Second-order recoupling of chemical-shielding and dipolar-coupling tensors under spin decoupling in solid-state NMR

The source of the residual line broadening in continuous-wave ~cw! decoupled spectra under magic-angle sample spinning conditions is reexamined. It is shown that an important contribution to the line broadening comes from a second-order recoupling of the heteronuclear dipolar-coupling tensor and the chemical-shielding tensor of the irradiated spin. Such an interference between the two tensors leads to a sum of a zeroth-rank, a second-rank, and a fourth-rank tensor component in the Hamiltonian. The zeroth-rank and the fourth-rank tensor components are not averaged out under magic-angle sample spinning ~MAS! conditions, requiring the use of higher-order averaging such as double rotation ~DOR! for obtaining narrow lines. This broadening is distinctly different from off-resonance decoupling effects which transform as a second-rank tensor and can be averaged out by MAS. The properties of this second-order recoupling as a source of structural information are explored, and the conditions for removing the broadening in systems with weak homonuclear dipolar-coupling networks are discussed. © 1996 American Institute of Physics. @S0021-9606~96!01132-4#