Selective Resolution Booster

When I announced my new blog, a colleague of mine told me that he felt very sceptical about blogs, as they used to be overwhelming and very dilute in general at the same time. I have to admit that I shared the same opinion but I think I’m changing my mind, slowly but at a steady pace. One reason for this change is that since I posted my first blog, I found that it caught the attention of many people and even though there are no public comments in the blog (I guess people don´t like to create Google or Blogger accounts), I have received a few emails with very good and interesting feedback, which will also be useful for future work on software.

For example, regarding Resolution Booster, I was asked about this:

So, why should I use Resolution Booster and not apodization?

First, let me say that I think that a discussion about the correct use of terms such as ‘Apodization’, ‘Weighting Function’, ‘Window Function’, etc, would be worth another blog entry, and maybe I’ll do it soon (unless someone else blogs about it before I do - Stan, are you there?) but for the time being I just want to compare the Resolution Booster algorithm with resolution enhancement algorithms traditionally used in NMR.

OK, in answer to the question, there are several aspects in which I believe Resolution Booster is superior, namely:

• It is easier to use
• It performs better (yields greater resolution enhancements)
• It generates less artifacts
• It eliminates the need for baseline correction
• It can be applied selectively to different areas of the spectrum

That´s a lot of claims. Let me write a little bit about each one of them:

(1) Resolution Booster is easier to use. I write this because with this algorithm there is no need to tune two parameters (as is the case with the Lorentzian-Gaussian function). Resolution Booster requires only one parameter to be optimized, the so called “Line Width” Parameter (there is a second parameter, Threshold, but it can be safely ignored in nearly all routine NMR experiments).

The Line Width parameter should correspond, approximately, to the natural line width, though it does not need to be very precise: making it smaller increases resolution and noise, making it larger goes in the opposite direction. However, a +/-50% deviation (and probably more) from the natural line widths is perfectly tolerable, and this also means that it is relatively easy to automate the selection of this parameter, making the algorithm even more accessible to the not-so-confident user.

(2) In general, the Resolution Booster algorithm yields a greater resolution enhancement than other methods.

(3) Traditional Resolution enhancement methods (e.g. Lorentzian-Gaussian) may introduce wiggles in the baseline because of the rapid truncation of the data that occurs in the tail of the FID with the application of the noise-reducing (Gaussian) function. As can be appreciated in the figure below, Resolution Booster does not present such artefacts, yielding cleaner spectra (note also in this figure the illustration of the point made above, about the greater resolution enhancements achieved with the algorithm)

(4) Spectra processed with Resolution Booster do not require baseline correction. It’s worth mentioning that none of these resolution enhancement techniques are well suited for quantification purposes. Some of these procedures change the intensity of the first points in the FID and thus proper values for integrals are not guaranteed. As for Resolution Booster, it can also change relative intensities. On isolated lines, in principle, it is approximately proportional to the second derivative which, when all lines have the same line width (as they often do) is proportional to the line height. However, broad lines can get suppressed and unresolved humps and shoulders get resolved, which is a positive thing, but their intensities and, to some extent, positions cannot be trusted.

(5) The Resolution Booster algorithm can be signal selective, and this is one of the main advantages to my mind. What I mean by this is that traditional resolution enhancement procedures are usually applied in the time domain by multiplying the FID by an appropriate function. In principle, this operation could be applied in the frequency domain by convolving the corresponding convolution kernel with the frequency domain spectrum. However, from a computational standpoint, the multiplication of the two functions on the time domain followed by a Fourier Transform is more efficient than the convolution of the two functions in the frequency domain (convolution is a more computationally expensive operation than a multiplication).
This implies that it’s not possible (or at least it’s not straightforward) to choose spectral windows (regions) in which the resolution enhancement procedure will act while leaving the other regions untouched.
Resolution Booster is capable of doing such a thing: it allows the user to easily apply it to specific regions and with different parameters, in such cases, for example, when a spectrum has peaks with different line widths (maybe due to exchange or coupling to 14N)
To illustrate this point, in the following figure I’m showing a simulated spectrum with 3 AB systems with different line widths each (10, 5 & 1 Hz) and different J(AB) (10, 5 & 1 Hz respectively). It’s possible to use the Resolution Booster to optimize the resolution individually for every AB system having different line widths by simply selecting the optimum parameter for each spectral region




An invitation

In the example above I have used a synthetic spectrum, mostly because I don’t have at hand any good experimental data sets (nor better ideas). From this blog I would like to invite you to find a real-life experiment in which this technique could be applied for real-life problems. Just drop me an email or post a comment in the blog.

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!

Let´s get started

NMR is a growing and exciting analytical technique, of interest to all areas of chemistry. After many years working in the processing and analysis of NMR data, I have been missing an ‘open’ blog, a blog which discusses all aspects of working with NMR data, not with one author, but a number of highly reputable contributors. This blog aims to become a valuable resource to the scientist using NMR by filling this gap and providing a forum for publication and sharing of high quality information, by having not only comments, but also a ‘Guest Contributor’ facility where I will invite experts in our fields to write on their specific interests. I will welcome both your comments and offers for contribution and I hope that all comers will enjoy the content and find it useful.

As for content, the objective of this blog will be to cover, specifically, the following areas

• Basic principles on NMR Data Analysis & Processing
• Tips & Tricks on NMR Data Analysis & Processing: How to get the most of your NMR data
• New Advances in Computer-Assisted Evaluation of NMR spectra
• Prediction of NMR spectra

And finally, a confession. On my choice of NMR software I am biased, having worked on the design and development of Mnova for the last 3 years, and therefore I will use Mnova for my postings and when illustrating processing, analysis and simulation tips in my articles. However, this is not an Mnova promotional site, and I will always try to make concepts and suggestions of general application independently of the software package used.

Welcome to nmr-analysis.blogspot.com. Enjoy and contribute!