Hybrid Orbital Theory

What is the Ground State Configuration of Carbon?

Let’s learn a little bit more about carbon. According to the hybrid orbital theory, the ground state configuration of carbon has two electrons in the 1s orbital, two electrons in the 2s and two electrons in the 2p.

According to this model, only the electrons in the 2p will be available to bond. But we know that in real life, the molecule of methane, for example, has four sigma bonds. So the ground state shows that only two electrons are available to form sigma bonds with only two hydrogen atoms. However, this is not what we see in nature.

So this model does not match what is found in nature. In order to understand what is coming up next, we need to go through the excited state. You’ll learn that the excited state is the bridge between the ground state and the hybridization state of carbon.

In the excited state, one electron from the 2s jumps to the 2p orbital. So now you have three electrons in the 2p and one electron in the 2s. This means that if this was true, you will have three bonds that are equivalent, but they will be in a 90-degree angle with respect to each other. Plus then you will have a short bond that will be another CH bond. This is also not observed yet, but we have learned that carbon has to hybridize. In order to have four bonds, it needs to do something.

From Ground State to Excited State to Hybridized State

What we have here so far is that in the ground state, we have learned that the ground state configuration of carbon will have two electrons in the 1s, two electrons in the 2s, and two electrons in the 2p. One of these electrons in the 2s will jump up to the next level. So in the excited state, you have two electrons in the 1s, one electron in the 2s, and then you have now three p electrons. The atom of carbon now does something interesting called hybridization.

In its hybridized mode, or sp³ in this case, one s orbital will combine with three p orbitals. And because they are in the second level, you have this two here, that’s why it’s called 2sp³ level. So now in the hybridized state, you have two electrons in the 1s, and then you have four electrons that are equivalent with the same energy, or degenerate.

Degenerate means they have the same energy. And notice that because you have combined or blend or mix these four electrons, the energy has averaged out. And so now these four electrons are in an energy level in between the 2s and the 2p. So it’s right here in the middle. They are lower in energy, more stable. These four electrons can then make four sigma bonds.

And that’s what we see in carbons. So here you have one s and one p orbital mixing. Now you have these hybridized atomic orbitals which look kind of like bowling pins.
There’s four of them and they will have four different directions. Those four directions represent four sigma bonds. And this molecule will have this hydrogens at 109.5 degrees separation. That will be the molecule of methane.

So let’s continue here. So for the sp² hybridized state, we’re going to, again, look at the ground state of carbon. And then one of these electrons is going to get excited. Now you have four electrons that could form bonds. One in the s, three in the p’s. But for the sp² hybridization, you’re going to combine one s and two p’s. So for the hybridized state, you have one, two electrons in the 1s. And then you have one, two, three electrons in the 2sp2 orbital. And then you’re going to have one untouched hybridized 2p electron.

These three electrons right here can form three sigma bonds, the sp2s. And this electron right here can form one pi bond. So in order to explain the molecule of ethane, we’re going to have to use two carbons, because otherwise this model will be truncated in half. So we cannot explain a half model, instead we have to explain a full model.

The combination of one, two s orbital with two 2p orbitals will produce three identical sp² hybridized orbitals. Now sp² means three directions. So you have one, two, three directions for this carbon here. And then you have one, two, three directions for this carbon right here. So in total you have three directions, therefore it’s sp². The angle here between these bonds is 120 degrees all around to make 360. Here you have in any pi bond, your first bond is always a sigma. The blue bonds here are the sigmas and the one green bond is your pi.

That’s what we have here. We have one, two, three sigma bonds for each carbon and one pi bond. On the next slide we’ll work with sp hybridization. And so here we start with the grounds there again. One, two, three, four, five, six. But one of them jumps and gets excited.

You can excite a molecule with light, some sort of energy will excite it. And so when a molecule is excited you can do different things. In this case this carbon would like to hybridize as an sp hybridization. in this case you mix or combine one s orbital with one p. So you will leave two untouched p orbital electrons.

In your hybridized state for the sp you have one, two electrons and then one, two and then one, two. These two electrons here will form two sigma bonds. And these two here in the p will make two pi bonds. The sp is a combination of one s orbital with one p orbital. And that produces two identical sp hybridized orbitals oriented 180 degrees from each other.

The blue bonds here are your sigma bonds. For this model we need two carbons to make the ethyne molecule. The first bond in blue in a triple bond will always be a sigma bond. The other two in green are two pi bonds. So a triple bond will have one sigma bond and two pi bonds. A double bond will have one sigma bond and one pi bond.

So here you have: electrons are shared in overlapping orbitals between the atoms involved. These orbitals that extend around more than one atom are called molecular orbitals or MO’s.