Pictorial Representation of Anisotropy and Macroscopic Reorientations of Samples in Solid-State NMR: First-Order Interactions

Abstract

The representation of second-order broadening effects in solid-state NMR by general fourth-degree surfaces is presented. Static second-order quadrupolar and “dipolar−quadrupolar” interactions are treated in a unified way. Most experiments involving the fast reorientation of samples such as magic-angle spinning, variable-angle spinning, dynamic-angle spinning, and double-rotation and multiple-quantum magic-angle spinning are also illustrated by using averaged fourth-degree surfaces. The equations of the surfaces are derived analytically and allow the derivation of most results concerning these experiments. This article is an extension of the representation of the first-order effects by quadrics to more complex broadening effects. Multidimensional experiments will also be discussed in this frame. It can be noted that this approach is essentially Cartesian. P2(cos θ) and P4(cos θ) Legendre polynomials are not explicitly used in this work.