Why don't two protons on the adjacent carbon atoms with identical environment show splitting in proton NMR?

Question

when protons on the adjacent carbon atoms have different chemical environment, they show spin-spin coupling which results as doublet/triplet/multiplet splitting in proton NMR spectra. but when two protons have identical environment, they do not split. Why don't they sense each other for coupling?

Answer 1

When two protons couple you expect to see two doublets.

If the protons have quite a large chemical shift difference then the four lines will be almost equal intensity.

If the chemical shifts are close then the outer parts of the lines are much weaker and the inner parts are stronger.

The transition probability for the outer lines gets less  due to the mixing of the wave functions for the two protons. Mixing is enhanced if the two protons have similar energies (chemical shifts). In the end the outer parts of the doublets becomes too weak to see and it appears that there is no coupling when the protons are chemically equivalent.

In unusual circumstances the coupling between two chemically equivalent protons can be seen in the spectrum - see 1,2-dichlorobenzene for example.