symmetry and energy matching
/ SIM-eh-tree and EN-er-jee MATCH-ing /
Two atomic orbitals do not combine just because they happen to be near each other. There is a kind of compatibility test, and an orbital pairing has to pass it. Two conditions matter most: the orbitals must have similar energies, and they must have the right symmetry to overlap without cancelling. Energy and symmetry matching is that compatibility test — the rule that decides which orbitals are allowed to mix into molecular orbitals.
Take energy first. Orbitals far apart in energy barely interact, like two pendulums of very different lengths that struggle to push each other. The closer two orbitals are in energy, the more strongly they mix and the bigger the bonding-antibonding split. Now symmetry: along the bond axis you can classify each orbital by how it behaves, and only orbitals of the same symmetry type combine. A hydrogen 1s can combine with a fluorine 2p that points along the bond, because both are symmetric about that axis; but it cannot combine with a fluorine 2p that points perpendicular, because their net overlap is forced to zero by shape. Symmetry sets which combinations are allowed at all; energy then sets how strong an allowed combination is.
These rules are why molecular orbital diagrams look the way they do. They explain why core electrons stay on their home atoms (their energies are far too low to match a partner), why some atomic orbitals end up nonbonding (no symmetry-matched partner), and why heteronuclear molecules have lopsided molecular orbitals (their atomic orbitals start at different energies). In the more advanced language of group theory, symmetry-adapted combinations of orbitals make this matching rigorous, but the everyday idea is simple: like talks to like.
In HF, hydrogen's 1s lies higher in energy than fluorine's 2s but is a good match for fluorine's 2p along the bond. Both have the same symmetry about the bond axis and similar enough energy, so they combine; fluorine's 2s is too low and its sideways 2p orbitals have no symmetry match, so they stay nonbonding.
Only orbitals matched in both symmetry and energy combine into a molecular orbital.
Symmetry is a yes-or-no gate: if the symmetry is wrong, the orbitals do not mix at all, no matter how close in energy; energy then governs only the strength of combinations symmetry has already allowed.