A bolder idea than overlap
Valence bond theory kept electrons mostly attached to their home atoms, just letting two orbitals overlap to make a bond. Molecular orbital theory is braver. It says: once atoms come together to form a molecule, the electrons no longer belong to any single atom at all. Instead they live in brand-new clouds — molecular orbitals — that stretch across the whole molecule. An electron in a molecule is, in a real sense, everywhere in that molecule at once.
This sounds abstract, but it is the natural endpoint of everything you've learned. We started with electrons pinned to atoms (Lewis), let them overlap between two atoms (valence bond), and now let them spread across the entire molecule. Each step let the electrons roam a little freer — and reality, it turns out, prefers electrons that roam.
Building molecular orbitals: add and subtract waves
Where do these whole-molecule orbitals come from? We build them out of the atomic orbitals we already have, using a recipe with an intimidating name and a gentle idea: linear combination of atomic orbitals, or LCAO. 'Linear combination' just means *add them up or subtract them*. Because orbitals are really waves (the electron is a wave, remember), two of them can be combined in two ways — and you get a different result each way.
Bonding and antibonding: helpers and saboteurs
The two ways of combining give the two faces of MO theory, the bonding and antibonding orbitals. When you add two atomic orbitals, the waves reinforce *between* the nuclei, piling electron density right where it glues the atoms together. That lower-energy result is a bonding orbital — putting electrons there stabilizes the molecule. It is the helper.
When you subtract them instead, the waves cancel *between* the nuclei, leaving a bare gap with almost no electron density there. That higher-energy result is an antibonding orbital — putting electrons in it actually pushes the atoms apart and destabilizes the molecule. It is the saboteur. Every bonding orbital comes paired with an antibonding partner sitting at higher energy, and whether a molecule holds together depends on which ones the electrons actually fill.
Bond order: the master number
Now we can answer the most practical question of all: does a bond even exist, and how strong is it? MO theory hands us a single tidy number, the bond order, computed by filling the molecular orbitals with the available electrons and then taking the difference between helpers and saboteurs:
bond order = (electrons in bonding orbitals − electrons in antibonding orbitals) / 2
This little formula is startlingly powerful. Two helium atoms? Their electrons fill both a bonding and an antibonding orbital, helpers and saboteurs cancel exactly, bond order comes out 0 — and indeed helium refuses to form He₂. A higher bond order predicts a shorter, stronger bond, every time. One number, drawn straight from how the orbitals fill, tells you whether atoms bond and how tightly.
Spread-out electrons: delocalization
MO theory also finally explains the resonance puzzle from guide 2. Remember ozone, where no single Lewis picture worked and the electrons seemed 'spread out'? Molecular orbitals make this literal: some orbitals genuinely stretch over three or more atoms, so an electron pair really is shared across the whole stretch rather than pinned between two atoms. That spreading is delocalization, and it is no longer a fudge — it falls straight out of letting orbitals span the molecule.
Delocalization is why the carbon ring in benzene is so stable, why graphite conducts electricity, why the dyes in your clothes have color. Spread-out electrons are lower in energy and freer to move. With MO theory you have climbed from a dot on paper to a picture where electrons belong to the whole molecule — the same physics that runs from a single water molecule to the simpler pictures we built along the way, now seen whole.