Nuclear magnetic resonance spectroscopy

Nuclear magnetic resonance spectroscopy, most commonly known as NMR spectroscopy or magnetic resonance spectroscopy, is a spectroscopic technique based on re-orientation of atomic nuclei with non-zero nuclear spins in an external magnetic field. This re-orientation occurs with absorption of electromagnetic radiation in the radio frequency region from roughly 4 to 900 MHz, which depends on the isotopic nature of the nucleus and increases proportionally to the strength of the external magnetic field. Notably, the resonance frequency of each NMR-active nucleus depends on its chemical environment. As a result, NMR spectra provide information about individual functional groups present in the sample, as well as about connections between nearby nuclei in the same molecule.
As the NMR spectra are unique or highly characteristic to individual compounds and functional groups, NMR spectroscopy is one of the most important methods to identify molecular structures, particularly of organic compounds.
The principle of NMR usually involves three sequential steps:

The alignment of the magnetic nuclear spins in an applied, constant magnetic field B₀.
The perturbation of this alignment of the nuclear spins by a weak oscillating magnetic field, usually referred to as a radio-frequency pulse.
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.
The most significant drawback of NMR spectroscopy is its poor sensitivity. Typically 2–50 mg of a substance is required to record a decent-quality NMR spectrum. The NMR method is non-destructive, thus the substance may be recovered. To obtain high-resolution NMR spectra, solid substances are usually dissolved to make liquid solutions, although solid-state NMR spectroscopy is also possible.
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 spectroscopy, the relaxation of the resonances is observed. As NOE depends on the proximity of the nuclei, quantifying the NOE for each nucleus allows construction of a three-dimensional model of the molecule.
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 0.5–5 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. Higher magnetic field also improves the sensitivity of the NMR spectroscopy, which depends on the population difference between the two nuclear levels, which increases exponentially with the 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 spectra of protons can be observed even in Earth magnetic field. 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 a better sensitivity and higher resolution of the peaks, and it is preferred for research purposes.

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 inventions.

NMR-active criteria

The key determinant of NMR activity in atomic nuclei is the nuclear spin quantum number. This intrinsic quantum property, similar to an atom's "spin", characterizes the angular momentum of the nucleus. To be NMR-active, a nucleus must have a non-zero nuclear spin. It is this non-zero spin that enables nuclei to interact with external magnetic fields and show signals in NMR. Atoms with an odd sum of protons and neutrons exhibit half-integer values for the nuclear spin quantum number. These atoms are NMR-active because they possess non-zero nuclear spin. Atoms with an even sum but both an odd number of protons and an odd number of neutrons exhibit integer nuclear spins. Conversely, atoms with an even number of both protons and neutrons have a nuclear spin quantum number of zero, and therefore are not NMR-active. NMR-active nuclei, particularly those with a spin quantum number of 1/2, are of great significance in NMR spectroscopy. Examples include ¹H, ¹³C, ¹⁵N, and ³¹P. Some atoms with very high spin are also extensively studied with NMR spectroscopy.

Main aspects of NMR techniques

Resonant frequency

When placed in a magnetic field, NMR active nuclei 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 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 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 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. The most widely used deuterated solvent is deuterochloroform, 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 change slightly between solvents, and therefore the solvent used is almost always reported with chemical shifts. Proton NMR spectra are often calibrated against the known solvent residual proton peak as an internal standard instead of adding tetramethylsilane, which is conventionally defined as having 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 extremely uniform throughout the sample volume. High-resolution NMR spectrometers use shims to adjust the homogeneity of the magnetic field to parts per billion 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 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 pulse, a nuclear magnetic resonance response a free induction decay 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 about 3–8 μs for the optimal 90° pulse. The pulse width can be determined by plotting the 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, slower for heavier nuclei and in solutions, and 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.