Relative orientation of quadrupole tensors from two-dimensional multiple-quantum MAS NMR

The Multiple-Quantum Magic Angle Spinning (MQMAS) technique enables the resolution of crystallographically inequivalent nuclei and also yield the quadrupolar coupling constant C-Q, quadrupolar asymmetry eta, and isotropic chemical shift delta(CS) of each crystallographic site. However, no information is obtained that relates one quadrupole tensor to another, such as internuclear distances or relative orientations. Here, we discuss a recently developed modification of the MQMAS NMR experiment that utilizes two-dimensional correlation of second-order (rank I = 4) broadened MAS line shapes to obtain the relative orientation of quadrupole tensors. This new method involves the insertion of a "mixing time", tau(m), into the MQMAS experiment such that magnetization transfer between two distinct nuclei within a crystallite during this period will result in a two-dimensional "cross-peak" correlating the two line shapes. The shapes of these cross-peaks are characteristic of the three Euler angles, alpha', beta', and gamma', that describe the relative orientation of the two quadrupole tensors.