Residual dipolar couplings between quadrupolar nuclei in solid state nuclear magnetic resonance at arbitrary fields

Second-order dipolar effects arise when a nucleus S is in close proximity to a quadrupolar spin I. These couplings originate from cross correlations between quadrupolar and dipolar interactions, and have the notable characteristic of not being susceptible to averaging by magic-angle-spinning. Therefore they can originate noticeable splittings in high resolution solid state nuclear magnetic resonance ~NMR! spectra, as has been observed repeatedly for S51/2. With the advent of high resolution half-integer quadrupole spectroscopy, such effects have now also been noticed in higher (S53/2,5/2,...) spin systems. Within the last year these couplings have been reported for a number of complexes and analyzed in the high-field limit, when I’s Larmor frequency largely exceeds its quadrupolar coupling. The present study discusses the generalization of these analyses to arbitrary quadrupolar/Zeeman ratios. The predictions of the essentially numerical treatment that results compare well with previously derived high-field analytical models, as well as with experimental solid state NMR spectra observed in a borane compound possessing a B– As spin pair. An alternative analytical variant that can account for these effects in the low-field limit is also derived on the basis of average Hamiltonian theory; its results agree well with the predictions obtained from general numerical calculations of one-dimensional S spectra, but present peculiarities in the bi-dimensional NMR line shapes whose origins are briefly discussed. © 2001 American Institute of Physics. @DOI: 10.1063/1.1357440#