Bond Order Calculator

Background.

A Lewis structure counts bonds by drawing lines between atoms, one for each shared pair. Molecular orbital theory counts them differently. The electrons in a molecule occupy orbitals that belong to the whole molecule, and those orbitals come in two kinds: bonding orbitals, which pile electron density between the nuclei and hold them together, and antibonding orbitals, which have a node between the nuclei and work against the bond. Bond order is the balance between the two, half the difference between the electrons in each.

The count earns its place because it gets right some cases that line drawings struggle with. Oxygen comes out with a bond order of 2, a double bond as the Lewis structure says, but the same orbital filling puts two unpaired electrons in antibonding π* orbitals, which explains why liquid oxygen is drawn to a magnet. Helium has two bonding and two antibonding electrons, so He₂ has a bond order of zero and does not form a stable molecule. The hydrogen molecule ion H₂⁺, with a single electron, has a bond order of one half, something no line diagram can show.

Across a related series, a higher bond order goes with a shorter, stronger bond: removing an antibonding electron from O₂ to make O₂⁺ raises the order to 2.5 and shortens the bond. That is a trend, not a measurement. The page does the subtraction and halving; deciding which orbitals the electrons occupy, and reading the result for stability, is up to you.

What is bond order calculator?

Molecular-orbital bond order is half the difference between the number of electrons in bonding molecular orbitals and the number in antibonding molecular orbitals. A value of 1 corresponds to a single bond, 2 to a double and 3 to a triple; half-integer values arise when an odd number of electrons is involved, and zero means the bonding and antibonding effects cancel and no net bond is predicted. It is most often applied to diatomic molecules and ions.

How to use this calculator.

1. 01Draw or look up the molecular orbital diagram for the molecule or ion and fill it with electrons, lowest energy first, adjusting the total for any charge.
2. 02Count the electrons in bonding orbitals (σ and π without an asterisk) and enter that number as bonding electrons.
3. 03Count the electrons in antibonding orbitals (σ* and π*) and enter it as antibonding electrons. Both must be whole numbers, and the antibonding count cannot exceed the bonding count here.
4. 04You can count valence electrons only or include the core: filled inner shells add equally to both counts and leave the bond order unchanged.

The formula.

Bond order = (N_b − N_a) ÷ 2, where N_b is the number of electrons in bonding molecular orbitals and N_a the number in antibonding ones. The division by two converts electrons into pairs, so that two net bonding electrons make one bond, matching the shared-pair picture of a single bond. Each extra bonding electron raises the order by one half and each extra antibonding electron lowers it by the same amount, which is why adding or removing electrons from an ion shifts the order in steps of 0.5. The page accepts only whole-number counts and an antibonding count no larger than the bonding count, so the smallest result it gives is zero.

A worked example.

Frequently asked questions.

References& sources.

1. [1]IUPAC Gold Book, bond order.
2. [2]OpenStax, Chemistry 2e, section 8.4, Molecular Orbital Theory.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.