Chapter 8.5 to 9: Molecular Orbital Theory & Hybridization

What does the sign (+/–) of a wavefunction represent?

The phase of the orbital, not charge. Phase matters for orbital interactions (constructive vs destructive).

What is a radial node?

A spherical region where the probability of finding an electron is zero. Formula: n – l – 1.

What is an angular node?

A planar (flat) region where the wavefunction changes sign. Count = l

Total number of nodes formula?

n – 1

Do atomic orbitals describe atoms or molecules?

Atoms. That’s why we need MO theory for molecules.

What is LCAO?

A method that combines atomic orbitals to create molecular orbitals.

Rules for orbitals to mix?

• Must be similar in energy

• Must overlap

• Number of orbitals is conserved

What happens when two atomic orbitals combine?

They form two MOs — one bonding (σ) and one antibonding (σ*).

What is a σ bond?

Overlap on the internuclear axis.

What is a π bond?

Side-to-side overlap; electron density above and below the axis.

What is a σ* orbital?

Antibonding orbital formed by destructive interference.

MO bond order formula

(bonding electrons – antibonding electrons)/2

What does a bond order of 0 mean?

The molecule does not form (ex: He₂).

How many p-p interactions are possible?

1 σ + 2 π (and similarly 1 σ* + 2 π*)

Why do some period-2 MOs have flipped ordering?

Small energy gap between 2s and 2p causes 2s–2p mixing.

Which diatomics have “flipped” ordering?

B₂, C₂, N₂ (σ2p is ABOVE π2p).

Which have “normal” ordering?

O₂, F₂, Ne₂ (σ2p is BELOW π2p).

O₂: paramagnetic or diamagnetic?

Paramagnetic — has two unpaired electrons in π* orbitals.

What determines hybridization?

The steric number (electron domains around central atom).

Steric number 4 → hybridization?

sp³ (tetrahedral electronic geometry).

Steric number 3 → hybridization?

sp² (trigonal planar electronic geometry).

Steric number 2 → hybridization?

sp (linear electronic geometry).

σ vs π bonding in single, double, triple bonds

• Single: 1 σ

• Double: 1 σ + 1 π

• Triple: 1 σ + 2 π

Why does hybridization happen?

To maximize bonding and stabilize the molecule by forming equivalent orbitals.

sp³ shape & bond angle

Tetrahedral, ~109.5°

sp² shape & bond angle

Trigonal planar, ~120°

sp shape & bond angle

Linear, 180°

Steric number 5 hybridization?

sp³d

Steric number 6 hybridization?

sp³d²

Why can’t double bonds rotate?

Rotation breaks the π bond because the p-orbitals must stay parallel.

What geometry does a π bond enforce?

Planarity around the atoms participating in the π bond.

Do electrons “jump” between resonance structures?

No — electrons are delocalized across the structure.

What does delocalization mean?

π electrons spread out over multiple bonds simultaneously.

What is the actual structure of a resonance-stabilized molecule?

The weighted average (hybrid) of all resonance structures.

Example of delocalization?

The π electrons in NO₃⁻ are spread equally among all N–O bonds.

What must be conserved when forming molecular orbitals?

Number of orbitals.

What are the types of MO interactions for p-orbitals?

σ, σ*, π, π*

What determines if a molecule is paramagnetic?

unpaired electrons in its molecular orbitals.

What kind of overlap makes a σ bond?

Head-to-head overlap.

What kind of overlap makes a π bond?

Side-to-side overlap of p orbitals.

What is the steric number?

Number of σ bonds + lone pairs on a central atom.

How do π bonds affect structure?

Prevent rotation; enforce planar geometry.

What is delocalization?

π electrons spreading across multiple atoms due to orbital overlap.