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Chemical shift
Chemical shift
Chemical shift
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In nuclear magnetic resonance (NMR) spectroscopy, the chemical shift is the resonant frequency of an atomic nucleus relative to a standard in a magnetic field. Often the position and number of chemical shifts are diagnostic of the structure of a molecule.[1][2][3] Chemical shifts are also used to describe signals in other forms of spectroscopy such as photoemission spectroscopy.

Some atomic nuclei possess a magnetic moment (nuclear spin), which gives rise to different energy levels and resonance frequencies in a magnetic field. The total magnetic field experienced by a nucleus includes local magnetic fields induced by currents of electrons in the molecular orbitals (electrons have a magnetic moment themselves). The electron distribution of the same type of nucleus (e.g. 1H, 13C, 15N) usually varies according to the local geometry (binding partners, bond lengths, angles between bonds, and so on), and with it the local magnetic field at each nucleus. This is reflected in the spin energy levels (and resonance frequencies). The variations of nuclear magnetic resonance frequencies of the same kind of nucleus, due to variations in the electron distribution, is called the chemical shift. The size of the chemical shift is given with respect to a reference frequency or reference sample (see also chemical shift referencing), usually a molecule with a barely distorted electron distribution.

Operating frequency

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The operating (or Larmor) frequency of a magnet (usually quoted as absolute value in MHz) is calculated from the Larmor equation[4]

where B0 is the induction of the magnet (SI units of tesla), and is the magnetogyric ratio of the nucleus — an empirically measured fundamental constant determined by the details of the structure of each nucleus. For example, the proton operating frequency for a 1-tesla magnet is calculated as

MRI scanners are often referred to by their field strengths B0 (e.g. "a 7 T scanner"), whereas NMR spectrometers are commonly referred to by the corresponding proton Larmor frequency (e.g. "a 300 MHz spectrometer", which has a B0 of 7 T). While chemical shift is referenced in order that the units are equivalent across different field strengths, the actual frequency separation in hertz scales with field strength (B0). As a result, the difference of chemical shift between two signals (ppm) represents a larger number of hertz on machines that have larger B0, and therefore the signals are less likely to be overlapping in the resulting spectrum. This increased resolution is a significant advantage for analysis. (Larger-field machines are also favoured on account of having intrinsically higher signal arising from the Boltzmann distribution of magnetic spin states.)

Chemical shift referencing

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Chemical shift δ is usually expressed in parts per million (ppm) by frequency, because it is calculated from[5]

where νsample is the absolute resonance frequency of the sample, and νref is the absolute resonance frequency of a standard reference compound, measured in the same applied magnetic field B0. Since the numerator is usually expressed in hertz, and the denominator in megahertz, δ is expressed in ppm.

The detected frequencies (in Hz) for 1H, 13C, and 29Si nuclei are usually referenced against TMS (tetramethylsilane), TSP (trimethylsilylpropanoic acid), or DSS, which by the definition above have a chemical shift of zero if chosen as the reference. Other standard materials are used for setting the chemical shift for other nuclei.

Thus an NMR signal observed at a frequency 300 Hz higher than the signal from TMS, where the TMS resonance frequency is 300 MHz, has a chemical shift of

Although the absolute resonance frequency depends on the applied magnetic field, the chemical shift is independent of external magnetic field strength. On the other hand, the resolution of NMR will increase with applied magnetic field.

Referencing methods

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Practically speaking, diverse methods may be used to reference chemical shifts in an NMR experiment, which can be subdivided into indirect and direct referencing methods.[5] Indirect referencing uses a channel other than the one of interest to adjust chemical shift scale correctly, i.e. the solvent signal in the deuterium (lock) channel can be used to reference the a 1H NMR spectrum.[5] Both indirect and direct referencing can be done as three different procedures:

  1. Internal referencing, where the reference compound is added directly to the system under study."[5] In this common practice, users adjust residual solvent signals of 1H or 13C NMR spectra with calibrated spectral tables.[6][7] If substances other than the solvent itself are used for internal referencing, the sample has to be combined with the reference compound, which may affect the chemical shifts.
  2. External referencing, involving sample and reference contained separately in coaxial cylindrical tubes.[5] With this procedure, the reference signal is still visible in the spectrum of interest, although the reference and the sample are physically separated by a glass wall. Magnetic susceptibility differences between the sample and the reference phase need to be corrected theoretically,[5] which lowers the practicality of this procedure.
  3. Substitution method: The use of separate cylindrical tubes for the sample and the reference compound, with (in principle) spectra recorded individually for each.[5] Similar to external referencing, this method allows referencing without sample contamination. If field/frequency locking via the 2H signal of the deuterated solvent is used and the solvents of reference and analyte are the same, the use of this methods is straightforward. Problems may arise if different solvents are used for the reference compound and the sample as (just like for external referencing) magnetic susceptibility differences need to be corrected theoretically.[5][8] If this method is used without field/frequency locking, shimming procedures between the sample and the reference need to be avoided as they change the applied magnetic field (and thereby influence the chemical shift).[5]

Modern NMR spectrometers commonly make use of the absolute scale,[8][5] which defines the 1H signal of TMS as 0 ppm in proton NMR and the center frequencies of all other nuclei as percentage of the TMS resonance frequency:[5][8]

The use of the deuterium (lock) channel, so the 2H signal of the deuterated solvent, and the Ξ value of the absolute scale is a form of internal referencing and is particularly useful in heteronuclear NMR spectroscopy as local reference compounds may not be always be available or easily used (i.e. liquid NH3 for 15N NMR spectroscopy). This system, however, relies on accurately determined 2H NMR chemical shifts enlisted in the spectrometer software and correctly determined Ξ values by IUPAC.[5][8] A recent study for 19F NMR spectroscopy revealed that the use of the absolute scale and lock-based internal referencing led to errors in chemical shifts.[9][10] These may be negated by inclusion of calibrated reference compounds.[9][10]

The induced magnetic field

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The electrons around a nucleus will circulate in a magnetic field and create a secondary induced magnetic field. This field opposes the applied field as stipulated by Lenz's law and atoms with higher induced fields (i.e., higher electron density) are therefore called shielded, relative to those with lower electron density. Electron-donating alkyl groups, for example, lead to increased shielding whereas electron-withdrawing substituents such as nitro groups lead to deshielding of the nucleus. Not only substituents cause local induced fields. Bonding electrons can also lead to shielding and deshielding effects. A striking example of this is the pi bonds in benzene. Circular current through the hyperconjugated system causes a shielding effect at the molecule's center and a deshielding effect at its edges. Trends in chemical shift are explained based on the degree of shielding or deshielding.

Nuclei are found to resonate in a wide range to the left (or more rare to the right) of the internal standard. When a signal is found with a higher chemical shift:

  • The applied effective magnetic field is lower, if the resonance frequency is fixed (as in old traditional CW spectrometers)
  • The frequency is higher, when the applied magnetic field is static (normal case in FT spectrometers)
  • The nucleus is more deshielded
  • The signal or shift is downfield or at low field or paramagnetic.

Conversely a lower chemical shift is called a diamagnetic shift, and is upfield and more shielded.

Diamagnetic shielding

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In real molecules protons are surrounded by a cloud of charge due to adjacent bonds and atoms. In an applied magnetic field (B0) electrons circulate and produce an induced field (Bi) which opposes the applied field. The effective field at the nucleus will be B = B0 − Bi. The nucleus is said to be experiencing a diamagnetic shielding.

Factors causing chemical shifts

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Important factors influencing chemical shift are electron density, electronegativity of neighboring groups and anisotropic induced magnetic field effects.

Electron density shields a nucleus from the external field. For example, in proton NMR the electron-poor tropylium ion has its protons downfield at 9.17 ppm, those of the electron-rich cyclooctatetraenyl anion move upfield to 6.75 ppm and its dianion even more upfield to 5.56 ppm.

A nucleus in the vicinity of an electronegative atom experiences reduced electron density and the nucleus is therefore deshielded. In proton NMR of methyl halides (CH3X) the chemical shift of the methyl protons increase in the order I < Br < Cl < F from 2.16 ppm to 4.26 ppm reflecting this trend. In carbon NMR the chemical shift of the carbon nuclei increase in the same order from around −10 ppm to 70 ppm. Also when the electronegative atom is removed further away the effect diminishes until it can be observed no longer.

Anisotropic induced magnetic field effects are the result of a local induced magnetic field experienced by a nucleus resulting from circulating electrons that can either be paramagnetic when it is parallel to the applied field or diamagnetic when it is opposed to it. It is observed in alkenes where the double bond is oriented perpendicular to the external field with pi electrons likewise circulating at right angles. The induced magnetic field lines are parallel to the external field at the location of the alkene protons which therefore shift downfield to a 4.5 ppm to 7.5 ppm range. The three-dimensional space where a diamagnetic shift is called the shielding zone with a cone-like shape aligned with the external field.

Induced magnetic field of alkenes in external magnetic fields, field lines in grey

The protons in aromatic compounds are shifted downfield even further with a signal for benzene at 7.73 ppm as a consequence of a diamagnetic ring current.

Alkyne protons by contrast resonate at high field in a 2–3 ppm range. For alkynes the most effective orientation is the external field in parallel with electrons circulation around the triple bond. In this way the acetylenic protons are located in the cone-shaped shielding zone hence the upfield shift.

Induced magnetic field of alkynes in external magnetic fields, field lines in grey.

Magnetic properties of most common nuclei

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1H and 13C are not the only nuclei susceptible to NMR experiments. A number of different nuclei can also be detected, although the use of such techniques is generally rare due to small relative sensitivities in NMR experiments (compared to 1H) of the nuclei in question, the other factor for rare use being their slender representation in nature and organic compounds.

Magnetic properties of common nuclei[11]
Isotope Occurrence
in nature
(%) 		Spin number I Magnetic moment μ
(μN) 		Electric quadrupole moment
(e × 10−24 cm2) 		Operating frequency at 7 T
(MHz) 		Relative sensitivity
1H 99.984 ⁠1/2⁠ 2.79628 0 300.13 1
2H 0.016 1 0.85739 0.0028 46.07 0.0964
10B 18.8 3 1.8005 0.074 32.25 0.0199
11B 81.2 ⁠3/2⁠ 2.6880 0.026 96.29 0.165
12C 98.9 0 0 0 0 0
13C 1.1 ⁠1/2⁠ 0.70220 0 75.47 0.0159
14N 99.64 1 0.40358 0.071 21.68 0.00101
15N 0.37 ⁠1/2⁠ −0.28304 0 30.41 0.00104
16O 99.76 0 0 0 0 0
17O 0.0317 ⁠5/2⁠ −1.8930 −0.0040 40.69 0.0291
19F 100 ⁠1/2⁠ 2.6273 0 282.40 0.834
28Si 92.28 0 0 0 0 0
29Si 4.70 ⁠1/2⁠ −0.5548 0 59.63 0.0785
31P 100 ⁠1/2⁠ 1.1205 0 121.49 0.0664
35Cl 75.4 ⁠3/2⁠ 0.92091 −0.079 29.41 0.0047
37Cl 24.6 ⁠3/2⁠ 0.68330 −0.062 24.48 0.0027

1H, 13C, 15N, 19F and 31P are the five nuclei that have the greatest importance in NMR experiments:

  • 1H because of high sensitivity and vast occurrence in organic compounds
  • 13C because of being the key component of all organic compounds despite occurring at a low abundance (1.1%) compared to the major isotope of carbon 12C, which has a spin of 0 and therefore is NMR-inactive.
  • 15N because of being a key component of important biomolecules such as proteins and DNA
  • 19F because of high relative sensitivity
  • 31P because of frequent occurrence in organic compounds and moderate relative sensitivity

Chemical shift manipulation

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In general, the associated increased signal-to-noise and resolution has driven a move towards increasingly high field strengths. In limited cases, however, lower fields are preferred; examples are for systems in chemical exchange, where the speed of the exchange relative to the NMR experiment can cause additional and confounding linewidth broadening. Similarly, while avoidance of second order coupling is generally preferred, this information can be useful for elucidation of chemical structures. Using refocussing pulses placed between recording of successive points of the free induction decay, in an analogous fashion to the spin echo technique in MRI, the chemical shift evolution can be scaled to provide apparent low-field spectra on a high-field spectrometer.[12] In a similar fashion, it is possible to upscale the effect of J-coupling relative to the chemical shift using pulse sequences that include additional J-coupling evolution periods interspersed with conventional spin evolutions.[13]

Other chemical shifts

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The Knight shift (first reported in 1949) and Shoolery's rule are observed with pure metals and methylene groups, respectively. The NMR chemical shift in its present-day meaning first appeared in journals in 1950. Chemical shifts with a different meaning appear in X-ray photoelectron spectroscopy as the shift in atomic core-level energy due to a specific chemical environment. The term is also used in Mössbauer spectroscopy, where similarly to NMR it refers to a shift in peak position due to the local chemical bonding environment. As is the case for NMR the chemical shift reflects the electron density at the atomic nucleus.[14]

See also

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References

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Revisions and contributorsEdit on WikipediaRead on Wikipedia

Chemical shift

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In (NMR) , the chemical shift is the resonant frequency difference of a nucleus relative to a standard reference compound, expressed in parts per million (ppm) using the symbol δ, which arises from variations in the local experienced by the nucleus due to its surrounding electrons and chemical environment. This phenomenon, known as magnetic shielding or deshielding, allows NMR to distinguish between nuclei in different structural positions within a , making chemical shift a for elucidating molecular structures in organic and . The chemical shift originates from the interaction between the applied external magnetic field and the induced magnetic fields generated by circulating electrons around the nucleus, which either shield (reducing the effective field and shifting the signal upfield to lower ppm values) or deshield (increasing the effective field and shifting downfield to higher ppm values) the nucleus. Key factors influencing the chemical shift include inductive effects from electronegative atoms that withdraw and deshield nearby protons, π-electron in unsaturated systems like aromatic rings that can cause variable shielding, and hydrogen bonding in functional groups such as alcohols or amines, which typically deshields protons and leads to concentration- or solvent-dependent shifts. For ¹H NMR, proton chemical shifts generally span 0–12 ppm, while ¹³C NMR shifts cover a broader 0–200 ppm range, reflecting greater sensitivity to electronic environments in carbon atoms. Chemical shifts are measured relative to (TMS), a standard reference with 12 equivalent protons that produces a sharp singlet at δ = 0 ppm and does not overlap with most organic signals, ensuring instrument-independent reporting. The value is calculated as δ = [(ν_sample - ν_TMS) / spectrometer frequency in MHz] × 10⁶, where ν represents the frequency in Hz, allowing consistent comparisons across different NMR instruments operating at varying field strengths (e.g., 300 MHz or 600 MHz). Solvent effects, such as using (CDCl₃) or (DMSO-d₆), can subtly alter shifts by up to 0.1–1 ppm due to solute-solvent interactions, necessitating standardized conditions for reproducible data. In practice, characteristic chemical shift ranges enable rapid identification of functional groups: for example, methyl protons (CH₃-) appear at 0.9–1.8 ppm, alkene protons at 4.5–6.5 ppm, and aldehyde protons at 9–10 ppm, providing essential diagnostic information for structural elucidation in fields like pharmaceutical development and . Advanced applications, such as multidimensional NMR, exploit chemical shift perturbations to study , binding, and dynamic processes at the atomic level.

Fundamentals of Chemical Shift

Definition and Basic Principles

In (NMR) , the chemical shift (δ) is defined as the difference in the resonance of a nucleus relative to that of a standard reference compound, expressed in parts per million (ppm) to render it independent of the spectrometer's strength. This dimensionless quantity arises because the resonance of a nucleus is proportional to the applied , so normalizing the frequency difference by the operating ensures comparability across different instruments. The basic principle underlying chemical shift stems from the local electronic environment surrounding the nucleus, which induces variations in the effective experienced by the nucleus. In NMR, nuclei with the same but placed in different molecular contexts—such as varying bonds, substituents, or geometries—encounter differing degrees of shielding or deshielding from surrounding electrons, leading to shifts in their absorption frequencies. This phenomenon allows NMR to distinguish between nuclei in unique chemical environments, providing structural insights into molecules. The term "chemical shift" was first coined in 1950 by Warren G. Proctor and Fu-Chun Yu during early NMR experiments, where they unexpectedly observed distinct frequencies for the two nuclei in (NH₄NO₃), attributing the difference to the chemical environment. Their discovery marked the recognition of how influences NMR signals, laying the foundation for high-resolution NMR . The chemical shift is quantitatively expressed by the equation: δ=νsample−νreferenceν0×106\delta = \frac{\nu_\text{sample} - \nu_\text{reference}}{\nu_0} \times 10^6 where νsample\nu_\text{sample} is the resonance frequency of the sample nucleus in Hz, νreference\nu_\text{reference} is the resonance frequency of the reference standard in Hz, and ν0\nu_0 is the operating frequency of the spectrometer (typically in MHz for protons). This formula derives from the Larmor frequency relation ν=γB0/2π\nu = \gamma B_0 / 2\pi, where small perturbations in the local field Blocal=B0(1−σ)B_\text{local} = B_0 (1 - \sigma) (with σ\sigma as the shielding constant) cause frequency differences Δν=ν0σ\Delta \nu = \nu_0 \sigma; dividing by ν0\nu_0 and scaling by 10610^6 yields the ppm scale for practical measurement. By convention, deshielded nuclei (experiencing higher effective magnetic fields) appear at higher δ values (downfield), while shielded nuclei (experiencing lower effective fields) appear upfield. A representative example illustrates this principle for protons (^1H): in alkanes, methyl (CH₃) protons typically resonate at 0.9–1.0 ppm and methylene (CH₂) protons at 1.2–1.4 ppm due to their non-polar hydrocarbon environment, whereas aldehyde protons (RCHO) appear far downfield at 9–10 ppm owing to the deshielding effect of the electron-withdrawing carbonyl group. Tetramethylsilane (TMS) serves as the universal reference standard, assigned δ = 0 ppm for protons.

Measurement and Units

In (NMR) , chemical shifts are measured by recording the resonance of a nucleus relative to a reference standard, initially expressed as a frequency difference in hertz (Hz). This difference arises from the local magnetic environment of the nucleus and is determined during the acquisition of the (FID) signal in the spectrometer. Modern NMR instruments, such as (FT) spectrometers, detect these frequencies in the time domain and convert them to the via , yielding spectra where peaks correspond to specific chemical environments. To achieve field-independent reporting, the frequency difference in Hz is converted to the chemical shift scale in parts per million (ppm), a dimensionless unit defined by the International Union of Pure and Applied Chemistry (IUPAC). The conversion is performed automatically by spectrometer software using the formula: δ=νsample−νrefν0×106\delta = \frac{\nu_\text{sample} - \nu_\text{ref}}{\nu_0} \times 10^6 where νsample\nu_\text{sample} is the resonance frequency of the sample, νref\nu_\text{ref} is the reference frequency (both in Hz), and ν0\nu_0 is the spectrometer's operating frequency (in MHz). Positive δ\delta values indicate deshielding (downfield shifts, higher frequency relative to the reference), while negative values denote shielding (upfield shifts). For 1^1H NMR in organic compounds, chemical shifts typically span 0 to 12 ppm, with rare negative shifts (e.g., -1 to -2 ppm) in cases like protons influenced by aromatic ring currents, and more negative values (down to -10 ppm) in organometallic hydride protons. The accuracy of these measurements relies on proper instrument , including locking and shimming. Locking involves using a lock signal (from a deuterated ) to stabilize the against drifts, while shimming adjusts coils to homogenize the field, minimizing linewidths and ensuring precise peak positions. Without adequate locking and shimming, spectral distortions can shift apparent peak frequencies by several Hz, propagating errors into the ppm scale. A key advantage of the ppm scale is its independence from the strength, allowing consistent chemical shift values across instruments operating at different frequencies, such as 60 MHz or 900 MHz spectrometers. For instance, a 600 Hz difference at 60 MHz corresponds to 10 ppm, just as a 9000 Hz difference does at 900 MHz, facilitating direct comparison of from diverse setups. Common sources of in chemical shift include sample impurities, which introduce extraneous peaks or broaden signals, complicating accurate peak identification and positioning. Poor , often due to inhomogeneities or low signal-to-noise ratios, can also lead to imprecise determination of peak maxima, with errors up to 0.1-0.5 ppm in low-quality spectra. These issues are mitigated by employing high-field NMR spectrometers (e.g., 500 MHz or higher), which enhance resolution through increased chemical shift dispersion and better separation of overlapping signals.

Theoretical Basis

Induced Magnetic Field

In (NMR) , the applied external B0\mathbf{B}_0 induces currents in the surrounding a nucleus, generating a secondary local magnetic field Bind\mathbf{B}_\text{ind} that modifies the field experienced by the nucleus. This induced field arises from the response of the molecular electron cloud to B0\mathbf{B}_0, creating circulating electron currents analogous to those in a loop of wire, which produce Bind\mathbf{B}_\text{ind} according to the Biot-Savart law. The direction and magnitude of Bind\mathbf{B}_\text{ind} depend on the electronic structure, typically opposing B0\mathbf{B}_0 at the nucleus in diamagnetic systems, thereby shielding it from the full external field. The effective at the nucleus, Beff\mathbf{B}_\text{eff}, is the vector sum Beff=B0+Bind+Bext\mathbf{B}_\text{eff} = \mathbf{B}_0 + \mathbf{B}_\text{ind} + \mathbf{B}_\text{ext}, where Bext\mathbf{B}_\text{ext} accounts for any additional external contributions, though it is often negligible in standard NMR setups. The resonance ν\nu of the nucleus is then given by the Larmor equation: ν=γ2π∣Beff∣,\nu = \frac{\gamma}{2\pi} |\mathbf{B}_\text{eff}|, where γ\gamma is the of the nucleus. Since Bind\mathbf{B}_\text{ind} modulates Beff\mathbf{B}_\text{eff}, variations in Bind\mathbf{B}_\text{ind} lead to shifts in ν\nu, with the induced field typically reducing ∣Beff∣|\mathbf{B}_\text{eff}| and thus lowering the observed compared to a bare nucleus. Approximating Bind≈−σB0\mathbf{B}_\text{ind} \approx -\sigma \mathbf{B}_0, where σ\sigma is the shielding constant (a between 0 and 1 for most cases), yields Beff≈(1−σ)B0\mathbf{B}_\text{eff} \approx (1 - \sigma) \mathbf{B}_0, directly linking the induced field to the chemical shift. The induced magnetic field encompasses both diamagnetic and paramagnetic contributions. In diamagnetic molecules, which lack unpaired electrons and dominate organic compounds, the diamagnetic term arises from the orbital motion of paired electrons and typically produces an opposing Bind\mathbf{B}_\text{ind} that shields the nucleus. Paramagnetic contributions, stemming from unpaired electrons, can enhance or reverse the field direction, leading to deshielding, but these are rare in standard diamagnetic samples used in routine NMR. Visual representations of the induced field often depict field lines circulating around the nucleus due to electron loops, with Bind\mathbf{B}_\text{ind} pointing opposite to B0\mathbf{B}_0 within the electron cloud, akin to the in a superconducting ring. This circulation creates a local environment where the field strength diminishes toward the nucleus, emphasizing the . The quantum mechanical foundation for Bind\mathbf{B}_\text{ind} was established using second-order to calculate the induced electron currents and their magnetic effects on the nucleus, as introduced by Norman Ramsey in 1950. This approach treats the external field as a perturbation that mixes excited electronic states into the wavefunction, yielding the shielding constant σ\sigma through integrals over electronic orbitals.

Diamagnetic Shielding

Diamagnetic shielding arises from the weak opposition to the external B0B_0 generated by induced loops of circulation around the nucleus, which reduces the effective BeffB_\mathrm{eff} at the nucleus. This contribution, denoted as σdia\sigma_\mathrm{dia}, is a key component of the total magnetic shielding in . The quantitative expression for diamagnetic shielding in atoms is given by the Lamb formula: σdia=e23mec2⟨∑i1ri⟩,\sigma_\mathrm{dia} = \frac{e^2}{3 m_e c^2} \left\langle \sum_i \frac{1}{r_i} \right\rangle, where ee is the , mem_e the , cc the , and ⟨1/r⟩\left\langle 1/r \right\rangle the expectation value of the inverse distance between an and the nucleus, averaged over the ground-state for all . This formula originates from a classical treatment of in the , assuming spherical symmetry of the electron distribution; it provides the leading-order term for the induced opposing B0B_0. In , the expression involves the α\alpha: σdia=α23⟨∑i1ri⟩\sigma_\mathrm{dia} = \frac{\alpha^2}{3} \left\langle \sum_i \frac{1}{r_i} \right\rangle (converted to ppm). The magnitude of σdia\sigma_\mathrm{dia} is typically 0–100 ppm for light nuclei like 1H^1\mathrm{H} and 13C^{13}\mathrm{C}, reflecting compact orbitals with smaller ⟨1/r⟩\left\langle 1/r \right\rangle; for heavier atoms, it increases significantly due to more diffuse orbitals that enhance this average. The total shielding is σtotal=σdia+σpara\sigma_\mathrm{total} = \sigma_\mathrm{dia} + \sigma_\mathrm{para}, with the paramagnetic term σpara\sigma_\mathrm{para} arising from excited-state contributions; in closed-shell molecules, σdia\sigma_\mathrm{dia} dominates because filled orbitals minimize paramagnetic effects. In , diamagnetic shielding exemplifies this dominance, as seen in 129Xe^{129}\mathrm{Xe}, where the atomic shielding reaches approximately 6600 ppm, driven by the high in the closed-shell configuration.

Factors Influencing Chemical Shifts

The chemical shift in NMR is modulated by several molecular and environmental factors that alter the and local around the nucleus, primarily affecting the diamagnetic shielding component. These factors lead to deshielding (downfield shifts) or shielding (upfield shifts) relative to a , enabling structural elucidation. Electronegativity of adjacent atoms plays a crucial role through inductive effects, where electron-withdrawing groups reduce around the observed nucleus, causing deshielding. For instance, the high of deshields the protons in CH₃F, resulting in a chemical shift of 4.26 ppm compared to 0.23 ppm for the protons in CH₄. This effect diminishes with distance from the electronegative atom, typically influencing protons within two or three bonds. Hybridization influences chemical shifts by changing the s-character of bonding orbitals, which pulls electrons closer to the nucleus and enhances deshielding. sp³-hybridized carbons exhibit shifts in the 0–50 ppm range for ¹³C NMR, while sp²-hybridized carbons appear at 100–200 ppm due to the higher 33% s-character compared to 25% in sp³. In aromatic systems, the pi-electron ring current generates that deshields protons in the ring plane; for example, the methyl protons in resonate at 2.34 ppm, deshielded by approximately 1.4 ppm relative to typical methyl protons near 0.9 ppm. Hydrogen bonding significantly deshields protons involved in the interaction by polarizing the electron cloud and reducing shielding. In alcohols, OH protons typically appear between 1 and 5 ppm, with the exact position varying with concentration: dilute solutions show upfield shifts (near 1 ppm) for monomeric forms, while concentrated samples exhibit downfield shifts (2–5 ppm) due to intermolecular hydrogen bonds. Steric and conformational effects arise from spatial arrangements that alter local electron distribution or anisotropic fields. In derivatives at low temperatures, axial and equatorial protons differ by about 0.5 ppm due to distinct orientations relative to surrounding bonds, with axial protons generally more deshielded. Solvent effects stem from interactions like hydrogen bonding or changes in the dielectric constant, which can deshield or shield nuclei. Polar solvents such as DMSO often cause greater deshielding than nonpolar ones like ; for many ¹H signals, this results in shifts of 0.5–1 ppm, with variations up to 4.6 ppm for polar protons.
FactorDescriptionExample
ElectronegativityInductive withdrawal by electron-withdrawing groups reduces electron density, deshielding nuclei.CH₃F protons at 4.26 ppm vs. CH₄ at 0.23 ppm (¹H NMR).
Hybridization/AnisotropyHigher s-character in sp² vs. sp³ increases deshielding; ring currents in aromatics create anisotropic fields.sp³ carbons 0–50 ppm, sp² 100–200 ppm (¹³C NMR); CH₃ at 2.34 ppm (¹H NMR).
Hydrogen BondingPolarizes bonds, deshielding involved protons; concentration-dependent.Alcohol OH 1–5 ppm, shifts downfield with increasing H-bonding (¹H NMR).
Steric/ConformationalSpatial orientation alters local fields, causing differences in conformers.Axial vs. equatorial protons in differ by ~0.5 ppm (¹H NMR).
Solvent EffectsPolarity and H-bonding capability modulate shielding via solute-solvent interactions.¹H shifts of 0.5–1 ppm from CDCl₃ to DMSO-d₆.

Referencing and Standardization

Chemical Shift Referencing

Chemical shift referencing is essential in nuclear magnetic resonance (NMR) spectroscopy to establish a universal zero point on the chemical shift scale (δ), measured in parts per million (ppm), thereby allowing consistent comparison of spectral data across different samples, solvents, instruments, and laboratories. Without a reference standard, the observed resonance frequencies would be arbitrary and dependent on the spectrometer's magnetic field strength, rendering inter-sample comparisons impossible. The IUPAC recommends a unified chemical shift scale for all nuclei based on the ¹H resonance of tetramethylsilane (TMS) as the primary reference, set at δ = 0 ppm, to ensure reproducibility and standardization. Internal referencing, where the standard is added directly to the sample solution, is the preferred method for most routine NMR experiments due to its simplicity and the homogeneity it provides in the magnetic environment, minimizing susceptibility differences. For example, a small amount of TMS (typically <1% v/v) is added to organic solvents like CDCl₃, where its methyl protons and carbon produce a single sharp peak at 0 ppm for ¹H and ¹³C NMR, respectively. In contrast, external referencing involves measuring the sample and standard separately—often using coaxial tubes or the substitution method—and requires corrections for bulk magnetic susceptibility differences between the sample and reference compartments. This approach is particularly useful for air-sensitive or reactive samples where adding an internal standard could compromise the sample integrity or introduce contaminants. Ideal reference standards must exhibit several key properties to ensure accurate and reliable calibration: chemical inertness to avoid reactions with the sample, low volatility to prevent evaporation during measurement (though TMS is used in dilute solutions despite its moderate volatility), and a single, sharp, intense resonance peak that does not overlap with typical sample signals. TMS satisfies these criteria exceptionally well due to its tetrahedral symmetry, which yields equivalent protons and carbons, and the low electronegativity of silicon, which shields its nuclei to position the signal at high field (0 ppm). For aqueous solutions, where TMS has limited solubility, IUPAC guidelines recommend secondary references such as sodium 3-(trimethylsilyl)propane-1-sulfonate (DSS), whose methyl ¹H resonance is set to 0 ppm, providing a water-soluble alternative with similar desirable properties. These 2001 IUPAC recommendations (building on earlier 1999 proposals for reporting standards) emphasize using secondary references only when primary ones like TMS are impractical, with their positions calibrated relative to TMS via the frequency ratio Ξ. To maintain field homogeneity and stability during spectral acquisition, NMR spectrometers employ a lock signal, typically from the deuterium (²H) resonance of the deuterated solvent (e.g., CDCl₃), which continuously monitors and adjusts for magnetic field drifts. This lock mechanism ensures that chemical shifts remain consistent throughout the experiment, with any necessary corrections applied based on the difference between the lock frequency and the ¹H reference frequency. By integrating referencing with the lock system, variations due to temperature, solvent, or instrumental fluctuations are minimized, upholding the precision of the δ scale.

Referencing Methods

Direct referencing involves adding a standard compound directly to the NMR sample to serve as an internal reference for chemical shift calibration. For proton (¹H) and carbon-13 (¹³C) NMR in organic solvents like CDCl₃, tetramethylsilane (TMS) is commonly used at concentrations below 1% volume fraction to avoid signal overlap or distortion, with the methyl resonance set to 0 ppm. In aqueous solutions, particularly for biomolecules, sodium 2,2-dimethyl-2-silapentane-5-sulfonate (DSS) is preferred at approximately 10 mmol/dm³, also set to 0 ppm for the methyl group, due to its solubility and minimal interaction with biological samples. The procedure typically entails acquiring a ¹H spectrum first to confirm the reference peak position before scaling other nuclei spectra accordingly. Indirect referencing relies on the deuterium (²H) lock signal from the deuterated solvent to calibrate the chemical shift scale without adding an internal standard, using predefined frequency ratios (Ξ values) from the IUPAC unified scale. For example, in DMSO-d₆, the residual ¹H signal of the CHD₂ group is set to 2.50 ppm relative to TMS in the ¹H spectrum, and the spectrometer adjusts the ²H lock frequency to maintain consistency across nuclei via the ²H Ξ value of 15.350609%. This method ensures reproducibility without altering the sample composition and is standard for multinuclear experiments. Secondary standards provide alternatives tailored to specific sample types, such as biomolecules in aqueous media. For ¹H NMR in water-based solutions, 3-(trimethylsilyl)propionate-2,2,3,3-d₄ (TSP) is often employed at low concentrations with its methyl resonance defined as 0 ppm, offering advantages in solubility for biological matrices despite some pH sensitivity that requires careful control. In contrast, DSS serves as a more robust secondary option in such environments due to its lower sensitivity to pH variations, maintaining shift stability across typical biological pH ranges (e.g., 4–8). Specialized methods address challenging sample states like solids or gases. In solid-state NMR under magic angle spinning (MAS), adamantane is used as a reference for ¹³C shifts, with its methylene (CH₂) carbon signal at 37.77 ppm relative to TMS, enabling high-resolution calibration without bulk magnetic susceptibility corrections. For volatile or gas-phase samples, low-pressure ³He gas serves as a temperature-independent standard, with a ³He Ξ value of 76.178976%, facilitating precise referencing in low-density environments. Common pitfalls in referencing include using impure standards, which can lead to peak broadening from contaminants interfering with the lock or reference signals, necessitating high-purity reagents verified by prior spectroscopy. Additionally, temperature dependence requires corrections; for instance, the TMS ¹H shift varies by approximately -0.0005 ppm/°C, potentially causing up to 0.01 ppm deviation over a 20°C range, so calibrations should specify and account for the measurement temperature.

Practical Considerations

Operating Frequency

The operating frequency of an NMR spectrometer, denoted as ν0\nu_0, is the Larmor frequency at which nuclei resonate in the applied magnetic field B0B_0, given by the equation ν0=γB02π\nu_0 = \frac{\gamma B_0}{2\pi}, where γ\gamma is the gyromagnetic ratio of the nucleus. Higher operating frequencies correspond to stronger magnetic fields; for example, a 400 MHz spectrometer for 1^1H nuclei operates at approximately twice the field strength of a 100 MHz instrument, leading to greater separation of chemical shift differences when measured in hertz (Hz). However, the chemical shift δ\delta in parts per million (ppm) remains constant across field strengths because it is a relative measure, independent of ν0\nu_0, ensuring comparability of spectra regardless of the instrument used. Increased operating frequency enhances spectral resolution by dispersing peaks over a wider frequency range in Hz, facilitating the separation of closely spaced signals. At 900 MHz for 1^1H NMR, aromatic protons in complex organic molecules exhibit significantly better peak separation compared to lower fields, allowing clearer identification of subtle structural differences. Digital resolution, which determines the precision of peak definition in the processed spectrum, is calculated as the sweep width (the frequency range covered during acquisition) divided by the number of data points acquired. This parameter improves with higher fields due to the expanded dispersion, though it requires careful optimization of acquisition parameters to avoid truncation artifacts. While higher frequencies boost sensitivity, with signal-to-noise ratio (S/N) scaling approximately as ν03/2\nu_0^{3/2}, they introduce practical challenges such as more difficult shimming to achieve field homogeneity. At ultra-high fields beyond 1 GHz, magnetic field instabilities and sample-specific susceptibilities complicate shimming, potentially degrading resolution despite the theoretical gains. In practice, low-field instruments operating at 60 MHz are commonly used in educational settings for straightforward spectra of small molecules, whereas high-field systems at 1 GHz or above are essential for resolving the crowded chemical shifts in complex mixtures like proteins. The use of ppm for chemical shifts is particularly advantageous here, as the raw frequency differences in Hz scale linearly with B0B_0, making absolute Hz values instrument-dependent and less useful for standardization.

Magnetic Properties of Common Nuclei

The magnetic properties of atomic nuclei, particularly their nuclear spin quantum number II, gyromagnetic ratio γ\gamma, and natural isotopic abundance, fundamentally determine their suitability for nuclear magnetic resonance (NMR) spectroscopy and the observable range of chemical shifts. Nuclei with I=1/2I = 1/2 produce sharp, well-resolved signals because they lack a nuclear moment, avoiding relaxation-induced broadening from interactions with electric field gradients. Prominent examples include 1H^1\mathrm{H}, 13C^{13}\mathrm{C}, 19F^{19}\mathrm{F}, and 31P^{31}\mathrm{P}, which are routinely used in multi-nuclear NMR for structural analysis due to their favorable properties. In contrast, nuclei with I>1/2I > 1/2, such as 2H^2\mathrm{H} (I=1I = 1) and 14N^{14}\mathrm{N} (I=1I = 1), possess a moment that often leads to significant line broadening in solution-state NMR, complicating spectral interpretation unless in highly symmetric environments. The γ\gamma dictates the resonance frequency for a given strength and influences signal sensitivity, as the equilibrium scales with γ3\gamma^3. High γ\gamma values, as seen in 1H^1\mathrm{H} and 19F^{19}\mathrm{F}, yield stronger signals and wider chemical shift dispersions, enhancing resolution for distinguishing subtle electronic environments. Natural abundance further modulates detectability; low-abundance isotopes like 13C^{13}\mathrm{C} (1.1%) require longer acquisition times or enhancements such as the (NOE) via proton decoupling to achieve practical signal-to-noise ratios. The following table summarizes key for common NMR-active nuclei, including typical chemical shift ranges observed in organic and biochemical contexts. These ranges reflect environmental influences on shielding, with broader dispersions for nuclei like 19F^{19}\mathrm{F} providing valuable structural insights in multi-nuclear studies. Shift values are relative to standard references (e.g., TMS for 1H^1\mathrm{H} and 13C^{13}\mathrm{C}, 85% H3_3PO4_4 for 31P^{31}\mathrm{P}, CFCl3_3 for 19F^{19}\mathrm{F}).
NucleusSpin IINatural Abundance (%)γ\gamma (MHz/T)Typical Shift Range (ppm)
1H^1\mathrm{H}1/299.9942.580–12
13C^{13}\mathrm{C}1/21.110.710–220
31P^{31}\mathrm{P}1/210017.24–50 to +100
19F^{19}\mathrm{F}1/210040.08–300 to +300
2H^2\mathrm{H}10.0156.540–10 (broadened)
14N^{14}\mathrm{N}199.63.08Variable, often broadened
Quadrupolar effects are particularly pronounced for 2H^2\mathrm{H}, where the I=1I = 1 spin results in a three-line pattern in the absence of rapid tumbling, but in deuterated solvents like CDCl3_3, the signals are sufficiently narrowed for use as a field-frequency lock despite lower sensitivity compared to 1H^1\mathrm{H}. Similarly, 14N^{14}\mathrm{N} spectra often exhibit severe broadening due to quadrupolar relaxation, limiting its routine application, though it provides complementary information in specialized cases. The high sensitivity and wide shift dispersion of 19F^{19}\mathrm{F} (nearly as sensitive as 1H^1\mathrm{H}) make it invaluable for probing fluorinated compounds, where shifts can reveal connectivity and through scalar couplings. For low-sensitivity nuclei like 13C^{13}\mathrm{C}, NOE enhancement from 1H^1\mathrm{H} irradiation can increase signal intensity by up to a factor of 3, enabling routine acquisition of high-quality spectra.

Advanced and Specialized Topics

Chemical Shift Manipulation

Chemical shift manipulation in NMR involves deliberate experimental adjustments to external conditions or addition of to modify the observed shifts of nuclei, thereby enhancing , assignment, or structural insights. These techniques exploit the sensitivity of chemical shifts to environmental factors, allowing researchers to probe molecular interactions, dynamics, and conformations without altering the core molecular structure. Common methods include varying solvents, , , , , and employing shift , each providing targeted control over shift values. Solvent variation is a primary method for manipulating chemical shifts, as the choice of deuterated influences hydrogen bonding, polarity, and solvation effects on nuclei. For instance, the OH protons of alcohols exhibit significant shifts depending on the ; in CDCl₃, the impurity appears at approximately 1.56 ppm, while in D₂O it resonates at 4.79 ppm, resulting in a downfield shift of about 3.2 ppm due to enhanced hydrogen bonding in aqueous media. Similar variations occur for exchangeable protons like OH and NH, with differences of 3-5 ppm often observed when switching from non-polar like CDCl₃ to polar ones like D₂O. Cosolvents, such as DMSO-d₆ added to D₂O, are frequently used to improve of hydrophobic compounds while minimizing unwanted shift perturbations, enabling NMR analysis of otherwise insoluble samples. Temperature dependence offers another controllable parameter, with many chemical shifts varying linearly with temperature, typically on the order of per . For ¹H nuclei in groups, the temperature coefficient is approximately -0.01 ppm/°C, reflecting changes in hydrogen bonding and vibrational averaging; this linear behavior allows extrapolation to standard conditions and is exploited to study conformational dynamics in peptides and proteins. Adjusting and directly impacts shifts of ionizable groups by altering states and electrostatic environments. In carboxylic acids, causes a notable shift in the ¹³C carboxyl by 3-4 ppm downfield, from ~175 ppm (protonated) to ~178-179 ppm (deprotonated). Buffers are essential for maintaining consistent and ensuring reproducible shifts, as uncontrolled variations can broaden peaks or obscure assignments. further modulates shifts by screening electrostatic interactions; increasing salt concentration (e.g., NaCl) can shift ¹H by up to 0.1-0.2 ppm in proteins, influencing hyperfine-shifted signals in metalloproteins. Isotope effects from deuteration provide subtle but precise manipulation, particularly for resolving overlapping signals. Deuteration at a carbon site induces an upfield shift in adjacent protons via the alpha effect, typically 0.01-0.05 ppm for remaining protons on the same carbon (e.g., in CHD vs. CH₂ groups), arising from changes in vibrational modes and reduced . shift reagents, such as Eu(fod)₃ ( tris(1,1,1,2,2,3,3-heptafluoro-7,7-dimethyl-4,6-octanedione)), introduce large paramagnetic shifts through coordination, amplifying differences for structural elucidation. These reagents bind to Lewis basic sites like oxygen or , inducing shifts up to 50 ppm via Fermi contact and pseudocontact mechanisms, which are particularly useful for determining in organic molecules by analyzing the directional dependence of shifts. In applications, these manipulation techniques enhance NMR analysis of complex systems. For protein NMR, pH titration monitors chemical shift changes to map ionizable residues, such as Asp and Glu carboxylates, revealing pKₐ values and electrostatic networks with shifts of 0.5-2 ppm per residue. Dynamic NMR leverages or variations to observe conformational averaging, where averaged shifts reflect equilibrium populations, aiding studies of flexible biomolecules like peptides.

Other Types of Chemical Shifts

In (NMR) , chemical shift anisotropy (CSA) arises from the orientation-dependent interaction between the and the local , described by a tensor that reflects the electronic environment around the nucleus. Unlike isotropic shifts in solution-state NMR, CSA in solids produces broad spectral lines due to the lack of molecular tumbling, with principal components spanning tens to hundreds of parts per million (ppm); for example, the 13C CSA tensor in polymeric materials typically ranges from 10 to 100 ppm, providing insights into molecular conformation and dynamics. Magic-angle spinning (MAS) techniques average the anisotropic components to yield an isotropic chemical shift, facilitating high-resolution spectra for in rigid systems like biomolecules and materials. Paramagnetic chemical shifts occur in systems containing unpaired electrons, such as metalloproteins, and comprise two main contributions: the contact shift, arising from delocalization of spin density onto the nucleus via covalent bonds (Fermi contact mechanism), and the pseudocontact shift, resulting from through-space dipolar interactions with the anisotropic of the paramagnetic center. The total shift is given by Δδ=Aρ+D3cos⁡2θ−1r3\Delta \delta = A \rho + D \frac{3 \cos^2 \theta - 1}{r^3} where AρA \rho represents the contact term (AA is the hyperfine coupling constant and ρ\rho the spin density at the nucleus), and the second term is the pseudocontact contribution (DD relates to the susceptibility anisotropy, rr is the metal-nucleus distance, and θ\theta the angle between the vector r\mathbf{r} and the principal susceptibility axis). These shifts, often exceeding 100 ppm in lanthanide-substituted proteins, serve as long-range restraints for structure determination, complementing diamagnetic NMR data. Isotope shifts in NMR manifest as small perturbations in chemical shift when one isotope replaces another, primarily due to vibrational and mass differences affecting the electronic environment; secondary isotope effects, such as those from substituting for in C-H bonds, typically amount to about 0.01 ppm for the proton shift. These effects are intrinsic to the molecular and are valuable for probing hydrogen bonding and conformational changes, as they provide sensitive indicators of isotopic substitution without altering the primary chemical identity. In (EPR) and , analogous "shifts" differ fundamentally from NMR chemical shifts by involving spins or nuclear gamma transitions rather than nuclear spins in a magnetic field. The g-shift in EPR measures deviations from the free- g-value (2.0023) due to spin-orbit coupling and local fields, akin to NMR's chemical shift but scaled to Zeeman energies (typically in mT units), while Mössbauer's shift reflects changes in s- density at the nucleus, comparable to NMR's contact shift but probed via recoilless gamma emission with resolutions down to 0.1 mm/s. These techniques complement NMR by accessing paramagnetic centers inaccessible to standard nuclear spectroscopy. Emerging applications include NMR for , where chemical shifts of metabolites in tissue are referenced to N-acetylaspartate (NAA) at 2.0 ppm to account for tissue-specific susceptibilities and enable quantification of neuronal markers like NAA and neurotransmitters such as GABA. (DNP) enhances NMR sensitivity in such contexts by transferring polarization from electron spins to nuclei, allowing detection of low-concentration metabolites without altering the intrinsic chemical shifts, though low temperatures may introduce minor thermal effects on linewidths. Historically, the shift, observed in metals during the early development of NMR in the and , represents a hyperfine interaction variant where conduction electrons polarize in the external field, shifting nuclear resonances by 0.1-1% relative to insulators; first reported in 1949 for metals like and aluminum, it provided early evidence of Fermi contact mechanisms in solid-state systems.

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