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Tuesday, July 4, 2017

Correcting NMR Spectra for Poor Shimming - Reference Deconvolution

The pleasingly symmetric and narrow Lorentzian resonances in a high resolution NMR spectrum are truly things of stunning beauty, appreciated by all NMR spectroscopists. Their majesty depends on the homogeneity of the NMR magnet around the sample. Inhomogeneous fields yield low resolution NMR spectra with broad asymmetric peaks pleasing no one. These repugnant, distasteful spectra are often obtained when automatic shimming routines are used on under-filled samples, samples with solids present (precipitates, floaters of suspended solids), samples with thermal gradients, poorly mixed samples etc…. Have you ever looked at such a spectrum and longed to recover the hidden beauty, resolution and information you know is present in the depths of its repulsive form? In many such cases reference deconvolution is a processing technique able to help. The distortions in a spectrum from an inhomogeneous magnetic field affect all peaks in the spectrum in the same way. The imperfect FID giving rise to the offensive spectrum, FIDexp(t), is essentially a perfect FID, FID(t) multiplied by an error function, E(t), resulting from the inhomogeneous field.

FIDexp(t) = FID(t) * E(t)

If we could find the error function and divide the experimental FID, by it, we could produce a perfect (or at least improved) FID, the Fourier transform of which would be a spectrum corrected from the effects of field inhomogeneity. In the reference deconvolution technique, one selects a high signal-to-noise ratio singlet peak as a reference in the experimental spectrum and sets all other points in the spectrum to zero. This spectrum is inverse Fourier transformed to produce an FID of the distorted singlet, FIDrexp(t). A synthetic FID, FIDrsyn(t) is constructed for what one would expect the time domain signal to be for a perfect reference peak (e.g. a sharp Lorentzian). The error function for the reference peak Er(t) is then determined by:

Er(t) = FIDrexp(t) / FIDrsyn(t)

Since all peaks in the experimental spectrum are affected equally by the inhomogeneity, E(t) = Er(t) and we can compute a corrected FID for the entire spectrum,

FID(t) = FIDexp(t) / Er(t)

The corrected FID is Fourier transformed yielding a much improved spectrum. This technique is available in newer NMR software processing packages and is particularly easy to implement in the MestReNova software package available to NMR users at the University of Ottawa. An example is shown in the figure below for a 300 MHz 1H NMR spectrum of a mixture of compounds.
The top two traces show portions of the spectrum obtained in a carefully shimmed magnet. The middle traces show the same portions of the spectrum obtained in a poorly shimmed magnet. The bottom traces were obtained by applying reference deconvolution to the spectrum obtained in the poorly shimmed magnet. Clearly, there is much improvement in the reference deconvoluted spectrum, allowing one to obtain much more information and recover some of the lost beauty. In fact, the corrected spectrum is very similar to the one obtained in the homogeneous field of a carefully shimmed magnet. The penalty paid is a lower signal-to-noise ratio, as the noise from the experimental reference signal is convolved into the error function which in turn gets convolved into the corrected spectrum. The loss in signal-to-noise ratio can be minimized by choosing a reference signal with a higher signal-to-noise ratio.

4 comments:

Anonymous said...

Hi Glenn,
This is based on Gareth Morris's FIDDLE algorithm published ...last century. It had been a part of Varian's VNMR and VNMRJ since the early '00s and has been implemented in various forms and with different names by all NMR processing software around, not just recent ones.
The important point, as you mention, is that it does not come for free. The price you pay is reduced signal to noise, as it is very nicely visible in your bottom spectrum. This can potentially be a very high one to pay if you start with a low S/N and overdo it a bit with your requested line width. In short people should shim their magnets;-)

Glenn Facey said...

Anonymous,
Thank you vey much for the background and information. Yes, there is always a trade off between resolution and SNR. I agree that one should always maintain a well shimmed magnet. There is no substitute for high quality data however the technique is very useful when dealing with imperfect data ( which is often the case)

Glenn

Anonymous said...

Dear Glenn,

Do you know if it is possible to perform this reference deconvolution with Bruker's Topspin? I have been searching through the software and the manuals but I have not been able to find it.
Thanks in advance

Glenn Facey said...

Anonymous,
Reference Deconvolution is available in TOPSPINN version 3.5 under "processing", "advanced". I was unable to find it in versions < 3.5.

Glenn