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Before We Start: Why Do We Need Molecular Orbital Theory?

Up until now, you've probably learned:

• Lewis Structures

• VSEPR

• Hybridization

 

These all belong to the Localized Electron Model.

Localized means:

Electrons belong to one atom or are shared between two specific atoms.

 

Example:

H—H

 

The bonding electrons are thought to exist only between these two hydrogen atoms.

This works really well...

 

BUT it cannot explain everything.

For example:

• Why O₂ is magnetic

• Why some molecules exist while others don't

• Why some bonds are stronger than others

• Resonance and delocalized electrons

So chemists developed Molecular Orbital Theory (MO Theory).

The Big Idea of Molecular Orbital Theory

Instead of electrons belonging to ONE bond...

MO theory says:

Electrons belong to the entire molecule.

Think of the molecule as one giant object instead of separate atoms.

Imagine two houses.

Localized model:

• Each family stays inside its own house.

MO theory:

• Everyone can move freely throughout BOTH houses.

Electrons are spread across the whole molecule.

This is called delocalization.

 

What is a Molecular Orbital?

First remember:

Atomic Orbital (AO)

An atomic orbital belongs to one atom.

Examples:

• 1s

• 2s

• 2px

• 2py

• 2pz

These are where electrons live before atoms bond.

 

Molecular Orbital (MO)

A molecular orbital belongs to the entire molecule.

Electrons no longer belong to just one atom.

Instead, they occupy orbitals that spread over both nuclei.

How Do Molecular Orbitals Form?

This is called:

LCAO

Linear Combination of Atomic Orbitals

Sounds scary.

It simply means:

We mathematically combine atomic orbitals together to make new orbitals.

Think of it like:

AO + AO → MO

Example:

1s + 1s

becomes

• one bonding MO

• one antibonding MO

This ALWAYS happens.

 

VERY IMPORTANT RULE

Whenever atomic orbitals combine:

The number of molecular orbitals formed ALWAYS equals the number of atomic orbitals used.

Examples

2 atomic orbitals

↓

2 molecular orbitals

4 atomic orbitals

↓

4 molecular orbitals

6 atomic orbitals

↓

6 molecular orbitals

Nothing disappears.

Orbitals are simply rearranged.

 

Two Types of Molecular Orbitals

Whenever two orbitals combine...

You ALWAYS get:

1. Bonding Orbital

and

2. Antibonding Orbital

You never get only one.

 

Bonding Orbital (σ or π)

These are the GOOD orbitals.

How do they form?

The waves line up.

Positive overlaps positive.

Negative overlaps negative.

This is called

 

Constructive Interference

Think about two ocean waves.

If both waves go upward together...

They make one BIGGER wave.

Same idea here.

 

What Happens?

Electron density increases between the nuclei.

That means:

More electrons sit between the atoms.

Those electrons attract BOTH nuclei at the same time.

Imagine two positive magnets.

Normally they repel.

Now imagine putting negative charges between them.

Those negatives pull both positives inward.

The atoms are pulled together.

A bond forms.

 

Bonding Orbitals Have

✅ lower energy

✅ greater stability

✅ electrons between nuclei

✅ stronger bonding

Lower energy always means more stable.

Antibonding Orbitals (σ* or π*)

These are the BAD orbitals.

Notice the star (*).

The star ALWAYS means

antibonding

Example

σ*

π*

 

How do antibonding orbitals form?

Positive overlaps negative.

The waves cancel.

This is called

Destructive Interference

Imagine two waves.

One goes up.

One goes down.

They cancel.

 

What Happens?

Electron density disappears between nuclei.

Instead...

A gap forms.

This gap is called

a node

What is a Node?

A node is

a region where there is ZERO probability of finding electrons.

No electrons exist there.

Since there are no electrons between the nuclei...

Nothing pulls the atoms together.

Instead...

The positive nuclei repel.

The bond becomes weaker.

 

Antibonding Orbitals Have

Higher energy

Less stable

Node between nuclei

Weaken bonding

 

Easy Memory Trick

Bonding orbital

↓

Electrons BETWEEN nuclei

↓

Atoms pulled together

↓

Lower energy

↓

Stable

 

Antibonding orbital

↓

No electrons between nuclei

↓

Atoms repel

↓

Higher energy

↓

Unstable

Sigma (σ) Molecular Orbitals

Now the slides move into p orbitals.

First...

Remember p orbitals have three directions.

• px

• py

• pz

Each direction can overlap differently.

 

Sigma Bonds from p Orbitals

The slides use

2pz + 2pz

The two p orbitals point directly at each other.

Imagine two balloons touching tip-to-tip.

This is called

End-to-End Overlap

This produces

σ2p

and

σ*2p

 

Bonding Sigma Orbital

The orbitals add together.

Electron density increases in the middle.

Lower energy.

Stable.

 

Antibonding Sigma Orbital

The orbitals subtract.

A node forms.

Higher energy.

Unstable.

Why is it Called Sigma?

Sigma overlap happens

DIRECTLY along the line connecting both nuclei.

Think

Head-on collision.

 

 

 

Pi (π) Molecular Orbitals

Now instead of pointing directly at each other...

The p orbitals sit side-by-side.

Like two hot dogs next to each other.

This is

Side-to-Side Overlap

 

This creates

π2p

and

π*2p

 

Again...

Adding orbitals

↓

Bonding π orbital

Lower energy

 

Subtracting orbitals

↓

Antibonding π*

Higher energy

Node forms

Why Are There TWO π Orbitals?

Remember

There are

px

and

py

Both can overlap sideways.

So you actually get

πx

and

πy

They have

• identical energy

• different orientation

This is called

Degenerate Orbitals

Definition:

Orbitals that have the same energy.

 

Sigma vs Pi

Sigma	Pi
End-to-end overlap	Side-to-side overlap
Usually stronger	Usually weaker
Electron density directly between nuclei	Electron density above and below bond axis
Forms first	Forms after sigma

Can Any Orbitals Combine?

NO.

Two things MUST match.

 

Rule 1 — Energy Match

Orbitals must have similar energies.

Example

2p with 2p

✅ Works

1s with 4p

❌ Doesn't work well.

Why?

The energy difference is too large.

They cannot mix effectively.

Think about trying to dance with someone jumping on a trampoline while you're standing on the floor.

The motions don't match.

 

Rule 2 — Symmetry Match

The shapes must line up correctly.

Even if energies match...

If the orbitals point the wrong way...

They cannot overlap.

Example

Two p orbitals facing each other

✅ Good overlap

One p orbital sideways while another points forward

❌ Almost no overlap

 

BOTH Conditions Must Be True

Good bonding requires

✔ Similar energies

AND

✔ Proper orientation

Missing either one means little or no molecular orbital forms.

 

Big Picture So Far

1. Atoms have atomic orbitals.

2. When atoms approach each other, their atomic orbitals combine.

3. Every pair of atomic orbitals forms:

   • one bonding orbital

   • one antibonding orbital

4. Bonding orbitals:

   • lower energy

   • electrons between nuclei

   • stabilize molecules

5. Antibonding orbitals:

   • higher energy

   • node between nuclei

   • weaken molecules

6. Sigma bonds come from head-on overlap.

7. Pi bonds come from side-by-side overlap.

8. Orbitals only combine if they have:

   • similar energies

   • matching symmetry

 Exam Tips

Memorize these:

Bonding

• Constructive interference

• Lower energy

• Stable

• Electrons between nuclei

Antibonding

• Destructive interference

• Higher energy

• Node

• Unstable

 

Sigma

• Head-on overlap

• Stronger

 

Pi

• Side-by-side overlap

• Weaker

 

LCAO

• Atomic orbitals combine

• Number of MOs = number of AOs

 

What is the Purpose of MO Diagrams?

Molecular Orbital (MO) diagrams show where electrons go after atoms bond.

MO diagrams help answer these questions:

• Does the molecule exist?

• How strong is the bond?

• Is the molecule magnetic?

• How many bonds are there?

Everything depends on where the electrons are placed.

 

 

 

Bond Order (BO)

Definition

Bond order tells you how strong a bond is.

It compares:

• Electrons that help form the bond (bonding electrons)

• Electrons that weaken the bond (antibonding electrons)

Formula:

Bond Order = (Bonding Electrons − Antibonding Electrons) ÷ 2

 

Why do we divide by 2?

Each complete bond contains 2 electrons.

Examples:

• 2 bonding electrons = 1 bond

• 4 bonding electrons = 2 bonds

That's why we divide by 2.

 

Interpreting Bond Order

Bond Order > 0

• The molecule exists.

• More electrons help the bond than hurt it.

Bond Order = 0

• The molecule does NOT exist.

• Bonding and antibonding effects completely cancel.

Higher Bond Order means:

• Stronger bond

• Shorter bond

• Harder to break

Examples:

• BO = 3 → Very strong bond

• BO = 2 → Double bond

• BO = 1 → Single bond

• BO = 0.5 → Weak bond

• BO = 0 → No bond

Memory Trick:

Bonding electrons "pull" atoms together.

Antibonding electrons "push" atoms apart.

 

Rules for Filling Molecular Orbitals

Electrons fill molecular orbitals exactly like atomic orbitals.

Rule 1: Aufbau Principle

Fill the lowest-energy orbitals first.

Electrons always want the lowest possible energy.

 

Rule 2: Pauli Exclusion Principle

Each orbital can hold a maximum of 2 electrons.

The two electrons must have opposite spins.

Correct:

↑↓

Incorrect:

↑↑

 

Rule 3: Hund's Rule

If two orbitals have the same energy:

• Put one electron in each orbital first.

• Pair electrons only after each orbital has one electron.

Correct:

↑ ↑

Incorrect:

↑↓ empty

 

MO Diagram for H₂

Step 1: Count electrons.

Each hydrogen atom has 1 electron.

2 H atoms = 2 total electrons.

 

Step 2: Form molecular orbitals.

Two 1s orbitals combine to form:

• σ1s (bonding, lower energy)

• σ1s* (antibonding, higher energy)

 

Step 3: Fill the orbitals.

Both electrons go into the lowest-energy orbital.

Electron configuration:

(σ1s)²

 

Step 4: Calculate bond order.

Bonding electrons = 2

Antibonding electrons = 0

Bond Order = (2 − 0) ÷ 2 = 1

 

What does this tell us?

• H₂ exists.

• It has one single bond.

• The bond is stable.

 

Magnetism of H₂

Both electrons are paired.

There are no unpaired electrons.

Therefore:

H₂ is diamagnetic.

 

Diamagnetic

Definition:

A substance with ALL electrons paired.

Properties:

• Not attracted to a magnetic field.

Easy Memory Trick:

Diamagnetic = Double = Every electron has a partner.

MO Diagram for H₂⁻

One extra electron is added.

Total electrons = 3

Electron configuration:

(σ1s)²(σ1s*)¹

 

Calculate Bond Order

Bonding electrons = 2

Antibonding electrons = 1

Bond Order = (2 − 1) ÷ 2 = 0.5

 

What does this mean?

• H₂⁻ exists.

• The bond is weaker than H₂.

Why?

The extra electron went into an antibonding orbital, which weakens the bond.

 

 

Magnetism of H₂⁻

One electron is unpaired.

Therefore:

H₂⁻ is paramagnetic.

 

Paramagnetic

Definition:

A substance with one or more unpaired electrons.

Properties:

• Attracted to a magnetic field.

Easy Memory Trick:

Paramagnetic = Partial pair = Someone is left alone.

Compare H₂ and H₂⁻

H₂

• Bond Order = 1

• Stronger bond

• Diamagnetic

• Stable

H₂⁻

• Bond Order = 0.5

• Weaker bond

• Paramagnetic

• Still exists

Important:

Adding an electron does NOT always strengthen a bond.

It depends on which orbital the electron enters.

If it enters an antibonding orbital, the bond becomes weaker.

MO Diagram for H₂⁺

Remove one electron from H₂.

Total electrons = 1

Electron configuration:

(σ1s)¹

 

Calculate Bond Order

Bonding electrons = 1

Antibonding electrons = 0

Bond Order = (1 − 0) ÷ 2 = 0.5

 

What does this mean?

H₂⁺ exists.

It has a weak bond.

 

One-Electron Bond

Normally:

• 2 electrons make one bond.

In H₂⁺:

• Only 1 electron forms the bond.

This is called a one-electron bond.

It is weaker than a normal bond but still exists.

 

Magnetism of H₂⁺

One electron is unpaired.

Therefore:

H₂⁺ is paramagnetic.

 

Compare Hydrogen Species

H₂

• Bond Order = 1

• Exists

• Diamagnetic

H₂⁺

• Bond Order = 0.5

• Exists

• Paramagnetic

H₂⁻

• Bond Order = 0.5

• Exists

• Paramagnetic

MO Diagram for He₂

Each helium atom has 2 electrons.

Total electrons = 4

Electron configuration:

(σ1s)²(σ1s*)²

 

Calculate Bond Order

Bonding electrons = 2

Antibonding electrons = 2

Bond Order = (2 − 2) ÷ 2 = 0

 

What does this mean?

He₂ does NOT exist.

The bonding electrons and antibonding electrons completely cancel each other.

No bond forms.

 

Why Doesn't He₂ Exist?

Helium already has a full 1s orbital.

When another helium atom approaches:

• The bonding orbital fills first.

• The remaining electrons must enter the antibonding orbital.

Those antibonding electrons cancel the stabilization provided by the bonding electrons.

Result:

Bond Order = 0

No bond forms.

 

Magnetism of He₂

All electrons are paired.

Therefore:

He₂ would be diamagnetic if it existed.

 

MO Diagram for He₂⁺

Remove one electron from He₂.

Electron configuration:

(σ1s)²(σ1s*)¹

 

Calculate Bond Order

Bonding electrons = 2

Antibonding electrons = 1

Bond Order = (2 − 1) ÷ 2 = 0.5

 

What does this mean?

He₂⁺ exists.

It has a weak bond.

 

Magnetism of He₂⁺

One electron is unpaired.

Therefore:

He₂⁺ is paramagnetic.

Summary of Helium Species

He₂

• Bond Order = 0

• Does not exist

• Diamagnetic

He₂⁺

• Bond Order = 0.5

• Exists

• Paramagnetic

Steps for Solving Any MO Diagram Problem

Step 1

Count the total number of electrons.

Step 2

Draw the correct MO diagram.

Step 3

Fill the orbitals from lowest energy to highest energy.

Step 4

Use Hund's Rule if orbitals have equal energy.

Step 5

Count the number of bonding electrons.

Step 6

Count the number of antibonding electrons.

Step 7

Calculate bond order.

Bond Order = (Bonding − Antibonding) ÷ 2

Step 8

Determine if the molecule exists.

• BO > 0 → Exists

• BO = 0 → Does not exist

Step 9

Determine magnetism.

• All electrons paired → Diamagnetic

• At least one unpaired electron → Paramagnetic

Key Rules to Memorize

• Number of molecular orbitals = Number of atomic orbitals used.

• Two atomic orbitals always form one bonding MO and one antibonding MO.

• Bonding orbitals are lower in energy and stabilize the molecule.

• Antibonding orbitals are higher in energy and weaken the molecule.

• Fill lower-energy orbitals first (Aufbau Principle).

• Maximum of 2 electrons per orbital (Pauli Exclusion Principle).

• Equal-energy orbitals fill singly first (Hund's Rule).

• Positive bond order means the molecule exists.

• Larger bond order means a stronger bond.

• All paired electrons = Diamagnetic.

• Any unpaired electrons = Paramagnetic.

 

Exam Tips

1. Adding an electron does NOT always make a bond stronger.

• If it goes into a bonding orbital → bond becomes stronger.

• If it goes into an antibonding orbital → bond becomes weaker.

1. You do NOT need to memorize whether molecules exist.

Just calculate the bond order.

• BO > 0 → Exists

• BO = 0 → Does not exist

1. You do NOT need to memorize magnetism.

Simply check the electrons.

• All paired → Diamagnetic

• Any unpaired → Paramagnetic

Molecular Orbital (MO) Diagrams for Period 2 Molecules (Li₂–F₂)

Why Are We Learning This?

So far, we only looked at hydrogen and helium because they only have 1s orbitals.

Now we're moving to Period 2 elements:

• Li

• Be

• B

• C

• N

• O

• F

• Ne

These atoms have 2s and 2p orbitals, making their MO diagrams more complicated.

The goal is to predict:

• Whether the molecule exists

• Bond order

• Bond strength

• Magnetism

 

Homonuclear Diatomic Molecules

Definition

"Homonuclear" means:

Both atoms are the same element.

Examples:

• H₂

• N₂

• O₂

• F₂

• Cl₂

"Homo" = Same

"Diatomic" = Two atoms

So a homonuclear diatomic molecule is simply two identical atoms bonded together.

Only Valence Electrons Matter

When drawing MO diagrams, ignore the core electrons.

Only use valence electrons because they participate in bonding.

Example:

Nitrogen

Electron configuration:

1s² 2s² 2p³

Ignore:

1s²

Use only:

2s²2p³

Reason:

Core electrons stay close to the nucleus and do not help form chemical bonds.

 

Number of Valence Electrons

Each molecule has a different number of valence electrons.

Examples:

Li₂

• 1 + 1 = 2 valence electrons

Be₂

• 2 + 2 = 4 valence electrons

B₂

• 3 + 3 = 6 valence electrons

C₂

• 4 + 4 = 8 valence electrons

N₂

• 5 + 5 = 10 valence electrons

O₂

• 6 + 6 = 12 valence electrons

F₂

• 7 + 7 = 14 valence electrons

Ne₂

• 8 + 8 = 16 valence electrons

Li₂

Lithium electron configuration:

1s²2s¹

Ignore the 1s electrons.

Only the two 2s electrons bond.

MO configuration:

(σ2s)²

Bonding electrons = 2

Antibonding electrons = 0

Bond Order:

(2 − 0) ÷ 2 = 1

Result:

• Li₂ exists.

• Single bond.

• Diamagnetic (all electrons paired).

 

Be₂

Beryllium electron configuration:

1s²2s²

Each Be contributes 2 valence electrons.

Total valence electrons = 4

Configuration:

(σ2s)²(σ2s*)²

Bonding electrons = 2

Antibonding electrons = 2

Bond Order:

(2 − 2) ÷ 2 = 0

Result:

• Be₂ does NOT exist.

• Bonding and antibonding cancel each other.

• Diamagnetic (all electrons paired).

Once We Reach Boron...

Starting with boron, atoms now have electrons in 2p orbitals.

This creates more molecular orbitals.

Instead of only:

• σ2s

• σ2s*

we now also have:

• π2p

• σ2p

• π2p*

• σ2p*

The diagrams become larger because there are more orbitals available.

Two Different MO Diagrams

This is one of the most confusing topics in General Chemistry.

There are TWO possible MO energy diagrams for Period 2 molecules.

Which one you use depends on the element.

 

Diagram 1

Used for:

• Li₂

• Be₂

• B₂

• C₂

• N₂

These have atomic numbers 7 or less.

 

Diagram 2

Used for:

• O₂

• F₂

• Ne₂

These have atomic numbers 8 or greater.

 

Why Are There Two Different Diagrams?

The answer is called:

2s–2p Mixing

Also called:

s-p mixing

 

What Is 2s–2p Mixing?

Normally:

2s orbitals and 2p orbitals are separate.

But for lighter atoms (Li–N)...

The energies of the 2s and 2p orbitals are very close together.

Because their energies are similar,

they interact and mix.

This changes the order of the molecular orbitals.

 

Easy Analogy

Imagine two students studying.

If they sit close together,

they can easily talk and help each other.

If they sit on opposite sides of the room,

they barely interact.

Same idea here.

If orbital energies are close,

they mix.

If orbital energies are far apart,

they do not.

 

cont

Large 2s–2p Mixing

Occurs in:

Li

Be

B

C

N

Reason:

Their 2s and 2p orbitals have similar energies.

Because they mix,

the MO energy order changes.

 

Small (Almost No) 2s–2p Mixing

Occurs in:

O

F

Ne

Reason:

The 2s orbital is much lower in energy than the 2p orbital.

They are too far apart in energy to mix significantly.

So the orbitals stay in their normal order.

 

The Important Difference

For Li₂ through N₂:

The π2p orbitals are LOWER in energy than σ2p.

Order:

σ2s

σ2s*

π2p

σ2p

π2p*

σ2p*

 

For O₂ through Ne₂:

The σ2p orbital becomes LOWER than π2p.

Order:

σ2s

σ2s*

σ2p

π2p

π2p*

σ2p*

THIS IS THE MAIN THING TO MEMORIZE.

The order changes because of 2s–2p mixing.

 

B₂ (Boron)

Each boron atom has:

3 valence electrons

Total:

6 valence electrons

Fill the orbitals using the Li₂–N₂ ordering.

Configuration:

(σ2s)²

(σ2s*)²

(π2p)¹

(π2p)¹

Notice something important.

The last two electrons go into separate π orbitals.

They do NOT pair up because of Hund's Rule.

 

cont: Magnetism of B₂

Magnetism of B₂

There are 2 unpaired electrons.

Therefore:

B₂ is paramagnetic.

This surprises many students because they expect all stable molecules to have paired electrons.

 

C₂

Total valence electrons:

8

Configuration:

(σ2s)²

(σ2s*)²

(π2p)⁴

Everything is paired.

Bond Order:

(6 − 2) ÷ 2 = 2

Result:

• C₂ exists.

• Double bond.

• Diamagnetic.

 

N₂

Total valence electrons:

10

Configuration:

(σ2s)²

(σ2s*)²

(π2p)⁴

(σ2p)²

Bonding electrons = 8

Antibonding electrons = 2

Bond Order:

(8 − 2) ÷ 2 = 3

Result:

• Triple bond.

• Extremely strong bond.

• Diamagnetic.

Fun fact:

Nitrogen gas is difficult to break apart because its bond order is 3, making it one of the strongest covalent bonds.

 

O₂

This is probably the MOST IMPORTANT molecule in MO Theory.

Lewis structures predict:

All electrons paired.

So oxygen should NOT be magnetic.

But experimentally...

O₂ IS magnetic.

Lewis structures cannot explain this.

MO Theory can.

 

O₂ Configuration

Use the O₂–Ne₂ orbital order.

After filling all orbitals,

the last two electrons go into separate π* orbitals.

Configuration ends with:

(π2p*)¹

(π2p*)¹

Each orbital contains one electron.

 

Magnetism of O₂

There are 2 unpaired electrons.

Therefore:

O₂ is paramagnetic.

This is one of the greatest successes of Molecular Orbital Theory.

It explains a real experimental observation that Lewis structures cannot.

cont

Bond Order of O₂

Bonding electrons = 8

Antibonding electrons = 4

Bond Order:

(8 − 4) ÷ 2 = 2

Result:

• O₂ exists.

• Double bond.

• Paramagnetic.

 

F₂

Total valence electrons:

14

After filling all orbitals:

All electrons are paired.

Bond Order:

(8 − 6) ÷ 2 = 1

Result:

• Single bond.

• Diamagnetic.

 

Ne₂

Total valence electrons:

16

Bonding electrons = 8

Antibonding electrons = 8

Bond Order:

(8 − 8) ÷ 2 = 0

Result:

• Ne₂ does NOT exist.

The bonding and antibonding electrons completely cancel.

Summary of Period 2 Molecules

Li₂

• Bond Order = 1

• Exists

• Diamagnetic

Be₂

• Bond Order = 0

• Does not exist

• Diamagnetic

B₂

• Bond Order = 1

• Exists

• Paramagnetic

C₂

• Bond Order = 2

• Exists

• Diamagnetic

N₂

• Bond Order = 3

• Exists

• Diamagnetic

O₂

• Bond Order = 2

• Exists

• Paramagnetic

F₂

• Bond Order = 1

• Exists

• Diamagnetic

Ne₂

• Bond Order = 0

• Does not exist

• Diamagnetic

 

Memory Tricks

Molecules that DO NOT exist

Be₂

Ne₂

Both have:

Bond Order = 0

 

Paramagnetic Molecules

Only remember these two:

B₂

O₂

Both have unpaired electrons.

Everything else in this section is diamagnetic.

 

Bond Orders to Memorize

Li₂ = 1

Be₂ = 0

B₂ = 1

C₂ = 2

N₂ = 3

O₂ = 2

F₂ = 1

Ne₂ = 0

Notice the pattern:

1 → 0 → 1 → 2 → 3 → 2 → 1 → 0

 

Big Picture

As you move across Period 2:

• More electrons are added to molecular orbitals.

• Bond order increases until N₂ (the strongest bond), then decreases as electrons begin filling antibonding orbitals.

• Filling antibonding orbitals weakens the bond.

• MO theory correctly predicts that O₂ is paramagnetic, something Lewis structures cannot explain

Heteronuclear Molecules, Ionization, and Combining MO Theory with Localized Bonding

Up Until Now...

Everything we've studied has been homonuclear diatomic molecules.

That means:

• Two identical atoms

• Same atomic orbitals

• Same orbital energies

Examples:

• H₂

• N₂

• O₂

• F₂

Because the atoms are identical, drawing MO diagrams is fairly straightforward.

Now we're moving to heteronuclear molecules.

 

Heteronuclear Diatomic Molecules

Definition

"Heteronuclear" means:

The molecule contains two different atoms.

Examples:

• NO

• HF

• CO

• HCl

"Hetero" = Different

"Diatomic" = Two atoms

So:

Heteronuclear diatomic = two different atoms bonded together.

Why Are They More Complicated?

Different atoms have:

• Different electronegativities

• Different orbital energies

• Different sizes

Because of this,

their atomic orbitals are NOT at the same energy level.

This makes the MO diagram less symmetrical.

 

Case 1 – The Atoms Are Similar

Example:

NO

Nitrogen and oxygen are next to each other on the periodic table.

Their orbital energies are fairly similar.

Because they are similar,

you can usually use the same MO diagram you already know for homonuclear molecules.

This makes the problem much easier.

 

Example: NO (Nitric Oxide)

Nitrogen contributes:

5 valence electrons

Oxygen contributes:

6 valence electrons

Total:

11 valence electrons

 

Which MO Diagram Do We Use?

Since oxygen is involved,

many students wonder whether to use the N₂ diagram or the O₂ diagram.

Your professor says:

Use the N₂ MO model for NO because nitrogen and oxygen are adjacent in the periodic table and have similar orbital energies.

cont

Electron Configuration

The slides don't list every orbital, but they tell you the important result.

Bonding electrons = 8

Antibonding electrons = 3

Bond Order:

(8 − 3) ÷ 2

= 2.5

 

What Does a Bond Order of 2.5 Mean?

Remember:

Bond order doesn't have to be a whole number.

A value of 2.5 means:

• Stronger than a double bond

• Weaker than a triple bond

It is halfway between.

 

Magnetism of NO

There is one unpaired electron.

Therefore:

NO is paramagnetic.

This matches experimental observations.

MO Theory correctly predicts what scientists actually measure.

 

Important Exam Point

NO has:

• Bond Order = 2.5

• Paramagnetic

These are two facts professors love asking about.

Case 2 – The Atoms Are Very Different

Example:

HF

Hydrogen and fluorine are very different atoms.

Hydrogen has:

1s orbital

Fluorine has:

2s and 2p orbitals

Their orbital energies are very different.

 

Can We Use the Same MO Diagram?

No.

When atoms are very different,

the standard MO diagrams no longer work well.

Instead,

a new MO diagram must be created specifically for that molecule.

 

Why Doesn't Every Orbital Bond?

Not every atomic orbital can combine.

Remember the two requirements from Part 1:

1. Similar energy

2. Correct symmetry (shape)

HF is a perfect example.

 

Which Orbitals Actually Bond?

Hydrogen contributes:

1s orbital

Fluorine has:

2s

2px

2py

2pz

The hydrogen 1s orbital mainly overlaps with the fluorine 2p orbital that points directly toward hydrogen (usually labeled 2pz).

Those orbitals have the correct orientation for a σ bond.

What Happens to the Other Fluorine Orbitals?

The remaining fluorine p orbitals do not overlap effectively with hydrogen.

They stay mostly unchanged.

These are called nonbonding orbitals.

 

Nonbonding Orbitals

Definition

A nonbonding orbital is an orbital that:

• Contains electrons

• Does not help form a bond

• Does not weaken a bond

It simply exists on one atom.

These electrons are usually what we call lone pairs.

 

Summary of HF

Hydrogen 1s orbital:

Forms a σ bond with fluorine.

Other fluorine orbitals:

Remain nonbonding.

This is why HF requires its own MO diagram.

Removing Electrons (Ionization)

Now the slides ask a very important conceptual question.

 

Question

Why does removing an electron from N₂ weaken the bond,

but removing an electron from O₂ strengthens the bond?

This confuses a lot of students.

The answer depends on which orbital loses the electron.

 

Removing an Electron from N₂

N₂ has:

Bond Order = 3

The highest occupied orbital is a bonding orbital.

When you remove an electron,

you remove one that was helping hold the atoms together.

Result:

• Fewer bonding electrons

• Bond order decreases

• Bond becomes weaker

 

Removing an Electron from O₂

O₂ has:

Bond Order = 2

The highest occupied orbital is an antibonding orbital.

When you remove an electron,

you remove one that was weakening the bond.

Now there are fewer antibonding electrons.

Result:

• Bond order increases

• Bond becomes stronger

Easy Way to Remember

Removing a bonding electron

↓

Bad

↓

Bond gets weaker

 

Removing an antibonding electron

↓

Good

↓

Bond gets stronger

 

This Is a Very Common Exam Question

Always ask:

"Which orbital is losing the electron?"

Not simply,

"Did we remove an electron?"

The orbital matters more than the electron itself.

 

Combining Two Bonding Models

The chapter finishes by comparing the two bonding models you've learned.

 

 

Localized Electron Model

This includes:

• Lewis Structures

• VSEPR

• Hybridization

Idea:

Electrons belong to one bond between two atoms.

Example:

A C–C single bond belongs only to those two carbon atoms.

 

Molecular Orbital Theory

Idea:

Electrons are spread over the entire molecule.

Instead of belonging to one bond,

they can be shared by many atoms.

This is called delocalization.

 

Which Model Is Better?

Neither.

Each explains different things well.

Localized Model is good for:

• Drawing Lewis structures

• Molecular geometry

• Hybridization

• Sigma bonds

MO Theory is good for:

• Magnetism

• Resonance

• Delocalized electrons

• Bond strength

• Bond order

Chemists often use both models together because each has strengths.

 

Benzene (C₆H₆)

Benzene is the perfect example of why both models are needed.

Kekulé's Original Model

In 1865,

Kekulé proposed that benzene looked like this:

Single bond

Double bond

Single bond

Double bond

Single bond

Double bond

A ring with alternating single and double bonds.

This was a great first model,

but experiments showed it wasn't completely correct.

 

Modern View of Benzene

Benzene is actually a resonance hybrid.

Instead of electrons staying in one double bond,

the π electrons are shared equally around the entire ring.

 

Delocalized π Electrons

The six p orbitals on the carbon atoms combine to form six molecular orbitals.

The π electrons move throughout the ring instead of belonging to one specific bond.

This is called delocalization.

 

What About the σ Bonds?

The σ bonds are still treated using the Localized Electron Model.

They remain between neighboring carbon atoms.

So:

σ bonds = localized

π bonds = delocalized

This combines both bonding theories.

What Does the π Cloud Look Like?

The six p orbitals overlap above and below the flat benzene ring.

This creates one continuous cloud of electrons.

Think of it as:

A "donut-shaped" electron cloud surrounding the ring.

The electrons are free to move around the ring instead of being trapped between two carbons.

 

Why Is Benzene So Stable?

Because the π electrons are delocalized,

their energy is lowered.

Lower energy means:

• Greater stability

• Stronger overall bonding

• Less reactive than expected

This extra stability is called resonance stabilization (or aromatic stabilization in more advanced chemistry).

 

 

Final Summary of the Entire MO Theory Chapter

Localized Electron Model

• Electrons belong to individual bonds.

• Best for Lewis structures, VSEPR, hybridization, and σ bonds.

Molecular Orbital Theory

• Electrons belong to the entire molecule.

• Explains bond order, bond strength, magnetism, resonance, and delocalized electrons.

Bond Order

• Bond Order = (Bonding − Antibonding) ÷ 2

• Higher bond order = stronger bond.

• Bond Order > 0 = molecule exists.

Magnetism

• All electrons paired → Diamagnetic.

• One or more unpaired electrons → Paramagnetic.

Homonuclear Molecules

• Same atoms.

• Use standard MO diagrams.

Heteronuclear Molecules

• Different atoms.

• Similar atoms (like NO) can often use a homonuclear MO diagram.

• Very different atoms (like HF) require a new MO diagram.

Ionization

• Removing a bonding electron weakens a bond.

• Removing an antibonding electron strengthens a bond.

Benzene

• σ bonds are localized.

• π electrons are delocalized over the entire ring.

• The delocalized π cloud makes benzene unusually stable.

 

Chapter "Must Know" Facts

• Molecular orbitals belong to the entire molecule.

• Bonding orbitals lower energy; antibonding orbitals raise energy.

• A positive bond order means the molecule is stable enough to exist.

• O₂ is paramagnetic because it has two unpaired electrons.

• NO has a bond order of 2.5 and is paramagnetic.

• Removing electrons from bonding orbitals weakens bonds.

• Removing electrons from antibonding orbitals strengthens bonds.

• Benzene's σ bonds are localized, but its π electrons are delocalized, making the molecule especially stable.