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Fitting a Simulated Spectrum Using the Frequencies Only

The reason why this long-standing approach is rarely used today is that magnetic field strengths have increased 15 times, compared to the those of the 1960s. Apart from this, the method is still precious and reliable. It doesn't require accurate processing of the experimental spectrum (the baseline, for example, can remain uncorrected), but requires the user to associate each experimental line to a theoretical line (or, at least, to verify that the computer has associated them in the right way). Because there are relatively few values to fit (the frequencies of a selected set of lines), the algorithm is fast and stable.

You can decide which lines to fit and which parameters iNMR will change. It goes without saying that the number of lines must be higher than the number of parameters.

To Parametrize a Spectrum Using the Line Frequencies:

Step 1

Process the experimental spectrum, calibrate the frequency axis, perform the peak-picking. If not all the lines are resolved, artificially increase the resolution. Only create the frequency labels for the lines you are going to fit.

Step 2

Create the simulated spectrum. You cannot use the X approximation and cannot simulate more than a single spin system if you want to use this algorithm.

Step 3

Import the experimental spectrum as an overlay.

Step 4

Put a check mark, into the sidebar, near the parameters you want to optimize, or click the button “check all” (on the Mac it's a round button with no title).

Step 5

If the frequency labels of the experimental spectrum (generated by peak-picking) are less than the number of lines in the theoretic spectrum, you need to specify, into the latter, which lines to use for the calculations. ⌘-click on them to create as many vertical marks (on Windows: Alt Gr-click). iNMR will select the nearest line for each mark.

Step 6

You can save the simulation at this stage. With this precaution, if you don't like the final result, you can easily restore the starting situation.

Step 7

Choose Simulation > Fit Line Positions. The list of lines appears.

Step 8

You'll see that the experimental lines have been associated to their theoretical counterparts, in frequency order. This can be incorrect, especially in some complex cases or when the two spectra are very different. For example, a weak signal can be assigned to a strong one. If you have a reason to believe that two assignments are incorrectly swapped, click their check-boxes into the first/last column. As soon as you click the second box, the assignments are reversed. If you have no clue, just go on.

Step 9

Click the big FIT button.

Step 10

It may happen that, after the calculation, two errors are significantly large and of similar magnitude, one being positive and the other negative. It is an indication that the initial assignment was wrong. Swap the two, as explained at point 8, and click FIT again. You should notice an improvement, both in the residuals (errors) and in the sum of their squares (Chi-2).

The first program where this algorithm appeared was named LAOCOON. The name is also used to indicate the algorithm itself.

Related Topics

Simulating a Spectrum

Total Line Shape Fitting

Parameters and Controls



Castellano and Bothner-By, J. Chem. Phys., 41, 3863 (1964)