Tuesday, 18 December 2007

Glenn Facey’s blog

In case you’re interested in experimental aspects of NMR, do not miss Glenn Facey’s blog at University of Ottawa. Whether you are an NMR facility manager or a scientist using NMR routinely, I’m sure you will find it a very useful resource.

Friday, 14 December 2007

Introducing 2D Resolution Booster ™ (RB)

In recent entries I presented Resolution Booster as a simple but robust method to obtain highly resolved NMR spectra and showed some of its properties. Today I want to show the preliminary results we are getting by applying an extension of this method to 2D NMR spectra.
In order to illustrate the performance of the algorithm I have simulated a 2D spectrum of an A2B3 spin system with the following parameters:

  • Spectrometer Frequency = 500 MHz
  • Shift A = 4 ppm (2000 Hz)
  • Shift B = 8 ppm (4000 Hz)
  • JAB = 30 Hz
  • Line Width = 30 Hz
  • Data points = 2048 x 2048

As the coupling constant is very close to the line width (they are actually exactly the same, 30 Hz), the multiplets are not resolved (2D spectrum at the left). After applying 2D RB, the spectrum achieved has a higher resolution along both dimensions, where all multiplets are now clearly well resolved.

We are still working on this method but the results we are currently getting are certainly very promising and we are confident that it will soon become a very valuable tool for automated 2D NMR processing. It is not available in the current version of Mnova but it will be included in the new release scheduled for the end of January 2008. Together with my friend Stan Sykora, we will be presenting a poster on RB in ENC 2008 at Asilomar. Should you be attending ENC, please stop by to see us. We will be delighted to discuss this (or any other) topic with you.

Friday, 7 December 2007

Automatic Processing & SNR

Manuel Perez brought to my attention a possible drawback of the automatic processing scheme for 13C NMR spectra I proposed in my previous post. Basically, his main concern was that small peaks in spectra with low SNR could get suppressed when this procedure is applied.
Of course, he is absolutely right if the method is carried out exactly as it has been described in my post. The problem is that I believe my post was somewhat misleading in the sense that it stated that the weighting functions to be applied should be just a linear ramp combined with a cosine bell function. Whilst this is correct, it’s not enough!. One should not forget that, usually, 13C NMR spectra are weighted with exponential functions in order to improve sensitivity, in particular when the SNR is not very good (as it often occurs). When such a function has to be used, it should also be applied in the automatic processing method I have proposed! Do not forget that a sine-like apodization function does not have the same sensitivity enhancement power as an exponential function does.
Because of the linear ramp employed, the sensitivity of the f-domain spectrum gets poorer and the cosine bell (or 90º shifted sine bell) function is introduced in order to somehow compensate for the decrease of the SNR caused by the linear ramp function. However, this does not mean that an exponential function must not be applied to further increase the SNR as it would be the case of routine 13C NMR processing.So, for example, when using Mnova, one should activate the following weighting functions:

It is important to note that merging of several apodization functions in this way it’s possible because weighting is a linear operation (as is the convolution process).

Let’s take a real-life example which will illustrate some of the points I’ve been talking about in the last two posts. In the figure below I show a 13C spectrum:

We can appreciate a very bad baseline and the intense solvent (Methanol-D4) peaks. For convenience, I will first get rid of the solvent lines by means of the cutting tool available in Mnova (note that this is just a visual tool, the peaks are not physically removed from the spectrum).

Baseline correction could seem quite tricky in this spectrum but it’s not. A polynomial baseline correction with an order higher than 4 or the Whittaker Smoother method included in Mnova will do the job very efficiently as it’s depicted below

Other operations that have been applied to this spectrum were (1) exponential weighting of 1 Hz and (2) phase correction. This is just the standard way to process this kind of spectra.
Now I will apply the ‘automatic’ method. First I will apply the linear ramp and cosine bell weighting function (excluding the exponential one) just to show the issue raised by Manuel. Remember the processing requirements:
  1. Apodization: Linear Ramp + Sine Bell 90º
  2. Magnitude calculation after FT

This is the resulting spectrum. It’s evident that the SNR has decreased significantly and several peaks get suppressed. The point to remember here is that the exponential weighting function has been excluded.

Let me introduce the exponential function again (in combination with the linear ramp and Sine Bell 90º functions) but this time I will use a line broadening value of 3 Hz. Take a look at the new spectrum stacked on top of the spectrum processed with the standard method:

Now the SNR is comparable with the ‘normal’ spectrum and no peaks are missing, whereas the resolution of both spectra is very similar.

I hope that things are clearer now. Should anyone out there find any other problem with this method or just want to give his feedback about it, I will be more than happy to respond.

Monday, 3 December 2007

Automatic Processing of 13C NMR spectra

The days in which chemists had a lot of time to spend in the processing and evaluation of their NMR spectra has probably gone. Synthetic or medicinal chemists should use their precious time working on their lab benches whilst NMR spectroscopists are usually devoted to get the most from the NMR instruments (optimizing or designing new pulse sequences) and resolving the most challenging cases in structure elucidation/verification. Thus, in my opinion, any method permitting to automate processing steps would be very useful in accelerating spectral analysis in the framework of NMR structure determination.

Here I would like to introduce a very simple processing scheme which can greatly simplify the automatic processing of 13C NMR spectra. For the time being I will simply outline the operations required but I will leave for a future blog entry an explanation on how the method actually works under the hood.

The method starts by first multiplying the FID by a Cosine Bell function (the squared version would also work) combined with a 45º linear ramp function:

Next, we will apply the Fourier Transform followed by the magnitude calculation of the resulting frequency domain spectrum. That’s it! The resulting spectrum will exhibit the same resolution as a standard phase corrected spectrum despite of being in magnitude mode!. As I wrote, I will explain why this is so in this blog shortly

So, the advantages of this method are that neither phase nor baseline correction are required. It is true that, in the last years, automatic algorithms for phase and baseline corrections have become very reliable, but they are not bullet proof and sometimes they require manual tuning in order to get optimal results. For example, in the figure below you can see (top) a 13C spectrum with a severe baseline roll caused by the corruption of the first points of the FID. Whilst backward linear prediction or efficient baseline correction algorithms (see this) could be used to resolve this problem, the method I presented here will yield a very good spectrum with no user intervention at all (bottom).

That is all for now. I will soon answer some questions such as why these window functions are used and why phase and baseline correction are not needed but in the meantime, should you need any clarification, just drop me an email or leave a comment here.

Thursday, 22 November 2007

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.

Monday, 19 November 2007

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!

Wednesday, 14 November 2007

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!