Molecular Orbital Theory - Video Tutorials & Practice Problems
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Molecular Orbital Theory allows us to predict the distribution of electrons within a molecule.
Molecular Orbital (MO) Theory
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Molecular Orbital Theory Concept 1
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Before we can talk about molecular orbital theory, let's have a quick recap on electron orbital diagrams. So we're gonna say recall that electrons are distributed 1 s to 2 s to 2 p and so on within 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 gonna say we have the Pauli exclusion principle and Hunt's rule. Under the Pauli exclusion principle, an orbital can hold a maximum of 2 electrons that have to have opposite spins, One points up and one points down. Remember, this affects our spin quantum number of m sub s. Hund's rule says that same energy orbitals, also known as degenerate orbitals, are first half filled before being totally filled. Right? So we for a p orbital, we go up up up and then come back around down down down if necessary. So again, before we can learn about molecular orbital theory, let's just recap electron orbital diagrams.
Electron orbital diagrams show electrons as residing within atomic orbitals.
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Molecular Orbital Theory Example 1
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Provide the electron orbital diagram for nitrogen atom. Nitrogen has an atomic number of 7. And since we're dealing with nitrogen atom, we're dealing with its neutral form, which means it also has 7 electrons. Following the Aufbau principle, we fill up 1 s completely before moving on to 2 s. Fill in 2s completely before moving on to 2p. So we'd say 1 up, 1 down, following the Pauli exclusion principle, electrons in the same orbital can must have opposite spins. So that's 2 so far, 1 up, one down. So so far we've drawn 4 electrons. We gotta get to 7, so we need 3 more. Now these next atomic orbitals are all 2p orbitals, so they're all degenerate. They have the same energy. So following Hund's rule, we have to half fill. So this would be electron 5, 6, and 7. So this would represent the electron orbital diagram for the nitrogen atom.
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Molecular Orbital Theory Example 2
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Now when we talk about molecular orbital theory, we're talking about more than 1 atom kind of combining their electrons together. So we're gonna say here, when atoms pool their electrons, the electron orbital diagrams are shown vertically. We're gonna say, even though they're shown vertically, we're gonna use the same three principles to draw these vertical electron orbital diagrams. So here it says, fill the electron orbital diagrams for 2 oxygen atoms that are combining their electrons. First of all, oxygen has an atomic number of 8. Oxygen's electron configuration is 1 s 2, 2 s 2, 2p 4. So we could think of this as being 1 oxygen atom here for this column, and 1 oxygen atom here for this column. And all we're gonna do here is we're gonna fill in their electron orbital diagrams vertically. So one s 2 means that we have 1 up, 1 down, 1 up, 1 down. 2 s 2, 1 up, 1 down, 1 up, one down. And then 2p4 orbitals are all same energy or degenerate, so we follow Hund's rule. We need to fill in 4 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 2 oxygen atoms. Here, we're still seeing them as 2 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?
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Molecular Orbital Theory Example 3
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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 2 elements. Now if we take a look here at this example, it says, fill in the molecular orbital diagram for when 2 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 three principles. They follow Aufbau principle as we start filling lower energy orbitals first and moving up. We also follow Hund's rule where degenerate orbitals, orbitals with the same energy, are first half filled before being totally filled. We also follow the Paul exclusion principle where 2 or electrons in an orbital must have opposite spins. Alright. So we're just gonna pull them together, and to do that we're gonna follow these rules. So if we take a look here at these rules, it says, if it is not given, determine the number of valence electrons for both elements. 2, we're gonna construct the molecular orbital diagram based on the location of the valence electrons. Period one elements would start out with 1 s, period 2 elements would start out with 2 s, and period 3 elements would start out with 3 s. 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 on, 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 1 s 22s22p4, but we're only looking at the valence electrons, so we're only looking at these electrons here. It has 6 valence electrons because it's in group 6 a. Alright. So we're gonna start filling in. We go 1 up, 1 down, 1 up, 1 down. We've already filled in all we can because in total we have 4 atomic orbital electrons, and we've just filled those 4 orbital, 4 electron orbital, electrons into these 2 molecular orbitals. Now next we're gonna have 4 here and we're gonna have 4 here, for a total of 8 electrons found within atomic orbitals. So now all we're gonna do is fill them in to these molecular orbitals. So up up, following Hund's rule, down, down. So we've used 4 electrons so far, meaning we have 4 left. So up, up, so that's 6. So we have 2 more electrons, up, up. So this would represent the molecular orbital diagram when we're talking about our 2 oxygen atoms. This is how they would fill in their valence electrons into these given molecular orbitals. So as we go further and further into molecular orbital theory, we'll see more and more of these molecular orbitals being used.
Molecular Orbital Diagrams represent chemical bonding as combination of valence electrons from atomic orbitals of elements into molecular orbitals.
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Molecular Orbital Theory Concept 2
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Now when combining the valence electrons between elements, there are 2 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 gonna 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 anti bonding molecular orbitals will decrease stability. So you have these two forces at work, one trying to form the bond, the other one's trying to prevent it. Now here we're going to say in terms of a molecular orbital diagram, we're gonna say electrons are delocalized, so they're spread out throughout the molecule, And we're gonna 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 1 s orbitals. So here we would say we have our 1 s atomic orbital, our one s atomic orbital. And here we're going to say let's say we're looking at he I'm 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's designated by the sigma sign, so sigma 1 s, and then remember if we see a star that means that we have an anti bonding molecular orbital. So this would be sigma star 1 s, which basically says we're dealing with an anti bonding molecular orbital. And remember, we would distribute the electrons found within our atomic orbitals into these molecular orbitals. So click on to the next video and we'll see how exactly this would work in terms of hydrogen and helium.
Bonding Molecular Orbital is region of high electron density between elements, promotes bond formation.
Anti-bonding Molecular Orbital is region with low electron density and prevents bond formation.
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Molecular Orbital Theory Example 4
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This example, we need to construct the molecular orbital diagram for the dihelium cation, which is HE 2+. 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 2 heliums. Remember, heliums have atomic numbers of 2. We'd also say that helium, they each have 2 valence electrons, so that'd be 2 times 4 2 times 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 dithium 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 1 elements like we are here, then we'd start out with 1s. If it's period 2 element, it's 2 s, and if it's period 3, it's 3 s. Step 3, we follow the three principles, so Aufbau principle, Pauli exclusion principle, and Hund'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 3 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 1 up, 1 down, and then we still have one more electron left that we need to fill in, and it would go here in the anti bonding molecular orbital. So this is what we would say our bonding our molecular orbital diagram would resemble. It would look like this. K, where we would fill in totally the bonding molecular orbital that is sigma 1s, and have half filled my anti bonding molecular orbital, which is sigma star 1s.