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  Fitting the Frequencies Only

Before total line-shape fitting, before interactive fitting, before the computer as we know it today, there was LAOCOON.
Castellano and Bothner-By, J. Chem. Phys, 41, 3863 (1964)
Note: The article presents LAOCOON II and doesn't mention the computer that they used, but contains a reference to a previous article: J. Am. Chem. Soc. 84, 743 (1962), which I haven't read.
The reason why this approach is rarely used today is that magnetic field strengths have increased 15 times. Apart from this, the method is useful and reliable and no simulation package is complete without it. Because there are relatively few values to fit (the frequency values of a selected group of lines), there is an high percentage of success.


You process the experimental spectrum, check that the frequency scale is properly referenced, and perform a peak-picking of the most significant lines (ideally all the lines predicted by quantum mechanics). You also introduce this experimental spectrum (as an overlay) in the window where you have simulated the spin system. Check the parameters (chemical shifts, J coupling, etc...) that need to be recalculated (they are into the drawer, at the side). Optionally, at this point, you can select which simulated lines to use. To select, put a vertical mark (Cmd-click). iNMR will automatically associate each mark to the nearest peak, so you don't have to be precise. If you don't put any vertical mark, all lines are automatically selected. It is essential that the same number of lines are selected in the two spectra. Also essential (and obvious): the number of parameters to recalculate must be less than the number of lines. Other two limitations are: the X approximation cannot be used and a single system must be declared.


After the command “Simulate/Fit Line Positions”, you are confronted with the two lists of peaks, in increasing order of frequency (Hz), and their difference, line by line. The program associates the lines, respecting the order. Afterwards, when some parameter is changed, two lines may swap their relative order in the calculated spectrum. iNMR will not change, however, the order in the table, it will only update the numerical values. The observed values, instead, never change. In some complicated cases, those where the algorithm is useful, the association of calculated and experimental lines is not trivial. You can visually inspect the spectra and consider if there is any mismatch in the intensities. You cannot associate, for example, a weak line with a tall one. To reassign the peaks check, in the table, the two lines that you want to swap. The experimental values will soon be swapped.
When you are satisfied with the assignments, click the “FIT” button. It may happen that, after the calculation, two errors are significantly greater than the others, one being positive and the other negative. It is an indication that the initial assignment was wrong. Swap the two and click “FIT” again. You should notice an improvement, both in the residuals (errors) and in the sum of their squares (Chi-2).
Whatever happens cannot be undone. Save the starting values of your parameters in advance.

See also

introduction to simulation

the dialog to define spin systems

the drawer

chemical exchange

total line shape fitting