00:00:00 Our next speaker is E. Bright Wilson, who is a professor emeritus in chemistry from

00:00:27 Harvard University.

00:00:29 He holds degrees from Princeton University, California Institute of Technology, and Harvard

00:00:35 University.

00:00:36 He's been a professor of chemistry at California Institute of Technology and at Harvard University.

00:00:44 His research area is quantum mechanics and chemistry, molecular dynamics, and microwave

00:00:50 spectroscopy.

00:00:52 He has received many honorary degrees and awards.

00:00:56 I want to describe two of these for you.

00:00:59 In 1962, he received the Peter DuBois Award in physical chemistry, and he was the first

00:01:06 recipient of the Peter DuBois Award in physical chemistry.

00:01:13 This is an award of the American Chemical Society.

00:01:16 As I told you earlier, it was established by the Humble Oil and Refinery Company.

00:01:22 It is now sponsored by the DuPont Company.

00:01:27 In 1972, Professor Wilson received the Pauling Award.

00:01:35 The Pauling Award is presented by the Oregon and Puget Sound section of the American Chemical

00:01:41 Society, and it's in recognition of contributions in chemistry meriting national and international

00:01:49 recognition.

00:01:50 I thought this was nice that Professor Wilson has received both the DuBois Award, named

00:01:57 after the person that we're honoring today, and has received the Pauling Award, named

00:02:03 after one of our speakers that we hope will be here this afternoon.

00:02:09 To us at Cornell, one of the most significant things, I think, that I would like to tell

00:02:15 you about Professor Wilson is that his sons, he has two sons that are professors at Cornell

00:02:22 University.

00:02:23 David is a professor of biochemistry and molecular and cell biology, and Kenneth is the James

00:02:31 A. Weeks Professor of Physical Science, and we appreciate having these sons as our colleagues.

00:02:42 Professor Wilson's lecture this morning is on extraction of barriers to internal motion

00:02:48 and other information about reaction paths from spectroscopic data with malhydride as

00:02:56 an example.

00:02:58 Professor Wilson.

00:03:31 Thank you.

00:03:43 Having been all wired, I've become an electronic object, which is supposed to be the timely

00:03:48 thing to be, I think.

00:03:52 I certainly am extremely honored to be able to take part in this occasion in honor of

00:04:00 the late Professor Debye.

00:04:02 I'm not sure whether Linus Pauling or I saw him first in our lives, not that it matters,

00:04:07 but I did first encounter him when I was a freshman, and he was giving a lecture in Philadelphia

00:04:15 on the dielectric theory.

00:04:17 I was very fortunate to be taken to the lecture by several of my professors at Princeton.

00:04:26 What I'm going to talk about today sounds fairly detailed, I know, and I'll try to

00:04:33 avoid some of the excessive detail as we go along, but I do strongly believe that science

00:04:41 is built out of a lot of very minute details, which add together to something in the end.

00:04:47 What I hope to accomplish is to show you how these things, how this particular set of observations

00:04:54 and analyses add together to give something of significance, I hope.

00:05:00 Now I'll start with the first slide, please.

00:05:04 See how that's going to work here.

00:05:06 Can you see that all right with the lights that's there?

00:05:09 Well, see, I'm going to talk about reaction paths.

00:05:13 There's much of a reaction as a hydrogen atom going from one oxygen to another in the same

00:05:18 molecule.

00:05:21 It has to pass over a barrier to internal rotation, I mean, a barrier, not from one

00:05:28 oxygen to the other.

00:05:31 And we can get a lot of information about this particular molecule, which is melanaldehyde,

00:05:40 by studying its microwave spectrum in some depth, and some of the things I've listed

00:05:46 here.

00:05:47 Now the next slide, please.

00:05:54 Now most of the information we're going to discuss is obtained from microwave spectroscopy.

00:06:02 And I have a bit of a bias on this subject, and I feel the following way about it.

00:06:08 If we can learn information entirely ignoring other people's information, well, that's

00:06:15 too much to ask.

00:06:16 So if we do not use, let us say, infrared, nuclear magnetic resonance, or other of these

00:06:24 powerful tools, but only stick to our own tool, and if we finally are surprised when

00:06:31 we get our answer, find out that everybody else has gotten the same answer, fine.

00:06:35 I've got independent verification now.

00:06:37 Whereas if I start out and say, now there's this fact from NMR, and this one from infrared,

00:06:42 and this one from microwaves.

00:06:44 Let's see if we can put them together in terms of a hypothesis.

00:06:47 But you can always do that, you know, with a finite number of pieces of information.

00:06:52 But I think the idea of doing it independently, and then finding out that you're in agreement,

00:06:57 or not, as the case may be, is a firmer way of sort of nailing down the benchmarks as

00:07:04 you go along.

00:07:07 And of course, microwave spectroscopy, everybody knows about these things.

00:07:11 Well, I think so.

00:07:12 When I see the size of this audience, there surely aren't that many people in the world

00:07:15 interested in microwave spectroscopy.

00:07:19 But it'll do a lot of things, as you can see from this slide, and we'll use a lot of them

00:07:23 in applying it to this molecule.

00:07:26 But why H-bonds?

00:07:27 Well, I hardly need to say that here, or any other place nowadays, when hydrogen bonds

00:07:33 are so important in biochemistry.

00:07:36 Seems everything has to be laced together by hydrogen bonds, or you can't live.

00:07:41 But I won't argue with that one much.

00:07:43 Let's go on to the next slide.

00:07:45 Well, we're going to talk exclusively about one molecule, and it's indicated in one of

00:07:52 its forms there at the top.

00:07:55 It occurs, and is supposed to occur, according to these other techniques, in a variety of

00:08:01 forms.

00:08:02 But microwave spectroscopy only works with vapors, low-pressure vapors, and that's what

00:08:07 we'll study, is the vapor phase form of this molecule.

00:08:11 And we're going to find that it does come in a ring, the ring being closed by a hydrogen

00:08:16 bond.

00:08:17 And one asks, then, why this molecule, and why put so much effort into it, as we have?

00:08:23 Well, it's one of the simplest internally hydrogen-bonded molecules, especially one

00:08:30 of the simplest where you have the possibility of a symmetric system, where it could be that

00:08:36 the hydrogen would appear to be in between the two oxygens, and halfway in between, perhaps.

00:08:41 It isn't, but that's where it could have been.

00:08:45 And furthermore, because of certain perturbations in the spectrum that I'll show you, you get

00:08:51 more information about a molecule of this kind through the perturbations than you can

00:08:55 get normally from just analyzing the ordinary rigid rotor or a similar spectrum.

00:09:02 Well, let's go on to the next slide.

00:09:07 Now, microwave spectroscopy, and this is true, of course, of every other branch of physical

00:09:12 chemistry, I believe, you start by making models to interpret the experimental data

00:09:18 that you have.

00:09:19 Now, it used to be, when I was an undergraduate in those dark days, you wrote down numbers,

00:09:25 and they meant something from the experiments you were at, or weighed something.

00:09:32 You had very little calculating to do to get a number that people were excited to publish.

00:09:37 Here's a number.

00:09:38 This is molecular weight, or concentration, equilibrium constant, or something.

00:09:43 They were pretty direct consequences of the measurements and observations that you made.

00:09:48 But of course, nowadays, it's not true at all.

00:09:50 You get thousands of numbers, a big printout, and you have to run the computer at full blast

00:09:56 for weeks to figure out what you've got.

00:09:59 So nothing is simple anymore.

00:10:01 It all comes from some complicated quantum mechanical calculation, or statistical mechanical,

00:10:06 perhaps.

00:10:07 Well, here, we'll start with a terribly simple thing.

00:10:12 We'll say, look, here's a bunch of spectra, or here's a spectrum from a given substance.

00:10:19 And I can account for most of these lower energy level lines, at any rate, with the

00:10:24 simplest possible model, just a solid blob of stuff, which only has three properties,

00:10:31 three principal moments of inertia, just mechanical moments of inertia, the masses times the square

00:10:37 of the distance from an axis, summed over the particles.

00:10:41 You don't ask anything else about it, except those three moments of inertia.

00:10:46 We adjust them to fit the low-lying spectral lines, and thereby, we extract from those

00:10:52 lines three moments of inertia of our model.

00:10:56 Well, we're not very much interested in just a solid blob of stuff.

00:11:00 So we want to go to a more elaborate model.

00:11:02 And of course, that's the chemist ball and stick model.

00:11:05 Laboratory is full of them.

00:11:07 We have point masses, and then we have rigid sticks, weightless sticks, holding the atoms

00:11:14 together.

00:11:15 And we need that extension.

00:11:18 Each one of these models, of course, has three moments of inertia.

00:11:22 It has the properties that the blob of stuff had before, but it obviously has more detailed

00:11:28 information telling us about the interatomic distances.

00:11:32 Well, most molecules have more than three interatomic distances.

00:11:35 So we can't do anything with just one spectrum, which gives us three moments of inertia.

00:11:42 But if we put in isotopic atoms, as you know, you can assume to a pretty good approximation

00:11:47 that the distances don't change.

00:11:50 The masses do, and therefore, the moments of inertia do.

00:11:53 So if you make enough isotopes, in principle, you ought to be able to fit these separate

00:11:57 spectra of these isotopic species and come out with the distances between the atoms,

00:12:03 which are the new parameters.

00:12:04 Well, that's fine, as long as we stick to pretty low-lying energy levels.

00:12:08 We go much higher, we discover that it doesn't fit exactly the rigid rotor and quantum mechanical

00:12:14 formulas.

00:12:15 And we can elaborate on that.

00:12:18 We can put in, you know, allow it to vibrate, allow small amplitude vibrations in the atoms.

00:12:23 Of course, we know they're there, that we should have put them in the first place.

00:12:27 This introduces certain changes, means that our moments of inertia have some kind of average

00:12:32 over the vibration, and that may give us some trouble later on.

00:12:36 And secondly, it introduces centrifugal distortion.

00:12:38 As the molecule rotates rapidly, these no longer completely rigid bonds begin to stretch.

00:12:46 So we've complicated life a bit, but also, we find we can get more information out of

00:12:51 it.

00:12:52 If we can see the difference between a rigid rotor spectrum and more higher energy parts

00:12:56 of the spectrum, if we can fit these differences, centrifugal distortion, for example, we can

00:13:01 get information about the stiffness of those chemical bonds and other properties.

00:13:06 Now, if we go further and say, well, look, we left out something there.

00:13:09 Hamiltonian isn't just the kinetic energy of rotation.

00:13:13 There is now this vibration going on in the molecule.

00:13:17 And these will be coupled through Coriolis terms, for example.

00:13:21 So we have to add the Coriolis terms.

00:13:23 Well, they don't amount to much at first in many ranges of the spectrum.

00:13:28 But we will find that they do in this spectrum, that they do introduce significant perturbations.

00:13:34 That's good, and it's bad.

00:13:35 First, it's more trouble to figure out what's going on.

00:13:38 But having done so, you get more information.

00:13:41 So at each stage of the game, we use more and more elaborate models, and we get more

00:13:46 and more information that required more work.

00:13:50 Now, we're going to use this kind of information to try to answer some questions about malonyl

00:13:54 aldehyde.

00:13:55 If I have the next slide now.

00:13:59 Here are the first questions.

00:14:00 Is it really a hydrogen bonded ring?

00:14:04 If it is, does the ring lie in a plane?

00:14:07 The atom's in a plane.

00:14:09 Where's the hydrogen?

00:14:10 It's between two oxygens, presumably.

00:14:13 It's going to form a hydrogen bond.

00:14:15 But is it nearer one oxygen to the other, or is it sitting in the middle?

00:14:19 And related to that, there's some carbon-carbon bonds in the molecule.

00:14:25 Are they single or double, and how about it?

00:14:27 Well, let's look at the next slide.

00:14:29 OK.

00:14:31 This is what we come to by analyzing the spectrum.

00:14:37 We'll discuss it in a little bit more detail.

00:14:39 We come to the conclusion that there are two forms.

00:14:42 Here's the hydrogen over next to this oxygen.

00:14:45 Over on the other side, the hydrogen's next to that oxygen.

00:14:47 If you go from one to the other, it just moves a fairly short distance.

00:14:52 Everything moves a little bit, as we should see.

00:14:54 We pass through this transition state, where

00:14:56 the bonds down here are equal, the two sides, and the hydrogen in the middle.

00:15:02 Now, it might be that this is an equilibrium position,

00:15:05 that there's a minimum energy.

00:15:07 But that is not what we find.

00:15:10 Walter Rowe, who was a student who worked on this first,

00:15:14 found that, really, it's this going through a transition state to that

00:15:18 and back in.

00:15:18 In other words, it's an unsymmetrical, two asymmetric equilibrium

00:15:26 configurations.

00:15:28 And the molecule is tunneling between those two.

00:15:31 So there are two energy minima and a maximum in between the transition state.

00:15:36 Well, how do we know that?

00:15:39 Well, the next slide, I point out Walter Rowe in 1975.

00:15:46 He found two rigid rotor spectra.

00:15:49 And they showed alternating intensities,

00:15:52 like our ortho para hydrogen, which is, of course,

00:15:55 if you go back to the previous slide, you find it has hydrogens.

00:15:58 It has one pair of hydrogens to get into change.

00:16:01 It should do that.

00:16:02 Furthermore, except for that alternating intensities,

00:16:05 the two spectra have essentially the same intensity.

00:16:09 Well, that's a little puzzling at first,

00:16:10 except we have plenty of historical precedent, of course, now.

00:16:15 What it means is that the two equilibrium configurations

00:16:18 are equal and equivalent.

00:16:20 And the molecule is tunneling back and forth,

00:16:23 as I said on the previous slide.

00:16:26 So he interpreted this that way, that the hydrogen was not

00:16:30 in the middle, that there was some kind of barrier between the two

00:16:33 equilibrium configurations.

00:16:36 And the barrier was of such a height that tunneling was occurring.

00:16:41 And we could see it as the spectrum was doubled.

00:16:45 There were two rigid rotor spectrum.

00:16:49 Now, the double minimum problem is not new.

00:16:53 It began, in fact, some of the very first work

00:16:55 in microwave spectroscopy was on the double minimum problem

00:16:58 in ammonia, which is where it goes through the planar structure

00:17:03 into either side, giving equivalent structures.

00:17:10 So lots of work gone into fitting that with simple formulas,

00:17:14 understanding it, and measuring it, and so on.

00:17:17 And even before microwave spectroscopy

00:17:22 was invented, so to speak, that was known about ammonia.

00:17:26 And later on, I should mention the beautiful work

00:17:29 on ring puckering and four-membered rings

00:17:32 by Gwynne and his students, actually

00:17:34 Harrison and Suni Chan and others.

00:17:39 That was a model set of papers.

00:17:42 And in principle, we sort of thought at first

00:17:45 we could just copy their stuff and apply it

00:17:47 to these spectra of this molecule.

00:17:50 But this turns out to be a little more complicated,

00:17:52 a little more trouble to handle than the four-membered rings,

00:17:56 unfortunately.

00:17:58 Well, the next slide is a question of structure.

00:18:02 Let's talk about quantitative structure,

00:18:04 because that's one of the things we

00:18:06 think microwave spectroscopy is pretty good at.

00:18:09 If you have a small polar molecule in the gas phase

00:18:12 and you can do enough isotopes, you can usually

00:18:15 get the structure pretty well.

00:18:17 Well, you need enough isotopic species,

00:18:19 because you only get three parameters for each species

00:18:22 you put in the machine.

00:18:24 You get your rigid rotor spectrum, let's say,

00:18:27 and you get three moments of inertia.

00:18:29 But if you have enough isotopic species,

00:18:32 then you can locate usually all the atoms.

00:18:35 Well, we have enough.

00:18:36 I think we have 29 species.

00:18:39 I think they got a little enthusiastic grinding out

00:18:44 these species.

00:18:45 Actually, I should point out that the chemistry was done

00:18:49 mostly by Dr. Richard Durst, who at that time

00:18:52 was at the University of Wisconsin, Eau Claire.

00:18:56 He spent a number of summers with us at Harvard.

00:18:59 And he also took home the workload

00:19:02 and shared it out to some of his undergraduate students.

00:19:05 So he made a lot of species labeled in all kinds of ways.

00:19:12 And we have used them.

00:19:13 We're still working on them.

00:19:15 Dr. Susanna Smith did a lot of the analysis of these spectrum.

00:19:23 I should mention first that Stephen Baucom was

00:19:29 a second student.

00:19:30 And he was important in the whole process.

00:19:32 And I'll give him specific acknowledgment later.

00:19:37 Now, in doing the structure here,

00:19:39 it turned out this is not an elementary operation.

00:19:44 It's not like the ordinary rigid molecule

00:19:46 because of the tunneling between the two structures.

00:19:49 And the question is, what are you

00:19:50 getting if you try to apply the conventional methods

00:19:53 of determining the structure?

00:19:55 What are you getting, an average over this quantum mechanical

00:19:58 state, which is tunneling back and forth?

00:20:01 Or are you getting the unsymmetrical individual

00:20:03 structures?

00:20:04 Well, we wanted the unsymmetrical equilibrium

00:20:07 forms of the molecule.

00:20:09 And we got them in a special kind of way.

00:20:12 Tunneling was messing us up.

00:20:14 So we stopped it from tunneling.

00:20:17 Cy Bauer is an expert at stopping things,

00:20:19 this kind of molecule, from tunneling.

00:20:22 He puts a different atom on each substituent on each side.

00:20:25 We put a deuterium on one side.

00:20:28 And if you have deuterium in the hydrogen bond, which

00:20:31 is easier to stop than a hydrogen in the hydrogen bond,

00:20:35 then when you put a deuterium on one side,

00:20:38 tunneling, for all practical purposes, is quenched.

00:20:41 Just enough asymmetry to the system to stop it.

00:20:45 You might say, well, that's nonsense

00:20:47 because we have the Born-Oppenheimer principle.

00:20:49 It shouldn't make any difference what

00:20:50 isotopes you have in the Born-Oppenheimer

00:20:53 level of approximation.

00:20:56 But we'll discuss that a little bit later.

00:20:58 It's an artifact, really, of the fact

00:21:00 that we're talking one-dimensionally

00:21:01 on a 21-dimensional problem.

00:21:05 So at any rate, we have a number of empirical evidences

00:21:08 that when you do this kind of asymmetrizing,

00:21:11 you stop the tunneling.

00:21:13 It actually took three deuterium because you

00:21:16 can't get one in hydrogen bond without putting

00:21:19 one on the opposite side of the ring at the same time.

00:21:22 So we have triply deuterated species,

00:21:24 which you'll see in a minute.

00:21:26 And then we have to put a fourth isotope in to find out

00:21:29 where that particular atom is.

00:21:31 So we'd like to label each and every atom in the molecule,

00:21:34 except these three separately, and then locate

00:21:38 all the atoms in that manner.

00:21:39 Well, we didn't quite reach that,

00:21:41 but we did a number of four-atom substitutions,

00:21:44 like the Durst did, and come out with contributions

00:21:48 to the structure.

00:21:50 The next slide, then, shows what we got.

00:21:53 Hope you can see those numbers all right in the back.

00:21:57 I'll just point out a few features.

00:21:59 First of all, I've labeled this deuterium over here

00:22:01 against hydrogen on the other side.

00:22:04 And over here, we have the hydrogen bond

00:22:07 with the deuterium in it.

00:22:09 So this is the asymmetrical species.

00:22:13 And these numbers are for its equilibrium configuration.

00:22:16 Now remember, it isn't tunneling.

00:22:17 It's just an ordinary molecule, so you

00:22:19 can read it in the ordinary way.

00:22:23 I won't comment very much.

00:22:26 There are a few of these numbers that aren't very good.

00:22:28 We don't know really where this atom is,

00:22:30 because it's sitting right on one of the axes.

00:22:32 They're very close, so we're a little uncertain about that.

00:22:35 Some of these are not quite.

00:22:37 But I'd say, in general, sort of a rule of thumb,

00:22:41 you can usually get these things to about a hundredth

00:22:44 of an angstrom bond length, and perhaps about a degree, maybe

00:22:47 half a degree in angle.

00:22:50 And you don't always do that well, but that's about it.

00:22:54 And when people talk about this next decimal place,

00:22:57 I tend to be a little skeptical.

00:22:58 But sometimes, it does seem to be

00:23:00 good to a few thousandths of an angstrom, but not always.

00:23:07 So we have a structure.

00:23:09 Well, let's look at the next slide.

00:23:13 What about calculations of this structure?

00:23:16 That's not quite so easy to see,

00:23:20 but this is the experimental R structure we've got.

00:23:25 This one over here is a calculated structure

00:23:27 from quantum chemistry.

00:23:29 There have been a number of those carried through.

00:23:31 There have been four or five calculations

00:23:33 in quantum chemistry.

00:23:35 This one is from Bicerano, Schaefer, and Miller

00:23:40 at Berkeley, and we're very grateful to get

00:23:43 their data ahead of time.

00:23:45 We're very careful not to let them have our data ahead

00:23:48 of time.

00:23:51 That's unfair.

00:23:53 And the day is going to come when

00:23:57 I hope it'll be possible to send to the National

00:23:59 Academy of Sciences or some such body a sealed envelope

00:24:03 and say, here's our results experimentally.

00:24:07 Those so-and-sos from the other place,

00:24:09 they've got theirs in an envelope,

00:24:11 and we'll deposit them in front of a notary public.

00:24:14 And then at some ceremony, tear open the two envelopes

00:24:17 and see how they agree.

00:24:19 That's really very important.

00:24:21 Really very important.

00:24:22 I mean it now.

00:24:23 I had a beautiful and a very ugly example of it,

00:24:26 I should say, and I'll mention later.

00:24:29 Well, the point I want to make here

00:24:32 is that it's really pretty darn good.

00:24:33 If you look around here, these distances and so on,

00:24:37 you'll notice that this is not the same as that,

00:24:40 because one of them's a double bond, one's a single bond.

00:24:43 Likewise down here, they're not quite the same.

00:24:46 But the agreement is roughly within that hundredth

00:24:50 of an angstrom limit that I mentioned.

00:24:53 However, it's not wholly so good,

00:24:55 because up at the other end, which is the interesting end,

00:24:58 they don't quite do it so well.

00:25:01 Now, that's assuming we're right and they're wrong.

00:25:04 And I can't say that for sure, but it does turn out

00:25:09 that I have more confidence in one of the distances

00:25:12 that doesn't show on these diagrams, the oxygen-oxygen

00:25:14 distance, because we were able to get that

00:25:17 in a number of different ways with different combinations

00:25:19 of isotopes.

00:25:21 And that does not agree well with their distance.

00:25:24 Likewise, this distance is not very good.

00:25:27 You see 1, 9 and 1, 6, 8 here.

00:25:31 So I conclude from this that we are stretching

00:25:35 the present day limits of a priori quantum mechanics

00:25:39 and handling a molecule with this number of electrons

00:25:43 and atoms.

00:25:43 I think it's really a rough job.

00:25:45 And yet, a lot of people have done it,

00:25:47 and they do have calculated it.

00:25:49 And I think the Vicerano and Miller and Schaeffer

00:25:56 had a quite elaborate, high-powered calculation

00:26:02 of this.

00:26:03 That's their calculation here.

00:26:05 And you see, even with a very large amount of computer time

00:26:10 and a very powerful computer, they

00:26:13 don't get the other end of the molecule too well.

00:26:15 And there's perfectly good reason for that.

00:26:17 See, this isn't a priori at all when

00:26:21 they talk about a priori calculations.

00:26:23 It's wholly guided by experiment,

00:26:25 because it's only by trying it and seeing whether it works

00:26:28 compared with experiment.

00:26:30 You know whether they're using the best basis sets

00:26:32 or a good basis set.

00:26:34 Or they have also a choice of configurations

00:26:36 if they have configuration interaction.

00:26:39 They don't know what configurations to mix in

00:26:41 until they've had some empirical experience.

00:26:44 Well, they've got quite a lot of empirical experience

00:26:46 with this kind of bonds.

00:26:48 They have relatively little about the hydrogen bond.

00:26:51 So it's not at all surprising or derogatory

00:26:56 when they don't come out too well up there.

00:26:59 Again, I repeat, I'm claiming that we're right

00:27:02 and they're wrong, and that may not be true.

00:27:06 And that's one of the things we've really got to find out.

00:27:08 So I think in the case of structure,

00:27:11 we're stretching the limits of what's practical at this time

00:27:16 with fair accuracy.

00:27:17 And we're going a little beyond it

00:27:19 when there's a hydrogen bond in the molecule.

00:27:23 So that's the point about structure.

00:27:26 And if I could have the next slide just summarizing this,

00:27:32 that the quantitative structure of the vapor,

00:27:35 both theory and experiment, give a planar hydrogen bonded

00:27:38 ring, and they always did from the beginning

00:27:40 when they were primitive calculations.

00:27:44 The later calculations all give a double minimum.

00:27:47 Some of the earlier ones gave a single minimum

00:27:50 with the hydrogen tunneling between the two

00:27:52 equilibrium configurations.

00:27:54 Distances and angles are good except these here.

00:27:58 And I repeat my comment that I don't

00:28:01 think they ought to call it a priori quantum mechanics.

00:28:04 It's pretty darn good in the absolute.

00:28:06 It's not quite good enough in the practical sense

00:28:08 that you'd like to have it better.

00:28:11 Now going on from the just one more comment about structure

00:28:17 from the next slide, because of the atoms

00:28:23 are vibrating in our model, and we've

00:28:26 got to somehow average over that motion,

00:28:29 it turns out there are lots of different kinds of distances.

00:28:32 And they aren't all the same.

00:28:34 I won't go down through them.

00:28:36 RS is where you use only the changes in moments

00:28:39 of inertia produced by isotopic substitution of one atom.

00:28:42 This is an average over the quantum mechanical motion.

00:28:45 This is the minimum energy of the Born-Oppenheimer

00:28:49 equilibrium.

00:28:50 Because we ought to be able to do better than Born-Oppenheimer.

00:28:53 We can't right now, but we should be able to do better.

00:28:57 And then we'd be in another kind of distance.

00:28:59 And I've discussed that once.

00:29:02 It's a very interesting question,

00:29:03 very interesting question whether a molecule has

00:29:05 any structure in a certain philosophical sense.

00:29:09 And it certainly doesn't know which one it has.

00:29:12 It has several kinds of.

00:29:14 They're not very different from one another,

00:29:16 but we're beginning to push on that limit a little bit.

00:29:20 Now the next slide goes on to something that really concerns

00:29:26 Professor Debye.

00:29:27 This is the great man on dipole moments

00:29:31 and his famous formula on the dielectric constant

00:29:35 as a function of temperature related to the dipole moment.

00:29:39 But since then, microwave spectroscopy,

00:29:43 by putting on an electric field and looking

00:29:45 at the effect on the spectral lines, the Stark effect,

00:29:48 you can get the dipole moment out of the spectrum

00:29:51 very readily and more accurately than you

00:29:55 can measure it other ways.

00:29:57 You get the separate components, x, y, and z, if any.

00:30:00 You can get values for isotope species and natural abundance,

00:30:03 for example, sometimes.

00:30:05 You can get the dipole moment as a function of vibration state

00:30:10 or even a rotational state.

00:30:11 If you go very high, you'll stretch the molecule a bit

00:30:14 and it spins.

00:30:15 So this is a very good method studying dipole moments

00:30:20 and various properties.

00:30:21 Next slide shows, in this particular case,

00:30:26 here are some of the species.

00:30:27 And I won't explain the notation.

00:30:29 They're different substituted, deuterium substituted species,

00:30:33 oxygen-18 species, and so on.

00:30:36 This one here, which is, I'm sorry to say wrong,

00:30:39 this is 6, 7, 8, since I haven't explained what the numbers mean.

00:30:45 It doesn't matter.

00:30:46 But one of these is the one I showed you

00:30:48 with the deuterium on one side.

00:30:50 And the other is the deuterium on the other side.

00:30:53 And you'll notice that if you have these parent

00:30:56 species or the symmetrically substituted ones,

00:30:59 they're tunneling.

00:31:00 So you don't get any component of dipole moment

00:31:04 crosswise in the molecule the way I presented it before.

00:31:08 But when you stop the tunneling, then you

00:31:10 get small dipole moments.

00:31:12 So we could determine the dipole moment

00:31:14 of these equilibrium structures, even though they never

00:31:17 stay in them.

00:31:18 They're always bouncing from one to the other.

00:31:20 I won't say more about that because we don't have time.

00:31:24 Go on to the next slide.

00:31:30 I just mentioned this.

00:31:31 This was not a great success.

00:31:34 Dr. Smith and I tried extremely hard

00:31:37 to extract the vibration, the fundamental modes,

00:31:43 frequencies of vibration for the molecule,

00:31:46 and the force constants.

00:31:48 First, by transferring force constants

00:31:50 from similar parts of similar molecules.

00:31:53 Secondly, by looking at the infrared spectrum that we had.

00:31:57 And we had some isotopic species with very little data.

00:32:01 That's much harder to get the kind of data

00:32:03 you need from the infrared, unless you're

00:32:05 getting into the laser machines of the near future.

00:32:10 With the conventional machines or the Fourier transform

00:32:14 machines, or even the best presently available laser

00:32:19 setups, it's hard work.

00:32:21 You need pure samples.

00:32:23 You need isotopically pure samples.

00:32:25 You need rather large samples.

00:32:27 And you need a lot of work to try

00:32:29 to get a reliable analysis.

00:32:32 Well, we did that the best we could.

00:32:35 And we got from the Berkeley group

00:32:38 their predictions of the vibration frequency.

00:32:40 We also got a set of predictions from John Popel,

00:32:43 Carnegie Mellon.

00:32:45 Now, these are very advanced and more advanced calculations

00:32:48 because now you're getting the derivative

00:32:49 and derivatives are coming in.

00:32:51 Get the force constants.

00:32:54 All I can say is the agreement was not very good.

00:32:57 And I think both of us are wrong, in my opinion.

00:33:02 After looking at their results and comparing with ours,

00:33:06 then I could see that we should have changed things a bit.

00:33:10 And after the fact, I shifted the frequencies a little bit.

00:33:13 And the agreement is much better.

00:33:16 But does that mean anything?

00:33:18 I was already spoiled.

00:33:19 I had sealed my envelope, sent it in, you see.

00:33:23 And now you can't go change it after that.

00:33:25 That's starting all over again.

00:33:27 I hope they will start all over again.

00:33:28 And I think we would be willing to try again if they would.

00:33:32 But I think we should both seal our envelopes.

00:33:34 Because I'll tell you, just human race

00:33:36 isn't capable of giving up that improvement.

00:33:40 You see that you can improve it by shifting everything over

00:33:43 or not, you're going to do it.

00:33:45 You hope it's right.

00:33:47 If you didn't know about it, you wouldn't have done it probably.

00:33:51 Well, I'll say no more about that.

00:33:53 Well, knowing the vibration frequencies

00:33:56 would be important to us, as I'll point out later.

00:33:59 And I'm sorry that we didn't do a totally successful job,

00:34:04 either of us, on that.

00:34:06 Now, look next, the next slide.

00:34:09 Here is a very schematic picture of the double minimum problem.

00:34:14 Here is the potential energy.

00:34:15 It really costs 21 degrees of freedom, not just one.

00:34:19 Here are the two lowest energy levels of the system,

00:34:23 split by this tunneling phenomenon.

00:34:26 And these things are meant to be rotational energy

00:34:29 levels built on top of these vibration energy levels.

00:34:32 If we have a deuterium tunneling,

00:34:34 this separation is about three wave numbers.

00:34:37 If we have hydrogen tunneling, it's about 21 wave numbers.

00:34:40 And if you think about three wave numbers, it's small enough.

00:34:45 So we should expect some of these rotational levels

00:34:48 to be quite close together, introducing a near degeneracy.

00:34:53 And when you have degeneracy between unperturbed systems,

00:34:57 if you have a perturbation on that,

00:35:00 it is very likely to enhance the effect of the perturbation.

00:35:05 But here, let's assume that we left out the Coriolis coupling

00:35:09 in vibration and rotation.

00:35:11 And we get some near degeneracies up here.

00:35:14 When we put the Coriolis coupling back in again,

00:35:16 it's going to shift those particular levels very much.

00:35:19 So if you look through the spectrum,

00:35:20 you'll find that a lot of them fit the rigid rotor

00:35:23 very nicely, but some don't.

00:35:25 Some go quite wild.

00:35:27 And you expect those to be perturbations.

00:35:30 On the next slide is a discussion of that.

00:35:34 Now, I don't want to get into the gory details.

00:35:37 But when people tell you about separating rotation

00:35:39 and vibration, it's an arbitrary, man-made thing.

00:35:43 You've defined a set of rotating axes.

00:35:45 And you can do it in an almost infinite number of ways.

00:35:49 You can let the axes be instantaneous principal axes,

00:35:53 in which case there are no cross products of inertia.

00:35:58 If you let them be so-called Eckart axes,

00:36:01 they minimize the Coriolis, the true Coriolis term.

00:36:05 There are a lot of ways of defining rotating axes,

00:36:08 and therefore defining the rotational energy

00:36:10 of your molecule.

00:36:12 Herbert Pickett made a choice, his so-called Pickett axes

00:36:17 nowadays.

00:36:18 And he wrote a computer program to fit it

00:36:22 while he was with us at Harvard.

00:36:25 And Steve Balcombe, for his thesis,

00:36:31 unraveled these perturbations, fitted Pickett's formulas

00:36:35 to them, and extracted information

00:36:38 from the molecule from these analyses.

00:36:41 Information is primarily the separation

00:36:45 of this lowest pair of energy.

00:36:46 In other words, the rate is a measure

00:36:48 of the rate of the hydrogen going back and forth

00:36:50 from one side to the other.

00:36:52 And also, a parameter having to do with Coriolis coupling.

00:36:59 And now, there were 20 parameters

00:37:01 in the fit for the hydrogen case, the parent molecule.

00:37:06 And I tend to believe the old story about the elephant.

00:37:11 You have 20 parameters.

00:37:13 You could draw an elephant and make it wag its trunk

00:37:18 and still fit the formulas.

00:37:20 Well, 20 parameters is a lot of parameters.

00:37:22 We had a couple hundred, 183 transitions.

00:37:27 But we tried all kinds of variations on this,

00:37:30 pushing things around.

00:37:32 And we really think that those 20 parameters are pretty well

00:37:35 determined by the fits of the spectrum.

00:37:38 And to make it extra sure, we predicted a set of frequencies

00:37:42 that had not been observed, because we

00:37:44 didn't have the original equipment

00:37:46 to reach up into that region.

00:37:48 We then did jerry-build an apparatus.

00:37:52 Steve Coy put one together and Susanna Smith, spare parts

00:37:56 we had around the place, and went

00:37:59 to look for those frequencies.

00:38:01 Found them all within a half a megacycle.

00:38:03 That is a part in 100,000 or so.

00:38:06 And we're all right there.

00:38:08 There weren't any others floating around

00:38:09 that we couldn't account for.

00:38:11 And I believe, therefore, that we really have

00:38:13 fitted this, got this information.

00:38:16 Let's have the next slide now.

00:38:20 Well, again, we've got all this gobbledygook of symbolism.

00:38:24 These are different isotopics.

00:38:26 Here's doubly oxygen 18, couple of deuteriums, and so on.

00:38:32 These are all symmetrical, so they're all tunneling species.

00:38:37 And here are the separations.

00:38:40 They're also, it's deuterium in the hydrogen bond.

00:38:45 So they're split by about three wave numbers, you see.

00:38:49 Now, the interesting point about this slide

00:38:51 is that there are some differences between those.

00:38:54 Again, there's this question about the Born-Oppenheimer

00:38:59 approximation.

00:39:00 Why does substituting make any difference to that?

00:39:03 Well, the answer, as I said before,

00:39:06 is that we're now talking about a one-dimensional model

00:39:09 of this situation.

00:39:11 And so we will see that any process which

00:39:15 reduces this 21 degree of freedom

00:39:17 problem to a one-dimensional problem

00:39:20 is going to put in some kind of an isotope effect in it.

00:39:24 And by the way, we can get this kind of accuracy if you want to.

00:39:29 I don't know what we do with it.

00:39:31 The next slide, then, says something

00:39:35 about this one-dimensional approximation.

00:39:38 How do we get a one-dimensional curve out of 21 dimensions?

00:39:42 Well, one way to do it is to start

00:39:45 making the joints in the molecule rigid.

00:39:50 Instead of the distances, the lengths between things,

00:39:54 instead of allowing them to change, vibrate,

00:39:57 we'll lock all those connections except one.

00:40:02 We'll have some kind of a motion of the molecule,

00:40:04 which we think describes the critical motion that's

00:40:09 going from one minimum to the other.

00:40:12 And then we'll freeze all the other motions out.

00:40:15 So our molecule will consist of two parts

00:40:19 that are rigid, moving in some way relative to one another.

00:40:23 That's what Glenn and company did with the four-membered ring,

00:40:27 puckering ring.

00:40:28 The ring pucker was the one motion,

00:40:30 and it froze out the others.

00:40:32 That gives you a one-dimensional,

00:40:34 but of course, you're making an approximation.

00:40:36 You're doing it.

00:40:37 And there, by the way, are several ways

00:40:38 of doing it in a given case.

00:40:41 And then you have to talk about a reduced mass,

00:40:45 some kind of an effective mass, which may

00:40:48 be a function of the coordinates.

00:40:50 Well, the effective mass, if you set up the kinetic energy

00:40:55 in terms of the inverse G matrix,

00:40:58 then you make all the internal motions zero.

00:41:04 You freeze them out.

00:41:06 So they give you zero kinetic energy terms.

00:41:08 And this is the one you have left,

00:41:10 and that's the reduced mass.

00:41:13 And it's then possible to use the same empirical function

00:41:19 that Glenn used, which was the one they found to be best,

00:41:23 was a combination of a cubic and a quartic term

00:41:27 with opposite signs.

00:41:29 And then you have a certain number of parameters to fit.

00:41:32 And this is the way you come out to go next to get

00:41:35 some idea of the barrier.

00:41:38 We've got the rate of the reaction, which

00:41:41 is measured by that splitting.

00:41:43 And we have the curve that we're going

00:41:49 to fit.

00:41:50 Everything is determined by the barrier height,

00:41:53 the separation of the two minima in space,

00:41:57 and the reduced mass.

00:41:59 Go to the next slide, please.

00:42:03 If you use that and use this empirical one-dimensional

00:42:09 potential energy function and this idea of reducing it

00:42:14 to one degree of freedom, then you

00:42:15 can plot the barrier height as a function of the reduced mass.

00:42:22 And you can plot this parameter f,

00:42:24 which also comes out of the experiments.

00:42:26 It's essentially a cross product of inertia

00:42:29 as a function of the mass.

00:42:31 And this enables you, from the data we have,

00:42:35 which is the splitting in f, to take f and come across here.

00:42:39 It gives you a mark.

00:42:40 Go up here, go across, get the barrier height.

00:42:44 So you can get a barrier height,

00:42:46 but it's not a very satisfactory approximation.

00:42:49 Obviously, we can't expect it to be too good.

00:42:52 This reduction to one dimension is just too drastic.

00:42:55 The next slide, please.

00:42:59 Here are some results, though, from that process.

00:43:03 So after we've analyzed these perturbations,

00:43:05 we've got these splittings.

00:43:08 We've got the f values from the perturbations.

00:43:11 You now go to this empirical formula and the calculations,

00:43:15 and we get various values of the barrier

00:43:17 for various isotopic species.

00:43:19 Well, that's not bad.

00:43:20 I mean, if I could stop there, I'd be quite happy.

00:43:23 You see 4, 4 and 1 half kilocalories,

00:43:26 the barrier height.

00:43:27 Unfortunately, if you go to the hydrogen species,

00:43:31 you get a larger number.

00:43:33 So our range of possibilities is probably 4 to 6,

00:43:36 or 4 to 6 and 1 half kilocalories,

00:43:39 something like that.

00:43:41 And the f values, these products,

00:43:42 cross products of inertia given here.

00:43:46 And this is another way of getting barrier height.

00:43:50 In this column over here, I only used only one isotope,

00:43:54 data from one isotope at a time.

00:43:57 And the other column here,

00:43:58 I used the effect of all of them put together,

00:44:02 and I won't try to explain that, I'm afraid.

00:44:05 That's quite a simple idea, but it's a little bit empirical.

00:44:09 And the next, and you see these are not bad,

00:44:12 not in violent disagreement, these over here.

00:44:15 But this is the weakest point in our analysis, I would say,

00:44:19 except the vibration frequencies.

00:44:22 Let's see what we have next.

00:44:23 Oops, that did it.

00:44:29 It's all right.

00:44:30 Let's let me use it like this for a moment.

00:44:33 So we have an estimate of the barrier, approximately.

00:44:36 Let's go to the next slide.

00:44:39 And this is the, I'll skip this one, go to the next one.

00:44:44 This is the other way of going about things.

00:44:46 And these kappas are the derivatives.

00:44:49 This is how much the reduced mass changes

00:44:53 as you put a substitute different isotopes in.

00:44:57 So just let me say that this is part of the procedure

00:45:01 of getting barrier by the second column.

00:45:03 However, I'd like to point out here that the,

00:45:08 mainly what's moving in this tunneling motion

00:45:11 is the hydrogen itself and moving along the sideways axis.

00:45:15 All the other atoms have got to move

00:45:18 because they switch from single to double bonds.

00:45:21 And as the hydrogen goes from one oxygen to the other,

00:45:24 you flip and interchange the double and single C-C bonds

00:45:28 and C-O bonds.

00:45:30 And therefore, every atom is going to move

00:45:32 an appreciable distance.

00:45:34 And this inversion takes place.

00:45:39 Now, if you say, look, all these things

00:45:42 are moving coherently together in a synchronous manner,

00:45:48 then you say, well, look, the oxygen and the carbons

00:45:53 are 12, 16, 16, 12 times heavier than the hydrogen.

00:45:58 And we must boost up the reduced mass

00:46:02 by taking into account their motions.

00:46:05 But if you look at this result,

00:46:06 because these are derivatives of putting an isotope in,

00:46:10 doesn't have a very big effect on the reduced mass.

00:46:13 Those derivatives are small, mainly.

00:46:17 How can you explain this?

00:46:18 How can you say, look, the heavy atoms moved

00:46:20 an appreciable distance, and yet the reduced mass

00:46:23 seems to be near one or near two for the deuterium?

00:46:28 Well, Boncombe, in his thesis,

00:46:31 claimed that they weren't moving synchronously.

00:46:36 To explain this, you have to assume

00:46:39 that the heavy atoms don't move

00:46:40 at the same time that the hydrogen moves,

00:46:42 or maybe there's some overlap.

00:46:44 And I tend to think that that is the explanation,

00:46:48 which I could prove it.

00:46:51 The property we're using here to get this reduced mass

00:46:55 is, after all, essentially the tunneling,

00:46:58 the splitting due to tunneling.

00:47:00 And that is largely determined by what goes on

00:47:03 in the neighborhood of the transition state.

00:47:06 That's the one place where the wave function

00:47:08 of the two localized wave functions overlap a little bit.

00:47:14 Therefore, you remember the reduced mass

00:47:18 is a function of position in general.

00:47:20 And I think these measurements are measurements

00:47:22 up at the top of the barrier, the transition state.

00:47:28 And therefore, I tend to believe

00:47:29 that the heavy atoms move a bit first,

00:47:32 maybe nearly halfway,

00:47:34 then the hydrogen pops across the other side,

00:47:37 and the heavy atoms finish their motions.

00:47:39 And we ought to be able to prove that

00:47:41 by finding some property that we can interpret this way,

00:47:45 which is determined by the values

00:47:47 in the neighborhood of the equilibrium configuration.

00:47:50 I think that may exist, but we haven't shown it as yet.

00:47:54 So I come to the end with the following comments.

00:48:01 Thinking of this, first of all, as an exercise

00:48:03 in extracting a lot of information about details

00:48:07 about a molecule from microwave spectroscopy,

00:48:13 I think that it's a success.

00:48:15 I think it has extracted a lot of information,

00:48:18 some of it pretty accurate, some of it not so accurate.

00:48:22 And we've done more than, not more than Gwynne did,

00:48:25 for example, with his tunneling of his four-membered rings.

00:48:29 I think we've done some useful things here on that score.

00:48:34 In addition, though, we have a series of tests

00:48:38 of quantum mechanics.

00:48:39 And there have been perhaps 10 people

00:48:42 who have made quantum mechanical calculations.

00:48:46 We can compare the structure, vibration frequencies,

00:48:49 the general qualitative question of tunneling,

00:48:52 tunneling splittings, and the barrier height, and so on.

00:48:56 I just mentioned the barrier height.

00:48:57 That slide got lost in my last slide, so the climax.

00:49:02 There wasn't a very impressive climax

00:49:04 for the following reasons.

00:49:06 The best calculations give a straightforward calculation

00:49:11 without configuration interaction

00:49:15 of about 11 kilocalories.

00:49:19 But then you start to start correcting that.

00:49:20 The first correction is that you put in configuration

00:49:23 interaction in a lot of it.

00:49:25 And the Berkeley group did put in a lot.

00:49:28 And it pulls it down quite a bit.

00:49:30 Then the next thing you have to do

00:49:31 is that that configuration interaction

00:49:33 wasn't the whole thing.

00:49:34 You can estimate additional factors

00:49:37 that would come from a more elaborate configuration

00:49:39 interaction.

00:49:40 They've done that, and it comes down some more.

00:49:43 But then finally, there's a big drop.

00:49:45 You put in the change of the zero-point energy,

00:49:47 the difference in zero-point energy

00:49:49 between the height of the top of the barrier

00:49:52 and the equilibrium configuration.

00:49:54 Well, nobody knows that except the Berkeley group,

00:49:58 I mean, in the sense that we don't have good vibration

00:50:02 frequencies.

00:50:02 And I don't think they do either.

00:50:05 And we don't have any vibration frequencies

00:50:07 at all from the top of the barrier.

00:50:12 We have to rely on calculations for that.

00:50:14 So until we get the vibration problem settled out,

00:50:18 then we can't really make this statement

00:50:20 that they have come close in their calculation.

00:50:24 But they have come pretty close.

00:50:26 They have brought their calculated barrier height.

00:50:29 It's right in the range of our uncertainty,

00:50:31 of our measurements.

00:50:33 But it does involve these several corrections,

00:50:35 and particularly zero-point energy.

00:50:38 So in several senses, this is an incomplete work.

00:50:42 I'm not sure I can persuade anybody else to work on it

00:50:45 again, but I hope other people will.

00:50:48 We get a clear-cut agreement between the theory

00:50:52 and the experiment.

00:50:53 And it's only when we do a series

00:50:55 of this kind of comparisons, we build up confidence,

00:50:59 which I think is sorely needed and important in quantum

00:51:02 chemical calculations.

00:51:05 But with that confidence, which is bound to come in time,

00:51:09 of course, it will change the whole face of chemistry.

00:51:12 And you can believe in quantum mechanical calculations

00:51:15 of this sort of thing, really use them for practical purposes.

00:51:20 But it will come close to locking the laboratory

00:51:24 in certain areas.

00:51:25 Thank you.

00:51:27 Thank you.

00:51:32 Thank you.

00:51:44 I wish to thank all the morning speakers and all of you

00:51:47 for attending.

00:51:48 And if I could make just a few announcements,

00:51:50 I forgot to tell you earlier that there's

00:51:53 an exhibit of some Dubai memorialia in the faculty

00:51:56 lounge, which is adjacent to the front foyer

00:51:59 where you picked up your name tags.

00:52:01 And we invite you to look at that.

00:52:05 If you are from out of town and need

00:52:07 to know where to find lunch, there's

00:52:10 information sheets on the front desk also.

00:52:13 Several people asked when Professor Pauling would

00:52:15 be speaking.

00:52:16 And it's my understanding that if he arrives,

00:52:19 he will be taking the place of Professor Flory on the program

00:52:23 and will simply replace that.

00:52:24 We'd like to ask you to come back and join us at 2 o'clock

00:52:28 for this afternoon's speakers.

00:52:30 Thank you very much.