Bond Order Calculator
Oxygen has a bond order of two AND two unpaired electrons — the prediction that settled molecular orbital theory.
The formula
bond order = (bonding electrons - antibonding electrons) / 2
Counting into and out of bonds
Molecular orbital theory pairs every bonding orbital with an antibonding one. Electrons in the first hold the molecule together, electrons in the second push it apart, and the bond order is the net divided by two. A bond order of zero means the molecule does not exist — which is exactly the case for He₂ and Be₂.
Oxygen is the reason the theory won
A Lewis structure for O₂ puts a double bond between the atoms and pairs every electron, predicting a diamagnetic molecule. Liquid oxygen is famously attracted to a magnet. Molecular orbital theory gets it right: the last two electrons go singly into two degenerate antibonding pi orbitals, giving a bond order of two AND two unpaired electrons. That single prediction is what settled the argument.
The order of the levels changes
Below oxygen the 2p sigma orbital sits above the pi pair; from oxygen onwards they swap, because s-p mixing weakens as the nuclear charge grows. The bond orders come out the same either way, but the magnetism does not — and that is measurable.
Models, and where they stop
Slater's rules, the Kapustinskii equation and Pauling's ionic-character expression are all empirical fits, not derivations. They were built to reproduce measured numbers with arithmetic simple enough to do by hand, and they succeed at that within perhaps five or ten per cent. Where a page here quotes one, it says which — a figure from a fitted rule and a figure from a Born-Haber cycle are not the same kind of thing, even when they agree.