WSOLIDS1: Static, Quadrupolar Nucleus

Description

This squeezed picture shows an example for the succesful simulation of a spectrum of a quadrupolar nucleus that shows the combined effect of chemical shift anisotropy and quadrupolar interaction in a powder sample. It is the ¹³³Cs NMR spectrum of cesium cadmium thiocyanate, CsCd(SCN)₃, and the results have been published in:

S. Kroeker, K. Eichele, R.E. Wasylishen, J.F. Britten:
Cesium-133 NMR Study of CsCd(SCN)₃: Relative Orientation of the Chemical Shift and Electric Field Gradient Tensors.
J. Phys. Chem. B 1997, 101, 3727-3733.

Click on the picture to have a better look.

Background

In addition to the chemical shift anisotropy (CSA), the spectrum of a quadrupolar nucleus will also depend on the nuclear quadrupolar interaction and the relative orientation of both interactions. The quadrupolar interaction is considered up to second order for the observed nucleus. Optionally, dipolar and indirect coupling to a heteronucleus can be added (note: quadrupolar interaction, if any, is neglected for the coupled heteronucleus).

Examples

The SVG images shown below were produced using the following tools: my own SpecPlot to plot the spectra, Platon or Ortep 3 for Windows to plot the molecular structures from X-ray data, and Inkscape to compose the picture.

The following examples show Cs-133 NMR spectra of static powder samples. Cs-133 has the nice properties of 100 % natural abundance, a great nuclear spin of 7/2, and the third-smallest nuclear quadrupole moment (after Li-6 and H-2). However, because it is heavier than Li-6 and H-2, it has a greater chemical shift scale and exhibits a greater chemical shift anisotropy. As a consequence, the static powder patterns show center and satellite transitions, the former basically showing chemical shift anisotropy, the latter the combined effects of quadrupolar coupling and chemical shift anisotropy as well as their mutual orientation.

Cs-133 NMR spectrum of a static powder sample of CsCd(SCN)3: this example uses the simulation of absorption and first derivative mode in separate spectrum windows. It is the spectrum shown in the description above. Unfortunately, I don't have the original experimental spectra anymore; the current example was generated from the figure in the publication, converted using SpecMake. You can download a zip file of the WSolids1 document: (ZIP) or have a look at the report generated from the WSolids1 document: (XML)

Cs-133 NMR spectrum of a static powder sample of CsPbBr3: this example is actually from the literature and was generated from Fig. 3 in the publication, a Cs-133 NMR spectrum simulated using TopSpin and converted using SpecMake. The conversion was then checked by re-simulating the spectrum with TopSpin. The publication: A. N. Gavrilenko, O. I. Gnezdilov, A. V. Emeline, A. V. Shurukhina, E. V. Schmidt, A. F. Ivanov, V. L. Matukhin, J. Appl. Spectrosc. 2023, 90, 769. DOI: 10.1007/s10812-023-01594-8 The reported TopSpin parameters: CQ = 195 kHz, ηQ = 0.01, δiso = 117 ppm, Δδ = 57 ppm, α = 0, β = 30, γ = 0, ηδ was not given, but my TopSpin check gave 0.55.

The conventions used by TopSpin are not clear, but the paper ventures to give some definitions. Translated to WSolids1, I have used the following parameters: the chemical shift parameters were entered in the Haeberlen convention, with δiso = 117 ppm, Δδ = 57 ppm was interpreted as "reduced anisotropy", therefore in our convention Δδ = 85.5 ppm, ηδ = 0.55; for the quadrupolar interaction, I used χ = 0.195 MHz, ηQ = 0.1. The values given in the paper in several instances for ηQ, about 0.01, did not agree with the simulation, both TopSpin and WSolids1 require ηQ = 0.1; a final matter concerns the mutual orientation of CSA and EFG. A value of β = 30 indicates the angle between the two principal axes. In this particular example, the principal axis of the CSA in the Haeberlen convention is δ11. WSolids works with δ33, hence β = 60 in WSolids1. The conventions in TopSpin for the xx and yy components are unclear, but it is likely that they differ from WSolids1. This is expressed in the fact that an α = 90 is required to get agreement between both simulations (see the final statement on EFG tensors). You can download a zip file of the WSolids1 document: (ZIP) or have a look at the report generated from the WSolids1 document: (XML)