NMR Spectroscopy Principles, Interpreting an NMR Spectrum and Common Problems

Nuclear magnetic resonance (NMR) spectroscopy is a physicochemical technique used to obtain structural information about molecules. It is based on the physical phenomenon of magnetic resonance that was first demonstrated by Isidor I. Rabi in 1938. In the 1940s, two research groups independently obtained the first successful measurements of NMR in condensed matter. The two principal investigators of these groups, Felix Bloch from Stanford University and Edward M. Purcell from Harvard University, were jointly awarded with the Nobel Prize in Physics in 1952 for their contributions to the field of magnetic resonance.^1,2,3

Since those early days, NMR spectroscopy progressed concurrently with advances in many other fields, such as mathematics, physics and informatics. In the 1960s, the implementation of superconducting magnets and computers to NMR equipment opened the door to a great improvement in sensitivity and the possibility to design new types of NMR experiments. As a consequence, scientists have developed a myriad of novel methodologies to study complex systems, such as membrane proteins, metabolically complex samples, or even biological tissues. NMR spectroscopy has become one of the most powerful techniques for structural determination of chemical species, as well as for the study of molecular dynamics and interactions.^4,5

What is NMR?

NMR spectroscopy is a physicochemical analysis technique that is based on the interaction of an externally applied radiofrequency radiation with atomic nuclei. During this interaction there is a net exchange of energy which leads to a change in an intrinsic property of the atomic nuclei called nuclear spin.

The nuclear spin is defined by a quantic number (I), which varies depending on the considered isotope. Only atomic nuclei with I ≠ 0 are detectable by NMR spectroscopy (NMR-active nuclei, such as ¹H, ²H, ¹³C and ¹⁵N). These NMR-active nuclei behave as tiny magnets (magnetic dipoles), capable of aligning with external magnetic fields (a process called magnetization). The force of those tiny magnets is defined by a constant known as the magnetogyric ratio (γ), whose value depends on the isotope. ^6,7

Nuclear spins of some NMR-active nuclei are able to adopt two different orientations when they align to an external magnetic field (B₀). One orientation corresponds to the lowest energy level of the nucleus (parallel to the external magnetic field), and the other one is associated to the highest energy level of the nucleus (antiparallel to the external magnetic field) (Figure 1, left panel). The difference between energy levels (ΔE) depends on the magnetic field and the magnetogyric ratio (Eq. 1) and affects the sensitivity of the technique (Figure 1, right panel). ^6,7

Figure 1: Nuclear spin orientations of a sample aligned (parallel and antiparallel) with the direction of an external magnetic field B₀ (left panel). Distribution of nuclear spin populations in the two possible energy levels in nuclei with I = ½ (right panel).

Magnetic resonance is achieved when nuclei are irradiated with radiofrequency. This causes transitions between energy levels, which involves changes in the orientation of nuclear spins.

When atomic nuclei are under the effect of a magnetic field, nuclear magnetic dipoles are not statically aligned with the magnetic field B₀, but rather move like a spinning top (precession movement) around an axis parallel to the direction of the field (Figure 2, left panel). The frequency of this precession movement, called Larmor frequency (ν_L), is defined by the magnetogyric ratio and the magnetic field: ^6,7

As a consequence of this precession movement, the magnetic vector (μ) associated with the nuclear magnetic dipoles possesses a component parallel to the magnetic field (μ_z) and another component perpendicular to the magnetic field (μ_xy), with this last one having a net value of zero in the absence of external perturbations. In an NMR experiment, it is not possible to measure the signal in the z direction, as the magnetic field is too intense in that direction. Therefore, it is necessary to transfer the magnetization of the z component to the xy plane. For this purpose, a magnetic pulse containing frequencies close to the Larmor frequency is applied perpendicular to B₀ to reach the resonance of nuclear spins, which generates a non-zero μ_xy component. After this pulse, a relaxation process takes place and the μ_xy component gradually recovers its net value of zero (Figure 2, right panel). As a consequence of this relaxation, energy is emitted as radiofrequency, producing a characteristic signal called free induction decay (FID) which is registered by the detector. This FID is subsequently transformed into a plot of intensities versus frequencies known as an NMR spectrum. ^6,7

Figure 2: Nuclear spin behavior under the influence of an external magnetic field (left panel). Scheme of a basic NMR experiment in which the magnetization is transferred to the xy plane upon the application of a magnetic pulse (right panel).

How does NMR work?

NMR spectrometers consist of three main components: a superconducting magnet, a probe and a complex electronic system (console) controlled by a workstation (Figure 3).

Figure 3: General design of an NMR spectrometer with its principal components.

The magnet is responsible for the generation of a strong magnetic field that aligns the nuclear spins of the atoms present in the sample. Nowadays, the magnets used in NMR spectroscopy are based on superconducting materials, and thus, they require very low temperatures to work (around 4 K). For this reason, NMR spectrometers contain a cooling system composed of an inner jacket filled with liquid helium which is refrigerated by an additional jacket filled with liquid nitrogen, and many layers of thermal isolating materials (Figure 4).^6,8

The superconducting magnet surrounds a cylindrical chamber known as the “probe”, which is a crucial component of the instrument. The sample is introduced into the probe and thus placed under the influence of the magnetic field. Additionally, the probe contains a series of magnetic coils that are also located around the sample (Figure 4). These coils have multiple purposes. On one hand, they are used to irradiate the radiofrequency pulses and to detect and collect the NMR signal emitted by the sample. On the other hand, they also enable control of the magnetic field homogeneity and the application of pulse gradients that are used in some NMR experiments. ^6,8

Figure 4: Internal components of an NMR spectrometer, including a detailed view of the probe. Credit: KissCC0.

Finally, the electronic system of the spectrometer controls all the experimental conditions and enables the set up and modification of every parameter of the NMR experiment through the workstation. This system is also responsible for data acquisition and subsequent mathematical transformation into an NMR spectrum. The spectrum contains a series of peaks of different intensities as a function of a magnitude known as the chemical shift that is derived from the Larmor frequency of the different atomic nuclei present in the sample. ^6,8

How to read an NMR spectrum and what it tells you

The signal detected by an NMR spectrometer (the FID) must be transformed prior to analysis. As the Larmor frequency is dependent upon the intensity of the magnetic field, it varies from instrument to instrument. For this reason, a mathematical transformation is performed to provide a relative magnitude called chemical shift (δ) (see Eq. 3). Unlike the Larmor frequency, this magnitude is independent of the magnetic field and the value can be compared across instruments. ^6,7,8

Where ν_L is the observed Larmor frequency of a nucleus and ν_L⁰ is the Larmor frequency of a reference nucleus, both in Hz. By convention, chemical shift is always expressed in parts per million (ppm). The zero value of the chemical shift scale is set using a reference compound (such as tetramethylsilane (TMS) or sodium trimethylsilylpropanesulfonate (DSS) for ¹H).

Figure 5 provides an example of a proton (¹H) NMR spectrum, meaning that only the protons of the molecule are detected.

Figure 5: ¹H solution NMR spectrum of acetic acid. The signals correspond to the two different ¹H nuclei present in the molecule and their areas are proportional to the number of nuclei contributing to the signal.

An NMR spectrum provides a lot of information about the molecules present in the sample. First, chemical groups within a molecule can be identified from chemical shift values. In the example provided in Figure 5, acetic acid (H₃C-COOH) has four protons so you could be forgiven for expecting to see four signals in the spectrum. However, the three protons of the methyl group (CH₃) are magnetically equivalent and therefore have the same chemical shift. This means that one signal comes from the CH₃ group and the other one, from the proton in the carboxylic acid group (COOH). Secondly, in ¹H-NMR spectra, signal area is proportional to the number of atomic nuclei producing that signal (this does not apply to ¹³C-NMR spectra). In this example, if the areas of both signals were to be calculated, the most intense signal will be three times larger than the other. This is in accordance with the fact that one signal represents the three protons from the CH₃ group (signal at δ = 2.0 ppm) and the other one the proton from the COOH group (signal at δ = 11.5 ppm).^9,10

The spins of two nuclei that are connected through a few chemical bonds can interact, causing a phenomenon known as scalar coupling which splits the signals. Typically, this coupling is only observable when the number of chemical bonds separating two nuclei does not exceed four. The splitting of the signals follows a pattern that depends on the number of coupled nuclei and on a coupling constant (J) defined by the type of nuclei and the distance (in chemical bonds) between them. The characteristic shape of a split signal is called multiplicity and provides additional information about the molecule. This multiplicity can be calculated using the N+1 rule. This rule states that if a proton shows scalar coupling with N protons attached to contiguous carbon nuclei, its signal will split into N+1 peaks with relative intensities defined by the Pascal’s triangle (Figure 6). Peak splitting because of the scalar coupling causes a reduction of the peak intensity. Finally, the observation of signals arising from an effect called the nuclear Overhauser effect (NOE) is essential for structural determination of macromolecules, since it emerges from the interaction of nuclear spins of atoms that are spatially close, but distant in the molecular sequence.^6,7,8,9,10

Figure 6: Example of a scalar coupling. If there is no scalar coupling (top), NMR signals from H_A and H_B appear as simple peaks. However, if the two nearby protons H_A and H_B show scalar coupling with a constant J (bottom), the signals will split. Both protons H_A and H_B are coupled with one proton attached to a contiguous carbon nucleus, following the N+1 rule each proton signal will split into two signals, forming a doublet and the split distance will be equal to the coupling constant, J.

In this context, to interpret an NMR spectrum it is necessary to use all that information to assign each observed signal to the corresponding atomic nucleus of the molecule(s) in the sample. This process is called spectral assignment and it can be difficult to achieve with complex molecules. For this reason, many types of NMR experiments providing different and complementary information are used to characterize a sample.¹¹

Upfield vs downfield NMR

As seen in Figure 5, the same kind of nuclei can generate signals with different chemical shift values. These chemical shifts differ as the magnetic field sensed by a particular nucleus strongly depends on its local chemical environment. The circulation of electrons in the surroundings of a nucleus creates small magnetic fields that oppose the applied external field. This “shielding” effect (σ) is directly proportional to the electronic density around the nucleus. As a result, the effective magnetic field acting on the nucleus is lower and the Larmor frequency is affected (Eq. 4). When there is a high electronic density around the considered nucleus, the shielding effect is high, the Larmor frequency decreases and so does the chemical shift (it moves upfield). On the contrary, when the electronic density is low in the vicinity of the nucleus, the shielding effect is low, the Larmor frequency takes higher values and so does the chemical shift (it moves downfield).^6,7,8,12

Therefore, in NMR spectroscopy, upfield and downfield are terms that refer to the regions of lower and higher values, respectively, within the chemical shift scale (Figure 7).^6,7,8,12

Figure 7: ¹H NMR chemical shift scale indicating the downfield and upfield regions.

Hydrogen nuclei from methyl groups or aliphatic molecules are strongly shielded and their typical chemical shift values are located upfield. On the other hand, hydrogen nuclei attached to electronegative atoms (such as oxygen or nitrogen) or close to electronegative groups (such as carboxylic acids or aldehydes) are deshielded and show chemical values located downfield. This illustrated and discussed further in a later section, NMR charts.

Proton NMR vs carbon NMR

The principal constituent elements of organic and biological molecules are hydrogen and carbon. As described above, NMR spectroscopy can only be applied on NMR-active nuclei (that is, nuclei with I ≠ 0). In the case of hydrogen, the most abundant isotope is NMR-active (¹H, 99.98%, I = ½). In the case of carbon, its most abundant isotope is not NMR-active (¹²C, 98.89%, I = 0). NMR spectrometers can only detect the isotope ¹³C, which has an abundance of 1.11%. Moreover, the magnetogyric ratio of ¹³C is also lower by a factor of four than that of ¹H (see Table 1). Both factors make ¹³C-NMR significantly less sensitive than ¹H-NMR (see Table 1). This difference in sensitivity leads to longer experimental times in the case of ¹³C (hours) compared to ¹H (seconds or minutes) ^13,14

The chemical shift of ¹H typically occurs in the range 0 to 14 ppm, whereas, the ¹³C chemical shifts occur over much a larger range, typically 10 to 220 ppm. This dependence of the chemical shift values on the type of nuclei arise from the fact that different nuclei possess different Larmor frequencies (as they depend on the magnetogyric ratio, as mentioned before). These increased shifts in ¹³C-NMR results in a better resolution compared to ¹H-NMR, as the signals are normally more dispersed.

Additionally, scalar coupling between ¹³C is rarely observed because, due to its low natural occurrence, two ¹³C atoms are unlikely to be found close enough to establish interactions between their nuclear spins. However, the coupling of ¹³C atoms with other nuclei is possible and it can further reduce the sensitivity of the technique. The reason for this is that ¹³C coupling constants are large and the reduction of signal intensity upon splitting (see section 3) is more marked when coupling constants are large. For this reason, ¹³C-NMR experiments are usually performed using special pulse sequences capable of removing the scalar coupling between ¹³C and ¹H.¹⁴

There are a number of ways in which the sensitivity of ¹³C-NMR can be improved, these include:

• ¹³C-enrichment of the sample
• Increasing the number of accumulated spectra, therefore reducing the signal-to-noise ratio
• Using NMR pulses to increase the population difference between nuclear spin energy levels¹⁴

Despite the limitations of ¹³C-NMR, it offers valuable information that is not accessible using only ¹H-NMR. The identification of primary, secondary, tertiary and quaternary carbons for example. For this reason, ¹³C-NMR and ¹H-NMR are often used jointly in NMR laboratories as a basic approach for molecular structure determination.¹⁴

Table 1: Comparison of ¹H and ¹³C NMR properties.¹⁵

	1H	13C
Natural abundance (%)	99.98	1.11
Nuclear spin quantic number, I	½	½
Magnetogyric ratio (rad·T-1·s-1)	2.68·108	6.73·107
Relative sensitivity a	1.00	0.016
Larmor frequency (MHz)b	600.130	150.903
Chemical shift range (ppm)	0 – 14	10 – 220

^a Considering a constant magnetic field and the same number of nuclei.

^b Considering a magnetic field with a flux density of 14.0954 T.

NMR chart

By convention, the chemical shift scale in an NMR spectrum is represented from right to left. As described above, the zero value is established using a standard compound whose carbon and hydrogen atoms are strongly shielded and hence, their signals appear in the furthest upfield region (as seen in Figure 7). The assignment of the NMR spectra is usually performed with the help of NMR charts or diagrams that facilitate the identification of the NMR signals.

Hydrogens or carbons that are highly shielded, such as the ones of methyl groups, have low chemical shift values. However, hydrogens attached to very electronegative groups (e.g., carboxylic acids, ketones or aldehydes) have high chemical shift values (Figures 8 and 9).

These charts represent typical chemical shifts, but sometimes the values could be displaced to other regions of the scale.¹⁶ For instance, in large macromolecules, a distant chemical group can be relocated due to spatial rearrangements of the tridimensional structure. This relocation could alter the chemical environment of the measured nucleus, leading to a change in its chemical shift value.

In order to facilitate NMR spectra assignment, there are public NMR libraries or databases (such as the Biological Magnetic Resonance Data Bank or the Spectral Database for Organic Compounds) containing NMR spectra and chemical shift values for thousands of biochemical molecules and chemical compounds.

Figure 8: ¹H-NMR chart showing the typical chemical shift values for different types of hydrogen atoms.

NMR variants

a.         2D NMR

Macromolecules, such as proteins, have a large number of NMR-active nuclei and, consequently, their NMR spectra are complex with many overlapping peaks. In addition, relaxation is faster in large molecules, which causes peak broadening and loss of resolution. To address these limitations, 2D NMR experiments generate spectra defined by two chemical shift axes (instead of one, as in 1D spectra), with signals that correlate pairs of different nuclei. Three examples of 2D NMR experiments are COSY, TOCSY and NOESY.^6,7,8,9 

• COSY (COrrelated SpectroscopY) spectra display peaks that correlate pairs of nuclei that are separated by a maximum of three chemical bonds. This correlation arises from the interaction between nuclear spins through scalar coupling (Figure 10).
  
  
• TOCSY (TOtal Correlated SpectroscopY) spectra show signals correlating pairs of nuclei that are part of the same spin system (a spin system is a set of nuclei whose spins interact with one another, that is they are coupled) (Figure 10).
  
  
• NOESY (Nuclear Overhauser Effect SpectroscopY) experiments are very important in the structural elucidation of macromolecules because they provide information about their spatial organization. NOESY spectra contain peaks that correlate pairs of nearby nuclei (typically, separated by less than 5-6 Å). Differently to COSY, NOESY correlation arises from the nuclear Overhauser effect, in which interaction occurs when two nuclei are spatially close, no matter the number of chemical bonds separating them. ^6,7,8,9 
  
  

Figure 10: Examples of ¹H,¹H COSY and ¹H,¹H TOCSY spectra for a molecule with the structure A-B-C-D and hydrogen atoms attached to each of them. The COSY spectrum only shows the peaks arising from the correlation between two hydrogens separated by a maximum of three chemical bonds (this is H-A-B-H; H-B-C-H; and H-C-D-H). The TOCSY spectrum shows the peaks arising from the correlation between two hydrogens belonging to the same spin system (in this case, all the possible H-H correlations).

b.    Solid-state NMR

In spite of the fact that most NMR analyses are carried out on samples in solution, the field of solid-state NMR has developed significantly in the last decade. Solid-state NMR is one of the most powerful techniques for the study of molecular structures and dynamics in solid samples. This NMR variant has special features and requires different experimental designs.¹⁷

Solution NMR and solid-state NMR show remarkable differences, mainly due to the fact that molecules in solution are able to move freely and nuclear spin interactions are averaged. However, in solid samples there is little or no molecular motion and, as a result, nuclear spin interactions depend on the spatial direction (this is termed anisotropic interactions). This anisotropy causes the broadening of the NMR spectral signals (Figure 11, bottom spectrum). To address this issue, scientists using solid-state NMR have developed special techniques that prevent the loss of sensitivity and resolution.¹⁷

The most well-known solid state NMR technique is magic angle spinning (MAS). The approach used in this technique involves placing the sample inside a rotor which is spun at high speed, forming a particular angle (magic angle ≈ 54.74º) with respect to the direction of the external magnetic field. The effect of this rotation is the cancelation of all the anisotropic spin interactions (including dipolar, chemical shift anisotropy and quadrupolar interactions) (Figure 11).¹⁷

Figure 11: Effect of MAS on the spectral line shape. When the solid sample is not rotating, the spectrum shows a broad signal (bottom spectrum). When the rotor is spinning, anisotropic effects are averaged and thus, resolution and sensitivity increases. When the spinning frequency is sufficiently high, all anisotropic effects are cancelled.

Strengths and weaknesses of NMR and common problems

NMR spectroscopy is a powerful technique that has many advantages over other techniques, but it has some limitations. These are summarized in Table 2:¹⁸

Table 2: Summary of the principal strengths and weaknesses of NMR spectroscopy.

NMR impurities

One of the most common problems encountered in NMR spectroscopy, as mentioned in Table 2, is the presence of interfering substances, such as traces of impurities or solvents, that give rise to the appearance of non-desired peaks in the spectrum.

The analytes contained in NMR samples are usually obtained by a synthesis and/or purification process in which many substances are involved. For this reason, it is not infrequent to find that certain amounts of those substances remain in the final sample as impurities. Occasionally, the analyte undergoes transformations or degradation, which can lead to the appearance of undesirable chemical species in the sample. If these impurities have NMR-active nuclei, they can hamper the correct assignment of the NMR spectrum. Generally, NMR impurities are found in trace concentration and therefore they are relatively easy to identify, as their NMR peaks show very low intensities compared to those of the analyte. To make it easier to characterize impurities, laboratories often make use of tables that summarize the chemical shifts of the most common impurities.^19,20,21

NMR solvent peaks

Solvents used in NMR spectroscopy usually contain NMR-active nuclei, especially ¹H, and hence, they can potentially cause interferences in the NMR spectra. Unlike trace impurities, the solvent is present in the sample at a very high concentration and peaks arising from it are usually huge. To avoid this problem, it is very important to know exactly the chemical shift of the solvent peaks to control to what extent they can be concealing any analyte signal. On the other hand, the customary strategy to reduce the effect of hydrogen-containing solvent peaks is to use deuterated solvents (some deuterated solvent must always be present in the sample as the lock system of NMR spectrometers uses the ²H signal to monitor the homogeneity of the magnetic field). These solvents have their ¹H nuclei substituted by ²H, thus considerably reducing the intensity of the solvent peaks. However, in spite of the fact that the usual percentage of deuteration is close to 100%, due to the high solvent concentration, their peaks can still be too intense and hinder the correct visualization of the analyte signals. For this reason, there are some NMR pulses available that are able to reduce the solvent peak perturbations in NMR spectra, especially for aqueous samples (for instance, pulses with presaturation or gradient-suppression pulses).^22,23,24

Applications of NMR

NMR spectroscopy is widely applied across many fields and is especially common in the fields of chemistry and the life sciences.

NMR applications in chemistry

In chemistry, the main application of NMR spectroscopy is the identification and structural elucidation of organic, organometallic and biochemical molecules. Generally, the identification of compounds is complemented with data obtained with other techniques, such as mass spectrometry, infrared spectroscopy and elemental analysis. Moreover, the proportionality between the area of the signals and the amount of nuclei that generate it allows NMR spectroscopy to be used as a quantitative analysis tool.¹⁵ Some examples of NMR applications in chemistry-related fields are:

• Chemistry: structural determination of new compounds, quality control of products and purity determination²⁵
• Pharmaceutics: study of structure, dynamics and molecular interactions for drug discovery, quality control and purity determination of drugs ²⁶
• Petrochemistry: analysis of rock materials to check the suitability of an oil reservoir to be exploited, solid state NMR composition analysis of petroleum derivatives, quality control of products²⁷
• Materials: characterization of new materials by solids state NMR ²⁸

NMR applications in the life sciences

Within the life sciences, NMR spectroscopy has been widely applied to the structural resolution of biological macromolecules, including peptides, proteins, lipids, carbohydrates and nucleic acids. These systems are highly complex, and it is therefore necessary to employ a special approach. This includes:

• Isotopic labeling to enrich the sample in ¹³C and ¹⁵N, or even in ²H
• The use of special NMR pulses to reduce signal overlapping and gain resolution
• Employing NMR experiments of high dimensionality (2D, 3D or even higher)

Once the NMR assignment is achieved, the data obtained are processed to obtain information about chemical shifts, torsion angles and distance restraints between atoms. This information is then used to calculate the molecular structure using a methodology that employs computer software developed for that purpose. The software generates molecular structures that fulfill the imposed restraints, minimizing their energy (since the lowest energy structures are the most stable and thus, the most probable).^29,30

Alongside the structural elucidation, NMR spectroscopy can also be used to extract information about molecular dynamics such as relaxation times, structural rigidity and chemical exchange as well as interactions between molecules (chemical shift perturbations, intermolecular magnetization transfer).^31,32 In this context, solid state NMR is useful to study proteins interacting with lipid structures or other biological systems that behave like a condensed phase.³³

Some examples of NMR applications in life science-related fields are:

• Molecular biology and biophysics: study of structure, dynamics and molecular interactions of peptides, proteins, nuclei acids, carbohydrates and other biomolecules^31,32
• Health sciences: analysis of biological fluids to obtain metabolic profiles related to diseases (metabolomics), use of NMR imaging techniques for medical diagnosis^34,35
• Food science: NMR fingerprint analysis to check quality or authenticity of food samples³⁶, wine and cannabis.

NMR abbreviations

COSY                     Correlated spectroscopy

DSS                         Sodium trimethylsilylpropanesulfonate

FID                         Free induction decay

MAS                       Magic-angle spinning

NMR                      Nuclear magnetic resonance

NOE                      Nuclear Overhauser effect

NOESY                 Nuclear Overhauser effect spectroscopy

TMS                        Tetramethylsilane

TOCSY                  Totally correlated spectroscopy

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