PROCESSING YOUR DATA
 
Chemical-shift referencing

In the section on Fourier transformation, the x-axis of the NMR spectrum was discussed in terms of frequency. However, a typical NMR spectrum does not present this axis in normal frequency or wavelength units, such as Hz or nm. Instead, it gives the frequencies in terms of parts per million, or ppm. While this looks like a unit of concentration, it actually refers to a frequency ratio.

The specific frequencies at which NMR peaks appear are proportional to the power of the system's magnetic field. The field strength is usually cited in MHz(1,000,000 Hz), corresponding to the resonance frequency of the 1H nuclide. This is not strictly correct, since the proper units of magnetic field strength are either Gauss (G) or Tesla (T, or 10,000G), but it is a form of shorthand commonly used by NMR spectroscopists.

Two peaks separated by 100 Hz on a 200 MHz (2.8T) system will be 200 Hz apart on a 400 MHz (5.6T) instrument, and 300 Hz apart on a 600 MHz (8.4T) spectrometer. Thus, it is impossible to directly compare results from two systems operating at different field strengths. Note, however, that the frequency ratio is constant:

In other words, if peak positions are divided by the operating frequency of the nuclide being observed, they can be compared. Numbers such as 0.0000005 are inconvenient, so the ratios are multiplied by 1,000,000 (hence parts per million), and the resulting values are called chemical shifts. In the case discussed above, the chemical shift between the two peaks is 0.5 ppm.
 

If a nuclide other than 1H is being observed, then the shift calculation must include the appropriate resonant frequency. For example, 13C resonates at about 1/4 the frequency of 1H. Thus, on a 2.8T system (200 MHz for 1H), 13C's resonant frequency is 50 MHz; on on a 5.6T system, it is 100 MHz. Therefore, a 1 ppm peak separation corresponds to 50 Hz on the weaker instrument, and 100 Hz on the stronger.

 
Note that peak separation has been defined in terms of a separation between two peaks. In practice, one of these peaks is a primary reference standard, a chemical with one peak, whose position is generally agreed to be equal to zero. Peak positions are then referred to as chemical shifts, designated by d. If feasible, the standard chosen resonates at a shift that is at one extreme of the range found for common compounds. For example, the chemical-shift reference standard for both 1H and 13C NMR is tetramethylsilane (TMS). In a normal NMR spectrum, TMS, at 0 ppm, would be represented at the right-hand edge of the spectrum. The other peaks would be displayed to the left, with positive chemical shifts increasing toward the left (this seemingly backwards presentation is a historical artifact); this is called the delta scale. While some unusual compounds (such as metal hydrides or organometallics) do give rise to negative chemical shifts, the vast majority of organic materials exhibit only positive shifts.
 
TMS, or any other shift reference, does not actually need to be present in the sample to be used as the standard. The chemical shifts of many compounds are well-known, and can be used as secondary shift standards. Solvents are well-suited to this role, particularly in 13C NMR. The chemical shift of chloroform-d, for example, is 77.23 ppm, and the spectrum can be properly calibrated if the CDCl3 peak is set to this shift value. Since CDCl3 exhibits only a very small residual 1H signal at 7.27 ppm, solvent-referencing is somewhat more problematic for this nuclide. If the identity of the sample is known, some of its resonances may be used for shift referencing.
 
Like many of the other routine operations used in NMR, the computer systems of all modern instruments perform these calculations automatically.