NMR in the quadrupole regime: Measurement of quadrupole and chemical shift parameters in single-crystal paradibromobenzene

The exact theory for the frequency of transition between the two lowest levels of a spin $\text{I =}\text{3}\text{2}$ nucleus experiencing a large asymmetric electric field gradient, an applied magnetic field, and an anistropic chemical interaction was presented in an earlier paper. Using the assumption that the quadrupolar and chemical shift tensors have the same principal axis system, the Hamiltonian was solved exactly — analytically for the applied field aligned along each of the three axes of the quadrupolar principal axis system, and numerically for arbitrary orientations.This theory is reviewed here and applied to our room-temperature experiments in single-crystal paradibromobenzene. The self-consistent least-squares fit to the field-dependencies and simultaneously the angular dependence (rotational pattern) of the resonance frequency was performed using the literature value for the pure quadrupole frequency $\text{ν}{}_{\mathrm{Q}}\text{(1 +}\text{η}{}^2\text{3}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 223·8}\text{MHz}$. The fit yielded values for the quadrupolar asymmetry η = 0·0461 ± 0·0004 and the chemical shift components σ_x = ?0·001 ± 0·001, σ_v = σ_z = 0·000 ± 0·001. Our value for η is in good agreement with values determined by other methods; it and our shift values are consistent with the information obtained by this method using a powdered specimen.The process of using the NMR signal itself to align the specimen yielded sufficient information for an unambiguous determination of the Euler angles of orientation of the crystal in its mounting within ± 0.6°.