Trigonometry for Dummies

This is a doublet of doublets. If you move one doublet towards the other, for example by increasing the smaller J, the central peaks will coalesce into a single peak of double intensity (the algebraic sum of the central peaks).


A triplet is a special case of doublet of doublets (the Js are identical).


Another doublet of doublets. This time the smaller coupling is anti-phase.
If we increase the small J, we'll see another algebraic addition.


This is a triplet. Right?

NMR for Dummies

Here is where the real fun begins. I was not joking with my previous post. You can really do these things at home. The simple instructions are available on another site, and they are illustrated. After completing the tutorial (it takes 5 minutes in total) a working application will remain in your hard disc, and you will be free to apply the same treatment to your own spectra.
iNMR has always been available as a free download (since 2005). Access is unlimited and the program never expires. Other specialized simulation modules are included to cover most of the needs of an advanced spectroscopist (the few exceptions are motivated by the fact that other needs were already covered by existing freeware).
My blog is three years old. Half of the comments have been dedicated to a single post, which is clearly (and purposely) the least representative of the blog. When people find something useful (and this is certainly the case today) and free, they don't comment.
If you are not going to comment, I will comment by myself.
COMMENT: although it's a serious work, although it contains a lot of maths (and maybe just for this reason) it's funny too.

Try this at home

Returning to the DQF-COSY of taxole, I have found this challenge:

I couldn't tell which kind of multiplet it was. I have extracted the section corresponding to the red line and moved it into my novel simulator. Then I have introduced 3 couplings and pushed the "Fit" button.

That's all. The goodness of the fit is convincing. It is a doublet of doublets of doublets and the Js are: 14.7, 6.4 and 9.9 Hz. The latter corresponds to an antiphase coupling. Not only I know which kind of multiplet it is, I have also measured the Js!
You might feel it's funny, I find it amazing, perhaps somebody will say it is useful. "The coupling constants were extracted from the DQF-COSY by the blogger's simulator".

Digitization

I am continuing my explorations on board of my new multiplet simulator. It has been easy to simulate an asymmetric doublet. Here the asymmetry is only apparent and is due to the limited digitization.

As explained yesterday, the black line belongs to an experimental 2-D spectrum (today I have chosen a TOCSY), the red line is a theoretical doublet acquired and processed under the same conditions.
My simulator allows me to change the frequency by dragging the blue label at the bottom.

In this way the coupling remains constant. It turns out that my spectrum was a middle-range case. With a slight increase of the chemical shift I can obtain a symmetric doublet, or even a singlet!

Natural Products

A reader asked me: "What is the shape of a 2-D peak?" and my answer was: "Exponential! (in time domain)". This is all you need to know, I think. The picture should help, as always. If you are reading this blog, it means that you have something like a computer. Even the iPhone is a computer (you can run programs on it) and can display my blog. I suspect, however, that you have a better computer, like I do.
You can use your computer to run simulations and more: you can ask it to fit a model spectrum to an experimental spectrum. This is what I have done. The black line is a (fragment of a projection of a) DQF-COSY. The red line is a model generated by the computer. All I said was:
1) the signal has an exponential decay;
2) it's an anti-phase doublet;
3) here is an experimental spectrum and here are its processing parameters;
4) please fit the model to my spectrum!
The goal was a better estimate of the coupling constant. The distance between the two peaks is 7.3 Hz, while the model contains a J = 8.88 Hz. My impression is that the model is more accurate by 1.6 Hz.
The calculation involved is very little (the whole process was faster than the blinking of an eye). The job of programming was more time-consuming. If you don't like spending time, find someone else that can do the job for you. They ask 0.99$ (0.79€) for an application (for the iPhone). Calculating the Js with more accuracy is certainly worth the price.
There is no secret, no new theory, should you need more explanations please ask.
If you want to know more, I can try to explain what was behind the question of the reader. It's not necessary, it's an un-necessary complication, but it's also well-know theory. If you submit to FT a function (e.g.: an exponential decay) you get a different function (in the example, a Lorentzian). They form a "Fourier pair". Being that most 2-D spectra are weighted with a squared cosine-bell my friend probably wanted to know which other function it makes a pair with.
Now you can realize that it is more a theoretical question than a practical one: if the final goal is to simulate an NMR spectrum, it's enough to know that the signal decays exponentially (and everybody knows it).
The program shown by the picture can simulate a multiplet (with 3 different J values). The multiplicities that can be chosen from the menus are:
but it's trivial to extent the menu and handle quintets and so on. Even without further modifications, you can already simulate a quartet of triplets of doublets."R" is the inverse of the transversal relaxation time. This kind of program can't simulate second-order spectra, but nothing prevents you from writing a program that simulates second-order spectra in time domain.
What happens when the user pushes the "Fit" button? The computer runs a Levenberg-Marquardt optimization, based on first derivatives. How have I found the derivatives without knowing the function that describes a peak? You know: life is simpler when you have a computer...