Line Fitting Primer

No previous exposure to iNMR is required to follow this tutorial. The pictures you will see have been generated with version 2.4.2. With older incarnations of iNMR you can get the same results, but through a different sequence of commands.
Our purpose is to measure the integrals of two multiplets on top of a hump (the water signal). It can be argued that what we are doing is not necessary, because the eye of a spectroscopist can reach the same result in a fraction of second. This is a primer and the example had to be simple. The fact that visual inspection leads to the same results should increase your confidence into the method, therefore this is an ideal spectrum for a primer. Once you have mastered the tools described here, you'll be able to solve more difficult cases.
The article includes step-by-step instructions, comments and further hints. It is easy-to-follow just because it's so long. The tutorial itself can be repeated in one or two minutes. It takes more to say it that to make it.
The pictures are conveniently small for a web site. When working at your computer, you are warmly invited to zoom all the windows up to their maximum allowed size. You can also close the iNMR palette, because we aren't going to use it, this time. iNMR is pleasure: the larger the windows, the bigger the pleasure.
Download this archive on your hard disc and decompress it with a double click. It contains a Bruker spectrum (a folder) whose origin doesn't matter. It's a proton spectrum acquired in DMSO-d6. It's our raw material.

Open the Spectrum

Open iNMR and, through it, open any of the files of the decompressed folder. The spectrum has already been processed. A simple, first-order, baseline correction has been applied. The water signal is centered at 4.09 ppm. It is closely surrounded by the two multiplets we are going to integrate. All the integral regions are already defined and the integral values normalized. It's important to normalize the integrals before starting the line-fitting module, because the latter will automatically inherit the same normalization factor and the final results will be expressed in the same units. We'll be able to compare the results of best-fitting directly with the other integrals of the spectrum. When the integrals are not normalized, the values are instead expressed as percentage of the total area.

Select the Region to Fit

Select the gray region shown below. To select a region click and drag the mouse.

selection

OPTIONAL: If you want to reproduce the same identical results of this article, there is a more complicated alternative to click-and-dragging:

Look how two tiny spikes on the tails of the water signal are left outside the selection. While it is advantageous, in general, to fit as many experimental points as possible, there is no necessity to sample the whole line-shape. Our model spectrum will only contain peaks of regular shape. It's impossible to formulate a model that explains the spikes, therefore it's better to avoid them. We are still forced to sample the biggest spike at 4.24 ppm, unfortunately! When the selection is gray, issue the menu command “Simulate/Deconvolution”. A new window appears, containing the captured region.

Improve the Automatic Guess

The program suggests an initial number of peaks. This initial guess is terribly cursory, with a reason. iNMR tries, at the first attempt, to include not only the peaks, but also the shoulders into the model. Unfortunately, with such a noisy spectrum and such a broad peak, almost every point corresponds to a shoulder and iNMR gets fooled. We have the option, however, to generate the initial model from a smoothed version of the spectrum. Click the icon “smooth”. Click it again. Click it a third time. Something happens each time. At the end your window will be exactly as shown here:

deconvolution module

Simulate the Water Signal

The number of peaks is now nearer to reality, but manually adjustment is still necessary. The upper part of the module contains a table. Select the row that begins with a “6” (click on the digit “6”). The corresponding peak will become red. Four little square handles mark the peak and let you move or resize it. Drag the bottom handle to the left, until it corresponds to the center of the water signal:

manual adjustment

Drag down the top handle, until it coincides with the top of the water peak. Drag either of the side handles to enlarge the red peak. We can't make it as large as we need: the maximum allowed by iNMR is less than the experimental width. Don't worry: it's enough for an initial guess.

water marked

Simulate the Quartet

Click on the leftmost green peak (the wide one). It will become red:

another peak selected

Drag the bottom handle to the left, until the red peak corresponds to the leftmost component of the quartet.

peak moved

Click the icon “split”. This creates two peaks of half intensity. Initially they look as a single peak because they are equal and superimposed. Drag the bottom handle to the right, until the red peak corresponds to the rightmost component of the quartet.

last peak

Run It!

Now we are ready for the calculations. Press the button “Check All”. This tells the program that all the parameters are to be recalculated (optimized for best-fitting). Click the “same %” button. It's located at the opposite side, just below the table. You have told the program to fit the spectrum with pure Lorentzian line-shapes. This is the most common and simple strategy. Click the icon “FIT” to run the optimization.

fitted peaks

Check the Fit

You can see that we had overestimated all the individual heights (with the exception of the hump). To appreciate the goodness of the fit, click the icon “toggle”. It will show a different kind of plot. Instead of the individual peaks, their sum is shown (in green) and the difference from the experimental spectrum too (in red). The residual error is reported numerically, in red.

plotted sum

To make sure that the best fit has been reached, click again the icon “FIT”. You can click it many times, because cycles are so fast. Even if the plot seems the same, some decimal digits change into the table. At the fourth additional run, no digits change anymore. It means that iNMR can't find anything better, given our initial guess.

Save the Results

The Deconvolution window is not saved into the original document. How shall we save our work? Click the icon “copy”. This copies the content of the table, as text, into the clipboard. You can paste the text into TextEdit, for example, and preserve it as a file. From there, it can be reintroduced, with the icon “paste”, into another deconvolution window, regenerating the table.

Examine the Results

On my computer, I get the following results:


Parameters for 8 peaks
frequency (Hz)     intensity      width (Hz)   Lorentzian %

1751.4712         0.0973         3.0791       100.0000
1744.4119         0.4027         4.3291       100.0000
1737.4297         0.4202         4.4088       100.0000
1730.3103         0.1050         3.0906       100.0000
1637.3000        13.5916       164.5764       100.0000
1545.8155         0.4567         5.0343       100.0000
1539.4415         1.0518         4.9630       100.0000
1533.0480         0.4853         4.8921       100.0000

The quartet (first 4 rows) has the total intensity of 1 hydrogen; the total intensity of the triplet (last 3 rows) is the double. Incidentally, the intensity pattern of the “quartet” (?) is 1:4:4:1, not 1:3:3:1; Interpreting it would lead us outside the scope of this tutorial.
Can iNMR calculate the areas of the multiplets? Instead of summing the individual components, we can remove the water completely and see what remains. It will be faster. Let's go!

Create an Artificial Blank

Delete, from the text above, all the lines but the water peak. It is easily recognized by the large values of intensity and width. You can also correct the “8” in the header into a “1”, if you like, to reflect the fact that there are less lines now, but it's not necessary (it takes more than a typo to make iNMR crash):


Parameters for 8 peaks
frequency (Hz)     intensity      width (Hz)   Lorentzian %

1637.3000        13.5916       164.5764       100.0000
whole spectrum

We have created an artificial spectrum with the same spectral width of the example. There is a single lorentzian curve and it is equivalent to the water hump. The file format is identical to that of an experimental spectrum and we can apply all the operations that iNMR allows for frequency-domain spectra.

pure water

Remove the Water

Return to the experimental spectrum (click that window). Issue the command: “Format/Overlay...”. Check the box at the top-left; it corresponds to the fake blank. Check the other box labeled “Subtract”. Wow!
Dismiss the dialog, the job is done.

final result

The Extra Trick

You may wonder why the numerical values are so perfect. The trick was explained into a previous tutorial.
The whole manual of the line-fitting module is shorter than this page. You can reach it by clicking the icon “help”.


 
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