Cross-correlated quadrupolar spin relaxation and carbon-13 lineshapes in the (13)CD(2) spin grouping

Lineshape calculations are reported for a spin system consisting of a spin-12 nucleus scalar-coupled to two magnetically equivalent spin-1 nuclei, e.g., a CD(2) group. It is found that, because of the differential line broadening, the peak height ratio of the five spin-12 nucleus transitions is expected to deviate from the integrated intensity ratio of 1:2:3:2:1. The deviation is dependent on the extent of cross-correlation between the two quadrupolar interactions. The theoretical predictions for peak height ratios and for bandshapes are tested for the carbon-13 spectrum of perdeuterated ethylene glycol, and iterative fitting is used to obtain an estimate of the extent of the correlation between the quadrupolar interactions for the two deuterons.