What is an example of converging energy?
Consider the following potential energy curve that details the change in potential energy as a function of the internuclear distance between two atomic nuclei:
The local minimum is the equilibrium bonding distance and that's where the difference in energy levels between the molecular orbitals are optimal for bonding.
As the atoms move farther apart, the energy levels of the molecular orbitals (MOs) converge and you just have some degenerate atomic orbitals (AOs).
For example, consider the
As the bonding distance increases, the energy levels of these MOs approach the energies of the AOs, and the energies converge; that's why the potential energy curve levels off at large bonding distances (internuclear separations); the atoms don't even interact anymore because they're so far apart. Thus their AOs must be in the state that they would be in if the atoms aren't bonded.
This is called the bond-dissociation limit.