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Most molecular bonds involve pairs of electrons. The two nuclei involved satisfy valence requirements by sharing two electrons. The sharing of an odd number of electrons is a relatively rare phenomenon. In special cases, two atoms may form a one-electron bond. This is the kind of interaction found in boron hydrides, for example. Another type of odd electron orbital configuration involves three electrons in a three-electron bond.

The three-electron bond may be best thought of as a resonance of two structures:

          A.:B  and  A:.B

sometimes represented as  A...B

It has been found both by calculation and experiment that this interaction has about half the bond strength of a regular bond. For the bond to be stable, A and B must be similar, if not identical such that the two resonance structures are energetically somewhat symmetric.

The simplest example of a three-electron bond is the helium molecule-ion (He2+. The bond has a strength of approximately 58 kcal/mol with an equilibrium distance between the two helium nuclei of 1.09 Å. The He...He+ bond energy is the same as that of the one-electron bond in H...H+ and about half the energy of regular diatomic hydrogen.

A well known molecule that also forms a three-electron bond as one of its resonance structures is nitric oxide (NO). It is one of the most stable of the odd-bond molecules. NO has a double bond and a three electron bond between the two atoms:

This explains some of the physical properties of nitric oxide. The internuclear distance of 1.14 Å lies somewhere between that of a double bond (1.18 Å) and a triple bond (1.06 Å). The electric dipole moment is very small as a result of the resonance distribution of the odd electron across both atoms.

Many other small molecules also have three-electron bonds such as complexes of sulfur, which have two three-electron bonds per molecule:
          ...        ...
	:S---O:    :S---S:
           ...         ...

Similar structures have been assigned for diatomic selenium and tellurium (Se2, Te2).
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.

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