ABSTRACT
There are several points to note in this expression. First, because of the (1 - 3cos20) dependence of the dipole-dipole interaction, this interaction van ishes when Θ is 54.7°, or the magic angle. For liquids in which the molecules are tumbling rapidly, the (1 — 3cos20) term must be integrated over a sphere, as all an gles 0 are sampled. This integration produces the result that the dipole-dipole in teraction is zero for molecules in solution (see Table 7.1). Additionally, the r -3 dependence of the dipolar interaction means that generally only directly bonded and nearest-neighbor protons will contribute to dipolar broadening at a specific carbon nucleus.
