Resolution Booster

As my very first blog entry, I thought it would be appropriate to cover one of the most important and exciting topics in NMR signal processing and analysis, resolution. In this first entry I will introduce some very basic concepts about resolution, why it is important and how it can be improved by means of data processing techniques. However, the most relevant point that will be mentioned here will be the introduction of a novel resolution enhancement technique, the so-called Resolution Booster which, I believe, will represent an important breakthrough in NMR.
Indeed, resolution is a key concept in high resolution NMR and considerable effort (e.g. shimming, digital filtering, etc) is usually devoted to ensure optimum resolution. High spectral resolution is important for the measurement of NMR parameters, especially for signal intensities, chemical shifts, and coupling constants. However, in many areas of high-resolution NMR the observed resonance lines are broadened in some undesirable way which may complicate, if not prevent, the accurate analysis of e.g. scalar couplings. Moreover, it is possible to directly measure accurate values of J only when the splitting is much larger than the linewidth. For example, the figure below shows two calculated Lorentzian peaks with linewidth of 10 Hz, separated by a coupling of 10 Hz, which would be mistakenly interpreted.

In this figure, the individual components of a doublet are plotted in red and green whilst the sum, which is the observable curve, is shown in black. The blue dashed lines indicate the true splitting, corresponding to the separation of the maxima of the individual components (10 Hz). On the other hand, the short yellow lines indicate the observed splitting, defined as the distance between the two maxima. It can be observed that the splitting value measured as the distance between the two peaks maxima in the sum spectrum underestimates the real J value (in the case of antiphase multiplets the result is exactly the opposite).

A real-world example will illustrate the problems caused by low resolution and how to sort them out by enhancing resolution via data processing procedures (such as the new Resolution Booster technique). So let’s take a look at the spectrum of dimethyl pyridine-2,5-dicarboxylate acquired at 250 MHz:

This spectrum has been processed without applying any weighting function and the resolution is 0.13 Hz/pt. If we look at the signals corresponding to proton 2 in the structure, we can appreciate a small splitting due to 4 bonds coupling with proton 6. Proton 6 shows a large splitting due to 3 bond coupling with proton 5 and a small splitting due to the 4 bond coupling with proton 2. Proton 5 appears as a double doublet because of the 3 bond coupling with proton 6 and a small 5 bond coupling with proton 2. The latter is barely appreciated in the figure because of the lack of resolution. In fact, the same splitting should show in proton 2 but this can not be seen at this resolution level.

The classical solution to the line broadening problem, other than using higher magnetic fields, and assuming proper shimming, is multiplication of the FID by a resolution-enhancement function. Typically this is achieved by using a window function with the goal of deemphasizing the beginning of the FID and amplifying the later part. Two well-known functions for this purpose are the Lorentzian-Gaussian and the Sine Bell function.
These functions are very effective in improving the resolution as can be appreciated in the figure below, but we have to pay the price in poorer SNR and peak shape distortions (significant negative lobes appear on either side).

Resolution Booster in action

As a new powerful and effective method for resolution enhancement I’m glad to introduce here the Resolution Booster algorithm, an algorithm which is currently available in Mnova software and comes from the fruitful collaboration with Stan Sykora. BTW, Stan has a well established blog.
This method is based on a second derivative calculation combined with a non linear filtering of negative peaks. At this time I cannot give further details, but a publication with all the technical details is on the way. As soon as it is published, I will comment further on some interesting points about it.
So let me show you the spectrum of the pyridine derivative once Resolution Booster has been applied:

In this case, resolution has been increased by ~230% thus making the calculation of the weak, long range coupling constants possible. For example, we can calculate the 5 bond coupling between proton #2 and proton #5, obtaining a value of 0.82 Hz.

I will have much more to say about Resolution Booster but I think that for a first introduction this is enough. If you are curious about it and want to try it out with your own spectra, just download Mnova and play with it. Of course, your feedback about it will be very welcome. In forthcoming entries I will give more examples of Resolution Booster applications and will comment some practical issues about its use so, please, stay tuned!