molecular orbital diagram
/ M-O DY-uh-gram /
A molecular orbital diagram is the single most useful drawing in this whole subject. It is an energy ladder. Down the left edge you draw the atomic orbital energy levels of one atom, down the right edge those of the other atom, and up the middle you place the molecular orbitals that form when the two combine. Higher on the page means higher energy. Once it is drawn, you simply pour in the electrons and read off the answers.
Building one follows a fixed recipe. List each atom's valence atomic orbitals on its side at the correct relative energies. Pair up orbitals that match in symmetry and energy, and for each pair draw a connecting bonding orbital lower in the middle and an antibonding orbital higher in the middle. Orbitals with no partner sit in the middle unchanged as nonbonding levels. Then fill the molecular orbitals with all the molecule's valence electrons from the bottom up, two per orbital with opposite spins (Aufbau), and spread electrons singly across equal-energy orbitals before pairing (Hund's rule). The diagram now shows, level by level, where every bonding electron lives.
From a finished diagram you read straight off the molecule's most important properties. Count bonding minus antibonding electrons, divide by two, and you have the bond order. Any orbitals holding lone, unpaired electrons tell you the molecule is paramagnetic — drawn to a magnet. The highest filled level is the HOMO and the lowest empty one the LUMO, and the gap between them governs color and reactivity. One diagram, read carefully, predicts strength, magnetism, and reactivity at once.
For N2, the diagram shows (from the bottom) sigma2s, sigma-star2s, then the pi2p pair below sigma2p (because of s-p mixing), all filled, with sigma-star2p and pi-star2p empty. Counting gives a bond order of three and no unpaired electrons, matching nitrogen's famously strong, diamagnetic triple bond.
Fill the ladder bottom-up, then read bond order, magnetism, HOMO and LUMO off the diagram.
MO diagrams normally show only valence orbitals; the core electrons are left off because their energies are far too low to mix and they contribute nothing to the bond order.