In the molecular orbital model, compare and contrast \(\sigma\) bonds with \(\pi\) bonds. What orbitals form the \(\sigma\) bonds and what orbit- als form the \(\pi\) bonds? Assume the \(z\) -axis is the internuclear axis.

The molecular orbital model explains the formation of chemical bonds through the merging of atomic orbitals. There are two types of bonds in this model: the sigma (σ) bond and the pi (π) bond. Both of these bonds are formed by the overlapping of atomic orbitals, but the way they form and their characteristics are different.

Sigma (σ) bonds are formed by the head-to-head overlapping of atomic orbitals. They are cylindrical in shape, symmetric along the internuclear axis (z-axis in this case), and have an electron probability distribution concentrated on the internuclear axis. The electron cloud in a σ bond directly overlaps between the two bonded atoms. Due to this direct overlapping, σ bonds are generally stronger, resulting in greater stability and more significant bond energy.

The overlapping of s orbitals (1s, 2s, 3s, etc.) and the z-axis component of p orbitals (pz) form σ bonds. For example, when two hydrogen atoms bond through their 1s orbitals, a σ bond is formed. 1s-1s, 2s-2s, 1s-2s, and 2pz-2pz overlapping combinations can produce σ bonds.

Pi (π) bonds are formed by the side-to-side overlapping of atomic orbitals. Unlike σ bonds, π bonds are not cylindrical nor symmetric along the internuclear axis. Instead, the electron probability distribution in π bonds is found above and below the internuclear axis. As a result, π bonds are generally weaker than σ bonds due to less effective orbital overlap and larger electron cloud separation from the internuclear axis.

The x-axis (px) and y-axis (py) components of p orbitals form π bonds. Since these components are perpendicular to the internuclear axis (z-axis), the resulting bond structure will have electron distribution above and below the z-axis. 2px-2px and 2py-2py overlapping combinations can produce π bonds. To summarize, σ bonds are formed by the head-to-head overlap of atomic orbitals (s orbitals and the z-component of p orbitals), while π bonds are formed by the side-to-side overlap of atomic orbitals (x and y components of p orbitals). Sigma bonds are stronger and more stable due to more effective orbital overlap, while pi bonds are weaker due to less effective orbital overlap and larger electron cloud separation from the internuclear axis.