Structural Interpretation of Asymmetrically Broadened NMR Fine-Structure Lines

Abstract

The determination of precise structural information about solids by means of NMR fine‐structure measurements is investigated theoretically. Attention is directed to the interpretation of broadening effects resulting from subsidiary dipolar interactions. Consideration is limited primarily to systems in which the fine structure is that produced by a strongly interacting pair of spin ½ nuclei, of which the water molecule in hydrate crystals is the prototype. It is shown that the fine‐structure lines are expected to broaden asymmetrically and that the asymmetry is a measure of the anisotropy in the pair distribution. The nature of the asymmetry can often be interpreted in terms of the relative angular position of nearby interacting pairs in the crystal. It is further proved that, within the validity of a first‐order perturbation theory approach, the center of gravity of a broadened fine‐structure line is the correct measure of the interaction responsible for the main splitting. This result is independent of the number or relative positions of the interacting pairs. The breakdown of the first‐order theory with increasing interpair interaction strength is discussed. Using a simple two‐pair model, calculations are made which show typical interpair distances at which one may expect a significant shift of the center‐of‐gravity position from that determined only by the intrapair interaction. Extension of the center‐of‐gravity theorem to other systems in which fine structure produced by a dominant interaction is asymmetrically broadened by subsidiary nuclear magnetic dipolar interactions is discussed briefly.