bond order from MO theory
/ M-O BOND OR-der /
Once you have a filled molecular orbital diagram, you can put a single number on how many bonds hold the two atoms together — even if that number is a half. Bond order is that count. It captures, in one figure, whether a molecule is loosely or tightly bound, and it can be a fraction, which the old single-double-triple bond picture cannot express.
The recipe is simple arithmetic. Count the electrons sitting in bonding molecular orbitals, count the electrons sitting in antibonding orbitals, subtract the second from the first, and divide by two: bond order = (bonding electrons - antibonding electrons) / 2. The division by two reflects that a full bond is a shared pair. Nonbonding electrons are left out — they neither help nor hurt. A bond order of zero means no molecule forms; one, two, and three correspond to single, double, and triple bonds; and values like 1.5 or 2.5 are perfectly allowed and quite real.
Bond order is the headline prediction of the whole theory, and it tracks measurements remarkably well. Higher bond order means a shorter, stronger, harder-to-break bond. It explains why N2 (bond order 3) is inert and N2-plus has a longer bond, why O2 (bond order 2) is weaker than N2, and why He2 (bond order 0) simply does not exist. Because it allows fractions, it also handles odd-electron radicals like NO that Lewis structures fumble — NO's bond order of 2.5 correctly sits between a double and triple bond.
For the nitrogen cation N2-plus, removing one electron from N2's bonding levels gives (7 bonding - 2 antibonding)/2 = 2.5. The lower bond order predicts a longer, weaker bond than neutral N2 — and indeed the bond in N2-plus is measurably longer.
Bond order = (bonding - antibonding)/2; higher means shorter and stronger, and fractions are allowed.
MO bond order can disagree with the simple count from a Lewis structure, and where they differ the MO value is usually the one that matches experiment (O2's bond order is two, but with two unpaired electrons that no single Lewis structure shows).