Total Line Shape Fitting

Typically, you simulate a spectrum to measure its chemical shifts and coupling constants, when they cannot be directly derived from the list of peaks.
Historically, the first approach was to minimize the differences between an experimental peak list and a simulated one. All least-squares methods require a starting guess provided by the user, and therefore belong to the class of optimization methods. If a spectrum is very complex (for example, when peaks overlap or are not fully resolved), it becomes difficult to create two peak lists containing the same peaks in the same order.

When the technology moved from analog (CW-NMR) to digital (FT-NMR) data, a more direct approach was developed, in which the differences are calculated, point by point, between the two spectra. This approach exploits all the available information. Beware that, if the spectrum contains an impurity, you must simulate it as well. You are in no way forced to fit the whole experimental spectrum.
In practice, the opposite is often true. It is better to fit, sequentially, a few diagnostic regions. In this way you avoid simulating the impurities and the solvent. The task of correcting the baseline is also simplified. Shape fitting is still a minimization technique and the chances of success depend on the fairness of your starting guess.

How to Fit a Portion of a Spectrum:

  1. Process the experimental data: correct the phase and the baseline, calibrate the frequency axis and increase the resolution, if necessary to resolve small couplings.
  2. Create a simulated spectrum and perform a preliminary manual fitting.
  3. Now it is time to take some strategic decisions. At this stage you can decide which parameters are already accurate (because you have measured them from a clear first-order multiplet or because they are in accordance with the literature or your experience) and which remain unknown (they require optimization by the computer).
    Also choose the battlefield: which cluster of peaks to fit first. We suggest going from the simplest to the most complex one. Select and expand the first (or only) cluster of peaks.
  4. The sidebar contains a list of parameters. Put a check mark on the chemical shifts and the couplings of the nuclei involved. Do not check the parameters that you want to remain constant. As a general rule, it is more effective to optimize n parameters together than to optimize them one by one. Leave out the parameters that have nothing in common with the cluster under study.
  5. Check any of the population parameters if you also want to recalculate the populations, but if you have already done it (during the manual fitting) it is better to keep them constant. During the initial stage of the optimization, it is not necessary to simulate the authentic line width. Use a line width that is approximately correct, or slightly smaller.
  6. Choose Simulate > Fit to Overlay. Only the visible part of the spectrum will be fitted. This command not only minimizes the difference, it also cuts away the regions of the simulated spectrum that are not visible. If you have fragmented the scale with the cutter, only the rightmost fragment will be considered. At the end of the calculation, before moving to another region of the spectrum, click the button refresh to restore the missing parts.
  7. If the first attempt fails, increase the parameter pull and try again.
  8. If the simulated and experimental regions are similar enough, keep constant the parameters adjusted so far and fit the other regions. Save the document often, so you can restore it if something goes wrong.
  9. When all the multiplets are roughly similar, you can set pull = 0 and try simulating the line widths. This step is seldom necessary, but can improve the overall accuracy. If the shape of the experimental peaks is not purely lorentzian (because you have weighted the FID), you should also change the parameter %Lor (or let iNMR optimize it).
  10. In the end, when you have found fair values for all the parameters, and if time permits, you may save the document and experiment with different optimization strategies.

Though by no means an art, this is a field where some experience pays off. You should start fitting simple spectra (even simulated ones!). Many users who have tried it have found the process surprisingly enjoyable.

Related Topics

Parameters and Controls

Spin Systems

Estimating the Concentrations in a Mixture

Why you May Want to Simulate a Spectrum

Web Tutorials

How to Fit an Abstract Spin System

How to Fit a Real Spin System

Reference

Stephenson and Binsch, J. Magn. Reson., 37, 395-407 (1980)