 Solution

Differentiate the Lennard-Jones potential. Its minimum satisfiesFor dilithium, the two wells consequently haveUnder an additional same-orbital, Hund-type exchange comparison, assign $(3.4,0.06)$ to the triplet and $(4.9,0.05)$ to the singlet: the lower-energy minimum is associated with the exchange-stabilized triplet state, as in part (a).

This assignment needs that extra orbital-parentage assumption. A scalar Lennard-Jones potential does not itself encode spin, and a common atomic dissociation limit does not specify a unique molecular electronic configuration or spatial symmetry. The two curves even cross at about $5.006$ bohr: neither lies below the other at every separation. Thus the minima and well depths are determined unambiguously; the spin labels are a conditional qualitative inference, rather than a unique consequence of the four supplied parameters. Neither “a triplet must always have a longer bond” nor a universal ordering of unrelated excited states is justified.