Molecular Orbitals, Lewis Acids, and Bond Rotation: General Chemistry Study Notes

Molecular Orbitals and Bonding

Introduction to Molecular Orbitals

Molecular orbital (MO) theory describes the behavior of electrons in molecules by combining atomic orbitals to form molecular orbitals. These orbitals can be bonding, anti-bonding, or non-bonding, and their occupation determines the stability and properties of molecules.

• Bonding Molecular Orbitals: Formed by constructive interference of atomic orbitals, resulting in increased electron density between nuclei and a stabilizing effect.

• Anti-bonding Molecular Orbitals: Formed by destructive interference, leading to a node between nuclei and a destabilizing effect.

• Non-bonding Molecular Orbitals: Orbitals that do not contribute significantly to bonding or anti-bonding interactions.

Example: The combination of two hydrogen 1s orbitals forms a bonding (σ) and an anti-bonding (σ*) molecular orbital.

Electron Excitation in Molecular Orbitals

Electrons can be excited from lower-energy molecular orbitals (such as π) to higher-energy orbitals (such as π*) by absorption of energy, typically in the form of photons.

• Ground State: Electrons occupy the lowest available energy orbitals.

• Excited State: Upon absorption of energy, electrons move to higher-energy orbitals (e.g., from π to π*).

Example: In a conjugated system, absorption of UV light can promote an electron from a π orbital to a π* orbital.

Orbital Occupation and Lewis Acids

A Lewis acid is a substance that can accept an electron pair. The orbital that accepts the electron pair is typically an unoccupied hybrid orbital appropriate to the geometry of the molecule.

• Key Point: For SiH3+, the new electron will occupy an unoccupied sp3 hybrid orbital, consistent with the tetrahedral geometry of silicon compounds.

Example: SiH3+ acts as a Lewis acid by accepting an electron pair into its vacant sp3 orbital.

Molecular Orbital Diagrams and Electron Placement

MO Diagram for C–F Bond in Fluoromethane

The molecular orbital diagram for a C–F bond includes both σ (bonding) and σ* (anti-bonding) orbitals. Adding electrons to this system will fill the anti-bonding orbital after the bonding orbital is filled.

• Key Point: If two more electrons are added to the C–F bond, they will occupy the σ* (anti-bonding) orbital.

Example: In the MO diagram, the σ orbital is filled first, followed by the σ* orbital as more electrons are added.

Formation of Molecular Orbitals from Atomic Orbitals

Types of Molecular Orbitals Formed

When atomic orbitals combine, the type of molecular orbital formed depends on their orientation and phase.

• σ (Sigma) Bonding Orbital: Formed by head-on overlap of atomic orbitals (e.g., s-s, s-p, or p-p along the internuclear axis).

• π (Pi) Bonding Orbital: Formed by side-on overlap of parallel p orbitals.

• σ* and π* Anti-bonding Orbitals: Formed when the overlap is out of phase, resulting in a node between nuclei.

Example: The combination of two p orbitals can result in either a π bonding or π* anti-bonding molecular orbital, depending on their relative phases.

Table: Types of Molecular Orbitals Formed

Atomic Orbital Combination	Bonding MO	Anti-bonding MO
Head-on (s-s, s-p, p-p)	σ	σ*
Side-on (p-p)	π	π*

Bond Rotation and Molecular Geometry

Rotation Around Double Bonds

Free rotation around a bond depends on the type of bond present. Sigma (σ) bonds allow free rotation, while pi (π) bonds restrict rotation due to the electron density above and below the plane of the nuclei.

• Key Point: In trans-hex-3-ene, the C3–C4 bond is a double bond (one σ and one π). The presence of the π bond prevents free rotation around this bond.

• Explanation: Rotation would break the side-on overlap of the p orbitals forming the π bond, which requires significant energy.

Example: Alkenes (such as trans-hex-3-ene) exhibit restricted rotation around the double bond, leading to cis/trans isomerism.

Table: Bond Type and Rotational Freedom

Bond Type	Rotation Possible?	Reason
Single (σ)	Yes	Electron density is along the axis, allowing rotation
Double (σ + π)	No	π bond restricts rotation due to side-on overlap

Key Definitions and Formulas

• Lewis Acid: A substance that can accept an electron pair.

• Bond Order: $\text{Bond Order} = \frac{\text{Number of bonding electrons} - \text{Number of anti-bonding electrons}}{2}$

• Molecular Orbital Energy Diagram: Shows the relative energies and occupation of molecular orbitals formed from atomic orbitals.

Summary Table: Molecular Orbital Concepts

Concept	Description	Example
Lewis Acid	Accepts electron pair into vacant orbital	SiH3+
Electron Excitation	Electron promoted from π to π* orbital	UV absorption in conjugated systems
Bond Rotation	Restricted by π bonds, allowed by σ bonds	Alkene vs. Alkane

Additional info: These notes expand on the original questions by providing academic context, definitions, and examples relevant to General Chemistry molecular orbital theory and bonding.