Fitting with a Simulated Spectrum Using the Frequencies Only
The reason why this long-standing approach is rarely used today is that
magnetic field strengths are now about fifteen times higher than they were in the 1960s.
Apart from this, the method is still valuable 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 with 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. The number of lines must exceed the number of parameters.
To Parametrize a Spectrum Using the Line Frequencies:
- Process the experimental spectrum, calibrate the frequency axis, perform the peak-picking. If not all the lines are resolved, artificially increase the resolution. Create frequency labels only for the lines you intend to fit.
- 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.
- Import the experimental spectrum as an overlay.
- Put a check mark, in the sidebar, near the parameters you want to optimize, or click the button “check all” (on the Mac it is a round button with no title).
- If there are fewer frequency labels (generated by peak-picking) in the experimental spectrum than lines in the theoretical spectrum, you need to specify, in the latter, which lines to use for the calculations. Command-click them to create as many vertical marks (on Windows: Alt Gr-click). iNMR will select the nearest line for each mark.
- You can save the simulation at this stage. With this precaution, if you do not like the final result, you can easily restore the starting situation.
- Choose Simulation > Fit Line Positions. The list of lines appears.
- You'll see that the experimental lines have been associated with their theoretical counterparts, in frequency order. This can be incorrect, especially in some complex cases or when the two spectra are quite different. For example, a weak signal can be assigned to a strong one. If you have reason to believe that two assignments are incorrectly swapped, click their check-boxes in the last column. As soon as you click the second box, the assignments are reversed. If you have no clue, just go on.
- Click the big FIT button.
- It may happen that, after the calculation, two errors are large and of similar magnitude, one positive and the other negative. It is an indication that the initial assignment was wrong. Swap the two, as explained in step 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
Reference
Castellano and Bothner-By, J. Chem. Phys., 41, 3863 (1964)