Theory and simulation of vibrational effects on structural measurements by solid-state nuclear magnetic resonance

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.