What are sigma and pie bonds?

The sigma bond is a bond formed by head to head overlap of orbitals. In sigma bonds the electron density is concentrated in between the two atoms. The sigma bond in a molecule is denoted by a single bond. Hence in a molecule, all the single bonds are sigma bonds. For example in ethane (CH3-CH3), there are seven single bonds. So, there are seven sigma bonds in ethane (six C-H and one C-C). Thus saturated hydrocarbons possess only sigma bonds. The formation of sigma bonds is shown below 


Pie bond is formed by the sideways overlapping of orbitals. In pie bonds, the electron density also concentrates between the atoms, but on either side of the line joining the two atoms. the shape of the molecule is determined by the sigma bonds but not by the pie bonds. Pie bond in fact shortens the bond length. A double bond is made up of one sigma bond and one pie bond. A triple bond is made up of one sigma bond and two pie bonds. Thus the multiple bonds in a molecule are called pie bonds. Pie bonds are found in unsaturated hydrocarbons. For example in ethene (CH2=CH2), there is a double bond between the two carbon atoms. This double bond actually consists of one sigma bond and one pie bond. Similarly in ethyne (CH≡CH), there is a triple bond between the two carbon atoms. This triple bond consists of one sigma bond and two pie bonds. The formation of pie bonds is shown below



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A description of the double bond is the sigma-pi model shown in Fig. 1. In this case only two of the p orbitals on each C atom are involved in the formation of hybrids. Consequently sp2 hybrids are formed, separated by an angle of 120°. Two of these hybrids from each C atom overlap with H 1s orbitals, while the third overlaps with an sp2hybrid on the other C atom. This overlap directly between the two C atoms is called asigma bond, and is abbreviated by the Greek letter σ. This orbital has no nodes:electron density exists continuously from around one atom to the other atom.

Figure 1 The sigma-pi model of a double bond. Three sp2 hybrids around each carbon atom are indicated in color. Two of these overlap directly between the carbon atoms to form the σ bond. Two p orbitals, one on each C atom, are shown in gray. These overlap sideways to form a π bond, also shown in gray.
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