Chemical-Shift Standards and Units

Chemical shifts always are measured with reference to a standard. For protons or 13C in organic molecules, the customary standard is a tetramethylsilane, (CH3)4Si, which gives strong, sharp nmr signals in regions where only a very few other kinds of protons or carbon nuclei absorb. Chemical shifts often are expressed in Hz (cycles per second) relative to tetramethylsilane (TMS). These may seem odd units for magnetic field strength but because resonance occurs at ν=γH, either frequency units (Hz, radians sec−1) or magnetic field units (gauss) are appropriate.

Ten years ago, most nmr spectrometers operated for protons with radio-frequency (rf) transmitters set at 60MHz (6×10⁷ cycles per second) but there has been a proliferation of different proton-operating frequencies and now 30, 60, 90, 100, 220, 270, 300 and 360MHz machines are commercially available. The cost of these machines is roughly proportional to the square of the frequency, and one well may wonder why there is such an exotic variety available and what this has to do with the chemical shift. High operating frequencies are desirable because chemical shifts increase with spectrometer frequency, and this makes the spectra simpler to interpret. A 12-fold increase in operating frequency (as from 30MHz to 360MHz) means a 12-fold increase in Ho at the point of resonance (remember ν=γH) and this means also a 12-fold increase in σHo. Thus resonances that differ because they correspond to different σ values will be twelve times farther apart at 360MHz than at 30MHz. This can produce a dramatic simplification of spectra, as can be seen from Figure 9-27, which shows the effect of almost a factor of four in ν on the proton nmr spectrum of 2-methyl-2-butanol.

Figure 9-27: Comparison of the proton nmr spectra of 2-methyl-2-butanol at rf transmitter frequencies of 60, 100, and 220MHz. The line at 165Hz in the 60-MHz spectrum is due to the OH protons, and this is off-scale to the left in the 220-MHz spectrum. The large single line in the center of the spectra arises from the resonances of the six methyl hydrogens. The line at 0Hz is TMS in each case.

To reiterate, chemical shifts are strictly proportional to spectrometer frequency, thus lines 100Hz apart at 60MHz will be 167Hz apart at 100MHz. This might seem to make comparisons of nmr spectra on different spectrometers hopelessly complex but, because of the proportionality of shifts to frequency (or field), if we divide the measured shifts in Hz (relative to the same standard) for any spectrometer by the transmitter frequency in MHz, we get a set of frequency-independent shifts in parts per million (ppmppm, which are useful for all nmr spectrometers. Nmr shifts reported in ppmppm relative to TMS as zero, as shown in Figure 9-23, are called δ (delta) values:

Thus, if at 60MHz a proton signal comes 100Hz downfield relative to tetramethylsilane, it can be designated as being (+100Hz×106)/60×106Hz=+1.67:ppm relative to tetramethylsilane. At 100MHz, the line then will be (1.67×10−6)(100×106)=167Hz downfield from tetramethylsilane. Typical proton chemical shifts relative to TMS are given in Table 9-4. The values quoted for each type of proton may, in practice, show variations of 0.1-0.3ppm. This is not unreasonable, because the chemical shift of a given proton is expected to depend somewhat on the nature of the particular molecule involved, and also on the solvent, temperature, and concentration.

A positive δ value means a shift to lower field (or lower frequency) with respect to TMS, whereas a negative δ signifies a shift to higher field (or higher frequency). The δ convention is accepted widely, but you often find in the literature proton shifts with reference to TMS reported as "τ values." The τ scale has the TMS reference at +10ppm, so most proton signals fall in the range of τ=0 to τ=+10. A τ value can be converted to the appropriate δ value by subtracting it from 10. Life with nmr spectra would be simpler if the τ scale would just go away.