Spin Systems

A fortnight ago we saw how to fit a spectrum with a collection of curves. A more evolute approach is to fit the spectrum with a collection of NMR parameters (shifts and Js in the first place). There are two reasons to prefer the latter approach:

1. you introduce logical restrictions into the model, for example you specify that the components of a triplet are in the ratio 1:2:1
2. you overcome the job of measuring shifts and Js from line positions

Simple line fitting to a generic collection of lines remains the best choice for singlets, simple multiplets and when you are not interested at all into the frequencies, but only into the intensities. Simplifying, curve-fitting (the so-called "deconvolution") is more about areas, spin system analysis is more about energies.
We have arrived to a large topic from an unusual path. We are in the field of quantum mechanic. It's easy in theory and, in practice, when the nuclei are few. When the number of nuclei in a spin system grows, no computer is fast enough to calculate precisely what happens. Somebody has also proposed to invert the roles, and create a super-computer with a large enough spin system (the quantum computer). That's even more difficult (try building a real molecule with 20 different nuclides!). When the number of nuclei is limited (e.g.: 10 protons), there is however no problem, at least with the older programs that diagonalize the Hamiltonian. I dedicated a post to the modern programs that can follow the evolution of a system under all kinds of effects. They have more calculations to do, are limited to smaller systems and, as it appeared from my old post, are oriented towards solid-state NMR.
Older programs are more popular in liquid-state NMR. I have already cited the free gNMR and SpiWorks. I have probably never cited Perch LE and Wind-NMR. Thay are all free (for academic users at least) and they all require Windows. Can you suggest a free solution for Linux and Mac users?
It's not a surprise that, which such an abundance of free solutions, the commercial applications, in this present moment, are ignoring the field. The race now is at predicting the spectrum directly from the chemical structure. That's the third level. At the first level we have the frequencies and intensities of the single lines. At the second level we have shifts and couplings. At the third level we have the structure. If you only have the third level, you can verify your spectrum against the prediction, but if you want to publish your data you need to extract the Js directly from the experimental data. You can't do that without the second level, unless you are glad to standardize all your reports into lists of unspecified multiplets, like:
7.24, m (2H); 4.14, m (2H), 2.36, m (8H).....
The simulation of spin systems is also becoming a popular exercise for chemistry students new to the world of NMR. It's amazing how fast the magnetic field can change, even by orders of magnitude. After a while the game becomes repetitive, but it remains highly instructive for newcomers. An excellent starting point is an article by Carlos on the NMR Analysis Blog. It should be, however, complemented by practice, more than by further references. There is a minimal library of ready examples for Mac users. It contains the classic cases (orto-di-chloro-benzene, DMF), plus templates for small and medium-sized systems of 1/2 nuclei. In the case of DMF you can change not only the magnetic field, but also the temperature.
I don't want to bother you with theory, but one thing at least must be said: geminal couplings usually have a negative constant!
One more thing on practice too: Carlos said that not all NMR signals are symmetric. Personally I still believe into the myth that they are symmetric, like the human body. To be precise, neither are symmetric, but in practice this precision is useless and misleading. I rely on the IDEA of symmetry to recognize a friendly face and I rely on the IDEA of symmetry to recognize NMR signals. By the way: they too are friendly!