Molecular Orbital Theory — Overview & Application

What is Molecular Orbital (MO) Theory?

It is used to describe molecular structure and bonding. This theory is useful because it describes the electrons better than valence bond theory (VBT). MO theory begins by looking at atomic orbitals (AOs) on each atom in a molecule. These orbitals are combined to describe molecular orbitals which are the combination of atomic orbitals.

Molecular Orbitals (MOs)

Molecular orbitals describe the location of electrons in a molecule. MOs are similar to AOs because they have energy levels, shapes, and are occupied by two electrons. If two AOs interact to from MOs, the number of MOs that from is the same as the number of AOs. This makes sense because if two AOs combine with two electrons in each, we will need two MOs to hold two electrons each.

Orbital Interactions

In MO theory there are two ways for orbitals to interact with each other and form two types of orbitals:

• Bonding molecular orbital: an additive combination where orbitals combine to form a shape resembling the combination of both orbitals. It is lower in energy than the original orbitals. Denoted as $\sigma$ or $\pi$ depending on the bond type.

• Anti-bonding molecular orbital: a subtractive combination where orbitals do not combine to form one shape, but from a node between each other. It is higher in energy than the bonding orbital and original orbitals. Denoted as $\sigma$ or $\pi$ depending on the bond type.

Molecular Orbital Diagram

MO diagrams are used to describe the energy and electrons in molecular orbitals. MO diagrams show the AOs on the atoms, the bonding orbitals, anti-bonding orbitals, electrons, and the energy of the orbitals.

Electron location is important in MO diagrams. The electrons are shown in the AOs, with opposite spins if there are two electrons in an orbital. Then when the MOs are distinguished, electrons are typically added to MOs starting at the lowest energy orbital. The electrons in the same orbital have opposite spins.

Bond Order

Bond order is very easy to distinguish from MO diagrams. Bond order describe the electrons between atoms. Examples of bond order are:

• 1 = single bond

• 2 = double bond

• 3 = triple bond

Bond order equation:

$$Bond\ order =\frac{ \#\ of\ bonding\ electrons\ - \#\ of\ antibonding\ electrons}{2}$$

For the $H_2$ molecule the bond order is:

$$Bond\ order =\frac{ 2 - 0}{2}\ =\ 1$$

This means there is a single bond between the hydrogen atoms.

(Video) Molecular Orbital Theory - Valence Bond Theory, Hybrid Orbitals, and Molecular Orbital Theory

By ProfessorDaveExplains

In this video, professor Dave explains the molecular orbital theory by reviewing atomic orbitals, hybrid orbitals, and the valence bond theory. He uses hydrogen to explain how the 1s atomic orbitals overlap to form a sigma bonding molecular orbital. He also uses oxygen to demonstrate how to use a molecular orbital diagram to determine bond order in a molecule.

Molecular Orbital (MO) Theory: MO Theory in a Nutshell

We've studied atomic structure. We started in the 1800s with Dalton's atomic theory. He stated that all matter consists of atoms. But what makes up atoms? We discovered electrons with the cathode ray experiment. But that left us with the confusing plum pudding model. Thankfully, Ernest Rutherford performed his famous gold foil experiment. We developed the nuclear model!

The nuclear model only got us so far. We didn't understand how electrons worked. Neils Bohr's model proposed that electrons reside in orbits. That helped account for Planck's quantum theory. But Einstein altered everything! How? He explained the photoelectric effect via the wave-particle duality. Soon after, Lewis De Broglie applied it to electrons. Suddenly, we entered the age of quantum mechanics!

Erwin Schrodinger developed the quantum mechanical model. Soon we understood that electrons reside in atomic orbitals. We describe them with quantum numbers. They tell us the energy, shape, and electron spin. But, we still didn't understand everything! We needed to figure out how bonding worked.

Previously, we studied valence bond theory. It's one of the two theories that use quantum mechanics to describe bonds. Today, we'll look at the Molecular Orbital Theory.

Basics of Molecular Orbital Theory

In valence bond theory, bonded atoms share electrons. The electrons experienced electrostatic attraction to each nucleus. The assumption is that they remain localized between the nuclei. But, let's think about atomic orbitals. Electrons can move around all sides of an atom. In molecular orbital theory, the electrons can move around the whole molecule. Why does this make more sense? Let's imagine a massive molecule. Something like octadecane. Its molecular formula is $C_{18}H_{38}$. The electrons can interact with any of the nuclei. There is nothing that keeps them between two atoms.

So, what happens to the atomic orbitals when two atoms bond? They combine into molecular orbitals. Every atomic orbital produces a molecular orbital. For example, let's consider a hydrogen molecule. Its two 1s-orbitals overlap. So, they create two molecular orbitals. How do we get two? Remember, we can describe orbitals as waves. So, the orbitals can constructively or destructively interfere. The constructive interference creates a bonding molecular orbital. Destructive interference generates an antibonding molecular orbital.

Here's how we write it mathematically.

$Bonding\, M.O=\Psi=1s_{a}+1s_{b}$

$Antibonding\, M.O=\Psi^{*}=1s_{a}-1s_{b}$

The fancy term for this math is a linear combination of atomic orbitals. Doesn't that sounds complicated?! But it just means addition and subtraction of the orbitals.

What does any of this have to do with bonding? The bonding molecular orbital is more stable. So, the electrons fill it first. The antibonding molecular orbital is at a higher energy level. So, it would be the excited state.

What about larger molecules? Like atomic orbitals, the p orbitals have higher energy than the s. So, when we draw our orbital diagram, s overlaps are below p overlaps. The only other thing we need to add is sigma and pi orbitals. Sigma orbitals form with a straight-on overlap. That happens between two s-orbitals or an s orbital and $p_{x}$ orbitals. The $p_{y}$ and $p_{z}$ overlaps generate pi orbitals. In pi orbitals, the overlap is lateral. They bend over the top or sides of the molecule. The sigma bonding orbital has the lowest energy. The sigma antibonding has the highest. The pi orbitals energies are between them.

Dioxygen Example

As an example, let's consider dioxygen. We have 12 valence electrons between the two oxygen atoms. Each oxygen brings a 2s orbital and three 2p orbitals. So, we would form eight molecular orbitals. But where do we put the electrons? Let's look at each set of orbitals.

• The two s orbitals form a sigma bonding and antibonding orbital. Each will hold a pair of electrons. That's four out of twelve electrons.

• The two p_{x} orbitals will yield a sigma bonding and antibonding set. Two of the electrons fill the bonding orbital. That's six out of twelve electrons.

• The $p_{y}$ and $p_{z}$ orbitals will each produce a pi bonding and antibonding set. An electron pair fills each of the pi bonding orbitals. What about the last two electrons? They each half fill one of the pi antibonding orbitals. That's all twelve electrons!

• The electrons only half-fill the pi antibonding orbitals. Why? Because unpaired electrons have lower energy. Remember, spin pairing increases the electrostatic repulsion. So, it's more stable to half-fill each pi antibonding orbital.

Advantages and Disadvantages of Molecular Orbital Theory

There seems to be a competition between Molecular Orbital Theory and Valence bond Theory. Many people will say that Molecular Orbital Theory is superior. But, they are two sides of the same coin. Computational chemists use both theories. Sometimes, one is more descriptive. Sometimes the other is easier to apply. It depends on the molecule. But, for any molecule, both theories should generate the same result. It's more about which model is more intuitive.

So, what are its advantages? The main benefit is that we get a picture of the whole molecule. For example, let's imagine dispersion forces. If the electrons can move freely about the molecule, it's easy to imagine a temporary dipole. Valence bond theory can still explain dispersion. But, when electrons are more localized, it's harder to envision. Another advantage is its explanation of excited states. Like atoms, molecules absorb and emit light. An electron can get excited into an antibonding orbital. That's the basic premise of UV-visible spectroscopy.

What are the disadvantages? Both ionic and covalent bonding become more abstract. It's easier to think of bonds between atoms. That makes intuitive sense. The electrostatic interactions keep everything together. But, in molecular orbital theory, we are thinking of orbitals. It's not always clear how overlapping orbitals make bonds.