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The bond order can then be computed by
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.