How are sigma and pi bonds formed from atomic orbitals?

Sigma and pi bonds are formed from atomic orbitals through the process of overlapping and sharing of electrons.

Sigma (σ) bonds are formed when atomic orbitals overlap along the axis connecting the two bonding atoms. This overlap can occur between any combination of orbital types (s, p, d, f), as long as they are oriented along the axis. For example, a sigma bond can be formed from the overlap of two s orbitals (as in H2), an s and a p orbital (as in CH4), or two p orbitals (as in F2). The overlapping of orbitals results in a region of high electron density between the two nuclei, creating a strong bond. Sigma bonds are the strongest type of covalent bond and are the first to form in a bond formation process.

Pi (π) bonds, on the other hand, are formed when parallel p orbitals overlap. Unlike sigma bonds, pi bonds do not form along the axis connecting the two bonding atoms. Instead, they form above and below this axis. This overlap creates two regions of high electron density, one above and one below the axis. Pi bonds are weaker than sigma bonds because the overlap is not as effective. They are usually found in double and triple bonds, supplementing the sigma bond. For example, in a carbon-carbon double bond, one of the bonds is a sigma bond and the other is a pi bond.

In summary, sigma and pi bonds are formed from atomic orbitals through the process of overlapping. The type of overlap (axial or parallel) and the types of orbitals involved determine whether a sigma or a pi bond is formed. The resulting regions of high electron density create the bond between the atoms. Understanding the formation of these bonds is crucial for understanding the structure and reactivity of molecules.