Molecular orbital theory

Introduction to Molecular Orbital (MO) Theory

Welcome to H3 Chemistry! If you’ve ever wondered why oxygen is magnetic, or why some organic molecules are brightly colored while others are clear, you are in the right place. In H2, we used Valence Bond Theory (hybridization like \(sp^3\)) to describe molecules. While useful, it doesn't tell the whole story. Molecular Orbital (MO) Theory is our "pro" upgrade. It treats electrons as belonging to the whole molecule rather than being stuck between two specific atoms. This is the foundation for understanding spectroscopy—how light interacts with matter!

Prerequisite Check: Remember your Atomic Orbitals (AOs)? Those are the \(s, p, d\) and \(f\) orbitals where electrons live in single atoms. In this chapter, we are going to "mash" them together to create Molecular Orbitals.

1. The Basics: How MOs are Formed

To create a Molecular Orbital, we use a method called LCAO, which stands for Linear Combination of Atomic Orbitals.

Think of it like this: Electrons behave like waves. When two waves meet, they can either reinforce each other or cancel each other out.

Constructive Interference (\(Bonding\))

When two atomic orbitals add together (in-phase), they create a Bonding Molecular Orbital. This orbital has high electron density between the nuclei, acting like "atomic glue" that holds the atoms together. These are lower in energy and more stable.

Destructive Interference (\(Anti-bonding\))

When two atomic orbitals subtract from each other (out-of-phase), they create an Anti-bonding Molecular Orbital. This creates a node (a region with zero electron density) between the nuclei. Because the nuclei are "exposed" to each other, they repel. These are higher in energy and less stable. We mark these with an asterisk (*), like \(\sigma^*\) or \(\pi^*\).

Non-bonding Orbitals

Sometimes, an atomic orbital doesn't have a partner to interact with, or the symmetry doesn't match. These remain at the same energy level as the original atomic orbital and are called Non-bonding orbitals (\(n\)).

Quick Review:
1. Number of AOs in = Number of MOs out.
2. Bonding MOs = Low energy (stable).
3. Anti-bonding MOs = High energy (unstable, contains a node).

2. Symmetry: Sigma (\(\sigma\)) vs. Pi (\(\pi\)) Orbitals

Just like in H2, we categorize these bonds based on how they overlap.

\(\sigma\) Symmetry (Head-on Overlap)

This happens when orbitals overlap directly along the axis between the two nuclei. Imagine two people shaking hands—the connection is direct and strong. \(\sigma\) orbitals are cylindrical and can be formed from \(s-s\), \(s-p\), or \(p-p\) head-on overlaps.

\(\pi\) Symmetry (Side-on Overlap)

This happens when two \(p\)-orbitals sit side-by-side and overlap above and below the nuclear axis. Imagine two people standing side-by-side and giving each other a "high-five" and a "low-five" at the same time. These are generally weaker than \(\sigma\) bonds.

Did you know? Because \(\pi\) electrons are further from the nuclei and held less tightly, they are usually the ones involved in "exciting" transitions when hit by light!

3. MO Diagrams for Homonuclear Diatomic Molecules

To visualize the electronic structure, we draw an MO Diagram. We fill these using the same rules we used for atoms: Aufbau Principle (lowest energy first), Pauli Exclusion Principle (max 2 electrons per orbital), and Hund’s Rule (don't pair up unless you have to).

Example 1: Hydrogen (\(H_2\))

Each H atom brings 1 electron (from the \(1s\) orbital).
1. Combine two \(1s\) orbitals \(\rightarrow\) one \(\sigma_{1s}\) (bonding) and one \(\sigma^*_{1s}\) (anti-bonding).
2. Total 2 electrons \(\rightarrow\) both go into the lower \(\sigma_{1s}\) orbital.
3. The molecule is stable because the bonding orbital is full.

Example 2: Oxygen (\(O_2\)) - The MO Superstar

In H2, Lewis structures showed \(O_2\) with all paired electrons. But MO theory shows something different! When we fill the \(\pi^*_{2p}\) orbitals for Oxygen, the last two electrons go into separate orbitals (Hund's Rule).
Result: Oxygen has two unpaired electrons, making it paramagnetic (attracted to magnets)! MO theory explains this perfectly while other theories fail.

Example 3: Fluorine (\(F_2\))

Fluorine has more electrons than Oxygen. Those last two spots in the \(\pi^*\) orbitals get filled up. With all electrons paired, \(F_2\) is diamagnetic.

Key Takeaway: MO diagrams help us predict bond order and magnetic properties.
\(Bond\ Order = \frac{1}{2} [(\text{Electrons in bonding}) - (\text{Electrons in anti-bonding})]\)

4. HOMO and LUMO: The Frontier Orbitals

These are the two most important levels in any MO diagram for spectroscopy:

HOMO: Highest Occupied Molecular Orbital. This is the "highest floor" of the molecule's "hotel" that actually has guests (electrons) in it.

LUMO: Lowest Unoccupied Molecular Orbital. This is the "lowest empty floor" where electrons can jump to if they get enough energy.

Analogy: Imagine a ladder. The HOMO is the highest rung you are currently standing on. The LUMO is the next rung up. To climb to the LUMO, you need a boost of energy (like a photon of light!).

5. Delocalized Systems: Benzene and Linear Polyenes

For the H3 syllabus, we focus only on the \(\pi\) symmetry orbitals for these systems.

Linear Polyenes (like Butadiene)

In a chain of alternating double bonds (conjugation), the \(p\)-orbitals overlap across the whole chain. Instead of just two \(p\)-orbitals mixing, four or more mix together. This creates a "ladder" of \(\pi\) orbitals.
Important: As the chain gets longer (more conjugation), the energy gap between the HOMO and LUMO gets smaller.

Benzene (\(C_6H_6\))

In benzene, the six \(p\)-orbitals form a ring. This creates a specific set of 6 \(\pi\) molecular orbitals. You don't need to do the math, but you should know that the electrons are delocalized in a giant "donut" shape above and below the ring. This makes benzene incredibly stable.

Common Mistake to Avoid: When drawing MOs for benzene or polyenes, students often forget that only the \(\pi\) system is being considered. The \(\sigma\) framework (the single bonds holding the atoms together) is treated as a separate, rigid skeleton.

Summary and Key Takeaways

1. MOs are Discrete Energy Levels: Electrons in molecules don't have random energies; they exist in specific, quantized molecular orbitals.

2. Spectroscopy Connection: When a molecule absorbs light, an electron jumps from the HOMO to the LUMO. The energy of the light must exactly match the energy gap (\(\Delta E\)) between these two levels.

3. Conjugation Effect: More conjugation = smaller HOMO-LUMO gap = lower energy light absorbed (moving from UV towards the Visible spectrum). This is why carrots (highly conjugated) are orange!

Don't worry if the shapes of the benzene orbitals look a bit wild at first. Just remember: more nodes = higher energy!