Field dependence of the magic angle spinning nuclear magnetic resonance line shapes of paired spin‐1/2 nuclei in solids

Proceeding from the average‐Hamiltonian theory, the effects caused by nonsecular terms of the spin Hamiltonian in magic angle spinning nuclear magnetic resonance spectra of a coupled pair of rare spin‐1/2 nuclei are described. Using doubly rotating coordinates with the Larmor frequencies (including isotropic screenings) measured in units of the rotation frequency, while the small frequency offsets between the actual Larmor frequencies and multiples of the rotation frequency were treated as small amplitudes within the Hamiltonian, a general formalism could be established that provides a universal description of the field‐dependent line shifts, broadenings, and splittings. Analytical expressions are given for a continuous range of experimentally accessible sample rotation rates, including the rotational‐resonance conditions where the Floquet theory fails. The second approximation includes the nonsecular terms and is sufficient to adequately describe the spectral features found. The anisotropic screening cross terms with the dipolar and J couplings generate in the high resolution spectrum of each single crystal at most four lines in the heteronuclear and up to eight lines in the homonuclear case. The positions and relative intensities of these lines depend both on the strength of the external magnetic field and on the mechanical sample rotation rate. In the powder pattern of a homonuclear pair, a broadened Pake‐like doublet appears over a limited magnetic field range. This splitting persists even at the highest attainable rotation rates. The splittings and line shapes can provide useful data about the relative orientations of the two nuclear screening tensors.