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5.111 Principles of Chemical Science, Fall 2005 Transcript – Lecture 28

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5.111 Principles of Chemical Science, Fall 2005 Transcript – Lecture 28 MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science, Fall 2005 Please use the following citation format: Sylvia Ceyer and Catherine Drennan, 5.111 Principles of Chemical Science, Fall 2005. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (accessed MM DD, YYYY). License: Creative Commons Attribution-Noncommercial-Share Alike. Note: Please use the actual date you accessed this material in your citation. For more information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms MIT OpenCourseWare http://ocw.mit.edu 5.111 Principles of Chemical Science, Fall 2005 Transcript – Lecture 28 All right. We have a few more PowerPoint things before I am going to attempt using the board. Again, we are in the transition metal unit. And today we are going to introduce something called crystal field theory. And this is in Chapter 16 in your book. Let me just tell you about two different theories. Again, chemistry is an experimental science. We collect data and then we try to come up with theories that explain the data, so the theories are not sort of 100%. And some are more simple and some are more complicated to try to explain what we observe. And some of these theories, although they are pretty simple approximations of what is really going on, do a pretty good job of explaining the things that we are observing. All right. There are two different kinds of theories that you will hear about with transition metals. You will hear about crystal field theory and ligand field theory. And so these were, again, developed to explain certain types of properties of coordination complexes of transition metals. There is observed data. And then people tried to think about how you could rationalize what was observed. The basic idea behind these theories is that if you have your metal ion with its given oxidation number and it is in the center of a coordination sphere, the energy levels of the d-orbitals for that particular metal are going to be altered when ligands are bound compared to sort of a free system. The binding of ligands around that metal, where there are those d-orbitals associated with that metal, is going to have an effect and create special properties. Crystal field theory, which is what we are going to be talking about, is based on an ionic description. Basically you are going to be considering your ligands as negative point charges, a negative charge. And you are going to ask the question is that negative charge pointed toward a d-orbital? If so, that will be repulsive. And that is going to have an effect. Ligand field theory includes covalent, as well as ionic description. It is a more powerful theory and it can describe things a little bit better, but we don't have enough time to cover it here. If you are interested in transition metals, you will probably go on and take another chemistry course called 5.03 which is inorganic chemistry. At this point, we are just going to be doing the more simple theory which just considers the ionic descriptions. But it does pretty well. You can explain some things with it, but you should be aware that you can do a little bit better with another theory. You should just be aware of that, that this is really the most simplistic kind of representation or theory to explain some of the properties of coordination complexes. All right. All of these theories require you to think in 3-dimensions about d-orbitals. Because they are all about the interactions with ligands, either covalent or ionic interactions, but they are all about the interactions of ligands with those d-orbitals. I mentioned last time that you need to know the shapes of the d-orbitals and you need to be able to draw them to some limited ability. We went through the names of the d-orbitals last time. Let's just review it now because we are going to be talking about this more today. What is this guy up here? That is dz2. And here is our reference frame. z is up here, y along here, and x is coming out toward you. What about this one? Dx2 minus y2. Down here, what is that one? dxy. The amplitudes are 45 degrees off the axes in the xy plane. Over here we have dyz, so now we are along z. And the last one is? xz over here. All right. Those are the five d-orbitals that we will be talking about a lot in the next few lectures. All right. Let me just show you. This is really 3-dimensional, so let's take a look at the 3-dimensional image of these d-orbitals. This is dz2. This isn't in your handout, obviously. It is a movie, but you can sort of get a little better sense of the 3-dimensions here. All right. The movie first rotates the axes. I am not sure why it does that. And then it is going to rotate the d-orbitals. You can see the doughnut in the middle with the hole and that the maximum amplitudes are along the z axis here. This is dz2. And the orbitals are right along the z axis, which is important. Now let's take a look at dx2 minus y2. The important point here is that the orbitals are directly on axis, and the axes are the x and the y. You can see how they are directly along those axes. All right. Here is the next one. Here we have dxy. And now the orbitals are not along the axes. They are 45 degrees in between, so they are not along, they are in between, which is the key point for this d-orbital in terms of what we are going to be talking about. Now we have some amplitude along the z axis. We have z and x. Again, the orbitals are 45 degrees off the axes. And we have one more. Now we have dyz, again 45 degrees off the axes. All right. Now you should have these sort of orbitals floating around inside your head. And, as we talk about bringing ligands in toward the orbitals, you can think about how those ligands are coming in and what orbitals they are going to be near. Again, crystal field theory is just considering the ionic interactions. And it is really considering the ligands as negative point charges. And so negative point charges are going to be repulsive with the d-orbitals. d- orbitals don't like it when you have these negatively charged ligand coming in and being near. It will be repulsive near the d-orbital. This is just another way to sort of draw that. And we have our octahedral frame. Here we are talking about a octahedral geometry. And we can think about how ligands are going to be affecting the d-orbital in these various places. If you had ligands on all of these positions in an octahedral arrangement around the metal. And you can think of these ligands as these negative point charges. And so this is just another depiction. Here are the d-orbitals again. It is a slightly different xyz frame, but not too much different. And so here are our orbitals. And these little green dots represent the point charges. What we will be thinking about today is the effect of ligands being close to the d-orbitals. You see here there is a ligand that is quite close up here and one down here. In this picture, these negative point charged ligands are also really close to the orbitals. Here they are not really as close. They are sort of off axis. And that becomes really important. All right. Let's now think about the different d- orbitals and the ligands when the ligands are arranged in an octahedral geometry. In this case, we have these ligands, these negative point charges coming in on all the different axes. And so, if we think about it, these are close. And I mentioned that in the last slide. A negative point charge along z is going to be very close to dz2 and it will be repulsive. For dx2 minus y2 the negative point charges along y and along x are also going to be very close to these d-orbitals. And that will, again, be repulsive. We are going to have a large repulsive interaction for these two orbitals with an octahedral geometry. These two d-orbitals are destabilized, and they are destabilized by the same amount. When they are destabilized by the same amount, what is that called? The energy of the orbitals are the same, what is that called? Yeah, they are degenerate. And so these two orbitals then will be more destabilized by those ligand negative point charges than the other sets of orbitals. Because they are off axis and the ligands are on axis. The negative point charges will be farther away from these guys. Let's take a look at that as well. Here we have our three other d-orbitals. And if ligands are coming in as negative point charges on axis, they are not going to be directly pointing at any of these orbitals. Because they are 45 degrees off axis. Ligands are on axis. It is not directly pointing toward any of them. These three orbitals then are stabilized relative to the other sets of orbitals we talked about and they are stabilized by the same amount.
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