III. Shimming, linewidths, and lineshapes - I

It is important to have a knowledge of proper lineshape of an NMR signal and how improper shimming contributes to poor lineshape. Examples of reasonably well-shimmed NMR spectra from the Unity+300 and VXR-S NMR spectrometers are illustrated in Figure III-1 and III-2.

NMR peaks have a Lorenzian lineshape. The mathematical expression of a Lorentzian line and the three parameters associated with the line are shown below.

The minimum obtainable linewidth at half-height is directly related to the resolution of an instrument, i.e., how close two peaks can be and still be distinguishable. Resolution is usually measured using o-dichlorobenzene, which has very narrow lines its ¹H NMR spectrum. The manufacturer’s resolution specification is usually around 0.20 Hz, although linewidths of less than 0.10 Hz are obtainable with expert shimming.

Manufacturers of NMR instruments, however, have traditionally separated the resolution specification from the lineshape specification. Lineshapes for ¹H NMR spectra are usually specified using CHCl₃ and the specifications are stated in terms of linewidth at 0.55% and 0.11% height of the CHCl₃. These percentages are chosen because they are the height of the ¹³C satellites of the CHCl₃ line and one-fifth this height. However, these values are meaningful only when compared with the half-height width (LW_1/2). From the mathematical equation for a Lorentzian line, the linewidth at 0.55% height is calculated to be 13.5 times the LW_1/2, while the linewidth at 0.11% height is calculated to be 30 times the LW_1/2. So, if the linewidth at half-height is 0.30 Hz, the calculated values are 4.0 Hz at 0.55% and 9.0 Hz at 0.11%.

For comparison, the manufacturer’s specifications are 10-15 Hz and 20-30 Hz at 0.55% height and 0.11% height respectively. These values are larger than the theoretical values because the linewidths at 0.55% and 0.11% height are very sensitive to how well shimmed the magnet is.