Isotropic second-order dipolar shifts in the rotating frame

Abstract

An experiment is described that utilizes the truncation of the Hamiltonian in the rotating frame by a radio-frequency field designed to yield an isotropic shift for the dipolar coupling. This approach allows the measurement of a normally orientation-dependent coupling constant by a single isotropic value. The dipolar isotropic shift is closely related to the field-dependent chemical shift in solids due to the second-order dipolar perturbation observed in magic-angle spinning experiments. In the rotating frame, larger shifts of up to 1000 Hz can be observed for the case of a one-bond C–H coupling compared to a shift of a few Hertz in the laboratory-frame experiment. In addition to the isotropic shift, a line broadening due to the P4(cos β) terms is observed when the experiment is carried out under magic-angle sample spinning (MAS) conditions, leading to the requirement of higher-order averaging such as double rotation (DOR) for obtaining narrow lines. As an application of this new experiment the separation of CH, CH2, and CH3 groups in a 2D spectrum under MAS is demonstrated. Implemented under DOR it could be used as a technique to select carbon atoms according to the number of directly attached protons.