Exact Simulation of Quadrupolar Lineshapes in Solids

The NMR spectra for quadrupolar nuclei in solids contain a great deal of structural information.  The evaluation of quadrupolar coupling constants, asymmetry parameters, isotropic chemical shifts, chemical shift spans, chemical shift skews and the angles relating the electric field gradient tensor to the chemical shift tensor is typically done by simulating the NMR spectrum with suitable software and fitting the simulated spectrum to the experimental data.  Almost always, the spectra of quadrupolar nuclei in solids have been simulated using perturbation theory where the quadrupolar interaction is treated as a perturbation on the much larger Zeeman interaction.  With the recent developments in the collection of ultra-wide line NMR spectra, quadrupolar nuclei with larger and larger quadrupolar coupling constants are being studied by NMR and the perturbation approach may not be valid.  Errors between simulated and experimental spectra appear when the Larmor frequency is not significantly larger than the quadrupolar coupling constant.

Recently, a new program called QUEST (QUadrupolar Exact SofTware) has been written by Frédéric Parras from the research group of David Bryce at the University of Ottawa.  As the name implies, this program is capable of simulating exactly the spectra of quadrupolar nuclei in solids without resorting to the assumptions of perturbation theory. QUEST is able to quickly calculate accurate lineshapes regardless of the ratio between the Larmor frequency and the quadrupolar coupling constant.  It even works in cases where the Larmor frequency is much less than the quadrupolar coupling constant (i.e. NQR). The figure below shows a series of spectra calculated for a spin I=3/2 nucleus as a function of the ratio of the Larmor frequency, ν_L , to the quadrupolar coupling constant, C_Q. The spectra near the top are NMR-like and those near the bottom are NQR-like.  QUEST is a fast, graphical, easy-to-use program able to handle multiple sites, export data in Bruker format, import experimental spectra for comparison to the simulations and simulate spectra as a function of the angle of the detection coil with respect to the magnetic field. The package also includes a very helpful well written pdf manual.  The program is reported and described fully here.  To take a look at the program in action, watch these tutorial videos prepared by the author.  The complete program is available for free download here.  I highly recommend it!