Bond order is the number of chemical bonds between a pair of atoms. A single bond has a bond order of 1, a double bond has a bond order of 2, and a triple bond has a bond order of 3. It tells you how strongly two atoms are held together: the higher the bond order, the more electrons are shared between the atoms and the more stable the bond. If the bond order between two atoms is zero, no stable bond forms and the molecule doesn’t exist.
How to Calculate Bond Order
There are two main ways to determine bond order, depending on the level of detail you need.
The simplest method uses a Lewis structure. Draw the molecule, count the number of bonds between the two atoms you’re interested in, and that number is the bond order. A single line represents a bond order of 1, a double line is 2, and a triple line is 3. For a molecule like nitrogen gas (N₂), you’d draw a triple bond between the two nitrogen atoms, giving a bond order of 3.
The more precise method comes from molecular orbital theory. Here, you look at how electrons fill molecular orbitals, some of which strengthen the bond (bonding orbitals) and some of which weaken it (antibonding orbitals). The formula is:
Bond Order = (Bonding Electrons − Antibonding Electrons) / 2
This formula works for any diatomic molecule or ion, including cases where the Lewis structure approach falls short. It also explains why helium doesn’t form a stable diatomic molecule (He₂): both the bonding and antibonding orbitals are completely filled, the electrons cancel out, and the bond order comes to zero.
Bond Order Can Be a Fraction
Bond order isn’t always a clean whole number. Many real molecules have fractional bond orders because their electrons are spread across multiple bonds through a phenomenon called resonance.
Ozone (O₃) is a classic example. You can draw two Lewis structures for ozone: one with a double bond on the left and a single bond on the right, and another with those positions swapped. Neither structure is correct on its own. The actual molecule is an average of both, with each oxygen-oxygen bond having a bond order of 1.5. Experimentally, both O-O bonds in ozone are identical at 127.2 pm, shorter than a typical single bond (148 pm) but longer than the double bond in O₂ (120.7 pm).
Benzene works the same way. Its six carbon-carbon bonds can be drawn as alternating single and double bonds, but measurements show all six bonds are identical at 139.9 pm, right between a typical C-C single bond (154 pm) and a C=C double bond (134 pm). Each carbon-carbon bond in benzene has a bond order of 1.5. The carbonate ion (CO₃²⁻) has three equivalent C-O bonds with a bond order of 1.33, the average of one double bond and two single bonds spread across three positions.
To calculate fractional bond orders from resonance structures, add up the total number of bonds across all resonance structures and divide by the number of structures. For carbonate: each structure has one double bond and two single bonds (total of 4 bonds), and there are three equivalent structures, so each C-O bond order is 4/3, or about 1.33.
How Adding or Removing Electrons Changes Bond Order
The molecular orbital formula reveals something that Lewis structures can’t easily show: removing or adding a single electron to a molecule changes its bond order. The oxygen molecule and its ions illustrate this perfectly.
- O₂⁺ (one electron removed): bond order of 2.5
- O₂ (neutral): bond order of 2
- O₂⁻ (one electron added): bond order of 1.5
- O₂²⁻ (two electrons added): bond order of 1
Removing an electron from O₂ actually makes the bond stronger because the electron that’s lost comes from an antibonding orbital. With one fewer electron working against the bond, the bond order increases from 2 to 2.5. Adding electrons has the opposite effect, filling antibonding orbitals and weakening the connection. Bond length increases in the same order: O₂⁺ has the shortest bond, O₂²⁻ the longest.
What Bond Order Tells You About a Molecule
Bond order correlates directly with two physical properties: bond length and bond strength. As bond order increases, the bond gets shorter and requires more energy to break. Carbon-carbon bonds show this clearly. A single bond in ethane (bond order 1) is longer and weaker than the double bond in ethylene (bond order 2), which in turn is longer and weaker than the triple bond in acetylene (bond order 3). The energy required to break a C-C triple bond is roughly 2.3 times that of a single bond.
These correlations make bond order a useful shorthand for predicting molecular behavior. A molecule with a higher bond order between its key atoms will generally be harder to break apart, less reactive at that bond, and more thermally stable. A lower bond order suggests a weaker link that’s more susceptible to chemical attack.
Bond Orders Above Three
While most chemistry stays within the range of single, double, and triple bonds, some metal compounds push the limits. Certain transition metals can form quadruple and even quintuple bonds. Molybdenum and chromium compounds are the best-known examples.
Quadruple bonds (bond order 4) were first identified in molybdenum-molybdenum compounds decades ago. More recently, chemists have synthesized chromium and molybdenum complexes with quintuple bonds (bond order 5), which consist of one sigma bond, two pi bonds, and two delta bonds. These quintuple bonds produce extremely short metal-metal distances, around 2.02 angstroms for molybdenum dimers. A true sextuple bond (bond order 6) has even been observed in diatomic molybdenum gas at low temperatures, with a bond length of just 1.93 angstroms.
These exotic bond orders require d-orbital electrons that only transition metals possess, so you won’t encounter them in everyday organic or biological chemistry. But they demonstrate that bond order is a continuous scale, not limited to the 1, 2, and 3 that cover most common molecules.