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Measuring the Area by Fitting to a Model

There are situations when the area is not an accurate measure of the intensity of a signal:

When another signal is so close that there is a sizeable overlap.

When there's too much noise.

The alternative solution consists in fitting a portion of the spectrum with a theoretical model, made up by one or more peaks. iNMR can do it both in 1-D and in 2-D spectroscopy. Here we describe the approach in 1-D spectroscopy. The model does not include the baseline and the peaks are perfectly symmetric, therefore you should preliminary correct the phase and the baseline, the latter at least in the proximity of the signal of interest. Digital resolution should also be high enough, in other words either set an adequate acquisition time or, if you haven't, increase the size of the spectrum by zero-filling.

To Deconvolute a Signal or a Group of Signals:

Step 1

Integrate at least one peak of the spectrum (any peak) in the traditional way and normalize the area. The estimated areas will be expressed in the same unit. You can't do it later, because there is no connection between the document window and the deconvolution window.

Step 2

Select a narrow region around the peak(s) of interest. Avoid selecting pure baseline, spikes and impurities that are difficult to model, at the cost of not selecting the tails of your peaks.

Step 3

Choose Simulate > Deconvolution. A new module is created. You can see the experimental spectrum in black and a series of proposed simulated peaks in green or red.

Step 4

iNMR automatically determines the number of peaks. This number can be wrong because any irregularity that creates a maximum is counted as a peak. If there are too many peaks, click smooth repeatedly until the number of simulated peaks is only slightly higher than what you really need.

Step 5

To remove an unwanted peak from the simulation, select it (click the peak and it will become red); then click the icon remove.

Step 6

To create an additional peak, select any peak and click split: the number of peaks will increase by 1 unit. Drag the new peaks where you need: first select a peak, then drag the handle that appears at the bottom. Drag the top handle to adjust the intensity.

Step 7

Click the button All, then click same %. You have told iNMR to optimize frequencies, widths and intensities of all the peaks and to simulate lorentzian line shapes.

Step 8

Click FIT. To verify the accuracy of the simulation, click toggle. Now you can see the simulated spectrum in green and the difference (experimental - simulated) in red. In this visualization mode, the value of the residual error is also reported. It costs nothing to click FIT again: there are chances that the error decreases.

Step 9

The area of each peak is reported into the table. If you have followed our advise to integrate a peak of the original spectrum, the values are expressed in the same unit. Otherwise, the unit is 1/100 of the initially selected area.

Curve fitting can be much simpler than this, when you only have an isolated peak, but also more complicated. Try a preliminary manual fit: drag the four handles that appear when you select a peak. If you are not sure about the shape of a peak (gaussian or lorentzian), uncheck the option “same %” and let iNMR optimize all the parameters. If the percentage of lorentzian character remains above 90, then you have lorentzian peaks indeed.

Related Topics

About Curve Fitting

Curve Fitting Commands

2-D Curve Fitting


Web Tutorial

Line Fitting Primer