Sigma and pi bonds

Sigma and pi bonds are the most popular forms of covalent bonds. In a covalent bond, chemical bonding is achieved by sharing of electrons. Atoms contain orbitals, and orbitals hold electrons. During chemical bonding, the orbitals of two different atoms come close to each other. And the orbitals overlap. The overlapping of orbitals can be virtually thought of as the sharing of space between two nuclei, where the probability of finding bonding electrons is maximum. The resultant orbitals after overlapping are called molecular orbitals.

Different orbitals make different types of overlap in different situations. And based on a type of overlap, we classify them as a sigma or pi bond.

Note: The covalent bond is not limited to sigma and pi bonds. There are other types, too, such as delta bonds.

Sigma bond

In sigma bonds, each orbital of two atoms overlaps with each other head-to-head. Consider the simplest case of the sigma bond, where a diatomic molecule is formed by sharing an s-orbital of each atom.

In the above diagram, the s-orbital of one atom overlaps with the s-orbital of the second. In the individual atoms, the electron density is higher toward the center of the atom, i.e., near the nucleus. But after the formation of the sigma bond, the probability of finding the bonding electrons is maximum between two nuclei of the atoms.

The line joining the two nuclei is the bond axis. The atoms are free to rotate along the bond axis.

In sigma bonds, the overlapping is head-to-head; in other words, it is a direct overlap. This makes sigma bonds the strongest covalent bond. Sigma bonds are stronger, stable, and are less likely to break over pi bonds during a chemical reaction.

The greek symbol “σ” is used to denote them, and the electrons belonging to σ bonds are termed σ electrons.

Besides the s-s overlap, we can have s-p, p-p, s-dz2, dz2-dz2, and so forth.

The sigma bond is also formed with a hybrid orbital, for example, s-sp3, sp3-sp3, and so on. 

As an example, in ethane (H3C-CH3), the carbon atoms are sp3 hybridized. Each carbon bonds with three hydrogens by s-sp3 sigma bonds. And the two carbons are bonded by an sp3-sp3 sigma bond.

Two different atoms can only have one sigma bond between them. For atoms having multiple bonds, the first bond is sigma, and the remaining are pi. As in a double bond, we have one sigma and one pi (e.g., -C=C-).

In a triple bond, there is one sigma and two pi bonds (e.g., -C≡C-).

In most cases, two atoms make a sigma bond first before making a pi bond.

The following diagram lights some insight into how the overlapping of the different orbitals looks. The overlapping differs based on the size and shape of individual orbitals. The resultant is called the molecular orbital.

Pi bond

In contrast to sigma bonds, pi bonds are formed by the side-to-side overlap. The two lobes of an orbital (p-orbital) overlap with the two lobes of an orbital belonging to the second atom. When we say the pi bond, we usually mean the overlapping of two p orbitals.

The pi bond is a lateral overlap, as shown in the figure below.

For the formation of a pi bond, the parallelity of the two p orbitals is a must. In the above diagram, the two p orbitals parallel to each other also share a nodal plane, which passes through both nuclei. A nodal region is a region where the probability of finding an electron is zero. 

The pi bond restricts the rotation of individual atoms; otherwise, the parallelity of the orbitals might break. Further, the lateral overlap is weaker compared to the direct overlap. Hence, the pi bonds are weaker bonds over sigma bonds. They are easy to break and less stable than sigma.

The greek symbol “π” denotes pi bonds; the electrons in the π bond are said to be π electrons. 

Unlike sigma bonds, two atoms can have more than one pi bond, as in the case of acetylene (H-C≡C-H).

In acetylene, the carbon atoms are sp hybridized. Each carbon makes two sigma bonds, one with carbon and the second with hydrogen. The two unhybridized p orbitals on each carbon overlap (py-py and pz-pz) with each other to form two pi bonds.