SIGNAL SHAPE
(SIMPLE COUPLING)
Why do the 1H's with neighboring 1H's split, look like multiplets and obbey the N+1 rule?
Remember that the 1H nuclei are tiny magnets whose population in the external magnetic field is divided almost in two halfs: an alligned one and another opposed one to the field.
The vicinal 1H's (two or three bonds apart) influence each other.
For instance, how do the two 1H's of a CH-CH group "see" one another?.
One 1H sees that the other's population is 50% alligned and 50% opposed to the external field.
In each molecule, the field-alligned 1H adds its tiny magnetic field to the main one whereas the field-opposed one substracts it.
Consequently, each 1H of the CH-CH group “feels” two slightly different magnetic fields, giving thus rise to a doublet. A vicinal 1H (N=1) induces the other be a doublet (N+1 "legs" or lines).
Two vicinal 1H's alligned and opposed to the magnetic field can do that in three different manners: the two alligned, the two opposed and one alligned and one opposed, the latter arrangement having double probability.
Considering this, it should be easy to understand why 2 1H's vicinal to another one makes it be a triplet, with "leg's" or lines intensity ratio of 1:2:1.
You have surely guessed why "quartets" exist!
Three neighboring 1H's can adopt four different alligned-opposed arrangements as shown in the scheme. That's why one 1H with three neighboring 1H's (N=3) is made appear as a quartet (N+1) with an intensity ratio of 1:3:3:1.
And so on and so forth...
In the case of ibuprofen, the CH group in the fragment (CH3)2CHCH2 should have nine "legs" or lines because is surrounded by 8 neighbors (N=8), isn't it?
The "Tartaglia" triangle allows you to calculate the relative intensity of the legs or lines of any multiplet.
The "legs" or lines of a multiplet arising from the "simple coupling" explained above are equally separated by a few Hz (in general up to 15 Hz), a value that is independent of the working frequency of the NMR instrument.
The interproton couplings solely depend on the coupled 1H's acting as tiny magnets towards one another.
That's why the coupling constants are frequency independent.
