Delta bond

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Formation of a δ bond by the overlap of two d orbitals
3D model of a boundary surface of a δ bond in Mo2

In chemistry, delta bonds (δ bonds) are covalent chemical bonds, where four lobes of one involved atomic orbital overlap four lobes of the other involved atomic orbital. This overlap leads to the formation of a bonding molecular orbital with two nodal planes which contain the internuclear axis and go through both atoms.[1][2][3][4]

The Greek letter δ in their name refers to d orbitals, since the orbital symmetry of the δ bond is the same as that of the usual (4-lobed) type of d orbital when seen down the bond axis. This type of bonding is observed in atoms that have occupied d orbitals with low enough energy to participate in covalent bonding, for example, in organometallic species of transition metals. Some rhenium, molybdenum and chromium compounds contain a quadruple bond, consisting of one σ bond, two π bonds and one δ bond.

The orbital symmetry of the δ bonding orbital is different from that of a π antibonding orbital, which has one nodal plane containing the internuclear axis and a second nodal plane perpendicular to this axis between the atoms.

The δ notation was introduced by Robert Mulliken in 1931.[5][6] The first compound identified as having a δ bond was potassium octachlorodirhenate(III). In 1965, F. A. Cotton reported that there was δ-bonding as part of the rhenium–rhenium quadruple bond in the [Re2Cl8]2− ion.[7]


  1. ^ Cotton, F. A.; Wilkinson, G. (1988). Advanced Inorganic Chemistry (5th ed.). John Wiley. p. 1087–1091. 
  2. ^ Douglas, B.; McDaniel, D. H.; Alexander, J. J. (1983). Concepts and Models of Inorganic Chemistry (2nd ed.). Wiley. p. 137. 
  3. ^ Huheey, J. E. (1983). Inorganic Chemistry (3rd ed.). Harper and Row. p. 743–744. 
  4. ^ Miessler, G. L.; Tarr, D. A. (1999). Inorganic Chemistry (2nd ed.). Prentice-Hall. p. 123–124. 
  5. ^ Jensen, William B. (2013). "The Origin of the Sigma, Pi, Delta Notation for Chemical Bonds". J. Chem. Educ. 90 (6): 802–803. doi:10.1021/ed200298h. 
  6. ^ Mulliken, Robert S. (1931). "Bonding Power of Electrons and Theory of Valence". Chem. Rev. 9 (3): 347–388. doi:10.1021/cr60034a001. 
  7. ^ Cotton, F. A. (1965). "Metal–Metal Bonding in [Re2X8]2− Ions and Other Metal Atom Clusters". Inorg. Chem. 4 (3): 334–336. doi:10.1021/ic50025a016.