Rudolph Marcus (2009) - From 'On Water' and Enzyme Catalysis to Single Molecules and Quantum Dots, Theory and Experiment

Much of theoretical chemistry has involved equations and their application to experiments, Debye, Debye-Hueckel, Transition State Theory, Kramers, LCAO, RRKM, among others

Well good morning and thank you very much. It’s a real pleasure to be here and to hear these various lectures and learn a lot and also to have this opportunity to tell you about some of the work going on and the interaction between theory and experiment and some of the ideas that are floating around. As you probably know, there’s been a major change in theory over the past half century. In earlier years, theoretical chemistry often consisted of various equations that are familiar to most of you, Debye-Hückle Theory, Eyring’s transition state theory, even the Electron Transfer Theory but that’s referred to. And with these equations they had the merit of being able to describe a wide variety of phenomena and to relate phenomena in different fields, different areas. During the past forty or so years there have been expensive developments in computational chemistry. And in fact computational chemistry could do some of the things that analytic formulations could not do. One could now calculate potential energy surfaces for reactions with far more accuracy, no comparison to what was done before and with them one could calculate rates and look at mechanisms, alternative mechanisms for example. On the other hand one could ask, this question is being asked, to what extent can computations replace analytical theory, in fact it’s even asked looking at new phenomena is there something new that you can treat with analytical theory. And those are some of the questions that I would like to address. You know one of the striking things in recent years and actually probably going way back are the number of new experiments, experiments with techniques that weren’t around many years ago. And so this field of experiment and interaction of experiment and theory is very much a growing one and I’ll try to describe some of the examples today. They include for example the use of some frequency generation methods to study surfaces and they include the use of single molecules to study various processes. And there the question of to what extent there are single molecule studies, to what extent do they replace the standard ensemble studies or to what extent are the two types of studies really complimentary to each other. The particular topics that I’ve singled out for discussion are these. There are others I could have chosen too from recent work that we and others have been involved in but these are the ones that I’ll focus on here. One is a rather striking development that was reported in 2005 by Barry Sharpless on what’s called On-Water Catalysis and we’ll say something about that. Another is this question of enzyme catalysis, there is a tremendous amount of work going on in transfers of protons and hydride ions and various things and enzymes. Now what are some of the, both qualitative and quantitative features of that, that bring out this question of analytical and computational chemistry. Then there is several single molecule studies that I’ll focus on and again emphasising the interaction of theory and experiment. One is on enzyme catalysis and the other is on semi-conductor nano particles, I’m calling them dots. So these are the particular topics that I’d like to talk about in the next two and a half hours (laughter). Okay. These are some experimental data of Sharpless and co-workers and the reactions studied, you perhaps can’t see it from way back there or even from close up. The reaction study is a cycloaddition reaction in which you add across a double bond and some of those reactions were catalysed by the so called on-water process. Now what is this on water process? If you take two organic reactants and shake them together, a particular example, that particular example, this one here took forty eight hours. On the other hand when he took those two reactants and shook them up with an excess of water it took ten minutes. Well that was hard to believe apparently and he tells me he sat on it for at least a year and didn’t have an explanation and then finally he said well let’s publish it anyway you know, one doesn’t like to publish a paper unless you, experimental paper unless you have an explanation and even a theoretician doesn’t like to publish a theoretical paper if he doesn’t have a theory to explain. Alright so here’s, here’s the experimental result. And this is the way it is in a number of experiments that we’ll try to deal with. A striking feature, a puzzle and the puzzle causes us to think about well at least qualitatively what could have happened and then once you formulate those ideas how can you put that into some sort of quantitative form. What do you need to do analytically to capture a picture as a whole and how can computations supplement that? So this is the first topic that I’ll discuss. The, what’s special about a water organic surface? Now remember this is shaken up so you really have an emulsion. What’s special about this emulsion water surface? The, the surface of water and air and water and oil has been studied by a number of people, and some of these, what these experiments showed, this is Wan Chen the specially at the UC Berkeley. What these experiments showed was that at the surface of the water, there are OHs that were sticking out from the water molecules. So there are OHs that were not hydrogen bonded. Inside the water most of the OHs are hydrogen bonded to other oxygens and what have you, but on the surface there’s about twenty five percent of them were determined by this relatively new method, some frequency generation where you mix an infra-red that tells you about the OH frequency and optical, you mix the two. Told you there was twenty five percent sticking out. So a computer sort of simulation, not of the ice, of the water surface, but here are one of the surfaces of ice and you can see all these, these hydrogens in that case sticking out, well you can imagine in water it’s not that, that abrupt. But and you have all sorts of wiggling around but nevertheless that’s what was found. And then that was found for example by looking at the peak of an OH that is not hydrogen bonded. Typically it’s at a higher frequency and you look at that peak and make your judgement. So the, the question is how could that particular fact explain the results of Sharpless and co-workers? Now you can well imagine that if you look at the reactants and you remember in reaction rate theory the reactants come together, they form essentially a critical configuration which then goes on to form products and the critical configuration is known as Transition State Theory. If in that Transition State Theory, if in that transition state the pair of reactants was more strongly bonded to the water than were the original reactants themselves because of the change in electronic structure, then you would have a catalysis and indeed that’s what happens with certain reactions. So here are, here’s a sort of a schematic picture of it. Here are the reactants just say this one is a little bit hydrogen bonded and the two of them together are more hydrogen bonded. Actually if you remember the reactants one was a nitrogen that was a double bond which becomes a single bond, that nitrogen is more basic, likes hydrogen bondedness more than the original one. And also there is some oxygens around that also change their structure a bit. And the reaction time, I showed this before, the neat reaction is forty eight hours, the on-water one was ten minutes and a reaction where you added some alcohol to make it soluble, a homogenous reaction took about four hours. So actually what you wanted, tried to explain with the theory are all three of those things. Now in applying a theory to this one has to take cognisance of the fact that you have three very different sort of a geometrical situations and in fact if you, as you know and when you measure reaction rates, you get, you try to summarise the data with some sort of a rate constant. The rate constant of all three things even has different units. So if you want a more, make a more direct comparison than just, what the reaction time is, you have to somehow convert your quantitative results to the same units. And it was impossible to do that by a simple statistical model which looked at things and probabilities and particles to get in together in the different situations. So when you do that, the catalysis actually you find is far bigger, it’s about a factor of ten thousand instead of it just, several hundred. And perhaps you can see the, the reason why there is that sort of multiplication is that when you’re doing on-water there are a lot of the reactants that are sort of buried inside the oil interface, can’t get close to the water, you have to correct for all that. And indeed one does that in trying to get at these rate constants. Of course the theory should be able to handle not only when there is catalysis but when there isn’t. And indeed there was an example where there was no catalysis, there were no oxygens or nitrogens involved or a change in their electronic structure but and indeed there is no catalysis there and when we made the calculations as you would expect, there was no catalysis in the calculations. Also with the theory you can explain why there is a difference between the homogenous and the other. In the homogenous case you have water molecules around the reactants, actually for them to catalyse you have to break some hydrogen bonds whereas at the surface you didn’t. So anyways, there are various things that we haven’t commented on. So this is an example, not really of a new technique, it’s really an old technique, the experiment. But used under different conditions and observation and here is an example of an analytic approach to the problem. But one where we supplemented it, which I hadn’t talked about, with a cluster of water molecules supplemented on by some computations using one of the methods available for that. It happens to be the Cohen-Method. Right, let me turn to another topic. Enzyme catalysis. As you know, with enzymes there are a variety of reactions that you can catalyse, some might involve proton transfer, some might involve the transfer of a hydrogen atom in one form or another, with H plus from here and electron from there perhaps. And some might involve a hydrid transfer and then there are others which involve other transfers. And these enzymatic catalytic reactions have been studied a great deal in recent years and there’s several recent symposia on this subject and a book recently on the subject. And one of the fascinations of the experiment as we were doing it has been to explore the question of hydrogen tunnel so, in many of these studies you’ll see a lot about hydrogen tunnelling. When you look at some of the experimental data and I’m showing one of the examples in the slide, you see some interesting features. This happens to be a thermophilic enzyme, so it operates best at the higher temperatures. There are other alcohol dehydrogenases which operate at the lower temperatures. Anyways when you study the rate of the reaction, the hydride transfer, this is a hydride transfer, when you study the rate of the reaction versus temperature, one over temperature, you find that a certain temperature in the order of thirty degrees, there’s actually a break in the slope, more pronounced with deuterium than with hydrogen. And if you look at these data, several things emerge, that stand out that you want to try at least to have a conceptual explanation of before you ever did any computation. I think that’s frequently true although often not done. For example, these curves here are parallel. That immediately tells us something, the ratio of the hydrogen transfer, the hydride to the deuteride transfer in that region of temperature is independent temperature. That’s not true of many other kinds of reactions. But it’s true here. And it tells one something about, to what extent is there a stretching of the hydrogen which will be different for the H to the D, the stretching of the hydrogen, prior to getting into something where you’re approaching the transition stage. And this really tells us that there’s very little of that. In fact, a model that’s often used for H transfers is patterned on a model for electron transfers. In electron transfer you have a light particle, the electron jumps from one reactant to the other, it can’t jump without something happening first because otherwise you can show as we did in a paper in ’56, you would violate the law of conservation of energy. So things have to happen. The whole environment has, dipoles have to reorganise, bond links have to change so you have to have something happening before the transfer and then when the two things are, so to speak, in resonance, they have the same energy before and after the transfer, that occurs and then things relax. And to some extent that’s true of a transfer of a, other light particles, not as strict but still, does that make sense, including a hydride transfer. And so if you think in those terms and if you think of, of the pair of reactants being just set so that all, when the, when you have the appropriate reorganisation of the environment, the appropriate reorientation of various dipoles and change of positions of various charges. When you have that, then everything is ready and the H jumps, we have this as one particular model. The H jumps but no energy change is permitted and you have your transfer. Anyways with the concepts like one can understand this parallelism. This reorganisation is isotope insensitive hence the parallelism. Then there’s this break, a break which so far has not been reproduced in any computations. And what does one see from the break? Well often one plots results as here versus log rate versus one over temperature and one gets a so called araneus expression. There is a pre-exponential factor of, called A. And A in this case down here for the hydrogens is ten to the seventeenth. Now perhaps too many of us in the audience here, ten to the seventeenth, ten to a hundred and seventeenth, what, what you know, what is the sort of expected result? The expected result indeed the one that’s above there, above that break point is about ten to the thirteenth. One understands that in terms of the vibration of frequency of some heavy nuclei. But this was, four orders in magnitude higher and the deuterium one was even maybe seven orders of magnitude higher. So how does one understand that dramatic thing? Computers have yet to, eventually they will, at least if you put in the right ideas. As you know, and when you do computations, what you get out is only as good as the model that you put in, no better. And so one has to put in something there. There is actually an analogy, if one looks at a glass transition and say in the case of silica, there is a corresponding huge change of five or six orders of magnitude and a pre exponential factor when one looks at the viscosity above it and below the glass transition. It’s known from other results in that temperature below there, the protein is more rigid. There is less, the rate of hydrogen deuterium exchange with the environment is slower for example. Klinman have shown that. So there are various features that are buried in here that you can analyse in sort of an overview way and then if one wants to make detailed computations as indeed one should and indeed some people have, then one can be guided by at least that qualitative thing, that qualitative view, before embarking on with detailed models that don’t stand a chance of working because they don’t have the right ingredients. Next thing I’d like to talk about is single molecule studies. As you know, for the past ten fifteen years or so there have been many single molecule studies. There are various properties that one measures in this way. Catalytic activity, or fluctuations in it. The change of a spectral fluorescence line, it jumps around, its energy jumps around because the species is in an environment that’s sort of fluctuating, jumping around. And also in quenching of the fluorescence or lifetime of the fluorescence I should say. So there are various properties that have been looked at of these enzymes, the single molecule techniques. And during the course of that one measures various correlation functions so the behaviour, one collects samples, one time looks at the samples later on. Looks at the correlation between the two and makes a plot of the correlation function. And one of my students Meher Prakash, one of the students, he’s now at ETH and doing some work in parallel. One of my students happened to see these results and one set of results and the other set of results and he took the two together and put them on the, to see if he could put them on the same plot, had to rescale a little bit. Put them on the same plot and you see the more or less the dark things and the light things, one is for spectral diffusion, the other is for catalytic fluctuations, they more or less fall on the same curves. That work that he happened to be, that he happened to notice in the literature, by the way he was a student who took time enough to look at the literature. Every morning he looked at the literature and came reminding us (laughs) almost every week so, in fact he was the one who brought the On Water work to our attention. Anyways, he looked at that and the question is this an accident, because this is a typical time scale, for, for the catalytic events in that time. Is this an accident or might there be a more fundamental reason? And in fact if you think of all three of the properties I’ve mentioned, these and the question of fluctuations in life time of a chromophore and the enzyme, think of all three. Do they have something in common that maybe you can derive a result, derive an equation that connects the two and so make predictions for other enzymes, other properties. And so he worked on that and he uses his main theme, a common theme that’s used in treating enzymatic catalysis and that is the importance of electric fields that are generated by the various dipoles and charges in the enzyme. And that if you have fluctuations in those fields, as indeed you do, it’s fluctuations of that type that permits say electron transfers to occur, hydride transfers to occur. If you have fluctuations of that kind then perhaps those fluctuations affect some of these properties similarly, if you look into the origin of the properties, drive equations related and so on. And if so this should not be an unusual thing but one should be able to look at other single molecule studies and see if they follow on the same curve also. And so he did that sort of analysis and derived an approximate equation that these various correlation functions, correlation functions, with catalysis fluctuations, spectral diffusion and florescent slow times were all approximately equal. He could relate all of them with a hypothesis to electric field fluctuations. And so he thought well that’s great, okay, this is a, this is consistent with those experiments that experiment, pair of experiments that I showed you. So now we’re, we’re on a roll. We’re ready to look at all these single molecule data and now see how well things work. Well of course a lot of the single molecule data was done without benefit of a theory relating various things and so an experiment was done here, an experiment was done there but there, other than this it turned out there is no enzyme for which, two or even three of these properties had been measured. So in all of this single molecule, in all of these single molecule studies, there is a, we didn’t have something to compare with but there it is anyway. Now if it is correct, that these sort of correlations are due to fluctuations on these electro statics, then when you look into relationships involving that you should be able to learn something about them naturally in a quantitative way from dielectric properties, the so called dielectric dispersion occurred. And so we thought alright well let’s look up the dielectric dispersion data for this particular enzyme that I showed the data on, was it there? There was some for other proteins but not for it. So we used a standard equation but we didn’t have the real data for the dielectric dispersion so we used some approximate parameters and of course, you can get things to fit but you really, this other system, really you need the dispersion data. Again it’s another example where theory can at least suggest its correlations and experiments that perhaps the experimentalist might not have thought of otherwise. One example actually where all of the data are available is in something which is not enzymes at all but some work that we did a number of years ago. This is what’s called the Time-dependent Stoke Shift. The spectral of the florescent shifts with time as the system relaxes after an oxidation and this compares, experiment in calculated with no adjustable parameters and this was a paper, so we’ve tested some of the ideas on different kinds of systems but we await the experimental data for this particular one. That brings us to our last topic, quantum dots. These semi-conductor nano particles have some very interesting properties. You shine light on them and they fluoresce, then all of a sudden the fluoresce stops, comes dark, continue shining light all of a sudden starts fluorescing again and you have this phenomenon of intermittent fluorescence. And this intermittent fluorescence as studied by people like people like Bawendi and others. Here’s an example of fluorescence and there’s dark periods. You can see these on off periods. You can take any one of these things expanded it, you see that is another example. And if you plot the data of the fluorescence, the lifetime. A particular dot is light for a while and then it becomes dark, make a note of that. Becomes dark for a while, becomes light, make a note of that. And look at the distribution of on periods, light periods, the distribution of dark periods and if you plot the log of that distribution versus the log of time you get a power law and sometimes a bit more complicated, it goes over into an exponential and this power is frequently close to one point five. And we saw those data and it occurred to us, there are a number of possible explanations for the power law. When we saw those data it occurred to us, one point five, well that’s characteristic of something, that’s characteristic of the diffusion light process when you look at a certain property. And so we set up with Chao Tang and later with Pablo Francisov, an approximate theory to treat this and this is just the very quick kind of description. Imagine that you have a number of levels down here in this cadmium selenide dot, I’ll call them dot. Sort of they would normally be the balance span of a rebulk system. Very closely spaced levels and you have a number of levels up here that would be part of the conduction band and when you’re absorbing a band edge, you’re say going from there to there, now if you think about the surface of these quantum dots, usually you’ve coded with something to protect it. Some trioctyl phosphal compound. Usually you then have selenium atoms, really ions, which are not being supported, strongly supported by, being surrounded by cadmium charges. So the electrons from that selenium there might be a bit more label, and you shine a light and there’s a, most of the time it will just fluoresce but there’s a possibility that an electron from there will rush into that hole while this electron goes up and provided this energy difference is roughly equal to that energy difference and you have a kind of resonance then you can get a transfer and once you have this once you’ve lost an electron from there, you got particles hanging around there, there’s a sort of residual particle hanging up there and you shine light again and other processes other than fluorescence can occur and in fact they can occur so quickly it’s called an O’Shea mechanism that the dot is essentially dark and until somehow the hole that’s there gets filled again by various processes that I have been trying to write down here when they retreated. So with this mechanism then if you look at details of it, of the electron transfer and how you, what’s involved in making that transition, what sort of structural fluctuations are involved in making the transition and if you linked that to the phenomenon that’s seen in these dots of spectral diffusion, the lines jumping around a little bit, there’s the structure sort of fluctuates, then you can design an approximate theory which is related to the electron transfer theory and this sort of exemplifies it. This is the state let’s call it the state, though there are really many states. Before the electron jumps from that selenium ion over to the whole and this is the state afterwards and the transfer occurs about there and when you look at not just the reaction problem but the so called reaction diffusion problem then you get things like this law that’s, well it’d be like this result that’s obtained from the distribution of times, dark times, light times, anyways there are a wide variety of experimental results on this. There are many things that I believe we can explain, there are certain things that so far are eluding us. We get a little bit closer but it’s not the sort of thing where one would bet one’s life on yes this is definitely the best approach but the thing is you can make predictions, for example we made one that was tested and verified last year about a change in power when you look at the details of the transfer there in building up a steady state and so on there’s a different power at the very beginning and that was confirmed experimentally. And there are various other things that sort of challenge the theory. The use of the dots as markers to follow cancer cells and various things, that’s one of the, well if you look at any of these quantum dot papers, you’ll see a long list of potential applications. And the, for us, the interesting thing is the sort of, what are the new phenomenon. I’ve just tried to focus on several of the new results, some of them with old techniques like that work of Sharpless, making emulsions and the rest of them with very new techniques to try to indicate that there really are a lot of phenomena in the literature. There are some that I haven’t discussed in the main, there are a lot of phenomenon in the literature. To be qualitatively explained and understood and then to follow it up with computations. It’s really a surprise that perhaps it’s in part because of the new experiments. Perhaps it’s in part because of the confidence of certain computer results if there was, given or given some, that make one go on and knowing that one can test things in more detail than was ever possible. So, or test so, but this field of theoretical chemistry and the interaction between theoretical and experiment is very much a living thing and I hope that many of you young people, I’m looking at the grey hairs too, many of you young people will be interested in at least understanding things at a reasonable depth and using that as a basis for further experiment. Thank you.

Rudolph Marcus (2009)

From 'On Water' and Enzyme Catalysis to Single Molecules and Quantum Dots, Theory and Experiment

Rudolph Marcus (2009)

From 'On Water' and Enzyme Catalysis to Single Molecules and Quantum Dots, Theory and Experiment

Abstract

Much of theoretical chemistry has involved equations and their application to experiments, Debye, Debye-Hueckel, Transition State Theory, Kramers, LCAO, RRKM, among others. In fortunate circumstances one can, as in a theory of electron transfer reactions, relate different experiments to each other without adjustable parameters, and indeed make predictions without computations. More recently a major focus in theoretical chemistry has been on computations for individual systems, on the specific rather than on the generic, and not on equations relating data in different fields. In practice the two approaches are complementary.

We choose for illustration two or three of the following topics where analytical theory, sometimes complemented by computation, is used to treat novel phenomena: catalysis of organic ‘on-water’ reactions in emulsions (1), enzyme catalysis, including several specific effects, the temperature independence of the H/D kinetic isotope effect for some enzymes operating under their natural conditions (2), an abnormal change in the Arrhenius pre-exponential factor for the catalytic rate of a thermophilic enzyme operating below its break-point temperature (2) (an analogy to a glass transition), predictions relating single molecule enzyme catalysis to other single molecule properties (3), and a topic drawn from the nanoparticle field, the intermittent fluorescence of semiconductor nanoparticles, interpreted in terms of an electron transfer, structural diffusion, and trap surface states theory (4). In particular what can be learned from single-molecule studies? Are they and the usual bulk ensemble studies complementary?

The research topics were each stimulated by puzzles arising from the experiments.

References and Notes5

1. Y. Jung & RAM, J.Am.Chem.Soc. 129, 5492 (2007).
2. RAM, in Quantum Tunneling in Enzyme Catalyzed Reactions, R. Allemann & N. S. Scrutton, eds. (2009).
3. M. K. Prakash & RAM, Proc.Nat.Acad.Sci.USA 104, 15982 (2007) and J.Phys.Chem.B 112, 399 (2008).
4 J. Tang & RAM, J.Chem.Phys. 123, 054704 (2005) and P. Frantsuzov & RAM, Phys.Rev.B 72,155321 (2005).
5. These references contain citations of the large body of experiments in these fields.

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