![]() They do it in order to get the best overlap. So let's look.įirst, I will assert that the best overlap you can get between hybrid orbitals on these carbons - if the nuclei are arranged in an equilateral triangle, so 60º angles - the best hybrids you can get point at the angles shown by the red arrows here. Okay? But analysis in terms of pairwise - that is, don't go over the whole molecule, just look at two atoms adjacent to one another, making a bond, so just a very local view - pairwise bonding overlap of hybrid atomic orbitals explains these two pathologies. Even if you believe that it gives you the right numbers, it doesn't tell you why. Right? So the answer is no, it doesn't provide understanding. Right? And there's so much other electron density in the molecule, with all complicated nodes, that it's very difficult to know where to look. Even if you grant - which is not easy to grant - that this is the proper orbital to look at, and that indeed the electron density of the red and blue, big red and blue lobes, are not on the line between we don't know why they are. But there are thirty-three of these occupied orbitals, and they put electron density every which way, and it's very difficult to understand why this is the way it is, why it's bent. And you see there is electron density in those - the wavefunction has big value in the region where those bonds are bent. That's the one we were just looking at, before we went on to the PowerPoint. And so we could look at the thirty-second of the thirty-three occupied orbitals, the next to the highest occupied orbital, and it looks like that. There's the framework of the molecule superimposed on this map, and that triangle on top there, on the right, is what we're looking at. Now, can we understand that, from the point of view of molecular orbitals, of Schrödinger's equation why it should look like that in this particular case? So would a computer's molecular orbitals provide understanding? So I was just showing you, as the class assembled, how you get these molecular orbitals, and I was showing you some of them. They don't lie on the line between the nuclei. So that bond isn't there in the electron density, the difference density. Professor Michael McBride: And one bond is missing. Student: And there's another bond that's missing. Professor Michael McBride: Some of the bonds are bent, and what else? And you remember what's funny about it? What's pathological? Dana? We looked at a cross-section through those three atoms, and it looked like that in the electron difference density. Right? When we were looking, we looked at this molecule and said that the bonding, from the Lewis point of view, was pathological. Okay, so let's see if we can understand some of the things that we didn't understand when we were looking at the molecule really, with X-ray diffraction. You're a chemist, and your goal is to understand things let the computer do the heavy lifting mathematically and you understand it. But you're neither the molecule - well you are a molecule - but you're neither the kind of molecule we're studying, nor are you a computer. You can't do it absolutely, but you can, depending on how much computer power you want to throw at it, you can do it close enough for most purposes. Right? And the goal of the computer is to approximate the Schrödinger equation. Or we can do a computer calculation, and if we do a careful enough computer calculation, we can get something that we believe is pretty close to reality, like the total electron density I showed you. We can look at the real molecule, for example, with X-ray. Professor Michael McBride: Okay, so now we have a number of different perspectives we can take on understanding what holds molecules together that is, on bonding. Criteria for assessing reactivity are outlined and illustrated. This is shown to be a generalization of the traditional concepts of acid and base. This lecture then focuses on understanding reactivity in terms of the overlap of singly-occupied molecular orbitals (SOMOs) and, more commonly, of an unusually high-energy highest occupied molecular orbital (HOMO) with an unusually low-energy lowest unoccupied molecular orbital (LUMO). Professor McBride begins by using previous examples of "pathological" bonding and the BH3 molecule to illustrate how a chemist's use of localized bonds, vacant atomic orbitals, and unshared pairs to understand molecules compares with views based on the molecule's own total electron density or on computational molecular orbitals.
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