Use the localized electron model to describe the bonding in \(\mathrm{C}_{2} \mathrm{H}_{2}\) (exists as \(\left.\mathrm{HCCH}\right)\).

Chemical bonding is the force that holds atoms together in molecules. It's a vital concept in chemistry, serving as the foundation for the structure and properties of matter. In the case of acetylene, or \(\mathrm{C}_2\mathrm{H}_2\), a specific type of chemical bonding takes place.

Each carbon atom in acetylene has to form four bonds, but these aren't just any bonds. Two types of bonding are at play: sigma (\(\sigma\)) bonds, which we'll explore soon, and pi (\(\pi\)) bonds, which arise from the lateral overlap of atomic orbitals. In acetylene, each carbon atom forms one \(\sigma\) bond with a hydrogen atom and shares another two \(\sigma\) bonds with the other carbon, which combined with the \(\pi\) bonds give rise to a triple bond. This triple bond is responsible for the unique properties of acetylene, including its linear shape and bond angles of approximately 180 degrees, making it an interesting study of how atomic interactions define molecular structure.

Sigma (\(\sigma\)) bonds are the strongest type of covalent bond and are formed by the head-on overlapping of atomic orbitals. In the context of acetylene's structure, each carbon atom in the molecule forms three \(\sigma\) bonds—two with the other carbon and one with a hydrogen atom.

It's these \(\sigma\) bonds that contribute to the molecule's structural framework. They provide the bond strength and rigidity that define the linear shape of the molecule. In acetylene, the \(\sigma\) bonds are made possible by the sp hybridization of the carbon atoms involved. The hybridization process involves merging the 2s orbital with two of the 2p orbitals, which then allows the carbon atoms to form strong, direct, and overlapping \(\sigma\) bonds with each other and with hydrogen.

Molecular Orbital Theory (MOT) is a sophisticated method for describing chemical bonding by using quantum mechanics. It treats electrons in molecules in a manner analogous to electrons in atoms, predicting how they occupy molecular orbitals that extend over the entire molecule.

In the creation of acetylene, MOT can further explain the electronic configuration and the nature of both \(\sigma\) and \(\pi\) bonding. Sp hybridization leads to the formation of new orbitals that are lower in energy and more stable than the original atomic orbitals. In MOT, when the sp hybridized orbitals of one carbon overlap with those of another carbon, or with the s orbital of hydrogen, it results in the creation of \(\sigma\) molecular orbitals. These are the orbitals occupied by the bonding electrons, and their symmetrical shape along the internuclear axis is what characterizes \(\sigma\) bonds. This theory helps to rationalize why bonds form as they do, providing a deeper understanding of the nature of covalent bonding and how it shapes the chemical and physical properties of molecules like acetylene.