Setting the magic angle using NMR spectra of oriented molecules

Abstract

High-resolution nuclear magnetic resonance in the solid state using magic-angle sample spinning (MASS) is now a very powerful technique in structural chemistry. In such studies, it is well known that the angle \theta which the spinning axis makes with the magnetic field direction should be as close to $54.7^0$ (i.e., \theta = $cos^{-1}$ $(1/ \sqrt{3})$, the magic angle) as possible since imprecise settings lead to line broadening. Difficulties and uncertainties in setting this angle have been discussed in the literature $(I, 2)$ and various methods for its adjustment have been proposed. The utility of a precise setting of the angle has also been pointed out (2). The more commonly used procedures are the measurement of $^{13}C$ NMR linewidths in the standard samples such as hexamethylbenzene and in the use of quadrupole nuclei such as bromine in KBr (1). In addition, the use of a laser beam to optically align the angle has also been suggested (2). The first two of the above methods require measurements of linewidths and line intensities and the last one needs additional optical accessories. Since the measurements of linewidths and line intensities are less precise than those of frequency separations, it would be ideal to discover a method using line separations. Such a procedure is suggested in the present note.