NMR in the quadrupolar regime: Chemical shifts, asymmetry parameter, and angular orientation

Degenerate perturbation theory, exact analytic solutions, and numerical calculations were used to determine the frequency of transition between the lowest two energy levels of a spin I = 3/2 nucleus experiencing a large quadrupole interaction in an applied field in a single crystal. It is shown how the field dependence of the appropriate resonance experiment may be used to extract the characteristic quadrupole frequency ν_Q and the components of the chemical shift tensor σ, and how the resonance position as a function of the angle $\mathrm{\phi \prime }$ of orientation of the crystal about the axis of the NMR receiver coil depends on the orientational Euler angles as well as on the quadrupolar asymmetry parameter η and the shift components. This theory is applied in our experiments to α‐para‐dichlorobenzene. In a combined self‐consistent least‐squares fit of the exact expressions to the field dependences and the $\mathrm{\phi \prime }$ dependence of the resonance position, using the value ν_Q = 34.262 MHz from the literature, the chemical shift components were found to be ${\sigma }_x{\text{=0.000± 0.001.\hspace{0.17em}σ}}_y\text{=0.003± 0.001}$ , and ${\sigma }_z\text{=−0.001± 0.001}$ , assuming that the principal axes of the chemical shift tensor are coincident with those of the quadrupole tensor. The asymmetry parameter was found to be $\text{η = 0.0712± 0.0005}$ : this and our own value for ν_Q are in excellent agreement with values determined by other methods. Additionally, the Euler angles of orientation of the single crystal in the mounting were determined (within an eightfold ambiguity) to within $\text{± 0.8°}$ .