### Perfect Looking Integrals

Can you honestly cheat? How do you define the integration limits in NMR? Are the two questions connected?

An ideal mono-dimensional proton spectrum contains a variable number of Lorentzian curves. Each cluster of such curves constitutes a multiplet and each multiplet corresponds (most of the times) to one or more protons, in other words to an integer number of hydrogen atoms. If you integrate the multiplets, the areas should be in the correct ratio and these ratio can be expressed with integer numbers.

The theory contradicts itself, because theoretical Lorentzian lines are always larger than the spectrum, so large that you can't measure their total area. What we normally measure is the central portion. (This is why broad signals always integrate for less than their expected values). The method works, in practice, because we are cutting the tails of all signals in a comparable way.

Having finished with the boring theory, let's have fun with iNMR. If you enlarge the region of an integral, the value at the bottom will increase by a small percentage; the opposite is true when you shrink the interval. If it doesn't happen, it means that your baseline is not correct. If you have time to spare (and the noise is at a low level), you can make all areas correspond to perfectly integer values. For example, when a value is, let's say, 2.1, you discard a little hump on the side and it becomes 1.99, then you add one more point and it becomes 2.00. There is no cheating, because the values are true and correspond to the selected regions, as shown by the plot.

It can be funny the first time, but I know better ways to enjoy myself. Mainly, there is no necessity of doing it manually, because iNMR can already play this game for you. After you have defined the integral regions and normalized them, open the console and type:

``` exact() <Return> ```

You will see no change. Now press <Esc> to force the window to redraw its contents. The integral regions have slightly changed and in many cases the areas correspond to integer values. Why not always? This algorithm is very prudent. If anything goes wrong (because of the noise or because of a local defect of the baseline) it stops. Prudent or stupid?

If you are extremely prudent, save your spectrum before running exact(). Doing so, you have the option of recovering the old integrals with the command “File/Revert to Saved”.