The bond order of a simple molecule can be determined by looking at the number of electrons in bonding and antibonding molecular orbitals. Like electrons in atomic orbitals , electrons in molecular orbitals fill the lowest energy orbitals first, but no more than two electrons can go in any given MO.

The bond order can then be computed by
0.5*(electrons in bonding orbitals - electrons in antibonding orbitals). (The 0.5 is due to the fact it takes two electrons to make a single bond.)

For the simple molecule H₂⁺, there is only one electron that must be placed in a molecular orbital. It goes into the lowest energy orbital as shown.

There is 1 electron in a bonding MO and none in antibonding orbitals: the bond order is thus 0.5*(1-0) = 0.5. H₂⁺ has a bond order of 1/2: fractions are ok! This bond has about 1/2 the strength of a normal H₂ covalent bond.

For H₂, there are two electrons. Both can fit into the bonding molecular orbital: the bond order is 0.5*(2-0) or 1.

For He₂, there are four electrons. Two can fit into the bonding MO, but the other two have to go into the antibonding MO.

This gives a bond order of 0.5*(2-2) = 0. There is no bond in He₂: the favorable interaction the electrons in the bonding MO get is canceled by the unfavorable one the antibonding ones have to deal with.

Example: What is the bond order of He₂⁺?

Solution: There are 3 electrons in the He₂⁺ molecule. 2 can fit into the bonding MO, one has to go into the antibonding.

The bond order is 0.5*(2-1) = 0.5. He₂⁺ is bound, with a bond strength about 1/2 that of a normal covalent bond.

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