# NMR - coupling of chemically equivalent protons

In Klein's Organic Chemistry 3rd Edition page 671, it states

This observation, called the n + 1 rule, only applies when all of the neighboring protons are chemically equivalent to each other.

However, in the following page, it states

Equivalent protons do not split each other

The first statement infers that for the n + 1 rule to be valid, the protons must be chemically equivalent - inferring that equivalent protons can couple, while the second statement directly contradicts this.

Could my misunderstanding be clarified?

The "n+1" rule refers to a situation where you have a proton of type A with $n$ protons of type B next to it. Proton A's signal will be split $n+1$ times by the B's. However, none of the B's will split each other because they are equivalent.

• Note: the Bs won't split each other if they are 'magnetically equivalent', which is a stronger condition than chemical equivalency. – AlaskaRon Jun 28 '18 at 6:30

The chemically equivalent proton energy levels are split by the static and local magnetic fields but nmr transitions out of some of these levels are forbidden by selection rules and those signals that remain are only the allowed transitions that give the appearance as if splitting has not happened.

The case for AX spectra is shown in the figure where the spin-spin coupling moves degenerate levels apart. The signals that are observed all have the same energy so appear as if nothing has happened to them.

(There are 2 spins labelled as $\alpha$ or $\beta$, $J$ is the spin -spin coupling constant and $h$ the Planck constant. The energy $A$ is given by $\gamma (1-\sigma)B_0/(4\pi)$ where $\gamma$ is the magnetogyric ratio, $\sigma$ the shielding constant and $B_0$ the static magnetic field).