Estimating the Concentrations in a Mixture
You normally measure concentrations by integration. For difficult cases you resort to deconvolution. In the case of complex mixtures containing known compounds you can try, instead, to exploit the module that simulates spin systems in a more inventive way. You can define each species as a separate system. This approach becomes efficient if you have many mixtures to analyze and the components are always the same. In this case you simulate the mixture the first time only, save the simulation document and reuse it for future analyses. Quite likely, the chemical shifts will change from sample to sample, and they need to be updated in the simulation too, but this is an easy job (you can click and drag the labels under the peaks).
Under normal circumstances, the simulation module does not change the population ratios during a fitting. It is usually assumed that the different systems of a document belong to the same molecule, therefore their populations must be kept identical. When you issue the command “Fit to Overlay”, if one or more populations are checked for fitting, iNMR will multiply (or divide) all the populations by the same factor in such a way that the total area of the simulated spectrum becomes equal to the area of the experimental spectrum. The population ratios are preserved. After this preliminary stage, the other parameters are fitted iteratively.
The case is different if one or more populations are checked for optimization and no other kind of parameter is checked. In this case, the selected populations will be individually optimized to fit the experimental spectrum. This mathematical problem of least-squares minimization is linear by nature, therefore it can be solved in a single step that leads to the global minimum. The process does not depend on the initial values. The rest of this page explains how to find the concentrations of known components in a mixture, using this approach. You should already be familiar with the interface of simulation documents.
Define each component of the mixture as a spin system (or with more systems sharing the same population). Add the experimental spectrum as an overlay and set the chemical shifts and the Js as accurately as possible. If you cannot adjust the line widths to fit the experimental lines, try to make them slightly thinner. Click in the sidebar, add check marks to the unknown populations and issue the command Simulate > Fit to Overlay.
It is rarely possible to simulate and fit the whole spectrum. Fit small regions separately. Each time, select only the populations of the species that appear in the displayed spectral region. This partial approach allows you to define far fewer components than might exist in reality. It is not even necessary to identify all of them.
As in the case of total lineshape fitting, the parameter pull is of fundamental importance, but the meaning is different here. In order to fit peaks of different widths, iNMR does not fit the spectra point-by-point, but bin-by-bin. In other words, the algorithm integrates many small regions and compares them. The rationale is that integrals are much less sensitive to linewidths and that binning reduces the need to reproduce the exact line shapes. Each small integral (not visible) contains the same number of points and this number is given by the parameter “pull”. If the peaks are well separated, you can use very large values and, by doing so, you can get a better fit. If the peaks are not separated and you set pull = 0, then you need to simulate the line widths very well.