A three-
electron bond occurs when two
nuclei share two
delocalised electrons in a
sigma molecular orbital, and a single
delocalised electron in a
sigma* orbital.
Sigma* is an
antibonding orbital, meaning that it has
more energy than an
s atomic orbital. Since
electrons tend to lower-energy
orbitals when possible, three-electron bonds are
weaker than normal
sigma bonds (about half the
dissociation energy).
Three-electon bonds, as noted above, have approximately the same dissocation energy as single-electron bonds. Let S be the energy of an electron in an S atomic orbital, S-d the energy of an electron in a sigma molecular orbital. Then an electron in a sigma* orbital has energy S+d, so we have that the total energy is (S-d) + (S-d) + (S+d) = 3S-d: d less than if there were no bond. In a single-electron bond, the electron has energy S-d, also d less than if there were no bond. Hence the two have the same strength, approximately half of the 2d dissociation energy of a normal sigma bond.