# Chemical shift

The chemical shift is the fractional variation of the resonance frequency of a nucleus in nuclear magnetic resonance (NMR) spectroscopy that results from its magnetic environment, expressed as a dimensionless ratio and reported in parts per million (ppm) on the δ scale.<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup> It is the quantity that lets a spectrum recorded on one instrument be compared with a spectrum recorded on another, and it is the primary observable through which NMR reports on molecular structure.

| Key fact | Detail |
|---|---|
| Definition | \( \delta = (\nu_{\mathrm{cpd}} - \nu_{\mathrm{ref}})/\nu_{\mathrm{ref}} \), normally expressed in ppm<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup> |
| Field independence | Because both \( \nu_{\mathrm{ref}} \) and \( \nu_{\mathrm{cpd}} \) are proportional to the magnet strength \( B_0 \), the ppm value is the same on any spectrometer<sup>[2](https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_%28Smirnov_and_McCarty%29/05%3A_Nuclear_Magnetic_Resonance_%28NMR%29_Spectroscopy_-_Introduction/5.03%3A_Chemical_shift_in_units_of_Hz_and_ppm)</sup> |
| Primary reference | The methyl ¹H signal at 0 ppm of internal [tetramethylsilane](https://www.edgepedia.org/tetramethylsilane) (TMS) in organic solvents, or sodium 2,2-dimethyl-2-silapentane-5-sulfonate (DSS) in aqueous solutions, for all nuclei<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> |
| Typical ranges | Almost all ¹H absorptions fall within 10 ppm of TMS; almost all ¹³C absorptions within 220 ppm<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup> |
| Physical origin | Electron circulation around the nucleus induces a field opposing \( B_0 \); the shielding constant σ enters the resonance frequency as \( \nu_{\mathrm{eff}} = \gamma \cdot (1-\sigma) \cdot B_0 \)<sup>[2](https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_%28Smirnov_and_McCarty%29/05%3A_Nuclear_Magnetic_Resonance_%28NMR%29_Spectroscopy_-_Introduction/5.03%3A_Chemical_shift_in_units_of_Hz_and_ppm)</sup> |
| Tensor character | Electronic shielding and the derived chemical shift are tensors, directional in the molecular frame; in isotropic solution fast tumbling reduces them to a scalar average<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> |
| Sign convention | Resonance lines to high frequency from TMS have positive δ values (deshielding); lines to low frequency have negative δ values (shielding)<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup> |

## Definition and units

IUPAC defines the chemical shift of a nucleus, with the symbol δ, as a ratio involving its resonance frequency \( \nu_{\mathrm{cpd}} \) relative to that of a standard, \( \nu_{\mathrm{ref}} \), both measured in the same applied magnetic field:<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup>

\[ \delta = \frac{\nu_{\mathrm{cpd}} - \nu_{\mathrm{ref}}}{\nu_{\mathrm{ref}}} \]

δ values are normally expressed in ppm, so in practice the ratio is multiplied by \( 10^{6} \).<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup> The ppm scale exists because the absolute resonance frequency in hertz changes with the strength of the magnet: the same sample gives different Hz values on a 300 MHz and a 400 MHz instrument. Since both the sample frequency and the reference frequency scale with \( B_0 \), their ratio does not, and a shift of 2 ppm means the signal lies \( 2 \times 10^{-6} \) of the spectrometer frequency away from the reference.<sup>[2](https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_%28Smirnov_and_McCarty%29/05%3A_Nuclear_Magnetic_Resonance_%28NMR%29_Spectroscopy_-_Introduction/5.03%3A_Chemical_shift_in_units_of_Hz_and_ppm)</sup> A worked example from the same source: on an 11.7 T magnet, a proton resonating 10,000 Hz from a reference at 500,010,000 Hz has δ = 20 ppm, a value that would be reproduced on any other magnet even though the Hz separation would change.<sup>[2](https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_%28Smirnov_and_McCarty%29/05%3A_Nuclear_Magnetic_Resonance_%28NMR%29_Spectroscopy_-_Introduction/5.03%3A_Chemical_shift_in_units_of_Hz_and_ppm)</sup>

By IUPAC convention, higher frequency is plotted to the left and corresponds to higher ppm and less shielding relative to the reference nucleus; chemical shift and shielding vary in opposite directions by definition.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> The older terms "downfield" and "upfield" are considered archaic and should no longer be used.<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup>

## Physical origin

When a molecule is placed in an external magnetic field, the response of its electrons leads to an additional induced magnetic field at each nucleus.<sup>[5](https://pmc.ncbi.nlm.nih.gov/articles/PMC12231273/)</sup> The effective field a nucleus experiences is therefore \( B_{\mathrm{eff}} = (1-\sigma) \cdot B_0 \), where σ is the magnetic shielding constant, and the resonance frequency follows as \( \nu_{\mathrm{eff}} = \gamma \cdot (1-\sigma) \cdot B_0 \), with γ the gyromagnetic ratio.<sup>[2](https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_%28Smirnov_and_McCarty%29/05%3A_Nuclear_Magnetic_Resonance_%28NMR%29_Spectroscopy_-_Introduction/5.03%3A_Chemical_shift_in_units_of_Hz_and_ppm)</sup> Nuclei in different chemical environments have different σ values, and so resonate at slightly different frequencies; this is what makes NMR useful for structure determination.<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup>

**What changes the shift.** Three main structural features affect the shielding of a nucleus: the electronegativity of neighboring atoms, the magnetic anisotropy of π systems, and hydrogen bonding.<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup> Electron-withdrawing groups reduce electron density at the nucleus, deshielding it and producing a larger chemical shift. In the methyl halide series the ¹H shift rises steadily with the electronegativity of X: CH₃F at 4.26 ppm, CH₃Cl at 3.05 ppm, CH₃Br at 2.68 ppm, CH₃I at 2.16 ppm, and CH₄ at 0.23 ppm, with TMS itself at 0.<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup> The effect is cumulative: CH₄, CH₃Cl, CH₂Cl₂, and CHCl₃ show δ = 0.23, 3.05, 5.30, and 7.27 ppm respectively.<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup> Circulating π electrons generate ring currents that deshield protons outside the ring: aromatic protons appear at 6.5 to 8 ppm, alkene protons at 4.5 to 6 ppm, aldehyde protons at 9 to 10 ppm, while the acetylene proton, shielded by its position relative to the π system, appears near 2.5 ppm.<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup> Hydrogen-bonded protons such as O-H and N-H are observed over wide shift ranges because the deshielding depends on dynamically varying hydrogen bond strength, solvation, concentration, and temperature.<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup>

## Referencing

Chemical shift values carry only relative meanings, so every reported δ depends on a reference convention.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> IUPAC recommends a unified chemical shift scale in which all shifts, for all nuclei, are referenced against the methyl ¹H signal at 0 ppm of very dilute (<1%) internal TMS in organic solvents or DSS in aqueous solutions, either directly or indirectly.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> For ¹H and ¹³C NMR the reference signal is usually that of TMS, strictly speaking in dilute solution in CDCl₃; other references appear in the older literature and for other solvents such as D₂O.<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup>

In routine work, when TMS or DSS is not added, the residual solvent signal (for example the ¹H resonance of CDCl₃ at about 7.26 ppm) or the ²H lock signal may be used for rough indirect referencing.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> The ¹H shift difference between TMS and DSS is generally below 0.03 ppm, and IUPAC states that data from the TMS and DSS scales may be validly compared without correction.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup>

**The Ξ scale.** For nuclei other than ¹H, shifts may be expressed relative to an agreed substance containing the relevant nucleus, or relative to the ¹H resonance of TMS as Ξ values.<sup>[1](https://goldbook.iupac.org/terms/view/C01036)</sup> Ξ is the ratio of a nucleus's resonance frequency to the TMS ¹H frequency, expressed as a percentage, measured to high precision and field independent; knowing Ξ and the observed TMS ¹H frequency fixes the 0 ppm point of any nucleus without the reference compound being present.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> IUPAC has further recommended that the published Ξ values be frozen, not subject to future change from remeasurement even where this increases accuracy, because chemical shifts have only relative meanings.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> Alternative secondary references should be avoided where possible; one accepted exception is ¹⁵N, where liquid NH₃ is commonly used instead of CH₃NO₂, which raises ¹⁵N shifts by about 380.5 ppm relative to the nitromethane scale.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup>

**Practical limits.** The shielding of TMS in solution, and of DSS in aqueous solution, varies only slightly with temperature but is subject to solvent perturbations of a few tenths of a ppm, which sets the practical accuracy of cross-laboratory comparisons.<sup>[6](https://publications.iupac.org/pac/80/1/0059/index.html)</sup>

## Chemical shift anisotropy and solids

Electronic shielding is a tensor, directional in the molecular frame, and the same is true of the derived chemical shift.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> In isotropic solution, fast and uniform molecular tumbling averages the tensor to a single scalar value, the isotropic shift; the residual components, the chemical shift anisotropy (CSA), contribute to nuclear spin relaxation.<sup>[3](https://nmr.chem.ucsb.edu/protocols/refppm.html)</sup> The isotropic shift is the average of the three principal components, \( \delta_{\mathrm{iso}} = (\delta_{XX} + \delta_{YY} + \delta_{ZZ})/3 \).<sup>[7](https://pmc.ncbi.nlm.nih.gov/articles/PMC4255364/)</sup>

In solids, molecular tumbling is absent, and the orientation dependence of the shielding produces broad powder patterns rather than sharp lines.<sup>[8](https://pmc.ncbi.nlm.nih.gov/articles/PMC8341432/)</sup> High-resolution solid-state NMR therefore relies on magic angle spinning (MAS), in which the sample is rotated rapidly about an axis at approximately 54.74° to the external magnetic field, averaging the anisotropic interactions to zero when the spinning rate exceeds their magnitude.<sup>[9](https://goldbook.iupac.org/terms/view/08377)</sup> MAS frequencies of 10 to 62 kHz are in routine use, and the highest attainable rate reported in 2014 was 110 kHz.<sup>[10](https://pubs.acs.org/doi/10.1021/ac504288u)</sup> At moderate MAS rates below 20 kHz, sites with large CSA show spinning sidebands whose intensities can be fitted to extract the principal values of the CSA tensor.<sup>[8](https://pmc.ncbi.nlm.nih.gov/articles/PMC8341432/)</sup> For most samples, the isotropic shifts measured in solution in a nonpolar solvent and in the solid state by MAS differ little or not at all.<sup>[11](https://www.sciencedirect.com/science/chapter/bookseries/pii/S0066410307620031)</sup>

## Use in structure determination

Because each chemically distinct nucleus gives a characteristic δ, chemical shifts serve as fingerprints for functional groups and local electronic structure. Almost all ¹H absorptions occur within 10 ppm of TMS, and almost all ¹³C absorptions within 220 ppm downfield of the TMS carbon, ranges narrow enough that tabulated shift regions identify proton and carbon types directly.<sup>[4](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)</sup> Beyond routine assignment, computed shieldings now support [NMR crystallography](https://www.edgepedia.org/nmr-crystallography): machine-learned shielding-tensor models for molecular solids reach a ¹³C isotropic root-mean-square error of 1.67 ppm against experiment, compared with 2.34 ppm for the GIPAW-PBE density-functional method on the same geometries.<sup>[12](https://arxiv.org/abs/2608.21313)</sup>

## References

1. [IUPAC Compendium of Chemical Terminology, 'chemical shift' (C01036)](https://goldbook.iupac.org/terms/view/C01036)
2. [Smirnov & McCarty, 5.3: Chemical shift in units of Hz and ppm, Chemistry LibreTexts](https://chem.libretexts.org/Courses/Western_Washington_University/Biophysical_Chemistry_%28Smirnov_and_McCarty%29/05%3A_Nuclear_Magnetic_Resonance_%28NMR%29_Spectroscopy_-_Introduction/5.03%3A_Chemical_shift_in_units_of_Hz_and_ppm)
3. [Chemical Shift Referencing, UCSB NMR facility (Hongjun Zhou, updated April 2022)](https://nmr.chem.ucsb.edu/protocols/refppm.html)
4. [13.3: The Chemical Shift, Chemistry LibreTexts](https://chem.libretexts.org/Courses/Smith_College/Organic_Chemistry_%28LibreTexts%29/13%253A_Structure_Determination_-_Nuclear_Magnetic_Resonance_Spectroscopy/13.03%253A_The_Chemical_Shift)
5. [Theory of Field-Dependent NMR Shifts in Paramagnetic Molecules, PMC](https://pmc.ncbi.nlm.nih.gov/articles/PMC12231273/)
6. [Harris et al., Further Conventions for NMR Shielding and Chemical Shifts, Pure Appl. Chem. 80, 59 (2008)](https://publications.iupac.org/pac/80/1/0059/index.html)
7. [a magic-angle spinning nmr method for the site-specific measurement of proton chemical-shift anisotropy in biological and organic solids - pmc](https://pmc.ncbi.nlm.nih.gov/articles/PMC4255364/)
8. [Solid-state NMR spectroscopy, PMC](https://pmc.ncbi.nlm.nih.gov/articles/PMC8341432/)
9. [IUPAC Compendium of Chemical Terminology, 'magic angle spinning' (08377)](https://goldbook.iupac.org/terms/view/08377)
10. [Magic Angle Spinning NMR Spectroscopy, Analytical Chemistry (ACS)](https://pubs.acs.org/doi/10.1021/ac504288u)
11. [Solid-State Effects on NMR Chemical Shifts, ScienceDirect](https://www.sciencedirect.com/science/chapter/bookseries/pii/S0066410307620031)
12. [ShiftML4: Machine-Learned NMR Shieldings in Molecular Solids, arXiv](https://arxiv.org/abs/2608.21313)

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