Three-center four-electron bond
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3-center-4-electron bond is a term for the axial bonds on a trigonal bypyramidal or octahedral molecule such as Phosphorous V Chloride. In this molecule, Phosphorous has an expanded octet, which is a violation of molecular orbital theory. So, the central atom shares a pi bond between the two atoms, creating resonant Lewis structures with ionic-covalent bonding.
For example, in Phosphorous V Chloride, the Phosphorous and two Chlorine atoms are the "3-centers" and the two bonds connecting the Phosphorous atom to each Chlorine represents "4-electrons." What happens in this type of bonding structure is that one Chlorine atom gains an electron and separates from the central Phosphorous atom. In the second resonant structure, the second Chlorine atom separates from the Phosphorous. This type of resonant continuum yields the phenomenon known as hypervalency or 3-center-4-electron bonding.
Contrary to prior belief, d orbitals are not involved in hypervalent bonding because the energy difference between a 3d and a 3p molecule is too great for stable bonding. 3-center-4-electron bonding is now growing in acceptance as the correct model for explaining hypervalency.