C 13 – 1 H dipolar-driven C13–13C recoupling without C13 rf irradiation in nuclear magnetic resonance of rotating solids

Two recently proposed C13–13C recoupling methods under magic angle spinning (MAS), resonant interference recoupling (RIR), and C13–1H dipolar-assisted rotational resonance (DARR), are examined on a common theoretical foundation using the average Hamiltonian theory. In both methods, a rf field is applied on not C13 but H1 to recouple the C13–1H dipolar interactions, and spectral overlap necessary to conserve energy for C13–13C polarization transfer is achieved by the C13–1H dipolar line broadening. While DARR employs time-independent C13–1H interactions recoupled by suitable rf irradiation to H1 spins, RIR uses time-dependent C13–1H interactions modulated appropriately by H1 rf irradiation. There are two distinct cases where C13–1H line broadening realizes C13–13C spectral overlap. For a pair of a carbonyl or aromatic carbon and an aliphatic carbon, spectral overlap can be achieved between one of the spinning sidebands of the former C13 resonance and the C13–1H dipolar powder pattern of the latter. On the other hand for a pair of spins with a small chemical shift difference, the two center bands are overlapped with each other due to C13–1H dipolar broadening. For the former, we show that both RIR and DARR occur in the first order, while for the latter, DARR recoupling is appreciable for time-independent C13–1H interactions. We refer to the former DARR as the first-order DARR recoupling and the latter as the second-order DARR. Experimentally, we examined the following C13–1H recoupling methods for DARR: H1 CW irradiation fulfilling a rotary-resonance condition or a modulatory-resonance condition, and H1 π pulses applied synchronously to MAS. For RIR, the FSLG-m2m¯m sequence is applied to H1. Several one-dimensional DARR and RIR experiments were done for N-acetyl1,2-13C, 15N DL-valine, and 2,3-13C L-alanine. It was found that the polarization transfer rate for RIR is larger than that for DARR except for fast spinning, while the rate for DARR is less sensitive to the spinning speed. Further, we showed that the efficiency of the second-order DARR recoupling is not significantly less than that of the first-order DARR. Among the C13–1H recoupling methods examined, CW irradiation at the n=1 rotary-resonance condition is superior for DARR because it gives a larger C13–1H dipolar broadening, leading to broadband recoupling. We showed that a broadband-recoupling experiment with the first and the second-order DARR by CW irradiation at the n=1 rotary-resonance condition is applicable to signal assignment as well as structural determination of a multiply/uniformly C13 labeled molecule as demonstrated by two-dimensional C13–13C DARR polarization-transfer experiments of uniformly C13, N15-labeled glycylisoleucine.