Fitting MQMAS Spectra with distributions of chemical shift and quadrupolar interaction

D.R. Neuville, L. Cormier, D. Massiot Geoch. Cosm. Acta 68 5071-5079 (2004)

 Example :  27Al 1D Spectrum of Glass with AlO4/AlO5/AlO6 sites  
References :

Important warning : for an efficient fitting of a 2D spectrum, restrict the sizes in both dimensions to a minimum value (see example spectrum for examples).

Step 1 : calibrate the indirect dimension of the MQMAS experiment...

 Load the 2D experiment (2rr file of XWinNMR or 'xxx.rr' file of WinNMR)
 call the Spectrum Parameter Dialog [Menu/File/Show Parameters] or click the "Spec Param" buttion on the left pannel.
 In the "F2 param" tab select the nucleus of the MQ experiment "27Al" for example.
 Click "F1 param" and "F2 param" tabs (there is a bug in the updating routine) to make the "Calibrate MQ..." button visible
 Click the "Calibrate MQ..." button which should show this window.

 The shear factor is computed for a 3Q experiment and the shift (as used in Bruker shearing routine) should show in the shift F1 place. If not correct, adjust values. The nFold value allows you to scroll the F1 dimension. Click the Ok button to process.
 Once calibrated you can show the diagonal (slope 1 in ppm) by going to [Menu/2D/DiagSlope] and setting the slope to 1 (if not already done) The spectrum should show as presented below.

 A good practice is now to save the calibrated spectrum : [Menu/File/SaveAs] "mycalibratedspectrum.rr"... Do nor forget the ".rr" extension.

Step 2 : Establish the fitting model... The better way is to do that from the fit of a 1D spectrum (see first how to fit a 1D spectrum and details on the Czsimple model )

 Load the 2D calibrated spectrum "mycalibratedspectrum.rr" that we just saved, go to [Menu/2D/Diagonal] and set a slope of 1 to obtain the 1/1 ppm diagonal.
 Load the 1D fit parameters [Menu/Decomposition/load Other]

 Remove from the fit parameters dialog [Menu/Decomposition/Fit Parameters] or all lines corresponding to the outer transition only keeping the lines of the central <1/2> transition "CzSimple" model (if you take my example file, also remove the smallest AlO6 component which dos not show up in the MQMAS spectrum).
 Expand the window to show the "Fit 1D" selection box at the bottom of the left pannel and change it to "MQMAS"
 Click the "Compute Button" [1234] to obtain the starting Model. This computation takes quite a while !!!

Important remarks

+ Because we now have an F1 axis we need to put a width in this dimension. This width has to be big enough to obtain a smooth model but not so big as to mask the expression of the NMR parameters. This "Width" is given in Hertz and should not be optimized.

+ As in the case of the 1D fit the EM serves to obtain a smoothed representation of the lineshapes and the distribution of isotropic CS is obtained with the "FWHM CS" value.

+ As in the case of the 1D fit the d parameter is better fixed to 5 to have a Gaussian Isotropic Model distribution.

+ Now the computation is long, this is normal as it has to compute for every point in the 2D spectrum.... Reducing the presentation widow results in quicker computation and optimisation !!!

+ As in the case of 1D fit with CZSimple, a proper integration is obtained in the  [Report] dialog by numerical integration... Be patient this is a very time consuming operation.

 [Menu/Decomposition/Load Fit] allows you to laod in the final fit (with 2 Czsimple lines) that give the following graph :

Good luck and be patient with 2D experiments, the more power you have for computing, the quicker the process...

The "CZSimple" Model  :

The "CzSimple" model implements a rapid version of the Czjzek distribution of quadrupolar interaction for the distribution of the isotropic chemical shift (Gaussian Isotropic Model for d=5) with an uncoupled distribution of isotropic chemical shift. See our paper in Geochimica Acta or the following references for use of this model.

The CzSimple model takes the following parameters :

 Amplitude : vertical scaling factor
 Position : Istotropic average value
 FWHM CS : Full Width at Half Maximum of the isotropic chemical shift gaussian distribution.
 EM au : line broadening used to smooth the discontinuities issued from the sampling of nuQ/etaQ and diso, use she smallest possible value and do not allow optimisation. Take negative values for gaussian apodisation. This is just a cosmetic parameter.
 nuQ : Peak value of the quadrupolar coupling of the Czjzek/GIM distribution (proportional to sigma values reported latest versions >2008)
 d : critical exponent of the Czjzek distribution, take d=5 for GIM, other values do not have physical sense even if they give better rendering.