I must admit, with a great deal of humility, that I’ve never taken an NMR myself. NMRs were always handled by my TA’s in undergrad. Provided my chemistry was clean, the NMRs always came back nice and neat, with huge signal-to-noise and no indication of any difficulty with actually obtaining the spectrum. I naturally assumed, then, that taking NMRs was a simple matter of dropping in the sample, turning on the magnet, setting parameters, clicking START and kicking back.
Of course, to quote Garson Hampfield, “that’s not how it works.” NMR works because application of a uniform magnetic field to a sample polarizes nuclear spins in the sample “with” and “against” the field lines, and the energy difference between these two states is directly proportional to the strength of the magnetic field felt by each nucleus (which in turn depends on the electronic environment around each nucleus). The problem? Applying a perfectly uniform magnetic field to a sample turns out to actually be kinda tough, and magnetic field gradients in the sample can lead to line broadening and distortion of spectra. The process of canceling out any magnetic field gradients in the sample (via the application of fields from “shim coils”) is called “shimming.”
The study of magnetic field gradients in NMR samples has led to some fascinating results. The exponent of the field variation with position is called the “order” of the gradient. First-order gradients can be constructed from the three Cartesian directions x, y, and z, which correspond conceptually with the atomic p orbitals. An arbitrary second-order quadratic gradient can be made from five independent first-order gradients, reminiscent of the five d orbitals. Seven independent third-order gradients (analogous to the seven f orbitals) form a basis for every possible cubic third-order gradient. Adjustable shim coils that can compensate for the “basis gradients” of a certain order can thus cancel out all possible gradients of that order. Shim coils up to and including fifth-order are now common on spectrometers. Gradients can also be distinguished by their direction relative to the axis of rotation of the sample–gradients aligned with the rotation axis are “spinning,” and those that aren’t are “non-spinning.”
Low-order gradients (first- and second-order) tend to affect the entire vertical profile of an NMR peak, while high-order gradients affect only the bottoms of peaks. Even-order gradients skew a peak asymmetrically, causing buildup of signal on one side of the peak or another, while odd-order peaks cause symmetrical line broadening. These frequency-domain effects correspond to characteristic distortions of the free induction decay signal, essentially the time-dependent NMR signal.
The integral of a particular sample peak is constant, but because peak asymmetry and line broadening cause the area under the curve to “leak” away from the frequency of peak signal, they cause a reduction of peak height. The basic idea of adjusting low-order shim coils, then, is to maximize the peak height of a standard, really strong singlet peak (TMS or CHCl3 in deuterated acetone, for example). Higher-order shims are actually best adjusted using multiplets, because the bottom-widening effect is amplified by the closely spaced peaks. Ortho-dichlorobenzene is often used.
Gerald Pearson of Iowa has written an extremely informative (albeit a bit ancient) guide to shimming superconducting NMRs.