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

Sigma (σ) bonds are the strongest and the most common type of covalent bond between two atoms, where the electron density is symmetric and concentrated along the internuclear (bonding) axis. In the molecular orbital model, σ bonds are formed via either end-on-end overlap of atomic orbitals or by a side-to-side overlap if the orbitals have proper symmetry.

Pi (π) bonds are covalent bonds formed by the side-to-side overlap of atomic orbitals, perpendicular to the internuclear axis. In the molecular orbital model, these are not symmetric around the internuclear axis, and the electron density is concentrated in two lobes on opposite sides of the atoms. When atoms form multiple covalent bonds, π bonds commonly occur after a σ bond has already been formed between them.

Sigma (σ) bonds form from various types of atomic orbital overlapping: 1. s-s overlap: Two s orbitals from different atoms can overlap end-to-end to form a σ bond, in which the electron density is concentrated between the two nuclei. 2. s-p overlap: An s orbital from one atom can overlap with a p orbital from another atom, with the p orbital oriented end-to-end along the internuclear axis. The axial orientation is critical, as an off-axis overlap would not lead to the desired symmetric electron distribution. 3. p-p overlap: Two p orbitals from different atoms can overlap end-to-end along the internuclear axis. This axial overlap creates a σ bond with electron density concentrated between the two nuclei.

Pi (π) bonds form from the side-to-side overlap of atomic orbitals, specifically p orbitals. When two p orbitals from different atoms interact side-to-side, they create a π bond in which the electron density is concentrated in two lobes on opposite sides of the internuclear axis. Therefore, π bonds are formed from p-p orbital overlap perpendicular to the internuclear axis.

After discussing the formation and basics of σ and π bonds, we can highlight their differences: 1. Orbitals Involved: σ bonds can occur between different atomic orbitals (s-s, s-p, and p-p overlap), while π bonds only form from the side-to-side overlap of p orbitals. 2. Electron Density: σ bonds have electron density symmetrically distributed along the internuclear axis, while π bonds have electron density concentrated in two lobes parallel to each other but perpendicular to the internuclear axis. 3. Strength: Since σ bonds involve end-to-end overlap of atomic orbitals along the internuclear axis, their electron density is concentrated between the nuclei, resulting in stronger bonds. On the other hand, π bonds have electron density above and below the internuclear axis, leading to weaker bonds and easier chemical reactions.