When the two atoms are no longer twins
In the last guide you built the molecular orbitals of homonuclear diatomics — N2, O2, F2 — where both atoms are identical. That symmetry made life easy: each atomic orbital met its exact mirror image at the same energy, so every bonding and antibonding pair was shared perfectly evenly between the two halves. The whole diagram was left-right symmetric, and the electron density of every orbital sat squarely in the middle. That is the special case, the one with a built-in mirror plane down the bond.
Now break the mirror. In a heteronuclear diatomic like CO, NO, or HF the two atoms are different elements, so their atomic orbitals do not start at the same height. The more electronegative atom holds its electrons more tightly, which is the same as saying its orbitals sit *lower* in energy — deeper in the well. Oxygen's 2p orbitals lie below carbon's; fluorine's 2p lies far below hydrogen's 1s. Everything strange and useful about these molecules flows from that single fact: the two sets of atomic orbitals are at different starting heights.
Why the orbitals tilt — and where polarity comes from
Picture the two atomic orbitals as the two ends of a seesaw at different heights. When they combine, the lower one (on the electronegative atom) and the higher one (on the electropositive atom) still produce a bonding orbital below both and an antibonding orbital above both. But the bonding orbital now leans *down toward the lower atomic orbital* — it ends up looking much more like the electronegative atom's orbital, with most of its electron cloud sitting on that atom. The antibonding orbital does the opposite: it leans up toward the electropositive atom and is concentrated there.
This is the molecular-orbital origin of bond polarity. The bonding electrons spend more time on the electronegative atom not because of some vague 'pull', but because the bonding orbital that holds them is physically fatter on that side. So the electronegative atom carries a small negative charge and its partner a small positive one — exactly the dipole you would have drawn from electronegativity differences alone. MO theory and the polar-covalent picture from the bonding rung agree; MO theory just shows you the actual lopsided cloud that produces the dipole.
There is a useful limiting case at the far end. When the two orbitals are *very* far apart in energy — or have no matching symmetry partner at all — they barely mix, and you get a nonbonding orbital: an orbital that is essentially a lone atomic orbital sitting on one atom, neither helping nor hurting the bond. Heteronuclear diagrams are full of these, because not every orbital on one atom finds a good partner on the other. Keep an eye out for them; one of them turns out to be the most important orbital in carbon monoxide.
Carbon monoxide: the molecule with backwards polarity
CO has the same ten valence electrons as N2 and the same triple bond, but its MO diagram is tilted because oxygen's orbitals sit lower than carbon's. Filling those ten electrons leaves two frontier orbitals doing the chemistry. The highest occupied one, the HOMO, is a sigma orbital — and here is the surprise: it is mostly carbon-based, a lobe of electron density pointing out from the carbon end like a lone pair. Even though oxygen is more electronegative, the way the orbitals mix leaves this particular top orbital sitting on carbon.
This carbon-heavy HOMO has a famous consequence: CO's dipole moment is tiny, and it points the *wrong* way — the carbon end is slightly negative, even though oxygen is the greedier atom. The simple electronegativity picture would predict a strong dipole with carbon positive; instead the carbon lone-pair lobe nearly cancels that, leaving a small dipole with carbon negative. It is a clean, honest reminder that electronegativity gives the gross trend but the detailed orbital arithmetic can override it. Two atoms differing in electronegativity does not guarantee the obvious dipole direction.
Now the part you will need again very soon. CO's lowest *empty* orbital, the LUMO, is a pair of pi-antibonding orbitals — and these are weighted toward carbon too. So CO offers a metal two things from its carbon end at once: a filled, carbon-pointing sigma lone pair ready to *donate* into the metal, and empty pi-antibonding orbitals ready to *accept* electron density back from the metal. That second move is pi back-donation, and together they are why a carbon monoxide molecule binds a metal so tightly through carbon in a metal carbonyl like Ni(CO)4. Hold onto this; the entire organometallic rung leans on it.
CO frontier orbitals (carbon on left, oxygen on right) LUMO === pi* (empty) lobes bigger on C --> accepts e- from metal ------------------------------------------------------ HOMO === 5-sigma (filled) lone-pair lobe on C --> donates e- to metal delta-EN tilts orbitals toward O, but orbital mixing pushes BOTH frontier orbitals back onto carbon.
Nitric oxide: the molecule with an odd electron
NO sits between CO and O2: it has eleven valence electrons, an *odd* number. Lewis structures hate odd electrons — you cannot pair everyone up — which is why NO is one of the classic odd-electron molecules that dot diagrams handle so awkwardly. MO theory takes it in stride. You fill the same diagram as before, and the eleventh electron simply lands by itself in the lowest available antibonding orbital, a pi-antibonding (pi*) orbital tilted toward the nitrogen end.
Counting bonds is just the bookkeeping you already learned: bond order is half of (bonding electrons minus antibonding electrons). NO comes out at a bond order of 2.5 — stronger than O2's double bond, weaker than CO's triple — and that single unpaired electron makes NO paramagnetic, exactly the kind of magnetism that Lewis dots could never have anticipated and that first sold you on MO theory through oxygen. The lone antibonding electron is also why NO gives it up easily to form NO+, which has a clean bond order of 3 and is even more strongly bound.
Hydrogen fluoride: the simplest lopsided bond
HF strips the idea down to almost nothing — two atoms, one bond, a huge electronegativity gap. Fluorine's 2p orbitals lie far below hydrogen's 1s. Only one of fluorine's three 2p orbitals points along the bond axis and has the right symmetry to combine with hydrogen's 1s; that pair makes one bonding orbital and one antibonding orbital. The other two 2p orbitals on fluorine point sideways, find no partner on the tiny hydrogen, and stay as nonbonding lone pairs sitting entirely on fluorine.
Because fluorine's orbital sits so much lower than hydrogen's, the bonding orbital that holds the shared pair is overwhelmingly fluorine-like — its electron cloud is pulled hard toward fluorine. That is the MO version of the very polar bond you would have drawn as H(delta+)-F(delta-): the shared electrons genuinely live closer to fluorine, and the picture and the dipole agree this time, unlike CO. The four electrons on fluorine that took no part in bonding are the two lone pairs you would have drawn in a Lewis structure — MO theory just relabels them as nonbonding orbitals.
- Place the two atoms' valence orbitals at their real heights — the electronegative atom's orbitals lower, the electropositive atom's higher.
- Match orbitals by symmetry first, then by energy: only similar-energy, same-symmetry pairs combine into bonding plus antibonding orbitals.
- Leave the orphans alone: any orbital with no good partner stays nonbonding, sitting on its own atom.
- Fill the molecular orbitals from the bottom up with all the valence electrons, then read off bond order, the HOMO, the LUMO, and any unpaired electrons.