Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 4 / 52 / e / Solution

In the slowly exchanging cubane A each methyl carbon is bonded to three equivalent ${}^6$Li nuclei with $I=1$. Its single carbon environment gives a septet, with first-order intensities $1:3:6:7:6:3:1$.

In B the three methyl vertices remain equivalent by the ideal threefold symmetry, but each carbon sees two equivalent Li of one type and one Li of the other. The carbon resonance is therefore a quintet of triplets (15 first-order lines if both couplings are resolved and unequal): the equivalent pair gives $1:2:3:2:1$, and the third Li gives $1:1:1$. Accidental equality of couplings can collapse this to a septet.

D has one methyl-carbon environment coupled to two equivalent Li, giving a quintet $1:2:3:2:1$. E has no methyl carbon. These patterns assume proton decoupling, resolved ${}^1{J}_{CLi}$, ideal aggregate symmetry and slow exchange; without proton decoupling each methyl-carbon pattern is additionally split by its three attached protons.