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Two recently proposed 13 C-13 C recoupling methods under magic angle spinning ͑MAS͒, resonant interference recoupling ͑RIR͒, and 13 C-1 H dipolar-assisted rotational resonance ͑DARR͒, are examined on a common theoretical foundation using the average Hamiltonian theory. In both methods, a rf field is applied on not 13 C but 1 H to recouple the 13 C-1 H dipolar interactions, and spectral overlap necessary to conserve energy for 13 C-13 C polarization transfer is achieved by the 13 C-1 H dipolar line broadening. While DARR employs time-independent 13 C-1 H interactions recoupled by suitable rf irradiation to 1 H spins, RIR uses time-dependent 13 C-1 H interactions modulated appropriately by 1 H rf irradiation. There are two distinct cases where 13 C-1 H line broadening realizes 13 C-13 C 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 13 C resonance and the 13 C-1 H 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 13 C-1 H 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 13 C-1 H 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 13 C-1 H recoupling methods for DARR: 1 H CW irradiation fulfilling a rotary-resonance condition or a modulatory-resonance condition, and 1 H pulses applied synchronously to MAS. For RIR, the FSLG-m2mm sequence is applied to 1 H. Several one-dimensional DARR and RIR experiments were done for N-acetyl͓1,2-13 C, 15 N͔ DL-valine, and ͓2,3-13 C͔ 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 13 C-1 H recoupling methods examined, CW irradiation at the nϭ1 rotary-resonance condition is superior for DARR because it gives a larger 13 C-1 H 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 nϭ1 rotary-resonance condition is applicable to signal assignment as well as structural determination of a multiply/uniformly 13 C labeled molecule as demonstrated by two-dimensional 13 C-13 C DARR polarization-transfer experiments of uniformly 13 C, 15 N-labeled glycylisoleucine.

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Vibrational effects on structural parameters obtained by solid-state NMR are studied by theoretical calculations and molecular-dynamics simulations. The structural parameters treated contain internuclear distances between directly bonded or remote nuclei including nonproton pairs in a molecule and bond and dihedral angles. In addition to the intramolecular normal mode vibrations, the libration of the whole molecule is considered in the theory. It is shown that the molecular libration as well as the intramolecular vibrations reduce dipolar interactions, and consequently lengthen the internuclear distances obtained from the dipolar interactions (RNMR). In contrast, the internuclear distances obtained by single crystal x-ray or neutron diffraction (Rcor) are proved to be shortened by the molecular libration. Molecular-dynamics simulations for glycine molecules in the crystal at room temperature reveal that RNMR are 1%–4% longer than Rcor, confirming the theoretical results. It is also demonstrated that the effect of the molecular libration on distances between nonproton nuclei is dominant over that of the intramolecular vibrations. Especially for long distances, the molecular libration is shown to be an almost unique vibrational effect and to give differences of 1% to 2% between RNMR and Rcor. On the other hand, the theoretical calculations on the vibrational effects on bond and dihedral angles determined by correlating two dipolar tensors show very little angular deviations, and it is confirmed by molecular-dynamics simulations for glycine molecules.