Molecular Orbital Theory - Online Tutor, Practice Problems & Exam Prep

Molecular Orbital Theory explains how valence electrons of atoms combine to form molecular orbitals, which are either bonding or antibonding. Bonding molecular orbitals, symbolized by the sigma (σ) sign, have high electron density that promotes bond formation and increases molecular stability. In contrast, antibonding molecular orbitals, indicated by a sigma star (σ*) sign, possess a node of low electron density that prevents bond formation and decreases stability. Electrons are distributed into these molecular orbitals following the Aufbau principle, Pauli Exclusion Principle—stating each orbital can hold two electrons with opposite spins—and Hund's Rule, which fills degenerate orbitals singly before pairing. This framework is essential for understanding the delocalization of electrons in molecules and the formation of stable chemical bonds.

Molecular Orbital Theory Concept 1

Now before we can talk about molecular orbital theory, let's have a quick recap on electron orbital diagrams. We're going to say. Recall that electrons are distributed S1 to S2 to P2 and so on within orbitals using what we call the Aufbau principle. And remember that electron orbitals themselves show electrons as residing within atomic orbitals.

Now with this whole thing of electron orbital diagrams and electrons, we're going to say we have the Pauli exclusion principle and Hund's rule. Under the Pauli exclusion principle, an orbital can hold a maximum of two electrons that have to have opposite spins, one points up and one points down. Remember this affects our spin quantum number of ms.

Hund's rule says that same energy orbitals, also known as degenerate orbitals, are first half filled before being totally filled, right? So for P2 orbitals, we go up, up, up and then come back around, down, down, down if necessary. Again, before we can learn about molecular orbital theory, let's just recap electron orbital diagrams.

Molecular Orbital Theory Example 1

Provide the electron orbital diagram for nitrogen atom. Nitrogen has an atomic number of seven, and since we're dealing with nitrogen atom, we're dealing with its neutral form, which means it also has seven electrons.

Following the off BOP principle, we fill up 1S completely before moving on to 2 S Fill in 2 S completely before moving on to 2P, so we'd say one up, one down. Following the Poly exclusion principle, electrons in the same orbital can must have opposite spins. So that's two so far, one up, one down.

So so far we've drawn 4 electrons. We've got to get to 7, so we need three more. Now these next atomic orbitals are all 2P orbitals, so they're all degenerate. They have the same energy, so following Huns rule we have to half fill. So this would be electron 5-6 and seven.

So this would represent the electron orbital diagram for the nitrogen atom.

Molecular Orbital Theory Example 2

Now when we talk about molecular orbital theory, we're talking about more than one atom kind of combining their electrons together. So we're going to say here, when atoms pool their electrons, the electron orbital diagrams are shown vertically. We're going to say even though they're shown vertically, we're going to use the same 3 principles to draw these vertical electron orbital diagrams.

So here it says film the electron orbital diagrams for two oxygen atoms that are combining their electrons. First of all, oxygen has an atomic number of eight oxygens. Electron configuration is 1S² 2S² 2P⁴, so we could think of this as being one oxygen atom here for this column and one oxygen atom here for this column. And all we're going to do here is we're going to fill in their electron orbital diagrams vertically.

SO 1S² means that we have one up, one down, one up, one down, 2S² one up, one down, one up, one down, and then 2P orbitals are all same energy or degenerate. So we follow Hund's rule. We need to fill in four electrons. So up, up, up come back around, down, same here, up, up, up, come back, around, down. So this is an illustration of us prepping the pooling of electrons for the two oxygen atoms.

Here we're still seeing them as two separate electron orbital diagrams. We haven't pulled them together yet. That's what's going to happen here in this space. So click on to the next video and let's see what happens when we start to pull together electrons found in atomic orbitals. Do they get a new description? What's going to happen?

Molecular Orbital Theory Example 3

From electron orbital diagrams we transition to Molecular orbital diagrams. They show chemical bonding as the combining of valence electrons from atomic orbitals of elements into what we call molecular orbitals. Now molecular orbitals are just a set of orbitals created from the combining of electrons between two elements.

Now if we take a look here at this example, it says fill in the molecular orbital diagram for when two oxygen atoms combine their valence electrons. So if we take a look here, we saw that we had our vertical electron orbital diagrams which were our atomic orbitals. So this portion here and this portion here, those electrons are pulled together into what we call our molecular orbitals here.

Now they follow the same 3 principles. They follow off Bob principle as we start filling lower energy orbitals first and moving up. We also follow Hun's rule where degenerate orbitals orbitals with the same energy are first half build before being totally filled. We also follow the poll exclusion principle where two electrons in an orbital must have opposite spins. All right. So we're just going to pull them together and to do that we're going to follow these rules.

So if we take a look here at these roles, it says if it is not given, determine the number of valence electrons for both elements. Two, we are going to construct the molecular orbital diagram based on the location of the valence electrons. One elements would start out with one S, period. Two elements would start out with 2S and period Three elements would start out with 3S. Remember your period is the row in which the element is found on the periodic table. And then finally we follow the three principles and fill in the molecular orbitals based on increasing energy.

So as we move off the energy increases. Here I've already given us the number of valence electrons for the oxygen atoms. So remember we'd say that oxygen is 1S22S22P4. But we're only looking at the valence electrons. We're only looking at these electrons here. It has six valence electrons because it's in Group 6A. All right, so we're going to start filling in. We go one up, one down, one up, one down.

We've already filled in all we can because in total we have 4 atomic orbital electrons and we've just filled those four orbital 4 electron orbital electrons into these two molecular orbitals. Now next we're going to have four here and we're going to have four here for a total of 8 electrons found within atomic orbitals. So now we're going to do is fill them in to these molecular orbitals. So up, up following Han's rule, down, down. So we've used 4 electrons so far, meaning we have 4:00 left, so up, up, So that's six. So we have two more electrons up, up.

So this would represent the molecular orbital diagram. When we're talking about our two oxygen atoms, this is how they would fill in their valence electrons into these given molecular orbitals. So as you go further and further into molecular orbital theory, we'll see more and more of these molecular orbitals being used.

Molecular Orbital Theory Concept 2

Now when combining the valence electrons between elements, there are two types of molecular orbitals involved. We have first our bonding molecular orbital. This is just regions where we have high electron density between elements that promotes bond formation. Now if we have bond formation then we have the opposite of that, bond destruction or bond prevention. This has to do with our anti bonding molecular orbital.

Here it's designated with a star. We're going to say this is a region of low electron density, also known as a node that prevents bond formation. What we need to realize here is that filled bonding molecular orbitals are going to increase stability and filled antibody molecular orbitals will decrease stability. So you have these two forces at work, one trying to form the bond, the other ones trying to prevent it.

Now here we're going to say in terms of a molecular orbital diagram, we're going to say electrons are delocalized, so they're spread out throughout the molecule. And we're going to say here valence electrons from atomic orbitals are combined into molecular orbitals. These are discussions that we talked about when first looking at molecular orbital theory.

So if we're talking about hydrogen and helium, their valence electrons are found in S1 orbitals. So here we would say we have our S1 atomic orbital, our S1 atomic orbital, and here we're going to say, let's say we're looking at helium. So helium would have electrons found in this atomic orbital and the other one those could be distributed into the molecular orbitals.

Here we have our what we call our bonding molecular orbital that is designated by the Sigma sign. So ΣS1 and then remember if we see a * that means that we have an antibody molecule orbital. So this would be ΣS1*, which basically says we're dealing with an antibody molecular orbital. And remember, we would distribute the electrons found within our atomic orbitals into these molecular orbitals. So click onto the next video and we'll see how exactly this would work in terms of hydrogen and helium.

Molecular Orbital Theory Example 4

In this example, we need to construct a molecular orbital diagram for the dihelium cation, which is HE₂⁺. All right, so the way we do this is we're going to determine the number of valence electrons for both elements. Here we're dealing with two helium's. Remember, helium's have atomic numbers of two. We also say that helium, they each have two valence electrons, so they'd be two times four 2 * 2, which is 4 valence electrons. But then here we're going to say this plus one charge means we've lost an electron. So in total we have 3 valence electrons for the diphthelium cation.

What we do next is we construct the molecular orbital diagram based on the location of the valence electrons. If we're dealing with period one elements like we are here, then we start out with 1S. If it's period two element it's 2S, and if it's. 3 It's 3S Step 3:00. We'd follow the three principles so off off principle, Poly exclusion principle, and Hun's rule, and fill in the molecular orbitals from bottom to the top.

If we come back up here to our image here, we're dealing with three valence electrons. So we'd actually erase one of these and we have 3 total valence electrons, which we would then distribute into these molecular orbitals. So we'd start out by filling out the lowest energy one according to Aufbau principle. So go one up, one down and then we still have one more electron left that we need to fill in and we go here in the anti bonding molecular orbital.

So this is what we would say are bonding. Our molecular orbital diagram would resemble it would look like this where we would fill in totally the bonding molecular orbital that is Sigma 1S and have half build my anti bonding molecular orbital which is Sigma star 1S.

Here’s what students ask on this topic:

What is molecular orbital theory?

Molecular Orbital Theory (MOT) is a principle for understanding the chemical bonding in molecules. It describes how atomic orbitals combine to form molecular orbitals, which are the energy states of electrons in a molecule. In MOT, when two atoms bond, their atomic orbitals overlap to create molecular orbitals that are spread out over the entire molecule, rather than being localized around individual atoms.

There are two types of molecular orbitals that can form: bonding orbitals, which have lower energy and can lead to a stable bond by housing paired electrons, and antibonding orbitals, which have higher energy and can destabilize a molecule if they contain electrons. Electrons fill the molecular orbitals starting with the lowest energy first, according to the Pauli exclusion principle and Hund's rule. The molecular orbital theory provides a way to predict the arrangement of electrons in molecules, the shape of molecules, bond order, magnetic properties, and the stability of the molecules.

How does molecular orbital theory differ from valence bond theory?

Molecular Orbital (MO) Theory and Valence Bond (VB) Theory are two approaches to understanding the bonding in molecules.

MO Theory views electrons as delocalized over the entire molecule, forming molecular orbitals that can extend over all the atoms in the molecule. These molecular orbitals are formed from the linear combination of atomic orbitals (LCAO), and they can be bonding, antibonding, or non-bonding. Electrons in bonding orbitals stabilize the molecule, while electrons in antibonding orbitals can destabilize it. MO Theory can also explain phenomena like resonance, magnetism, and the color of molecules.

On the other hand, VB Theory describes bonds as localized between pairs of atoms, with electrons shared in the overlapping regions of atomic orbitals. It emphasizes the concept of hybridization, where atomic orbitals mix to form new hybrid orbitals suitable for pairing electrons to form covalent bonds. VB Theory is often used to describe the geometry of molecules and the types of bonds (single, double, triple) between atoms.

In summary, MO Theory gives a more global view of electron distribution in molecules, while VB Theory provides a more localized picture of bonding between atoms.

How do you draw an electron orbital diagram?

To draw an electron orbital diagram, you'll need to represent the electrons and orbitals of an atom according to the principles of quantum mechanics. Here's a step-by-step guide:

1. Determine the number of electrons in the atom by looking at the atomic number on the periodic table.
2. Familiarize yourself with the types of orbitals (s, p, d, f) and their shapes, but for a simple diagram, you'll just need to know the order they fill: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc. This is known as the Aufbau principle.
3. Start filling the orbitals with electrons. Each orbital can hold a maximum of two electrons.
4. Apply Hund's rule: when you're filling orbitals of the same energy (like the three p orbitals), place one electron in each orbital before you start pairing them. Electrons in the same orbital must have opposite spins, represented by arrows pointing up or down.
5. Continue filling until all the electrons are placed in the appropriate orbitals.

Your diagram will consist of a series of lines or boxes that represent orbitals, with arrows indicating the electrons. The lines or boxes are labeled with the corresponding orbital designation (e.g. 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, etc.).

How do you draw a molecular orbital diagram?

To draw a molecular orbital (MO) diagram, follow these steps:

1. Count the valence electrons of the atoms involved in the molecule.
2. Draw the atomic orbitals for each atom. For diatomic molecules, you'll typically deal with 's' and 'p' orbitals.
3. Combine the atomic orbitals to form molecular orbitals. Each atomic orbital can combine with another to form one bonding (lower energy) and one antibonding (higher energy) molecular orbital.
4. Fill the molecular orbitals with the total number of valence electrons, following Hund's rule and the Pauli exclusion principle. Start from the lowest energy level up, and each orbital can hold two electrons with opposite spins.
5. For heteronuclear diatomic molecules, consider the difference in electronegativity between the atoms, which affects the energy levels of the molecular orbitals.
6. Once filled, count the electrons in bonding and antibonding orbitals to determine the bond order: (bonding electrons - antibonding electrons) / 2.
7. The bond order gives you an indication of the stability of the molecule; a higher bond order generally means a stronger bond.

Remember that the specific details can vary depending on the complexity of the molecule, but these steps provide a general framework for constructing a molecular orbital diagram.