Vibrational averaging of chemical shift anisotropies in model peptides

The effects of chemical shift anisotropy (CSA) are evident in line-shapes or side-band analysis in solid-state NMR, in the observed line positions in partially oriented samples, and in relaxation effects in liquid-state studies. In all of these cases, the effective shielding tensor is influenced by fast vibrational averaging in addition to larger-amplitude internal motions and to overall libration or rotation. Here we compute the contributions of vibrational averaging (including zero-point motions) to the CSA relaxation strengths for the nitrogen and carbonyl carbon in two simple peptide models, and for snapshots taken from a path-integral simulation of a small protein. Because the (15)N shielding tensor is determined by all the atoms of the peptide group, it is less influenced by vibrational motion than (for example) the N-H dipolar interaction, which is more sensitive to the motion of the light hydrogen atom. Computed order parameters for CSA averaging are hence much closer to unity than are N-H dipolar order parameters. This leads to a reduction by about 9% in the magnitude of the amide nitrogen CSA that is needed to fit liquid-state relaxation data. Similar considerations apply to the carbonyl carbon shielding tensor, but in this case the differences between dipolar and CSA averaging are smaller. These considerations will be important for making comparisons between CSA tensors extracted from various NMR experiments, and for comparisons to quantum chemical calculations carried out on static conformers.