice of the body is then a matter of computer graphics.

Context

Scientists make significant use of spectroscopic methods in the study of matter. Since its discovery shortly after the end of World War II by Nobel laureates Bloch and Purcell, NMR spectroscopy has developed from a versatile research tool into a workhorse technique used by every chemist. Applications of NMR cover the entire spectrum of science, from solid-state physics to chemical analysis to biological structure. Scientists use NMR to generate three-dimensional images of plants, animals, and humans and to determine the structure of molecules, the concentration of species, the properties of metals, the nature of nuclei, and the dynamics of molecules on a time scale ranging from seconds to picoseconds .

NMR is a clear-cut case of industrial research making significant contributions to progress in science. It emerged as a routine technique with the announcement of the first commercial spectrometer in 1950. This development, which required years of investment, was a technical tour de force and made extensive use of state-of-the-art technology such as digital plotters and lock-in amplifiers.

Both science and technology advance best when there is a close synergism between the two. The state of NMR spectroscopy advanced greatly with the application of Fourier methods, the province of electrical engineers and mathematicians. Although the first attempts were published by W. A. Anderson and R. R. Ernst in 1966, progress was very slow because laboratory computers were prohibitively expensive. Rapid progress became possible with the production of inexpensive computers, and progress in NMR has continued to be tied to advances in technology and computer science.

Principal terms

CHEMICAL SHIFT: a measure of the influence that the electrons around the nucleus have on the magnetic field at the nucleus, reported in parts per million

NUCLEAR OVERHAUSER EFFECT: the transfer of energy between two magnetic nuclei that can be caused by the through-space interaction between the nuclei

SPIN: a type of angular momentum associated with magnetism and the Pauli exclusion principle

SPIN-SPIN COUPLING CONSTANT: a measure of the interaction between two nuclei that is effected through the chemical bonds connecting the nuclei

Bibliography

Abraham, Raymond J., J. Fisher, and P. Loftus. Introduction to NMR Spectroscopy. 2nd ed. New York: Wiley, 1988. Print. This well-written text describes the full range of NMR techniques.

Carrington, Alan, and Andrew D. McLachlan. Introduction to Magnetic Resonance. New York: Harper, 1967. Print. This text covers the full range of magnetic-resonance techniques available at the time and is the clearest-written exposition of the theory of magnetic resonance spectroscopy.

Günther, Harald. NMR Spectroscopy: Basic Principles, Concepts, and Applications in Chemistry. 3rd ed. Weinheim: Wiley, 2013. Print.

Levitt, Malcolm H. Spin Dynamics: Basics of Nuclear Magnetic Resonance. 2nd ed. Chichester: Wiley, 2008. Print.

Maciel, Gary E. "High Resolution Nuclear Magnetic Resonance of Solids." Science 226.4672 (1984): 282–88. Print. This short article reviews the techniques used in solid-state NMR and the information that is obtained.

Nanni, Emilio A., et al. "THz Dynamic Nuclear Polarization NMR." IEEE Transactions on Terahertz Science and Technology 1.1 (2011): 145–63. Print.

Shulman, R. G. "NMR Spectroscopy of Living Cells." Scientific American Jan. 1983: 86–93. Print. This short review of the applications of in vivo NMR is written in nontechnical terms by one of the pioneers in the field.

Silverstein, Robert M., Francis X. Webster, and David J. Kiemle. Spectrometric Identification of Organic Compounds. 7th ed. Hoboken: Wiley, 2005. Print. This text clearly outlines the application of all spectroscopic techniques to the identification of carbon compounds.

Wuethrich, Kurt. NMR of Proteins and Nucleic Acids. New York: Wiley, 1986. Print. This volume is a product of the Baker lectures that Wuethrich delivered at Cornell University in 1983. The techniques for determining the structure of biopolymers were developed in his laboratory, and his monograph is the standard treatment of the subject. Describes the two-dimensional techniques that were developed by his colleague Richard Ernst.