Bond Order Calculator
This bond order calculator works out the bond order of a diatomic molecule or ion using molecular orbital theory, the model chemistry students meet when the simple line-drawing of single, double and triple bonds is no longer enough. Bond order is defined as half the difference between the electrons sitting in bonding molecular orbitals and the electrons sitting in antibonding orbitals, so you enter those two counts and the calculator returns the bond order along with a plain reading of what it means. A bond order of 1 is a single bond, 2 is a double bond and 3 is a triple bond, while fractional values like 1.5 turn up for ions and radicals that carry an odd number of electrons. The number matters because it predicts a great deal about the molecule: a higher bond order means a shorter, stronger bond that takes more energy to break, and a bond order of zero means the electrons cancel out so the molecule is not expected to form at all, which is why helium never pairs up. To use it, fill a molecular orbital diagram for your molecule, count the electrons in bonding orbitals and the electrons in antibonding orbitals, and read off the result. You can count all electrons or just the valence electrons, since the core orbitals cancel and the bond order comes out the same either way.
A bond order of 3 indicates a triple bond. A positive bond order means the molecule is expected to exist, with higher orders generally giving shorter, stronger bonds.
Bond order equals (bonding electrons minus antibonding electrons) divided by 2. Counts should be whole numbers of electrons. Educational estimate for main-group diatomic species.
How it works
Molecular orbital theory combines the atomic orbitals of two atoms into molecular orbitals, some that lower the energy and hold the atoms together (bonding) and some that raise it and push them apart (antibonding). Bond order measures the net bonding after the two are set against each other: take the electrons in bonding orbitals, subtract the electrons in antibonding orbitals, and halve the result. Dividing by two reflects that a full bond is a shared pair of electrons. A result of 1, 2 or 3 lines up with the familiar single, double and triple bonds, values between whole numbers are normal for radicals and ions, and a result of zero says there is no net bond so the species should not form.
Worked example
Take nitrogen gas, N2, the standard teaching example. Filling its molecular orbital diagram places 10 electrons in bonding orbitals and 4 in antibonding orbitals. The bond order is (10 minus 4) divided by 2, which is 6 divided by 2, giving 3. That triple bond is why nitrogen is so unreactive and so strong: it takes a large amount of energy to break, which is the whole reason atmospheric nitrogen is hard to fix into fertiliser. Swap in oxygen, O2, with 10 bonding and 6 antibonding electrons, and the bond order drops to (10 minus 6) divided by 2, which is 2, a double bond.
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