Valence Bond Theory and Sigma/Pi Bonding: Structured Study Notes

Valence Bond (VB) Theory

Concept and Principles of Valence Bond Theory

Valence Bond Theory explains how covalent bonds form through the overlap of atomic orbitals, resulting in a shared pair of electrons between two atoms. The theory provides a quantum mechanical description of bonding and is foundational for understanding molecular structure.

• Orbital Overlap: Covalent bonds form when atomic orbitals from two atoms overlap, allowing electrons to be shared.

• Electron Pairing: Overlapping orbitals hold two electrons of opposite spin, typically one from each atom.

• Localization: Bonding electrons are localized in the region of space between the nuclei, with a higher probability of being found there.

• Simultaneous Association: Both electrons are associated with both nuclei, stabilizing the bond.

Key Principle: A covalent bond forms when orbitals of two atoms overlap and a pair of electrons occupy the overlap region.

• Opposing Spins: The electron pair must have opposite spins.

• Maximum Overlap: Greater overlap leads to stronger bonds.

• Hybridization: Atomic orbitals may mix (hybridize) to maximize overlap and achieve specific molecular geometries.

Example: The formation of the H2 molecule involves the overlap of two hydrogen 1s orbitals, resulting in a stable covalent bond at an optimal internuclear distance.

Additional info: The energy diagram for H2 shows that as two H atoms approach, energy decreases until reaching a minimum (bond length), then increases due to nuclear repulsion.

Sigma (σ) and Pi (π) Bonding

Atomic Orbital Overlap: Sigma and Pi Bonds

Covalent bonds can be classified based on the type of orbital overlap: sigma (σ) bonds result from end-to-end overlap, while pi (π) bonds result from side-to-side overlap of unhybridized p orbitals.

• Sigma (σ) Bonds: Formed by end-to-end overlap of orbitals. Electron density is greatest along the axis connecting the two nuclei.

• Types of Sigma Overlap:

  • Overlap of two s orbitals

  • Overlap of an s and a p orbital

  • Overlap of two p orbitals (along the axis)

• Properties: Sigma bonds describe single bonds and allow free rotation around the bond axis.

Example: In H2, the bond is a sigma bond formed by two 1s orbitals.

• Pi (π) Bonds: Formed by side-to-side overlap of two unhybridized p orbitals. Electron density is concentrated above and below the internuclear axis.

• Node: The internuclear axis is a node (no electron density).

• Properties: Pi bonds restrict rotation due to the electron density distribution.

• Bond Composition: All single bonds are sigma bonds; double bonds consist of one sigma and one pi bond; triple bonds consist of one sigma and two pi bonds.

Example: In ethylene (C2H4), the C=C double bond consists of one sigma and one pi bond.

Visual Representation of Bonding

The diagrams show how atomic orbitals overlap to form sigma and pi bonds. Maximum overlap occurs when orbitals are oriented along the direct line between the two nuclei.

Bond Type	Orbital Overlap	Electron Density Location	Rotation
Sigma (σ)	End-to-end (s-s, s-p, p-p)	Along bond axis	Free rotation
Pi (π)	Side-to-side (p-p, unhybridized)	Above and below bond axis	No rotation

Additional info: Pi bonds are always associated with sigma bonds in multiple bonds. The presence of pi bonds restricts rotation and affects molecular geometry.