Lecture Series 7Hybridization of Atomic Orbitals and its Influence on Molecular Structure(?)HHHHCFigure 2. The assembly of CH4, based on the shapes of the atomic orbitals on the C atom, which is located at the origin of the coordinate system I have drawn. C1C2H1Figure 1. An incorrect bonding picture of the molecule HCCH. The molecule is linear, and so we have both C2 and H1 bonded to C1 through the px orbital. Lecture Series 7Hybridization of Atomic Orbitals and its Influence on Molecular StructureAt the beginning of Lecture Series 6, I wrote the following: “Many of the structures that we have been covering – especially the organic-molecule structures, should have raised some questions. For example, when we learned about the atomic orbitals that are used by a carbon atom, we had a 2s orbital, and 3 2p orbitals. Each 2p orbital is aligned with an axis, so we had 2px, 2py, and 2pz. The 2s orbital was spherically symmetric. If these are the atomic orbitals that we will need to form molecular orbitals, then shouldn’t the molecular shapes somehow resemble the spatial distribution of the atomic orbitals? In other words, since all of the p-orbitals are at right angles to each other, shouldn’t carbon be characterized by bond angles that are 90o, instead of 180o (AB2), 120o (AB3), and 109.5o (AB4)? Think about this question. It is important.“Let’s consider a second, but related anomaly. Some of the molecules that we have mentioned do not appear to be in contradiction to the shapes of our molecular orbitals. For example, HCCH is linear both in fact, and by VSEPR theory. Consider just the carbon on the right side of this molecule. It is bonded to a hydrogen and another carbon, as shown in Figure 1. This can’t happen! What we are doing is taking 1 atomic orbital, the 2px orbital on C1, and generating two bonding MO’s from it. We can only get one bonding MO, and one antibonding MO. Look at it this way. C12px + C22px will give us one bonding MO, and one antibonding MO. C12px and H11s will give us one bonding MO, and one antibonding MO. Thus, we have used 3 atomic orbitals to generate 4 MO’s. This is not possible to do. We can only generate as many MO’s as we have atomic orbitals. Therefore, even the simple structure of acetylene (HCCH) can’t be explained by our current view of atomic orbitals and MO theory. Either the atomic orbitals or MO theory is wrong. Let’s consider another molecule -- methane, or CH4. The Lewis dot structure, combined with VSEPR theory, states that this molecule is tetrahedral. This is confirmed by experiment. However, based on the atomic orbitals that we have at hand, we might start assembling this molecule as is shown in Figure 1. In this figure, we have brought in 3 hydrogen atoms, and located them so that they are s/p- bonding with the px, py, and pz orbitals. Based on the above discussion of acetylene, we know that we can’t bring in the fourth hydrogen atom and form a bond with one=+=2s2pxFigure 4. Adding and subtracting 2s and 2p orbitals from each other. 90o109.5oFig. 3. At left is the structure of CH4 predicted by simply considering the shapes of the p-orbitals. The binding sites are denoted by the oval pads. A 4th H is apparently swimming around the structure. At right is the structure of CH4 as it actually exists. The HCH bondangles are noted. of the ‘unused’ lobes of a p-orbital.Those lobes only appear ‘unused’ in the cartoon. They are actually used up in the already formed carbon-hydrogen bonds. The carbon atom does have one other orbital available for binding to the hydrogen atom, and that is the 2s orbital. However, the 2s orbital is spherically symmetric. Thus, whatwe might expect to form is a methane molecule with 3 hydrogenatoms located at right angles to oneanother, and a fourth hydrogen sortof swimming around the molecule, bound to the 2s orbital on the carbon. This is in contradiction to the actual tetrahedral structure. Wecompare these two structures in Figure 3. It turns out that the answer to these apparent contradictions is that the atomic orbitals we know and love actually change when we begin to consider bonding. They hybridize. What does this mean? All it means is that the orbitals ‘mix’ with each other to form new orbitals. Let’s look andsee how this happens by mixing a single s orbital with a single p-orbital. When we mix orbitals, we add or subtract them from one another. There are two ways to do this. The first is the knucklehead way, and it entails looking up the arithmetic functions in chapter 13 that describe the atomic orbitals. Then we simply add or subtract those functions from one another, and we plot the result. These would be the hybridized orbitals. The second way is much smarter (because it is simpler), and we show it in Figure 4. Here, we just take the graphical representations of the orbitals and add or subtract the graphs. Look at the left side of Figure 4. Here we are adding 2s + 2px together. Note that when the positive 2s orbital is added to the negative lobe of the 2px orbital, we get a very small lobe. Of course we do! We are adding a positive and a negative number. The answer is going to be smallerthan the magnitude of either of the two numbers that we are adding together. However, when we add the positive 2s orbital with the positive lobe of the 2p orbital, we find that the two contributions addspx hybridsHHC1C2C2Figure 5. sp-hybridized orbitals and bonding in the molecule HCCH. Both carbons are sp-hybridized. At top we show the bonds separately, and at the bottom we shown them as they are in the molecule.C12pzC22pzC22pyC12pyFigure 6. The  bonds in HCCH. The H’s and the hybridized orbitals are not shown. constructively to give a really large lobe. When we subtract these two orbitals, we of course get the opposite answer. What we have done is to take two atomic orbitals, and generate two new atomic orbitals. Notice that these orbitals can be used to solve the HCCH problem that we introduced these lectures with. We show this in Figure 5. Now we can use the sp-hybridized bonds to attach a hydrogen and a carbon (C2) to C1) in a linear bonding geometry. According to the Lewis Dot structure, HCCH has a triple bond between the two carbons. In fact, this is observed experimentally as well. With the sp-hypridized orbitals, we have only established a single bond – it is a -bond, since the