 Thank you. Well, thank you for the invitation to present. I'm sorry that we didn't get to do it in person. I have had previously some nice visits to Triesta and also to Kerala. I was at the ISO in Kerala and I've also been to Tata Institute. Some of my collaborators I will talk about are Indian Institute of Science in Bangalore. In the first part, I wanted to do a tutorial and talk about effective Hamiltonians for quantum dynamics in functional molecular materials. And Christina kindly mentioned my blog, Condensed Concepts. And so I put slides, copies of the slides on the blog so you can find them there. But there's also wide-ranging discussions about many scientific issues that relate to the theme of this meeting and also some broader comments and job advice, especially for young people. So this in the tutorial, first of all, explain what I mean by functional molecular materials, including biomolecules. And then I'll give some examples of quantum dynamical processes. And then a key idea in modeling is to partition the whole system into a discrete quantum system and an environment. An environment, maybe a solvent or a protein. And then I'll introduce the form of model effective Hamiltonians because they often have a common form. And then a particularly important idea is that of diabetic states and how they lead to potential energy surfaces. And in the second half on the research, I'll talk about diabetic states and hydrogen bonding. And then just to illustrate what these models can do, I'll talk about one of the simplest possible models, the spin boson model. Okay, so in terms of the big picture, we have a scientific and a technological challenge. And that is that at the atomic and molecular level we want to understand and learn to control a number of processes, charge transport and charge separation, whether it involves electrons or protons want to do energy conversion, like converting light to chemical energy or to electrical energy, and we want to transport energy and store energy. And we also want to selectively break and make chemical bonds. And particularly to do it in a very efficient way. And so to do cut catalysis. Well, biomolecules do all these things very well. So hopefully by studying them, we can get ideas of how artificial systems, we might be able to do these things, but there's not just a technological challenge, it's also a despondental scientific interest. This is just one example of, you know, how your eye works. You see things. Well, there is here is there is this molecule here, redoxin, and this is in a protein retinal. And you can see that it's embedded in some membrane protein. And the key thing of what happens is a photon is absorbed by the redoxin, and then he does assist double bond, and then there's a twist of the bond in response to the excitation by light, and then you have a new confirmation of the chemical, and then this leads to charge separation in the protein, and a electrical signal, that's how your eye works and so this is a highly efficient and fast conversion of photons to electrical energy. So we'd like to understand that. And we'd also like to find ways to mimic it. So these are examples, other examples of quantum dynamical processes in functional materials. So a photovoltaic cell, take a photon produces an exciton, which can be viewed as an electron hole pair, and then you want to connect that to decay into a separated electron and a hole, and that will then produce a voltage, or a light emitting diode is the reverse process, where a voltage produces a spatially separated electron and hole, and then you want them to combine to produce the exciton which will then decay radiatively to produce a photon. Basically, this kind of functionality requires some transitions between different quantum states, and so we would like to be able to describe those transitions, and so there's quantum dynamics involved, but how are we going to model this? This is just another example, and this is just to illustrate the complexity. This is an organic LED based on this chroma 4, and this will have more than 40 nuclei and more than 300 electrons. And so there's actually 10 to the 100 electronic quantum states, and so you're going to have to simplify things a lot. And that's just to describe the chroma 4, let alone the environment. And so there's some big picture observations here, and particularly this is where I come as a physicist, is there's a tension between specificity or particularity and universality. And so when, in different words, for complex molecular materials, when do the details, when do the details matter. Now physicists generally say the details don't matter, physicists think cows are spherical, and like to use the smallest possible model. But chemists say the details really do matter, and biologists say the details are a map of life and death, because you just have one mutation, and then before you know it, you have end up with cancer or some disease. So, this is the theoretical challenge is to, to find a balance between these different perspectives and thinking because if there's quantum dynamics involved, you can't do any modeling that involves every treating every single atom quantum mechanically. And so there's different levels of theory and modeling. And it's not that one is better than another. We actually need all of them. So it's simple for nonmology, where you just have a theory without atomic and molecular details, like when you do classical break equations, and some things systems you can understand. And so what's going on. Now in classical molecular dynamics, generally include all of the atoms but you're treating them. They're not allowing for quantum effects. And in computational quantum chemistry you're starting with Schrodinger's equation, or a density functional for all of the electrons, or some subset of them. What I'm going to be talking about is something different, which is very common in condensed metaphysics, which is my background, where you work with model effective Hamiltonians. Famous ones are Hubbard model Heisenberg model, Anderson model. They describe the low energy degrees of freedom. So you're not treating all everything there. So to make this concrete in terms of the kind of systems people interested in this workshop is a picture of the photo active yellow protein. And there's a chromophore here, and then it's surrounded by a protein, but there's also water, and the water environment. And so a key idea is to partition the system in the following manner that you think of that there's some subset here, which may involve a relatively small number of atoms such as the chromophore. And you have just a limited number of electronic states you focus on, such as the ground state and electronic excited state. And then there's an environment, and then in biomolecules you'll have the protein, you also have the water bound to the protein and then there's bulk water out here. And that can all of these can play a significant, a significant role. And so shortly I'll give you an example of how you might do this. So there's a general form for the effective Hamiltonian. And this basically does this partition, if you like, where you have the molecular electronic states, and I'll talk about diabetic states shortly, but there's also the molecular nuclear coordinate so this is generally just the chromophore. And then you have all these environmental degrees of freedom. And so then that you can partition the Hamiltonian into three parts, one part is just describing the system, which we would call, this would be the, the basically the molecule, the chromophore. And the, and then there's the environment, and the, and then there's the system environment interaction. So I, if you look in the, the literature that there's sort of a common form that these effective Hamiltonians have. And so the first part is where you think in terms of a limited number of diabetic states, but then they have coefficients which depend on the molecular vibrational coordinates such as the stretching of bonds or angles involved and later I'll show an example from hydrogen bonding. Now, if we look at the eigenvalues of this matrix because this is not necessarily diagonal, that will give you potential energy surfaces. Now the way to model the environment the simplest possible model is just an infinite collection of harmonic oscillators. And then you need a system environment coupling. And the simplest possible form is where you have some vibrational coordinate from the environment that's coupling linearly to the to these electronic states, but then you can also couple the vibrational coordinates. Now the details aren't here aren't so important, but just that that's a general form. So let me talk about diabetic states. And so it's good easiest way to understand them is to think of a simple example. Suppose we had a sodium chloride molecule. Well, at we know that the ground state is going to be ionic, there'll be a sodium plus iron and a chlorine minus iron. And then we can think about as that electronic state. As you vary the distance between the two at the ions, then that's how will that energy evolve. And that is this curve here. And we call this a diabetic state, because of this is not the electronic character isn't saying it's changing. So all that's happening as I go from here up to here I'm maintaining the electronic character. Whereas in contrast, if I have the neutral atoms at large separations when they're part of the ground state, the stable state is the neutral atom atomic state. And then as you move those two neutral atoms closer together, then that energy of that state will electronic state will increase up to here. Now in reality, though, those two states are coupled together. And so the actual Eigen states, or we should call the adiabatic states which define potential energy surfaces. These two curves here. And so the ground state is a sodium chloride ion, but the first excited state is the neutral atoms where you have charge transfer. Now, in terms of generally, the key properties of diabetic states is that they're many body electronic quantum states, and they don't, the electronic part doesn't vary significantly with the nuclear coordinates. And this, though, some of the power of this is it connects with chemical intuition. We can just think of simply more high school chemistry of ionic states neutral states. And so the energy of these states has a simple dependence on the nuclear coordinates. And so we are now to what most of us are more familiar with which is potential energy surfaces, and they're basically the adiabatic states which are the energy Eigen states. And so this is where you have the the Born-Oppenheimer approximation, and you might have some complex molecule and this would be the ground state surface. And this would be the excited state surface. And one thing that's a particular importance from phytodynamics is these surfaces can touch at what's called a conical intersection. And you can have very fast non-radiated decay through this conical intersection. And that's particularly important in, for example, fluorescent proteins. Okay, so the adiabatic states have many advantages. They can elucidate the conical intersections between potential energy services. They have a simple coupling to the environment, and they can be constructed from quantum chemistry. And they also allow going beyond the Born-Oppenheimer approximation. So now let me talk about a concrete example. And this is probably the simplest possible model that could describe non-trivial quantum dynamics where you have a system plus environment. So this is called the spin boson model. And the spin bit is there's no physical spin. It's just because you use polymatrices to describe two quantum states. So you have two quantum states and there's an energy difference between them. And so he epsilon, you have a term for that with the Z polymatrix. And then there's this term, which is coupling the two states together. Now then there is an environment is described by an infinite collection of harmonic oscillators. And so here's the harmonic oscillators. And then you consider the simplest possible coupling of these harmonic oscillators, which is a creation annihilation operators, and to the sigma Z. Now this model is very simple to write down, but it has very non-trivial quantum dynamics, and it can describe a whole range of processes that would be of interest to people at this meeting. So we can describe electron transfer, forced or resonant energy transfer, internal conversion, non-addict rate of decay, intersystem crossing due to spin orbit coupling, and then also hydrogen bonding and proton transfer. And the second talk I'll describe that. So in terms of the system, trying to parameterise it, what's interesting is that even though you have this complex form that the two, the effect of the environment on the quantum dynamics of the two states is completely determined by this quantity, which is known as the spectral density. And so it's a measure of the coupling to the quantum system and to the different modes and also what the frequency of those modes are of the environment. And then there's sort of two main parameters that parameterise the spectral density. One is called the reorganisation energy, which is the tote, which is an integral over J of omega, and then there's the typical relaxation frequency of the bath or the harmonic oscillators. So then if you study the model, then I'll show you the different types of quantum dynamics. But in terms of what kind of dynamics happens, determined by the fact that you've got competing energy and time scales. So for example, you've got the thermal energy, about 200 centimetres, the minus one at room temperature, and that corresponds to a temperature scale of like 25 temp seconds. But then you have this reorganisation energy, the relaxation time of the environment, the coupling of the two states, the energy difference. Now in biomolecules, depending on the process that you're involved in, these energy scales can span from one to a thousand centimetres minus one. And so at some times, one of them is much larger than another. It just depends on the system. So let's look at the dynamics. So this is, turns out to be highly non-trivial, just to show, to establish these three curves. But Legit and Tony Legit and Caldier and Weiss and others have spent a lot of time working on this, but it turns out there's three possibilities. And so this is an example where I'll show for, if you had FRET, where here you had an excited state of one molecule and the other molecule was not an excited state. And then there's transition to when you transition to the excitation moves on to the other molecule. And so you can start, it depends on the regime, but you can start in a situation where the excitation oscillates backwards and forwards. And so we call this coherence because that involves quantum coherence between these two states. And so this is showing the location of the excitation versus time. Now incoherent transfer is where there's no oscillation and then there's just exponential decay of slowly this is moving from the excitation from here to here. The other possibility is when the coupling to the environment is strong enough, the excitation is just completely localized on one of the molecules. And that will only happen at zero temperature or effectively very low temperatures. So, and Delta is the scale of the frequency of the oscillation here. So there's quite a lot of interest and controversy about between further synthetic systems to what extent you have this quantum coherence. And quantum coherence makes things interesting, but the coherence is actually good to because of that for functional processes, you actually want complete transfer you want to go from, you know, from one state to the other so. And so here, even though this coherence in the end, you end up with transfer of the energy excitation. I just give you another example of something analysis you can do in the incoherent regime. And this is the Marcus hush theory for electron transfer that Marcus received a nugget prize in chemistry for and so that's in a particular parameter regime. And what you find you can calculate the rate of transfer and there's a nice analytic form for that which Marcus and hush derived independently. And I'll just give you an example of how this can give you if you like a design principle that if you look at this rate as as a function of the energy difference between the two electronic states. And you see a exponential plate as a parabola this is a logarithmic scale. And so there's a particular energy difference, the maximum rate, when the relaxation energy equals the energy difference between the states. And this was this graph here shows experimental data for a whole range of different molecules where there's electron transfer. And it nicely is consistent with the theory. And you can apply these ideas in other contexts to explaining the concept of looking at design principles for organic solar cells. So I should move along here. And just mention, finally, this to give if you want a concrete example in a bi molecular system of how you might do this modeling. So you'd have a dipole, which might be excited state of a molecule. And so that's the chroma for, and then it's embedded in some protein. And that is then embedded in in the solid. And in this paper we are able to investigate the different regimes, and particularly because of that this different dielectric constants and different dielectric relaxation on the times. So I should finish up that there are lots of outstanding questions here. And so I won't go over these now. And these are just some of the papers that I have been involved in over the years of addressing some of these issues, but particularly in the second part, I'll talk about hydrogen bonding and proton transfer. So let me end there and I'm open to having questions. Yes. Thank you very much for this very nice introduction. So you can write your questions in the chat, or you can simply switch on the microphone and ask. Don't be shy. You can, you can ask some questions. I will start with the first one. I really appreciate this general idea of having effective amiltonians in order to describe and to investigate very complex systems. The first question is how do you convince chemists that the details do not matter, because this is an issue I think. And the other question is about the parameterization so are you usually take the parameters from the experimental from the experiments or do you think it is better to go to have another approach. Okay, so the first question of convincing chemists, yeah, that all the details don't matter. Yeah, that's a thing I think and I think sometimes the details do matter that's, and that's the tension that is is figuring out what details do matter and I think that the best way to convince them is some success so I will talk about the second half I'll talk about work I did on hydrogen bonding and and that's definitely I mean being much more successful than I thought it would be and and so there's chemists who are using the model I developed so I think that that's the only way to, you know, and that's enough to convince people is to show that sometimes simple models can capture details of very wide ranges of materials. So, in terms of the parameterization. So the two ways you can do things, and I think both have strengths and witnesses, you can do parameterization, often from some quantum chemistry or molecular dynamics. But you can also sometimes from experiment, you can parameterize things so this paper here, I mean we did both. So, the key quantity that you're interested in is this some spectral density. And so there's a way you can extract this from it from experiment. By looking at the time decay of optical excitations. And so that can be done and so in the paper there's a big long table with parameters for all sorts of proteins and with chroma force, but we also in that paper we had this model, the on saga type model where you've got a doc, you've got sort of three dielectric mediums, each has a dielectric constant and relaxation time and from that you can extract a form a functional form for the for the spectral density, and you can also get the spectral density from classical molecular dynamics in the simulations as various tricks for for for doing that. So, and then with the green fluorescent protein with set awesome we were able to characterize the you know the diabetic states. Yeah, so it's a. It's very important to to do both because of that quantum chemistry has its limit eight molecular dynamics have their limitations, but their strengths but then, and then extracting things from experiment is not always straightforward but can be quite insightful. Thank you. So, we have a question in the chat from mesh mesh do you want to ask yourself or. Oh, okay so the question is, can you elaborate how the coherence can be useful. Well, maybe it's that. If. Yeah, so this goes back to, let me go back to someone I was saying. Yeah, okay. Well, it's put it this way, if you. If you flip it around and say, right, maybe I should have put it this way, coherence can be useless. Because if you had complete coherence, for example, then this thing would just oscillate backwards and forwards from perpetuity. And so if you're thinking about elect, you know, electron transfer, for example, and you would be in a completely coherent regime. That would mean that the electron would just oscillate backwards and forward between the donor and the acceptor. And so you'd never get the process you want happening so in your eyes, you know the photon would be absorbed and you'd get an electron in a hole say and they would just be oscillate they would never get separated from from each other. So, so in that sense, yeah, it's a good question I probably should say that it put it around the other way that coherent pure complete coherence would would be useful for useless for any real process you wanted. Yeah. Okay. Okay, other comments from the audience. If not, possibly, the quantum state, there is something about a comment about a comma readout but I cannot understand. So can you switch on your microphone and ask. Yes. So hello Mr. Ross Thank you for this presentation. My question is about, we are talking here about molecules and we are talking about quantum physics. Remember that for quantum physics, the state of the state we don't have with we have a probability to find a state to to to have a particle in state. For example, here we are talking about the electronic structure of our molecules. So this will not meet a problem in experience when we are talking about applying quantum physics in this field of biology. Now, so this is a controversial issue of, of, you know, most of biology you think of in terms of classical physics that you know the, you know the protein is in a definite confirmation and then maybe the protein changes to another information you don't have a Schrodinger's cat state where the protein is in the two confirmations simultaneously. And similarly you don't have a chroma four in the ground state and the electron, the electronic besides at the same time. But there are processes, you know the biomolecular level when you get down to the size of, you know, a chroma four, such as when you have fret, or what you have exit on transfer between chroma fours and by the synthesis that where that there can be quantum coherence there. Now, that's the the time scale of that is often quite short it's often, you know, tens of femtoseconds maybe hundreds of femtoseconds. But I think the controversies, well there's controversy about to what extent this happens in different biomolecular systems, but also whether it's important for the functionality of the of the of the biomolecule and I'm on the camp that that I'm very skeptical that that is important for the functionality, and also that I think some of the experiments that were done and got a lot of attention claiming quantum coherence in photosynthesis I think were over interpreted and since then that it's there. There's simpler explanations are so so but um yeah so for most of biology quantum physics I don't think is relevant but if we're looking at short time scales and short distances, you know everything is quantum mechanical like it's you know chemistry, once you're breaking and making chemical bonds that's I'd say that's intrinsically quantum yeah. Okay. So, I think it is time to move to the second part of the talk. And of course we will have time at the end for for other questions. So, everyone's seen the the something about hydrogen bonding. Okay. So, I also put copies of the slides on the blog, if you want. So I'm going to talk about the effect of quantum nuclear motion on hydrogen bonding in complex molecular materials and just following up on that last question this is the case where you do see quantum effects in some by molecular system. And just to, to motivate that. I will show. This is just a recent paper from Steve boxes group at Stanford unusual spectroscopic and electric field sensitivity of chromophores with short hydrogen bonds green fluorescent protein and this is the yellow fluorescent protein as model systems and this is a picture of the chroma for and then there's a hydrogen atom or proton that can transfer between the protein and the molecule and the details here are not important but this what I'm going to talk about but the point is these kind of pictures, this is you're going to see again and again the talk, and this and boxes group they use this model that I'm going to talk about now to interpret a lot of the experiments so let's go to the, to the model now. Okay. And so, you know, physicists, not a chemist looking at a violators looking at hydrogen bonding. And so my three goals are to find the simplest possible model to describe a wide range of phenomenon materials and to elucidate the role of quantum physics so if you're looking at chemistry textbook. In high school, even first year university, it will, you know, have this kind of cartoon of the hydrogen bond and that it's all electrostatic interactions and this is a classical picture. And often that that's in a lot of situations that is capturing the essence, but it's not in all cases. And so that's what this talk is about. And so, we've got this concept of potential energy surfaces. And, you know, this underscores so much of our understanding of chemistry. And that basically you can understand most of chemistry in terms of the dynamics of atoms is described by classical motion on a potential energy surface. And this is based on the Born-Oppenheimer approximation. I want to show you an example where this is not the case. So, I'll talk about this simple model for potential energy surfaces for hydrogen bonds. And it turns out quantum nuclear effects are necessary for quantitative description of correlations between donor accepted distance. They are big R and bond lengths and vibrational frequencies. And the quantum effects which you can see through isotope effects where you replace hydrogen with deuterium are largest and most subtle for when you have moderate to strong symmetric hydrogen bonds and the relevant distance is about 2.4 to 2.5 angstroms. So, this is a very important picture for this talk. And so, and I'll keep showing it just so you don't forget, but let's suppose you have this hydrogen bond where you've got some molecule, now X here could be something very complicated. I mean, it could be part of a protein or something. And then there's a covalent bond to hydrogen atom and then there's this hydrogen bond to some other complex molecule. And we call this the donor and the acceptor. Now, there's four parameters here. One is just what's the distance between the donor and the acceptor between X and Y. And that turns out to be a very key variable. And then there's also this distance, this length. And then there's this angle. So let's see how important that is. So what was established over many years and nicely summarized by this book by Gilly and Gilly, I think father and daughter, and is that you can find all these correlations for hundreds of different chemical compounds. And so I'll show you some of these correlations now to get the flavor of things. So, the bond length, that is the distance between the donor, well, the donor, in this case it's OH. Now, normally in isolated atom, this would be like about one angstrom. Now, as you vary this distance between the X and the Y and these are, now this is for a symmetric complex. What you see is there's a definite trend here. Okay, and these, and this is for each data point here is a different chemical compound from the Cambridge crystallographic database and sometimes these are quite complex molecules. And so this is something we want to be able to explain both qualitative and quantitative why you get this correlation here. And then you can also measure the stretch frequency. And what you see is again there's a definite trend. Now an isolated OH stretch would be about 3500 centuries to minus one. But what you find is that that gets incredibly soft as the the hydrogen bond gets shorter and shorter, and that when it's down towards 2.4 angstroms, as in the distance here between the two oxygen atoms. The frequency has dropped by like four folds. Now that's a huge change. I mean, most chemical bonds, the vibrational frequencies might change by a few percent, not by a factor of three or something. So this is something also then that needs to be explained. And again, each one of these is a different compound. And so there's some universality here. Okay, and so we need a potential energy surface. And I'm going to show a simple model Hamiltonian which really only has two free parameters. It's physically and chemically transparent. And it gives a unified picture of different types of hydrogen bonds and of proton transfer. And it can give a semi quantitative description of all these empirical correlations. And so we come back to the diabetic states. And so the idea is to construct diabetic states for a hydrogen bond. Well, again, you go to chemical intuition. And so you think about, well, let's have, we have an isolated covalent bond between the X and the proton. And then you have a long way away, you have the Y, which is the acceptor, or you move the proton over here. And so that's a second electronic state. They just differed by transfer of a proton. Now you can describe the energy of these states, just individually by a more potential. And so you can parameterize that just from a, from what you know about these isolated bonds. So you can just take gas phase values for isolated molecules. Now you want the key thing though is how do you couple these two diabetic states together. And so there's this off diagonal coupling. And there's a intuitive way again to parameterize this and that if we think about, if this is a linear situation, you don't have to worry about this angle. And then we would just expect that this would decay exponentially as the R gets bigger. There's the overall scale here, which we call delta one. So that's one parameter. And then there's B here, which is just describing how that falls off exponentially. Now then if you think in terms of simple overlaps of molecular orbitals, you can argue that as you vary the direction of the bond that then there'll be this simple dependence. And so there's no new parameters there. Okay, so now you look at the energy eigenvalues of two by two matrix, you know what the eigenvalues are, they look like that and that defines potential energy surfaces. And so this is what the surface would look like. And so if you say you chose a distance of 2.9, and this is for when the symmetry here between the donor and the acceptor. And so this is what you see is the these are the two diabetic states as we coupling, and then there's a large potential energy barrier to transfer the proton. And this is a weak hydrogen bond. But then as you move the molecules closer, just to 2.6 angstrom, what you find is that that potential energy barrier is now getting a lot smaller. And so an example of this would be this, where you have hydroxyl and a water molecule. And the Zundal cation is another one. And so, if you then look and we will shortly a quantum mechanically that the first case, when you have this high barrier on the barrier is very little splitting or tunneling between the states is only tunneling up here. But when the barrier is low. There's only actually one state below the barrier. And so this is called a low barrier hydrogen bond and there's a lot of controversy about whether or not they, to what extent they exist in proteins and whether they're important for catalysis. And so this is actually the Zundal cation. And now when the distance is much shorter, there's actually no barrier here. And so the proton would be completely delocalized between the two. So now, let's try and do a, so this review, this captures three classes of hydrogen bonds, weak bonds, strong bonds, moderate bonds, local also known as low barrier hydrogen bonds, and also can describe a proton transfer reaction, and there's something called the PKA equalization principle, which really and really come up and this also captures this and this just relates to moving the bar, the diabetic states relative to one another. Okay, so now I want to talk about quantum nuclear effects. So we use the Born-Oppenheimer approximation but we need to find the Schrodinger equation for the vibrational eigenstates for say an x-h stretch. So this is the eigenvalue that gives the potential energy surface. And then here you have the nuclear mass. And so this is going to be different for hydrogen and for material. And so if you solve this equation, suppose this regime, you have this barrier, and then there's a ground state here. So this would, and then the, that's the energy, that's the zero point energy. And then here, this is the ground state probability energy density. And so you can note that the proton is more or less completely delocalized between the two, the donor and the acceptor. But you also note that if it was classical, the proton would sit right here. Okay, that would be the, it would, it would be localized there. And that would be the bond length. Okay, but if it's more delocalized, the most probable place to find it would be here or here. So that is a different length. And that would be the bond length you would measure in a neutron scattering experiment. Okay, so let's now take that, the information. Okay, so this is all the data I showed before. This is the length of the, this bond, XH versus big R. And so that's all the data. And if it was, if things were classical, this would be where the line would occur. That's where the minimum of the potential energy is. But if you allow for the quantum effects, what you see is that it's significantly different and you'll get this red curve for, and that's for hydrogen and then you'll get this curve for juterium. And so this is also predicting a isotope, geometric isotope effect that hydrogen and juterium, they would have different bond lengths. Now, there's more you can do is that you calculate the frequency. So here, if this was the well, and then there was a small splitting, there would be an energy difference between those two, which is here. But the excited that you would see in a infrared absorption experiment will be a transition from this state to that state. And so that's what this curve is. And so again, that can capture a lot of the trend that's seen in experimental data. Now, if it was purely classical, then if you were looking at just the parabola down here, you would have this curve. And so it shows that the zero point motion is quite, is quite important, the quantum effects are quite important. But also that, as though the model is quite simple, it can quantitatively describe all, you know, this, this very broad trend over many materials. Now, suppose you think about bending. So this is where the this angle with the oscillating, and you can calculate that. And what you see in this is compared to data. And again, there's no new parameters coming in here. And that trend is, is well captured. So notice that as are very here, this frequency is getting as they get further apart, that frequency gets smaller, whereas when the the oscillation, the linear oscillation, the stretch gets gets harder. And so there's the opposite trend. And so this is an important point is that the stretch in decreases with decreasing are, but the, the bend increases with decreasing up. So there's some zero point energy associated with this. And that's decreasing and decreasing are and the bend zero point energy is increasing with decreasing are. So, there's actually a competition between these two. And this is an important concept. And it turns out, and that the chemists, particularly Tom Markland at Stanford theoretical chemists, a lot of the path integral Monte Carlo simulations, such that he done that this model can can nicely capture the trains. And so the zero point energy is the main source of these isotope effects to the secondary geometric effect. Okay, and so let me just show you that now. So suppose that you replace the hydrogen with deuterium, then this distance is going to change. Now it only changes by about 100th of an angstrom. And then this is a graph of that change, but for many different compounds, versus are versus the distance between the donor and accept it now, you could look at this and think oh there's no trend here at all. And also you could think oh there's pretty bad data but bear in mind you're measuring bond lengths to within 100th of an angstrom. So, but if you do a detailed analysis with this, with this model. What you, what you find is the is the following that if you only do the calculation with the stretch zero point energy, you get this, but if you do it with the stretch and the Ben zero point energy and so they're competing with each other. And so there's a distance out here at which you get the sign of the geometric isotope effect changes. And it turns out water is sort of just in this regime, and this is something Markland and others had noted earlier that they see this subtle competition between the two effects. And so in order that can sorry about that, and what are the competing quantum effects are almost cancel it's almost exactly cancel each other. And, okay. So, and again we're not introducing any new parameters to describe this this data. Okay, so the model we've extended to other context. So in proteins. And you will do isotopic fractionation where you add heavy water and then you find out how much two terium ends up in the protein at particular sites. And so you can use this as a, as a measure of the hydrogen bond length and so on this paper, which was done with people at Indian Institute of Science, like the one of the earlier papers. That gives quite good insight into that. Then, you can also talk about double proton transfer, the diabetic state model for that. And then more recently we looked at the infrared absorption intensity so hydrogen bonds greatly enhance the infrared absorption intensity and so this is a detailed analysis of that. So, let me end. So this two diabetic state model provides a nice parameterization of potential energy surfaces on a very broad range of materials, and the quantum nuclear effects are necessary for a quantitative description of correlations between donor accepted distance and bond lengths and vibrational frequencies and these isotope. Oh, sorry. These isotope effects which are a measure of the, the quantum nuclear effect the largest and the most subtle when you have moderate to strong symmetric bonds. And this is the regime where, yeah, this quite really short. But yeah, well, these bonds occur in quite a few proteins, including the ones I alluded to originally with some of the fluorescent proteins. This is if you want to learn more this is probably the best paper to start. And I put copies of the slides on the blog and there's lots of discussion on the blog about related issues is probably like 50 posts on hydrogen bonding or something. Yeah. Okay, so. Thank you. Oh, thank you very much for this very nice lecture and I think that the results are quite impressive. In the sense that a very simple model is able to reproduce a lot of experimental data. So, is there any yes there is a comment Anna, please. Possibly you cannot unmute. Okay, now, now it's all they have to give me a permit. Iris, thanks for the beautiful talk very elegant as usual is the case with your talks and your work. Just a curiosity, of course, you have this most probably is a stupid question but when you have shorter distances, you're basically you have a not a single minimum almost so in the ground state. But then you have the excited state potential in the surface, which is the energy of these excited state and which is the natural of these excited state these are accessible experimentally. That's a wonderful that's a super guy that's a one that's one of my favorite questions let me take me a minute let me just get to where that's addressed. Okay, so I, this is actually yeah very important question because this is a, if you like a sort of a smoking gun for whether this model is actually correct, because the question of well what is this state well this isn't excited. This is an electronic state, and some people would call the twin state because she and, and so in this excited state, the, the, the one of the signatures of it and this you do see this twin state in benzene and alvaline, not which are not hydrogen bonding but this is an analogous thing where you've got these two coupled electronic states, and one of the signatures of it is that this state is is harder. And so the frequency, the oscillation frequency is larger than it is in the ground state and now that's the opposite of what normally happens with chemical bonds normally when you go to the excited state. The bond is is softer, and you do see this in benzene and so the, I would love to see someone do an experiment looking for this for this state, but you should also see it in in the quantum chemistry. And so this is one example where this melon aldehyde here. Again, this is another Indian paper maha paratha. And so, um, yeah that that they see it in quantum chemistry. This excited state so it should be there in high enough level quantum chemistry calculations but you should be able to see it experimentally so I would like it if people you know looked for it yeah. You can comment make a sort of. Well, first of all, these are the name of the excited state frequencies are there also in polyacetylene you remember for sure that in the old time of police. But apart from that, I have a comment, perhaps for the people working on these strange excited state in sorry in aggregate of amyloid or things like that. So this strange excited state is strange fluorescence come from these phantom state and these hydrogen strongly hydrogen bonded system, this is a question. Oh, I'm not qualified to answer to some clear you're saying in the some of the amyloids, this is exactly there is fluorescence and unexpected fluorescent unexpected fluorescence in amyloids. Okay, no I don't yeah no I'd have to. Maybe you could send me. Yeah we could correspond on email I would just know more about that. The expert here are looking at the. Yeah, yeah. I, I think that Ali has a comment, possibly. Yes. Thanks, Christina. Thanks, Ross. Good to see you. I saw. I have two curiosities before I get to Anna's question. So the first one is, you. So you know that d2o is toxic. Right, I mean life, life did not emerge in d2o. So my first question is, you know, the percentage of short hydrogen bonds that are 2.4 is there they're not insignificant but it's not that they have a large proportion of them. So, do you have, do you have a sense on why life did not evolve in d2o and is, can it be related somehow to these subtle differences and how things change in these potential energy surfaces so that's number one. Number two is, I don't know if you know this but d2o actually tastes sweeter than H2O. And they've been some speculations and ideas on how this may be related to a subtle hydrogen bonding effects with sweet receptors in the tongue. So this may seem like very esoteric questions but I'm just curious if how to, yeah, how to relate these to these things. Yeah, yeah, no, I think that's interesting. So the first. Yeah, okay, about, yeah, complexities of origins of life and life evolving and so on. I mean, there just isn't much d2o in the, you know, in the universe, so to speak. So I think it might be a bit unfair to say that, you know, suppose everything was d2o, we don't know we don't have a what do they call a counterfactual. Yeah, yeah, yeah. That would be one thing. But I, but then I'd also say, I mean I agree with what you were saying earlier that that that it's some that these these short hydrogen bonds are very rare. And that in terms of a percentage, you know, so you can find hundreds of, you know, you can find hundreds of proteins in which there's a couple of these short hydrogen bonds and often they are near an active site for some functionality. But first of all, it's only a few of the bonds within one protein. And then most of the, you know, the 99% or even more of the proteins, you don't have these short hydrogen bonds. Right, right. Yeah, so I don't. Yeah, I'm to me that chose that. Yeah, I just, I'm always skeptical. Yeah, they're just that these are, I think they're fascinating from a science point of view, and there are certain specific systems in which they're certainly important. But yeah, I really not convinced that most of biology that they really do. Yeah, yeah, yeah. Yeah. Okay. No, thanks. Thank you. Yeah, but thank you. Good questions. Yeah. Well, now I remember. Ali, you have on the amyloid team right you. That's, that's right. That's right. That's right. Yeah, so. Yes, yes. Okay. Yeah, so I mean, well, you know, I mean Luca can chime in here as well but you know, before this work with Luca, we thought that short hydrogen bonds were and this is a response to Anna's question that short hydrogen bonds could be one of these. The origins of this anomalous fluorescence but it turns out that they are systems without the short hydrogen bond that also exhibit. So I can't say that this is the necessary criteria to see it. Okay, we have another question in the chat. I know that we are running out of time but since after that we have the poster session maybe we can at least comment about this. Ross, can you read because the, okay. In an escape route from in out of a protein, would it be more efficient to have a restricted high dense area of sectors rather than just one. I mean, do these acceptor act as competitors for each other or do they kind of help the rate of the electronic state. Okay, so this is, I think to do with just with charge transfer electron transfer. And so, yeah, it seems that, again, I'm no, you know, expert on electron transfer and proteins but it just seems generally that most biomolecules, you know, things are very specific in terms of that. You've just got one donor and one acceptor occasionally, you know, there's exceptions people talk about bifurcated hydrogen bonds for example, they do occur but they're pretty rare. So, yeah, so I think that it's probably. Finally, there's just going to be one acceptor, you know, maybe there would be, maybe there would be two. Yeah, I don't know if that's answering the question. Yeah. Okay. Yeah, good. Yeah. Okay, so let me thank again, Professor Ross McKenzie for this very interesting lecture, and now it is time for the coffee break and we will be here in 10 minutes for the poster session.