Chemical shift is defined as the relative difference in resonant frequency compared to a standard signal. Conventionally this is the signal of the compound tetramethylsilane (TMS) for 1H-NMR and a standard fraction of this frequency (Ξ Greek letter Xsi) for all other nuclei. For aqueous solutions, sodium 2,2-dimethyl-2-silapentane-5-sulfonate [DSS, also known as 3-(Trimethylsilyl)-1-propanesulfonic acid sodium salt] is usually used instead of TMS. Put in the form of an equation this becomes
δ = (ν - ν0)/ν0
where δ is the chemical shift ν is the resonant frequency and ν0 is the reference frequency, that of TMS (dissolved in the sample) for 1H-NMR or Ξ times νTMS for other nuclei where Ξ is the frequency ratio of the nucleus. Chemical shifts are usually small and are quoted in ppm. For 1H-NMR the chemical shift range is just over 10 ppm, for 13C-NMR it is just over 200 ppm but it can be much larger for more esoteric nuclei such as 59Co-NMR where the chemical shift range is 20000 ppm (or 2%).
A secondary reference of known chemical shift can be used instead of TMS. The most common secondary references are the residual solvent signals. Table 1 lists the most common solvent signals for 1H, 2D-NMR (used as the lock reference) and 13C-NMR.
Table 1. Solvent chemical shifts of commonly used pure NMR solvents at 25°C
Slight variations in chemical shift occur on addition of solutes but this table is sufficient for routine work
| Solvent | 1H solvent chemical shift relative to dissolved TMS | 2D solvent chemical shift relative to 1H of dissolved TMS | 13C solvent chemical shift relative to 1H of dissolved TMS |
|---|---|---|---|
| Acetone-d6 | 2.053 | 2.101 | 28.91, 205.18 |
| Acetonitrile-d3 | 1.939 | 1.974 | 0.30, 117.31 |
| Benzene-d6 | 7.157 | 127.99 | |
| Chloroform-d | 7.262 | 7.290 | 76.99 |
| Deuterium oxide | 4.783 | 4.88 | None |
| DMSO-d6 | 2.502 | 2.559 | 39.98 |
| Methanol-d4 | 3.306, 4.848 | 3.354, 5.077 | 47.67 |
| THF-d8 | 1.724, 3.578 | 1.759, 3.616 | 24.40, 66.43 |
| Toluene-d8 | 2.089,6.974,7.014,7.095 | 19.97,124.57,127.47,128.37,136.87 |
To illustrate the calculation of chemical shift (normally all the calculations are done by the spectrometer so don't worry too much about the math) consider the 1H signal of benzene resonating at 400.13286373 MHz and that of TMS at 400.13000000 MHz. The chemical shift is calculated as follows.
δ = (ν - ν0)/ν0
= (400.13286373 - 400.13000000)/ 400.13000000
= 0.000007157 = 7.157 ppm
For other nuclei we use the 1H signal of TMS multiplied by a standard ratio (Ξ) for that nucleus. For example, for 13C, Ξ is 25.145020%. If the 13C signal of benzene resonates at 100.62561376 MHz and the 1H signal of TMS resonates at 400.13000000 MHz then the chemical shift is calculated as follows.
ν0 = Ξ νTMS
= 0.25145020 × 400.13000000 = 100.61276853
δ = (ν - ν0)/ν0
= (100.62564596 - 100.61276853)/100.61276853
0.00012799 = 127.99 ppm
The above definition assumes that the chemical shift of TMS is constant for the purposes of the experiment. For routine NMR spectroscopy and most other cases this assumption is sufficient and one can use the chemical shifts in table 1 for calibration. ONLY WHEN COMPARING DIFFERENT SOLVENTS should table 2 be used to adjust for variations in the chemical shift of TMS in different solvents.
Complications arise when comparing chemical shifts under different chemical or physical conditions or where TMS reacts with the solvent. In such cases the chemical shift is measured by exchanging the sample for a reference sample of dilute TMS in CDCl3 at 25°C under a standard atmosphere.. It is important to measure the samples without lock and not to reshim between samples. The chemical shift of TMS has been measured to be between -0.8 and 0.2 ppm depending on solvent and has a temperature dependence of about -0.0005 ppm K-1. This is because the chemical shift of TMS varies from sample to sample and that the resonant frequency of different samples is affected by the difference in their magnetic susceptibilities.
Table 2. TMS chemical shifts and solvent susceptibilities in commonly used pure NMR solvents at 25°C
These corrections should only be used when comparing chemical shifts in different solvents
| Solvent | 1H TMS chemical shift relative to TMS in CDCl3 | Magnetic susceptibility/ppm (SI units) |
|---|---|---|
| Acetone-d6 | -0.166 | -5.74 |
| Acetonitrile-d3 | -0.014 | -6.70 |
| Benzene-d6 | -0.508 | -7.51 |
| Chloroform-d | 0.000 | -9.28 |
| Deuterium oxide | -0.078 (DSS -0.095, TSP -0.079) | -8.99 |
| DMSO-d6 | 0.061 | -7.80 |
| Methanol-d4 | -0.109 | -6.76 |
| THF-d8 | -0.111 | -8.01 |
| Toluene-d8 | -0.460 | -7.95 |
For a regular NMR sample (45 mm in depth with the bottom 20 mm below the coil center) in a 5 mm tube, the chemical shift is given by the equation below.
δ = (ν - ν0)/ν0 - 0.327(κ - κ0)
where κ is the magnetic susceptibility (in SI units) of the sample and κ0 is the magnetic susceptibility of the reference sample. (Note that the values of magnetic susceptibility for diamagnetic solvents are negative and of the order of a few ppm – see table above.) The value 0.327 in the equation differs for differently shaped samples (see R. E. Hoffman, J. Magn. Reson., 178, 237-247 (2006)).
For example the signal of C6HD5 in C6D6 resonating at 400.13286373 MHz and the signal of dilute TMS in CDCl3 resonating at 400.13000000 MHz. The magnetic susceptibility of C6D6 is -7.51 ppm and that of CDCl3 is -9.28 ppm.
δ = (ν - ν0)/ν0 - 0.327(κ - κ0)
= (400.13286373 - 400.13000000)/400.13000000 – 0.327(-7.51 × 10-6 + 9.28 × 10-6)
= 0.000006578 = 6.578 ppm
Here we see that the routine measurement of chemical shift in C6D6 of 7.157 ppm has been changed to 6.578 ppm when comparing it with the chemical shift as defined in CDCl3. For routine purposes the convention has it that we stay with the value of 7.157 ppm (relative to TMS dissolved in the same solvent C6D6) and only change the value to 6.578 ppm when comparing the chemical shift with that obtained under different conditions.
More solvents and information on temperature dependence can be found in the literature (R. E. Hoffman, "Variations on the chemical shift of TMS", J. Magn. Reson., 163, 325-331 (2003), R. E. Hoffman, "Standardization of chemical shifts of TMS and solvent signals in NMR solvents", Magn. Reson. Chem., 44, 606-616 (2006), R. K. Harris, E. D. Becker, S. M. Cabral de Menezes, P. Granger, R. E. Hoffman and K. Zilm, "Further conventions for NMR chemical shifts", Pure Appl. Chem., 80, 59-84 (2008).)