Splitting goes with overlap

One of the figures on bonding models: Valence bond, molecular orbital and hybrids, drawn as descriptions of one thing rather than as competing pictures.

Three essays draw this figure, each at the values its own argument needs rather than at the setting shown above. What each one uses it to show is below, in the words of its own caption.

Exactly zero

Splitting drawn in proportion to overlap. The pairs that overlap split; the pair that symmetry forbids sits exactly where it started, which is what non-bonding looks like on an energy diagram.

Molecular orbital and valence bond

The molecular orbital picture in its simplest form: atomic levels on the outside, combinations in the middle, split by an amount that goes with the computed overlap. Everything about the framework is in that diagram.

Two hydrogen 1s orbitals at the bond length. Molecular orbital theory forms their sum and puts both electrons in it; valence bond theory pairs one electron in each and lets the pair be shared. Both accounts are drawn from this one splitting, and at this separation the splitting is large — which is the case where the two descriptions differ least.

The molecular orbital bookkeeping at its smallest: one pair of atomic levels, a bonding combination below them and an antibonding one above, split by an amount set by the computed overlap. Valence bond theory has no such diagram at all, because its objects are bonds rather than orbitals of the whole molecule — so there is nothing for its levels to be levels of.

A bond with nothing in the middle

The two combinations’ energies against separation. They cross at the separation the overlap changes sign, because one is proportional to the other.