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# CHEM 125a: Freshman Organic Chemistry I

## Lecture 6

## - Seeing Bonds by Electron Difference Density

### Overview

Professor McBride uses a hexagonal “benzene” pattern and Franklin’s X-ray pattern of DNA, to continue his discussion of X-ray crystallography by explaining how a diffraction pattern in “reciprocal space” relates to the distribution of electrons in molecules and to the repetition of molecules in a crystal lattice. He then uses electron difference density mapping to reveal bonds, and unshared electron pairs, and their shape, and to show that they are only one-twentieth as dense as would be expected for Lewis shared pairs. Anomalous difference density in the carbon-fluorine bond raises the course’s second great question, “Compared to what?”

Professor McBride’s website resource for CHEM 125 (Fall 2008)

http://webspace.yale.edu/chem125_oyc/#L06

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html## Freshman Organic Chemistry I## CHEM 125a - Lecture 6 - Seeing Bonds by Electron Difference Density## Chapter 1. Understanding Diffraction Patterns: Continuing the Case of the Hexagonal “Benzene” [00:00:00]
And this was the pattern that came out, this thing that looked a little bit like a snowflake, and I’d like you to understand why that hexagon of dots gives a snowflake. So we take the hexagon of dots, and what do we look for to see where scattering might be, to see — what’s the — remember what the trick is? The trick is to look at things that lie on equally spaced planes. Try to choose a set of planes so that as many of the electrons as there are will fall on or near that set of evenly spaced planes. So And this is two dimensions, so we’re looking for lines, or cross-sections of planes, right? So how can we draw lines on here, evenly spaced lines, so that all the dots will fall on them? Well we can do it this way, right? So they’re evenly spaced, three of them, and all the electrons fall on or near them. Notice, they don’t have to fall exactly on, because if they’re displaced a little bit, the phase of the wave will change a little bit, compared to the others; but only a little bit. So it just has to be near, not exactly on. Okay, so there we have it. Now, so that means that you’ll get scattering in that direction, where they will reinforce one another. Let’s go back to the display we were looking at before, here. Okay? We were talking about this just as class started. So a wave comes in, makes these things all move up and down, the electrons, here and here, at the same time. Actually, let’s make all three of them vibrate for current purposes. Okay. Now we’re interested at what angles light can come out and all these things will help each other out, reinforce one another. So as we go here and look at that vertical line, we see that they’re not all in-phase at that angle. But as we increase the angle, when we get to say here, it looks not so bad. The top and the bottom are actually exactly in-phase, but the middle one is exactly out-of-phase, and it’ll cancel out the top one. And if there were a whole row of these, the second one cancels the first, the fourth would cancel the third, the sixth would cancel the fifth, and so on; there wouldn’t be anything coming out. And now we go a little bit away from that. And it’s worth making a point here. Suppose that this were a very, very, very long line of scatterers, right? And the first two — let’s get to this place here where they’re all exactly in-phase; that’ll obviously be a very strong angle. But suppose we looked at another angle that was close to that, but just a teeny bit off. So the first two are off by just 1° in-phase, and the next one’s off by 2° in-phase; not much off, okay? So are we going to get pretty strong light coming out from that? Russell?
Now, when you take a slide with a regular lattice of these benzenes, then — remember, if you took just one, you get this snowflake pattern. If you take a whole row, across the top, like that — — oh pardon me, I meant to say that one will be very weak, you can hardly see it. What you need is a bunch of them to cooperate, to see something that you can see. Now first we could take the whole row along the top, and we’re going to look only at scattering in the vertical direction; so I’ve narrowed in on the picture. But if we take that whole row along the top, remember, they’ll all scatter in-phase at the specular angle, because — for scattering up and down. So now it gets more intense because they’re all cooperating. For other directions they wouldn’t all be in-phase from one hexagon to the next, but for scattering up and down, where they’re all at exactly the same level, they’ll all be exactly the same. Okay, now suppose I add the next row. Will they be in-phase, for the same direction of scattering up and down, where that top row is all in-phase? So we would get the scattering shown here, right? Stronger than it was before because it’s a bunch of these things now, right? But still not really strong. But let’s add in the next row. Is that going to make them all stronger again? No, most of the time they’ll be out-of-phase, from the next row, for scattering in this direction. Right? Most of the time they’ll be out-of-phase, but for
Now, there are two, quote, spaces that get talked about: direct space or real space; and diffraction space or reciprocal space. Okay? So the crystal is the real thing that you’re interested in, and diffraction photo is in diffraction space; you see these dots that Lowy Laue saw, for example, for copper sulfate. Right? So in real space you have a unit cell structure; that is, the thing, the pattern that then gets repeated to make the crystal. But you have the pattern, right? And that gives rise to this fuzzy pattern, like a snowflake in reciprocal space. And then you have a crystal lattice, a regular repetition of these patterns, right? And that’s as viewing through the holes in the pegboard. Okay? And remember that decreased spacing in real space corresponds to increased spacing in reciprocal space; which is of course why it’s called “reciprocal”. Okay, so that’s what we want to understand about how it works. Right? There are patterns which give rise to patterns in reciprocal space, that fuzzy thing, and then if you have a repeating lattice of that, it gets concentrated into particular points; but it’s the same underlying pattern. So there’s the pattern, which is the structure of the molecule, and there’s the lattice, which is the structure of the crystal. ## Chapter 2. Double Helices and DNA: Even and Offset Planes [00:15:11]Okay, now let’s look at the light bulb filament, the last thing we looked at, and see why the scattering from that looks the way we do — — looks like this X with dots along it. Okay, so we take — — we want to find if there are electrons on this helix, right? We can find a set of evenly spaced, parallel planes like the yellow ones here. So we’ll get scattering perpendicular to those planes. And sure enough there it is, that spot. But we could also take a set of planes, and it goes not only up but also down, both branches; both directions of that particular branch of the X, come from the same planes. Okay? But you could make planes that are twice as close to one another. Right? What will those give rise to?
But there’s something funny. The intensity doesn’t just evenly decease as you go out. Instead of being strong, not quite as strong, less strong, weaker, very weak, as you go out, it goes weak, strong, strong, very weak, strong. Now why is that? Why do you get such a funny pattern of intensities? Let’s look here at this thing again. Remember where, if we looked at the first, second, third and so on, we saw that they come in and out of phase. But let’s suppose — so it would be, if you have things that are twice as close together here, as in the first case, what effect does that have on the actual pattern we see? The pattern we saw, if we had only every other one, was here the direct beam, first reflection, second reflection, third reflection, fourth reflection. How does it differ if we add one in between? Okay, here’s the first reflection — can we see that, if we have all three. ? That’s what would’ve been the first reflection if we didn’t have the intermediate one. Do we see a reflection here, if we have a whole row of them? No, because every other one cancels out. So we won’t see that one. How about the next one?
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Okay, so knowing the molecule’s electron density, as we knew our artificial sort of benzene, or this DNA, it’s easy to calculate the crystal’s diffraction pattern, especially if you have a computer to help you out; but it’s not an intellectual challenge, it’s just work. Right? Using pretty heavy- duty math, people got the Nobel Prize for developing it; or a canned program, (that’s what they got the Nobel Prize for), you can go the other way and go from the X-ray pattern to what it was that was causing it. Right? What we did was go from what’s causing it to the pattern, but in fact you can go the other way now when you press a button on a machine. And you get out the electron density at every point in space. ## Chapter 3. Revealing Bonds and Unshared Electron Pairs via Electron Difference Density Maps [00:29:04]Okay, that’s the yield from an X-ray structure. Why don’t you get the nuclear positions, why do you get the electron positions? [Students speak over one another]
This is taken from a book written at that time by Stout and Jensen. And you drew these by hands because you didn’t have a computer that could draw — that could figure out where to draw it and so on. So here were atoms in a particular crystal structure. Then you had a whole bunch of sheets of paper for different slices, through the electron density; stack them up, right? Now sometimes the particular slice you’re working in went right through the middle of an atom, so you got very high electron density. Sometime it just barely touched the atom, right? So you see here that that one, that atom, this particular slice, was very near the nucleus, so we got high electron density. But that one, the nucleus was not in this plane, so you just got a little glancing blow at it. Okay? But you could draw these things on acetate or plastic sheets and stack them up, right? So this was the model made for the first determination of the structure of penicillin; in fact, the potassium salt of penicillin. Where’s the potassium atom? How can you distinguish potassium from nitrogen or carbon or hydrogen or oxygen?
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So first look up there. There are some very dense contours, right in the middle up there, and that’s the hydrogen which was not subtracted, right? So it’s the biggest game left in town, once you’ve subtracted the spherical carbons. Okay, so that’s — and the total amount of intensity in that region is one electron, which is what you expect. Now the total amount of deformation density in this region, where there’s a single carbon-carbon bond, is only 1/10th of an electron. What would Lewis have said? Two electrons, it’s 1/10th of an electron. Okay, now let’s slice that — and within the carbon-carbon bonds of the ring, the aromatic ones, it’s bigger. Why bigger? Because it’s partially double bond in the resonance structures, right? Okay, so it’s 0.2 electrons for those ones in the ring. Now let’s slice it and turn it so we can see its cross-section. And it’s round; no surprise there. But let’s slice the ones in the ring and turn them. It’s oval, not round, the bonds are not round. Why?
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## Chapter 4. The Second Great Question: “Compared with What?” [00:43:23]So here’s another example done by Dunitz in Switzerland and these people who were the — Schuyler Seiler and Schweizer, who were Swiss, who were the progeny of watchmakers and people that do very precise work; because to do this you have to have [Students speak over one another]
[Technical adjustments] Come on baby. I worked hard on this. Okay, I’ll tell you what it says. [Laughter] [Technical Adjustments]
Okay. [Laughter and applause] “What do you think of him?” “Compared with what sir?” “Exactly.” That’s the second question,
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