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Sigma and Pi bonds

sigma bonding and antibonding orbitals from valence bond theory

Core Concepts

In this article, you will learn about the basics of sigma and pi bonds and their importance to organic chemistry. You’ll also have the opportunity to apply what you know with some worked examples.

Topics Covered in Other Articles

Basics of Sigma and Pi Bonds

Sigma and pi bonds are an aspect of valence bond theory and molecular orbital theory that explains the existence of double and triple bonds. To start, we must explain both bonds: Sigma(σ) and Pi(π). Sigma bonds form when the available orbital with the highest energy of each atom overlaps one another. The constructive interaction will thus lead to the formation of a sigma bond between the two atoms with a higher electron density shared between the two nuclei.

Illustration of sigma and pi bonds between different molecular orbitals
Different sigma and pi bond combinations

Any additional bonds between two atoms are explained with the formation of pi bonds. This occurs when the un-hybridized (filled) p orbitals of each respective atom overlap to form a higher electron density between the two atoms outside of the established sigma bond. This bonding will also create an anti bonding orbital. Once this orbital is filled, the bond between the 2 atoms breaks. Thus to conclude, single bonds between atoms have a sigma bond; any additional bonds between the two atoms are pi bonds; double bonds have 1 sigma and 1 pi bond and triple bonds have 1 sigma and 2 pi bonds. Referring to a molecule like diatomic nitrogen, the formation of N2 would need 1 sigma and 2 pi bonds between the two nitrogen atoms to satisfy the triple bond.

Pi Bonds and Rotamers

As you may notice, pi bonds form combined electron clouds that are a little displaced from the axis between the two nuclei. This has important ramifications for molecule in question with pi bonds.

Specifically, single bonds allow for free rotation around the axis of the two nuclei. This means that each atom in a single bond can rotate independent of one another. Single bonds allow this because they only have one bond, a sigma bond, which connects the two nuclei precisely along their axis. Chemists call the different orientations these atoms can have with respect to one another rotamers, which have a lot of importance in organic chemistry. Often this rotation can occur very rapidly; ethane, for instance, completes 1010 full rotations around its C-C bond per second.

ethane has sigma bonds but no pi bonds
Ethane has free rotation around its pi bond, allowing for an infinite number of rotamers. Source.

However, once a pi bond forms between two atoms, all free rotation ceases. Due to the displacement of the pi electron cloud, any change in orientation between the atoms decreases orbital overlap. This means that the groups attached to the atoms participating in the pi bond have a constant relative orientation. The different possible orientations (before pi bond formation) are also called “rotamers”, though sometimes they go by the name “geometric isomers“.

The 4th bond?

The overlapping of un-hybridized filled p orbitals form π bonds. It is important to note that their orientation is orthogonal, as well as being displaced somewhat, to the initial sigma bond and parallel to the p orbital of the other atom. Unlike normal sigma bonds which can freely rotate, the addition of pi bonds prevents a bond from rotating. As you can tell from the picture, only 2 of the 3 p orbitals can be perpendicular to the σ bond. This means that the third of the p orbitals is parallel to a given sigma bond and thus the atom will require invoking the d orbital in order to form quadruple bonds. In addition, in order to rotate an atom about a double bond, the pi bonds must break first.

Image of the orientation of 3 p orbitals and 1 s orbital. Illustrates how a 3rd pi bond can't be formed.
P orbitals are orthogonal to one another which prevents the formation of pi bonds between each to the same atom.

Practice: Determine the number of sigma and pi bonds.

1:How many σ and π bonds are in Ethyne?

image of ethyne, to determine the number of sigma and pi bonds

2: How many σ and π bonds are in glucose?

molecule of glucose

3: How many σ and π bonds are in salicylic acid?

salicylic acid, which has sigma and pi bonds

Answers:

1: Ethyne forms 3 σ and 2 π bonds

2: Glucose forms 29 σ bonds

3: Salicylic acid forms 12 σ and 4 π bonds