welcome to Physics Colloquium. We are absolutely delighted to have Alexander had shank or as a speaker. Today, Alexander is a Professor of Theoretical condensed matter physics and the head of theoretical chemical physics group and the head of the department of physics and material science. The University of Luxembourg. Alexander is also distinguished visiting professor at the Technical University in Berlin. Alix received his undergraduate degree in computer science and a PhD in physical chemistry at the Universidad Autonoma Metropolitan that in Mexico City in 2007. From 20082010. He was Alexander Von Humboldt fellow at the Harvard Institute of the Max Planck Society in Berlin. Out of that Alex state at the same institution and lead an independent research group until joining the University of Luxembourg in 2015. In his research, Alex combines quantum mechanics, statistical mechanics, and machine learning to develop accurate and efficient first principles, computational models to study a wide range of complex materials, aiming at qualitative understanding and quantitative prediction of their properties at the atomic scale and beyond. And Alex is one of the leaders in the field. He's extremely productive, published over 180 papers, is ancient, exists 71, with more than 25 thousand citations. Alex is also in the top 1% of highly cited researchers from 2018 to 2020 want. He has also received a number of awards, including a girl for Eric Young Investigator Award of the German Physical Society, Dirac Medal from the World Association of theoretical and computational chemists and a Wander Walls Prius or what, 2021 International Conference on non-covalent interactions. Alex is also fell off of American Physical Society. We're all absolutely happy that Alix accepted our invitation. And without further ado, Alex, please, we're all eager to hear your talk. Thank you very much. And they say for this kind introduction, let me try to share my slides. Okay. Do you see my slides? Yes. Okay. Excellent. Great. So yes, thank you again, say and thanks for for this kind invitation. So as I said, it's a bit late here and in old Europe, but I think I'll manage the first time. I think scientists, they have to stay late work. But I think our work as enjoyable, so on. I'm thank you very much again for the invitation. And they think they hope that I can pass at least part of this enjoyment during my talk. So so I understand this is a broad colloquium. And so I tried to give a broad overview on, on few different topics that forever it can on and find a unified topic. And the unifying topic that I will be discussing here is force field. So, so force fields are some effective representations of the forces that nuclei feel in a certain molecule or material. And this force field, the, the, the, There's a definition for forceful to come off or it's busy and Warner behind approximation. So, so this will be ubiquitously used during my talk. Everything will be born Oppenheimer approximation. And that allows you to define always effective forces for a given nuclear configuration. And the question is, of course, all this forces are coming from electrons, right? So they are coarse-grain electrons and representing them effectively as some interactive and Adams, and the question is, how can we do this effect? So this of course, has been done in the field of computational chemistry and computational biology and material science for a very long time. In fact, for the Nobel Prize in Chemistry in 2013 was avoided for construction of biomolecular for students. A few years ago, new tool came into our toolbox. This is machine learning and machine learning allows the construction of sophisticated and flexible, non-linear forms for this, for students. And so for some time people thought this is sort of a lifesaver right now is machine learning. And we can construct universal force fields for essentially any monocular mature. But of course, once again, those force fields, those atomic forces are coming from interacting lecture. So the question is, when under which conditions we can map interacting electrons into effective for students. And, and I will try to tread on this topic during my talk. So in my group in general, we are interested in quite a complex problem of stops a large systems, large molecules, large materials. And this is a complex problem that involves physics, chemistry, material science, and computer science scientists represented by machinery and so on. People can mean from my group has different backgrounds. They're physicists, chemists, mathematicians, and computer scientists. And there are a few very important people to highlight here. Eager scheme. I'm, I'm, I'm showing you here. Here's a group leader in my group who is leading a small subgroup that works on combining physics and machine learning. And in particular Gregory von Sekhar and financing the lingual. There'll be two people whose work I will mention it. Now. The combination or physics and machinery and require strong experts from the physics side and from computer science side. And so we've established for about 10 years ago, a strong collaboration with a group of close Robert Mueller, who is one of the most renowned machine learners in Germany. He is working at the Technical University of Berlin and in particular to people Stefan Camila and those yellow cells header. Key players also did tremendous contributions to everything I will be describing. So, so a lot of this verb is really a combination between strong expertise and machinery and, and strong expertise in physics and chemistry. So we start from, in our breakfast, start from first principles and for us our standard model, these the Schrodinger equation and in particular born Oppenheimer approximation applied to the Schrodinger equation where we separate the electronic and nuclear degrees of freedom. But they are interested in understanding and solving the Schrodinger equation for large and heterogeneous systems. So for example, proteins, liquids, molecular crystals, or two-dimensional materials. And of course the interactions, the wide range of interactions and all the system's complicated. The solution of the Schrodinger equation because we are talking about thousands or even tens of thousands of interacting electrons. So this is a complicated problem. And you would like to develop approaches, efficient approaches that enable ear increasingly accurate solution of the Schrodinger equation for this complex. So that's our final goal. Of course. This goal of yeah, not the first group overcome this. There are thousands, tens of thousands of groups working on this. And in the modelers toolbox, there is a whole hierarchy of approaches for approximating the solution of the Schrodinger equation. Now it's well-known of course, that exact analytical solutions to the Schrodinger equation exists only for certain model systems or for one electron atoms, like a hydrogenic atom. So when we have more than one electron, which is the case for all systems of our interest, we need to approximate the solution of the Schrodinger equation and particularly to approximate the wavefunction. The most dumpy of approximating it is sort of rate and empirical, but actually the force that's forgetting about all electrons and just say, well, they're effective forces that Adams, you. And this can be done by following the Hellman Feinman theorem of squares. And just write some non-linear function that expressed as the at the, the force that an atom fields in a given confirmation of a molecule or a solid. Going a bit more sophisticated, you can introduce electronic degrees of freedom, for example, why are semi-empirical methods based on density functional theory or quantum chemistry? So you can introduce, for example, a small basis set is more than the basis that you can fit some parameters and get sometimes a reliable ancestral for certain class of systems. The real workhorse in the field of electronic structure theory East density functional theory, because as proven by Hogan broken corn and then constructed effective theory by corn and some density functional theory in principle as an exact theory. But of course, you have to approximate quantum mechanical many-body interactions and hands introduce approximately functionals. And this gives you, of course, errors and pencil. And going up, of course, in principle, we have numerical ways to exactly solve the Schrodinger equation y, a so-called full configuration interaction methods where you write electronic configurations and you write a linear expansion is some coefficients and then you obtain those coefficients. Or you can do Monte Carlo based solutions, so-called quantum Monte Carlo methods. And in principle, if you are lucky and if you have enough flexibility in those wave functions, while you can get, in principle, you can approximate the exact solution to the Schrodinger equation. Now. The nice thing here is that when you go up in this hierarchy, the accuracy of predictive power of your methods increase, but there is a price to pay and the price as computational cost. And another price which is especially important for physicists, is that you lose conceptual insights. Write wavefunctions are extremely high dimensional objects. And getting insights from wavefunctions of say, system, the cells of the electrons is not very easy. And so methods such as DFT or semi-empirical methods actually give you many more insights than methods that are here at the top of this, of this letter. And so the real question, and that's where machine learning comes. How we use the nice ideas, nice conceptual ideas at the lower rungs of this ladder. But we still keep the accuracy that we have and the higher ranks of the ladder, That's ray machinery. But machine learning instead of democratizes this whole hierarchy of methods here because you can use different techniques from different methods and you can combine them in a nice way. For example, you can use aspects of semi-empirical methods for describing a certain molecule, a material, but then train a machine learning method on high level data coming from, for example, quantum, high level quantum mechanical methods. But of course, if your reference data is garbage, right, for example, you took some approximations that are not good enough to describe your system, then machinery will only give you also a garbage, right? And so the question is how to appropriately combine reference data? Which level do you use to produce reference data and which level of theory to use to describe your system. And those are two questions that are still being investigated in our field. So now in the next couple of slides, I would like to delve a bit further into this question of how can we obtain reliable quantum mechanical data and how we can know that we are producing reliable quantum mechanical data for systems of our interests. So I will give you now two examples. One example is of a methodology and approximate methodology, which allows you to obtain very reliable reference data compared to experiment for very complex systems and molecular crystals. And then I will show you a case where you use the highest level of quantum mechanics to different highest levels of quantum mechanics. It turns out that both of them disagree, and this means that one of them or both of them are giving you garbage data, which we cannot actually use for parameterizing machinery and production. So before I started actually machinery numeric, a lot of the work in my group was on developing effective physical methods for describing a long-range electronic correlations. So this are ubiquitous many body effects, right? Where many electrons correlate or large land scales. And you don't want to describe those correlations explicitly, right? Because electro electronic degrees of freedom, because it's just too hard, it's too computationally expensive. So we've developed the so-called MDD, or many-body dispersion method that basically describes the response of electrons in a molecule of material, wire quantum harmonic oscillators and then the coupled or spinlock harmonic oscillators is a long range potential. And we solve the Schrodinger equation for oscillators, not for electrons. And we then couple that energy to a semi local density functional theory functional. And so we get this semi local quantum effects from DFT. We get non-local quantum effects from MBE Hamiltonian. And this is a nice combination of two different methods that we then applied to a variety of molecules and materials. And I will just show one particular obligation of this. And this application conserves, concerns a predictive modelling of so-called, so-called phenomenon of polymorphism in molecular crystals. This phenomenon is ubiquitous phenomenon. So basically, it turns out the Judaic one molecule, for example, this one, this is a drug candidate from actually from Pfizer. And then you try to crystallize it. When you crystallize it in from solution or some other environment, you realize that it can pack in a wide variety of different crystalline arrangement. And that is because there are many types of interactions. Electrostatics, polarization, dispersion, powder repulsion that guide the packing of those molecules in the crystalline phase. And those crystal packets often have almost degenerate lattice energies. So you can have within a window or for, let's say kcal per mole, which is so-called chemical accuracy. You can have 10, 20, 30, 40 of those polymers, right? A huge number, despite the fact that they are. Almost also degenerate. The different polymers can have completely different physical chemical properties. For example, different colors, different solubility is different than cities melting points, conductivities or whatever, whatever property your image. But you really need to know which polymorph is global energy minimum and these polymers or meta-stable states, and this is a very tough problem because we are talking about 1% of the largest temperature, right? That is what determined the differences between this point and this is a very, very tiny energy. And for a long time people thought this problem is completely, it cannot be dealt. Is quantum mechanics simply because the energy difference. And so we've actually applied our methodologist to this problem. And we tried to do this in a blind fashion. So we don't, we don't cheat as, as often we do in theory. The sort of take experimental data and then the calculations. And we then compare back to other experimental data by, by the often biased because we already used experimental data. In this case, what I'm showing you here is a real blind prediction. So, so these are results of so-called blind test of organic crystal structure prediction organized by Cambridge crystallographic data send them. So basically what they do is they collect experimental data, different polymorphs of molecular crystals. They hide this data. You don't know his unpublished data. And they asked experiment, they asked theoretical groups to predict those structures and then they compare the predicted structures which you submit to the experimental ones. And you need to predict both structures, right? Result knowing n structural information on the Norwegian structure of the molecule itself and energies as well, right? And so here I'm showing you overlays between our predict structures legally blind liberty. Rigid crystal structure prediction procedure. We put different crystal groups, we optimize the molecules. And these are optimized, completely geometry optimized structures. And our predictions are colored wildly. Experimental structures are the gray and it's pretty hard to see differences in most cases, the root mean square deviation for 20 molecules and the supercell is about 0.15 angstrom per molecule. It's a really tiny difference. It's mostly invisible here. And so this is, this result can only be obtained when you do density functional theory was a good hybrid functional, been easier or functional, so-called modern empirical hybrid functional. Plus our full many-body description that includes long-range correlations and the full many-body fashion. So here are structural information, so this is pretty good. But of course the question is, are those structures really the global mean? Because experiments often see global minimum. And it turns out that they are when you go to the highest level of theory. So what I'm showing you on this slide, our results for four different molecules. So the molecules they indicated here as this two-dimensional diagrams, the global minimum structures are shown in this unit cell pictures. And what I'm showing you on this diagrams, for example, here on the left, is for different levels of theory. As you move to the right, you increase the sophistication of your level of theory and the accuracy, right? And the there I bought a 100 structures and bottle. That's a 100 polymorphs that we predicted and the experimental structures and rat. And so in the best case, the experimental structure in red should be the global minimum. So it should have a 0 energy on this, on this diagram. And in fact, this is the case for all of this for different systems. When we go to the highest level theory, which includes a high appropriate to be B 0 DFD functional misses a function that describes semi local exchange correlation effects blast the many-body dispersion. So the full many-body treatment of long-range correlations. Glass also vibrational entropy is computed at room temperature. And so as you see here for all these four systems, the, the experimental structure turns out to be the global minimum at our landscapes, which is the best possible prediction you can make. So actually, when we presented this results originally 2016, nature sounds if gene actually nature all this news and views article saying that the volume of prediction problem is solved. I don't really agree with that statement. I think it's not solved. And movie, it's presented really good results. It's surprising results for five different systems. I'm showing four out of five systems. But there's still quite a lot to do. And it took us actually about four years to really finalize everything and writing this paper. Okay, So, so this is an example where Experiment 3 to experimental data. Tells you that your quantum mechanical reference calculations are good enough grade for this particular problem. And this is a very, very tough problem, the problem of prediction problem. But there is also a tremendous problem here because doing all these calculations is computationally very expensive. So I'm showing just part of the results. The total amount of computer time that we had to spend for this study is about 20 million CPU hours. But you can do on, on, on computer is especially in the US, right? If you have access to beak HIPC facilities. But it's not something you want to repeat for every new morning and spill here immediately. The question comes, well, if you have all this data, you could also use this data to construct effective machinery and potentials, for example. And you can learn from increasingly larger chemical space. It says your January data. You can construct those potentials and you can make them more and more general as you produce more when more reliable D. And that's something which has not yet been done in this field in a, in a, in a systematic way, let's say. But the data is in principle, there is just not easy to construct machine learning potentials for this large systems, as I will discuss in the second part of my book. So here's an example of reliable predictions with quantum mechanics, which you can then use for machining. Let me give you now a completely opposite case where, where you cannot decide what quantum mechanics aid and to actually use so, so, you know, in our field of development of quantum mechanical methods, there are two different paradigms to go over. It's heaven, right? Reaches the exact solution to the Schrodinger equation. One is called post Hartree Fock method. This means that you'll construct a Hartree Fock solution which respects anti-symmetry or fermionic, so fermionic statistics of electrons. Then what is missing is so-called the electron correlation energy, which is what I've described already, is the MEG method, which captures long-range correlation energy. But if you want all correlation energy between electrons in an exact way, you can do this wire so-called quantum mechanical methods. In particular, the gold standard in the field, the so-called couple of cluster map, but the single, double and perturbative triple excitations. In fact, this method originally comes from high-energy physics, from nuclear physics. And it was abandoned there because it was not giving good results, but four electrons, strained relations that gives great results. Most of the time they'd been people for that reason really cord goals then. But there's an alternative math, right? So if you have just one that, that you cannot really trust its results because there's just one number and you have to take it for granted. It would be great to have an alternative method. And in fact, there is an alternative method that's called quantum Monte Carlo, which is a completely different way to obtain to approximate an exact solution, I'm afraid your equation. So you write an ansatz for the wave function and you then optimized parameters and it's very flexible ansatz. And the principle of the ansatz flexible and app you get an exact solution and training. And so we've applied this to alternative ways, gold standard ways in quantum chemistry, in quantum physics communities to actually study the interactions between morning, I'm indifferent morning. It's ranging from benzene dimer of year two, this buckyball getchar complex. So this is a C 60 molecule embedded in this cycle of birth and that NRI. And we want to understand the binding energy between the right. And it turns out that when the molecules are small or when interactions are not so strong balls methods. So more gold standard, it's coupled cluster and the quantum Monte Carlo if essentially indistinguishable results. But the surprise is when you go to higher to larger systems and this has simple systems and just non-covalent interactions. There's nothing fancy bulb and it's not strong. Correlations is no oxides are some really strange or Bornstein buttons here. But nevertheless, for such systems, you just increase system size, the interaction, of course, the strength of the interaction increases a bit. You both methods give competitor different reasons and the difference is huge. It's order. Well, I would say, yeah, All order of magnitude more than what one would expect. So, so here the mean difference is eight kcal per mole between the two methods. But the largest difference is 12 kcal per mole. And this is a big surprise. And so we'd be sort of coined this puzzle. And of course now the question is, what do you trust as a reference for machinery? Is that this blue line or is it this red line? Right? And if you put the two different numbers, you will get completely different parameterization for, for, for the machinery enforced. And so, so this two examples sort of GIF. So define the first part of my talk where I wanted to talk about the reference state, okay, So you really have to be critical to your reference date. Sometimes when you use the highest level of quantum mechanics that you have. Disposal, you'll get reference data you can more trust at the moment. While in other cases, for much more complicated examples like molecular crystals, you do have methods that seem to give you reliable and quantitative results which you can use for construction of machinery first. Okay, So, so that's summarized some of the first, or we might talk about reference state and now let me talk about machine. So despite the fact that sometimes we don't, but we cannot produce reliable reference data. Let's say we have cooled reference data. And so we can now produce, for example, energies and forces for molecules as a function of their confirmation degrees of freedom. So we move some functional groups, right? And we know how the forces change on atomic forces change. And that allows us to construct a certain non-linear neural net for poor or current rich regression procedure. To feet, those are reproduced or atomic forces. So of course, we want to really do a complex systems that's where we want to goal and it is full accuracy of quantum mechanics. But at the moment, we are somewhere here, right at present, where machine-learning force fields can be used. Studying smaller organic molecules, I think this is, this part is largely solved or small organic molecules up with maybe three agonist is sort of a soft topic already. Or ordered materials. Are those materials have also been studied by many groups and they're very many. Would machinery methods to construct force was for this things. But if you look at disordered materials or the peptide from biopolymers, they are not there yet and a year classical force fields are still the, the de facto standard. But another thing which is extremely interesting is that children force fields are not, cannot only be used to construct This representations of how atomic forces change with molecular or solid state geometry. But they are becoming new, completely new methodologies in their own right. Because you can study of things which were not possible to study this previous classical force fields. You can study electronic effects. You can start the reactivity, try it so your atoms can change their, their bonding patterns, which was not possible to do this classical force fields. You can construct models for ground state and excited states. And so you can do nonlinear dynamics, you can do optical excitations example. You can easily study nuclear quantum effects, which was not possible to do is classical force fields. Because in their parametrization, people would mix experimental data that includes quantum nuclear effects and theoretical data of each does not those defects and so you cannot mix them. They sat, problem of double counting and so on. And so machinery enforces really enable a much wider set of applications in, in physics, chemistry and chemical physics and physical cans. And this is really where it gets pretty exciting because many of those simulations were simply impossible. Before machine reinforced feels really came into, into the game. Though. When we started working on this field. Aiming at first producing machinery enforced fields for molecules, for small money. That's where we started. We wanted to do something which is quite different to what most people were doing. The sort of put a very challenging problem in front of us. So we wanted to construct a machinery for short, which is general. It can be applied to any potential want to go up to a certain size. It should be transferable, right? It should be scalable and it should represent them all quantum mechanical interactions. So you cannot impose any couples, you cannot predict and the energy of the molecule as some of our atomic energies because this is not possible to move as the Schrodinger equation. And that's what most people were doing before. And so this led us to really reconsider the most basic aspects of all four forces. So what is typically done? They feel that something like this. So you're given a molecule, let's say a benzene molecule like the one shown here as one of the simplest molecules. And you are given the different conformations of the molecule, right? So you have a set of conformations. And of course, different conformations have different atomic forces. And so what we typically do is you write an energy model. And an energy model, right, is written as a sum over atomic energies. And this is already a big problem because Schrodinger equation does not allow you to define it on mechano. She's, the only thing you can do isn't born Oppenheimer approximation is define atomic forces. This is an observable in due to the home and find length here. And so doing this is not allowed by the Schrodinger equation, but nevertheless because of computational. Efficiency and because of permutation symmetries, people do this, but this is wrong. This shouldn't be done prints. Now what we decided to do is different thing. So we start with this confirmations and the right model, a force-field explicitly for atomic forces. And once you write that model, if this model is energy conserving by construction, you can actually integrate it out and get a potential energy surface, right? And the only question is, how do you do this? Energy conservation in the forest them, right? But this is of course well-known because we know how to construct a conservative force fields. You know, the, the curl of the force will have to be 0 there. But it was defined the conservative, conservative forceful. And so what is done in, in, in practice is something like this. So I'm giving you an example, a toy exam. So, so let's say we have this force field, two-dimensional force for this our ground truth. This are two coupled harmonic oscillators are a couple of parameters. And let me just take this and we take six data points at run out of this force here. And we impose the requirement that the curl of the force field has to be 0. By construction, this isn't our machinery model by default. So we work and for his domain. And then we try to reproduce the ground truths to learn from just 66 examples. And we get this field here. So if you compare this conservative fields which you learned to the ground truth, while it has all the features, it's not quantitative, but it's semi-quantitative. But if you'd drop the requirement of energy conservation, so, so you then learn the components of this force, the x and y components, you get this vector field, which is completely nonsensical compared to the ground truth, right? It has a different attractor here and has a completely different for, right? So, so energy conservation in general, in the domain or for force fields, extremely constrained requirement. And it's a requirement that really helps you to learn, right? Then it reduces the need for, for data, for the number of data points that it has a lot of interesting aspects actually that I don't have time to go. And now let's move beyond our toy examples, right, to real morning. So, so now we have a molecule and what we do in our approach, we call it gradient domain machine learning. And S stands for symmetrized gradient domain machinery because we use all the symmetries, global and local symmetries of our system. So global symmetry is this time invariance, which gives you energy conformation, right? And they have of course to rotational and translational invariance and v impulse per mutational and variance, which we discover from in a data-driven way, right? So for example, if, if you have a metal groups which rotates in the dynamics and of course, permuting all the hydrogen atoms on, on, on the methyl group is, is equivariant, right? For the, for the forces and saw the discover those images from the data from the molecular dynamic state. So we produce some liquid and that makes for a given molecule these simple efficient method. We then subsample the recover all the permutation symmetries. We do multi-part. I mentioned there is a lot of Blackmagic going into this, but that's explained in our papers. And then once we do that, we then construct a kernel matrix in the hessian domain because the covariance between 4 atomic forces is given by the Hessian matrix. And then we have a vector of coefficients which is obtained from our training data. Okay? Once we learn this vector of coefficients, this is a convex problem. You can obtain those coefficients by just matrix inversion. You then can integrate this kernel and analytically and get a model for the potential energy surface, right? That's a big sum here, but it doesn't matter. It's an analytic numerically exact solution. So, so then you can plot, for example, potential energy surfaces. And here is one example for one particular molecule shown over here are now this approach is extremely efficient. So for a realistic molecule, such as aspirin, beneath, it has 24 atoms, 60, I think, 68 degrees of freedom, if I remember correctly, we need only about 300 confirmations out of molecular dynamics trajectory to obtain force field, which is accurate to 0.3 kcal per mole, which is really, really accuracy which you can use to run molecular dynamics. And because you only need a very small number of conformations, the reference data can come from the highest level of quantum mechanics. And so we can, for example, train these force fields to couple of class than data, which is, as I said, is a sort of a gold standard for, for small molecules at least. And it works really, really well for those. And once we have obtained this force field. We have now a force-field that includes all the electronic effects within the born Oppenheimer approximation to essentially arbitrary accuracy. So it's almost essentially exact solution of the Schrodinger equation. And then in order to treat quantum mechanics of the nuclei, we use the so-called us integral molecular dynamics. This is based on find one cup plus integral representation of quantum statistics, which in the limit of an infinite number of beads gives you an exact quantiles to this 644 for your quantum particles. And with that we can, we now can really do, I would say embarrassingly quantum simulations because bores our nuclei and our electrons, essentially treated at the exact level of quantum mechanics is in Warner been Homer approximation and of course views in bosonic treatment of the nuclei. And so here is an example of this calculations. This is ethanol molecule, one of our favorite ones. And so it has three different minima, is a so-called trans and gauche minima. And we can calculate, for example, occupation probabilities of those minima. And when we look at our exact simulations and compare experiment essentially get exact results. And this is really resent error bar For experiment. While if you drop, if you, for example, train a force-field at the level of density functional theory, or you do classical molecular dynamics, you will not get this degree. And so say, the agreement is really destroys. You need quantum mechanics or balls, the electrons and the nuclei at the highest level theory. This is just an example of something we can compare to experiment, but they can also do new discoveries. So, so for example, you can compare the effective binding mechanisms to squat. Classical dynamics are the nuclei, are quantum dynamics are the nuclei. And you'll find something very surprising that quantum dynamics often dense to stabilized meta-stable states of molecules. For example, this happens in aspirin, where the global minimum is heavily stabilized. A local delocalization of the nuclei, the molecule is globally standardized and this is actually quite a surprise in fact, and we explain that by fluctuations of negative and positive charges. So call this by star and transitions. And this is the chemical. In chemical. Similar effect happens in this stall when molecule, so Darwin molecule is just a benzene ring of is a methyl group and this methyl group classically is just a broader, it's a free rotor. Classical dynamics just make this, this benzene toluene metal group also lead free. But if you do quantum dynamics, you find that this oscillator here actually starts to localize. And that's again a surprising finding because quantum effects localize this rotor, right? So it essentially just localized on the left side, on the right side. And this is also an electronic, quieter, complex electronic interaction. So this kind of facts that we can find now by this explicit usage or machinery and forceful. So this was not possible to do before result machine learning because those calculations would take essentially decades on, on, on supercomputers if you use this level of theory that we use. But now we can do this calculations and essentially an hour or so or even less. So. So this really demonstrates a huge acceleration that machinery in brains into the field of computational physics and competition against. Okay, So up to now, I've mainly discussed small molecules, but we can do much larger systems now. So of course everyone wants to go to real applications, for example, molecular crystals, D and E nanotubes. And we've actually extended our GDM, our framework by doing, instead of doing exact inversion, we can do precondition into to enable large-scale calculations that we've now extended GDM up to about 400 atoms. We get this double walled knowledge to prevent bliss of unpublished. We are finalizing this week. We've also extended our approach to materials for banks who didn't periodic boundary conditions. We call this Bravais inspired GD and malware big HTML. And all this will be coming out pretty soon. Just an example of an application that can actually do now in a very short time is for exams or the dynamics of a benzene molecule on top the Griffey. So this is fully periodic oscillation graphene and benzene aperiodic systems, right? It's a brute Excel. And we are running the dynamics of this benzene molecule and they're looking at how it fluctuates in terms of the vertical position and in terms of the angle between the vertical and the the plane of the molecule. And what you realize is something again, very, very interesting. Classical electrodynamics, the molecule is delocalized so it's rotating and translating over, over the surface quite widely. While in present ago molecular dynamics. So when you treat the nuclei quantum mechanically, the molecule dense to localize. And this is again counter-intuitive because buzz integral of molecular dynamics delocalize is the nuclei locally. But because the delocalize as nuclear locally, so most carbon distances and carbon-hydrogen distances are larger and effectively, the polarizability of the molecule grows and that increases the funding lines attraction between benzene and graphene. The same thing happens in graphene. The carbon atoms are effectively at larger distances and that increases the polarizability of graphene. And so the fun towards attraction become stronger because of quantum effects. And this is a very counter-intuitive fiend which I would not have predicted result actually running those simulations. So, so this application demonstrates the state of the art that we can do today in the bulk buying this or machine learning force field advance. Okay, So this is all nice and wall and this is a very nice applications I think. And not only ours, but many other groups have demonstrated extremely interesting results for many, many different systems. I would like to spend the last five minutes to talk about challenges. So, so there have been a lot of advancements. But actually I think that we've barely scratched the surface on the field of combining physics, chemistry, and machine learning. And there are many, many challenges and the recently tried to describe them in this prospective article with Igor. The, the main themes are accounting for long-range interactions. So up to now, most people have concentrated on short range chemical effects. The datasets that we have up, it's not really clear how to fully construct them in a systematic way and how to use everything that is there in the data sets. There's still a lot of physics that we have not incorporated into our, I'll get actress. And finally, there are some examples in the recently published literature where people find new phenomena from machine learning. And sometimes this correspond to false discovery simply because you're, you do extrapolation where you shouldn't really be doing. Okay. The 1 they wanted time, which is really close to my heart and that's related to the first part of my talk is how neuroscience it really Electrons are, right? That comes back to the data. Electrons of machinery and forceful. So, so how far away do we need to meet Adams? See rain. So, so what are the whole long range or the contributions to atomic forces from Adam's far away. And this question, of course, has bothered many physicists. So for many, many years. And in fact, the way to corn was a well-known Nobel laureate. Together There's Emily brought down, have written this nice article in PNAS called near sightedness of electronic mail. And many people in computational chemistry side that beeper as a proof that electronic matter is near. Now of course, what is near science? I mean, that is a very strange concept because if you ask someone seated and looking at the window, Well, they see a house far away, right? Which is meaning meters or kilometers away. So for him, maybe near sightedness is a 100 meters. But if you ask, say computational chemist, how neuroscience it is a benzene molecule, maybe they will tell you a few angstrom. So is it really a few angstrom is a 100 angstrom, is it Saul's an angstrom always a damn micro meters or even more and no one really norms. And so this interesting paper sort of setups in an hour based on the simple models, mostly the non-interacting inlet Mongols. And the question is like this. So you have a certain material which is represented here by this cloud. And you have a certain point are 0, and then you have a certain point r prime. And you want to ask a question of whether you can find a critical radius r. Ray fish for all points are 0, would confine all interactions that exist, right? Between our 0 and R prime. And so this means that for every r prime, there is a certain footprint in terms of interactions, right? This region w r prime, which never intersects this sphere via a critical radius r. Now what is the radar is unclear, and this paper has a very interesting last section. This is actually computed section of the paper which talks about interaction from it. So most of this paper is about non-interacting fermions where this radius r is exponentially decay and it's, it's, it's, it's, most of the time it's pretty small. But for interaction fermions of what the corn rates, the following thing. He says, however, charged insulating fermions are classically far sighted in the sense that a sufficiently large distances the fermions see the classical long-range total potential, where rho of t in this integral is the dawdle perturbing charged density, including depolarization. And what this means is that in a periodic materials, the electric field, this typically depolarized and especially involve or written materials because electric fields from different sites on the center of an atom, they can. But in real materials, such as biological molecules, two-dimensional materials, or a liquid, even this is no longer the case. You can have polarization or depolarization in different directions and you electric field is in general delocalized. So if you apply, if you extend this argument to real materials and all materials have insulating charged for nuance. You could say that the interactions there are actually quantum mechanically far-sighted because they also depend on the frequency for the electric field, which is neglected here for, for, for simplicity. And beg them into 1000, five or four is, there are no real calculations to show how I entered the electronic metal is, but now we have the ability to do those calculations. And I will give you two examples of different kinds of fire safety. The first one comes from electronic exchange. So this a hardship for calculation. There is no electronic correlations here for a system of carbon chain terminated with Mason groups. So this is so-called accumulate money. And what I'm doing here is I'm changing the land or this chain and I'm doing or even alternation. So for all even number of carbon atoms, a good this conical shape of the potential energy surface as a function of the rotation angle of one dimensional groups. For an odd number of carbon atoms, I'm getting this parabolic shape and it alternates, right, as I change the number of carbon atoms. So this calculations are pretty easy to do with your favorite hearts before called. Now, if you want to machine learn them, you can use a binary machinery methods. They completely fail because they are unable to describe this non-local you fact and this, this alternation between conical shape and parabolic shape happens because of long-range charge transfer events. And this is absent in all our localized machinery reinforcements, Of course. Now this is quantum exchange effect. Now what about quantum correlation? So we've done this analysis on correlation effects for biological systems. And in particular, the question of how far sighted are fun device I training correlation that lead to find a way it's interactions between the protein and water in wire. And so here I'm showing you calculations using two different approximations to a long-range find a way interactions. And i'm, I'm showing you a radial distribution function for the energy now and I don't have time to read it. See how we compute this for the quantum mechanical case. But there is a way to approximate this pair distribution function. And so here is the protein surface. And, and so if you use a standard pair-wise dispersion models, so for example, using Lennard Jones potential in this case be used so-called Pachinko shuffling about that features it also pairwise aspersion member, all interactions decade above five angstrom away from the surface of the protein. And this is expected, this is r to the minus sixth decade. But if you know what an explicit quantum mechanical many-body calculation using our MVD Hamiltonian, you see that interaction is actually propagate up with five angstrom away from, from the surface. And so this is actually quite far I say Today I will say and provides an illustration of how far sighted balls electron exchange and the electron correlation effects again. And this is of course, still quite a challenge to extract. Now this for aesthetic calculations, but we can prove the same thing for Dynamics. So here is dynamics of two different molecules, you know, build radial distribution function for glycine, which is a small molecule and for ease of benzene, which is a larger molecular switch. And for glycine, everything is localized to five angstrom because it's small molecule. But for ease of benzene interactions propagate up to ten to 12 angstrom. And if you now try to machine learn them, you realize that different machine learning methods for different bytes of the potential energy surface, they have different accuracy is one. Here is another mechanism. And if you look at the errors for different missionary and methods, they are different. And that just reflects the complexity of morbid involves chemical bonds and non-local electronic interactions over large distances. And so this is really an unsolved problem in this field. Okay, That brings me to the end of my talk. So everything that I have described, all the software that we've developed is open source. So Wars, there's TDMA and neural network, but then shows that we've developed are all available online to you. Feel free to download them and play around with them. Always happy to hear feedback or things that work and things that don't work, of course, which is even more important. And finally, I would like to leave you with a challenge slides. So, so I've tried to, first part of my talk, we could discuss how we produce reference data, what reference data is useful, and what reference data is not useful. In a second part, I tried to show how we can use quantum mechanical reference data and develop machine learning force fields to utilize it to the full extent which now have enabled us to really reach exact dynamics is Bohr's quantum electronic and quantum nuclear effects fully captured. But as I sat in the last part of my talk, as I've demonstrated, we still have a lot of challenges to solve. Accounting for long-range interactions is an unsolved problem simply because those long-range interactions involved many interacting electrons with braille large landscapes. In convey to that right, chemical bonds are simple because they involve only a few electrons interacting over at short length scales, right? So, so those short length scales are easy to treat. Long length scales are hard to treat. And in addition, there are many, many other challenges remaining to be solved. Related to data science related construction or descriptor is related to incorporation of different physical laws. And really tight marriage between machine learning and physics, chemistry and that, thank you very much for your time. Thank you, Alex, for a very good talk. Now we'll get some time for questions. Shift up for you and I go, Hey, thank you for the nice talk. And goes like say. So my question is, so what is in your opinion on the, the physical reason for those differences between a couple of class that diffusion Monte-Carlo forms of bigger molecules, dimers. Yeah, so, so we've tried to analyze many possible reasons. In our paper. You've not been able to completely explain them. And I I have two so I have two reasons. One of them to Blaine KMC and funnel them to blame coupled cluster. The way that it's done correctly. So saw on the coupled cluster side, I think that atomic basis sets or localized that plumbing basis sets are a big problem for large systems because they don't have sufficient flexibility to model fluctuations in the vacuum space between the molecules and outside the molecules. The polarizability of those large molecules is very large. And I think the polarizability density, density response is pretty localized. And so that's something that is not easy to treat because even if you put basis functions in vacuum space, which you can do, it's not clear how to do this systematically. And of course, you also get a lot of problems with degeneracies in the Hartree Fock solution when you do so. And hence, this is not a practical solution. So I think on the coupled cluster side, this can be big problem. And, and so the basis that extrapolation procedures that people use I don't think are reliable for this large molecules on the quantum Monte Carlo side, but also the construction of the gestural factor I think is still probably not sufficiently well investigated harm problem aspect in the, in the treatment of many, but I think there could still be issues on that side. So I think Moore's methods have still issues to be solved and I'm not sure which one of them has the largest potential uncertainty. So if I may comment, I agree on COP of class. That'll basically, and what I like about it is, which is already the same thing because you wanted to say that when you do those calculations are big molecules cannot use augmented basis sets. Condition is really important ability and for long-range interactions, you can not doing because you have dependencies. And that's the problem and extrapolation. Now prove the acceleration picks upped up those effects. So that's one thing. But in case of quantum Monte Carlo, I think it's also the node problem. There's no prove the notes are good enough and it may, in some cases, cancel other problems. In some cases, they may have up to larger arrows. And who knows? I mean, you're right, your right leg was known. We know that all beryllium is also of course, enters the gestural factor as well. And yes, sometimes they can compensate, sometimes they can accumulate. That's right, that there's no real numerical proof of that. Yeah. And in the coupled cluster, of course, we used a singly augmented basis sets, right? Read went up to OCC CPV, PV 50, z. But probably you actually need double or triple augmentation, right? And that's impossible to do for the sludge systems as you graduates. Thank you. Any other questions? Maybe from students? I don't see any other questions. Can I ask a question? Yeah, Of course. Yeah, I saw that you had the sun result of fully quantum treatment, lowering the energy of some molecule when compared to classical. And you mentioned this is kind of surprising. Yeah. Yeah. There was a picture like with two curves. So this, the difference between the two curves is basically that you're treating CLI quantum mechanical in the red case. That's right. Yes. Yeah. And so why would this be surprising? I mean, I'm thinking from a different perspective of condensed matter physics, for example, of magnets. So what happens in that case is that what is your new apply would be like a spin. And in physics of magnets there is lecture no army of people are using classical macro magnetics based on the Lipschitz equation, which is the same pretty much as classical molecular dynamics, which creates more visionary snow pliers or a classical Newtonian. Barney again. But then vein. And then if you look at some, you know, if you look at them, Ferro magnets, yeah, it's the same thing in classical quantum usually is very similar, as long as the spin is not 1.5, which is a kind of mass. But then when you go into anything which is not parallel, which means y county fair, I'm arguments. Anything non-colinear, chromiums and things like that. Then every time you touch quantum mechanics, which means you start treating spin as it should be done. Using quantum mechanics operators rather than using and olives shipped equation. Then you always find the quantum mechanics slows down the energy of people. You know, people call this or it's the 0 fluctuations quantum computation. Of course, all these words are kind of watch yours until you start writing equations. Non-linear, slight writing equations. What you see is that it is the superposition of many states which are generating better ground state energies. And I mean, I can even think of the simplest example which is nothing like fancy crystals are just a double well potential. You put a particle in one while and it's classically stock. But if your tunneling and that's actually a very complicated problems. So this one is also sold by the way, like a multiple tunneling to double well, we're taking into account all possible instant. Don't ask the antecedent compares is beyond any standard perturbative treatment that could also lead to a lowering or find them just to somehow kicking in quantum mechanics and superpositions of quantum states in Singapore. Yeah, I would always wore suits, maybe Africa, mystery, but we do not understand the role sort of ammonia Gail. So, so, so what I what I said, it was surprising. I mean, I didn't tell the whole story, but typically what has been found previously by not full dynamics by just include gene for example, vibrational free energies, right? Quantum mechanical free energies or 0 energies, is that quantum mechanical effect destabilize molecules. Now here, this effect really is stabilizing because you go doing full dynamics and including quantum nuclear effects. Dynamics, let's say make this charges five traits. So you have, let's say a positive and a negative charge. They fluctuate, right? Dynamically. Their beach they would do even in classical dynamics. But then in addition, I had zero-point energy is make them correlate in such a way that they actually stabilize the system. And so there are two different file. And then in the end, you have to do the full thing as you correctly say, right? Well, you have to write the equations and decompose terms. But what you, what you see from the full treatment is that compared to classical dynamics, the quantum one stabilized does it while, if you don't do dynamics, but you just compute some effective curves, include in 0 energies, the opposite effect. So, you know, that's real. Lines less than anybody else. I came. Why it's going on. I don't know. It was something else. Something else? Yeah. Okay. So that's so is there or is there a rule I'm just writing today a paper on this stuff. Hml spins how big the spin has to be to shift between quantum and classical. So here's the rule in this world on how big the Notewise should be or how small the NAPLEX should be sorted. You must use quantum mechanics, Burger King, or Newtonian equations. Well, not really because it's not only the mass of the nucleus, but it's also this trend of the forces, right? So if you look at semi-classical Lifshitz like perturbation, know if she's late perturbation theory for quantum effects. Then what you realize is that there's balls, the mass of the particle, and the strength of the force that the important parameters that define the, the, the dullness of your fluctuations. And in so, so for example, you know, if you have hydrogens, they fluctuate more. But in graphene, for example, the quantum of facts and they increase the fluctuations of carbon-carbon bonds by about 30 percent compared to classical dynamics, which is quiet a large effect. And you only get it by Ryan and explicit dynamics because otherwise by symmetry you don't see any, any difference. So going back to burped example, Yoko bridge was benzene molecule for putting on the top or graphene. So this is not power spending a little icon out. That's on our client. Okay. Because I was searching for it, but it didn't show up. Probably google is now focused on selling things rather quickly giving a scientific information. So like if I take a piece of DNA which is actually something quite relevant. Because a decade ago, many people experimentally started looking at whether graphene can sequence DNA by responding to different nucleobases. So what would that example require? Switching to anything to for an apply. If I just put a NACLO base and add the name or guanine on the top of the cases there was a whole show. You drill a hole in graphene and tried to shoot this NACLO basis through the hole to see what is inside them. That's how your sequence. I find Mickey has no clear dynamics would be very important in really dictating the nuclear quantum effects will be important in detergent and dynamics of this, of this process. Because you share the army of people, for example, creator of MIMD would be shooting these things day and night, throw the whole in graphene and looking at all possible orientations. But it was quite massive and you just do pure classical mentoring. And the other thing, the other problem of course, which has nothing to do with no clear is that all the parameterization of force fields, four carbons they use in market dynamics is very far away from solid state physics like they don't know that you are now delocalized. Walk, fades and stuff like that. They basically trip graphene as a bunch of benzene molecules stuck together. So you'll do your thing that, but so would that actually be amenable format to shovel like graphene on something? Well, one nucleobase, of course, is not a big deal, but it would have to be a graphene and NACLO base. And then all the junk around richard gill like water molecules and potassium chloride ions and that kind of stuff. So for that, you need to include long-range effects. I think both electrostatics and, and correlation in, I would say it is physical models. And so that really comes back to mind one of my last points in the training in the current challenges. Also, this will be fun. So problem IDS, I mean, if you want to get. Reliable results. So you can try, you can make localized pretensions and you would get something, but it all depends on how long range You effects are. And even classical electrostatics become squared long-range trade when you have an interface between graphene and mortar, so on. Okay, thanks, or Google's own, fruitful. Thank you. Uh, how we're how we're one of our guests named Henry has raised his hand and Henry want to ask a question. Yes, I word this is the the quantum level stuff is way over my capabilities. But a, B and a euro thing chemists for several, several decades. My question is, on your machine learning a very large molecules, how do you know that you have met the minimum state when you manufacturer may have some sort of internal stress built into the molecule at the end. I can't talk your language so I'm sorry, if it doesn't make sense. So you mean if you want to apply in any machine learning method for a large enough molecule, how do you know that? You can relax that to save some global minimum or some low line? Yes. Yes. Well, I mean, so so depends what large means raid, as I said, currently, is the technology that we have and provided that enough data is there in brands are both treating same molecules up to 100 atoms is visible at all the facts right, is all local, non-local effects. So, so in principle, that should be quite a reliable as long as you can run molecular dynamics or just generate an ensemble of minima that VM on. Let us do that. You can always find another stable or will upon meaning my even. And you can be sort of brothers sure that you are somewhere close to it. But if you're talking about more complex things or are you in periodic materials with some complex unit cells than I think we have. We're not there yet in the sophistication of our methods to really make sure that we have all the required interactions built in. Okay? Yeah. Now, I dealt with 50 thousand molecular weight, your things. We can never give them their loss stability state, right? Right. They would always. The whole dynamics of math, making the molecule was more important thing we could do. You mean kinetics? Kinetics becomes more important basics? Yes, Yeah. Yeah. I mean that's so for this polymorphism problem, that's often also that sometimes for large molecule that's also the case. I mean, exper, experiments often for many systems can get to the global minimum, but not always. And in polymorphism, right, there is a well-known disappearing polymorph problem where suddenly people have produced a polymorph for ten years. And then suddenly to the small change in fabrication conditions, you get to a more, much more stable state. It right? So you find that only after 10 years, don't make me have my nightmares again, right then you produce clones of that material rate and suddenly something happened and everyone, all, all, all, all, you know, batches come out as a new point. And so yeah, that's right, That's unplanned you. But, but so for that, rate, doing prediction is extremely important. Because then you can, for example, you, if you have an experimental structure and you can calculated, but then if you can explore the potential energy surface and you can say a is actually much more stable structure, right? That was really helpful. Yes. Thank you. Any other questions? I want to make sure that Alexander is quite late for you the mind. That's okay. That's okay. No problem. Of course, this is going to be on the, uh, on the machine learning and data science size. And I find it interesting that when in Quantum and condense matter you talk about machine learning. You Qian, very often people just talk about machine learning in general. And I find that it seems to me that the majority of those models or deep neural networks. So and maybe asking some Gaussian process is application. But so this goes back to what you were saying earlier. Like the language is different, right? So can I ask you from your perspective, you had to give it a definition of what is machine learning? How would you define it? And am I right? That primarily it's deep neural networks and the graph networks that are being applied. Or am I missing something? Yet? Been mainly talking, is the kernel, kernel methods like Gaussian process reference, right? And we also use neural net for when we have enough data or when we want to go through chemical space and we have no fit mostly understanding of how to construct a non-linear transformation. Then we just throw the data at a very deep neural network and, and we hope for the best friend and so, so in, in our field, balls approaches are widely used. So most of people who are just interested in, in, in interpolation data is using neural networks. But then even there, there's a lot of interesting work on incorporates in variances and covariances. And so there are this interesting methods that the couple rotation on permutation of degrees of freedom in quiet interesting ways. When you want to describe quantum states, right? So I've talked about force fields, but you can also do work on wave functions, for example, right? And then you have symmetries which have really, really higher level symmetries. And you can build those symmetries in principle directly in neural networks. So, so, so yeah, so most people are using neural networks and as you see, convolutional neural network is a graph neural networks. But people who are in our field who are trained to understand what the LDR trade we extract some in science than the small, sleeker and ridge regression approaches. So just non-linear regression. And then, yeah, and then in principle you can reformulate rate, you can reformulated kernel lake and neural metric. The other way around is a bit harder but, but there is more and more approaches that try to find a sweet spot between how much data you need and how much physics you put in your description of the system. Thanks. Thank you. Any other questions? All right. Someone asked collapsed question. We just actions that are similar to the previous one little bit expanding talk towards a new area. And you feel that's called quantum machine learning is when you use quantum computing algorithms applied to machine learning or develop algorithms for quantum computers to do machine learning. Are you excited about these? So you're following this field, you think where we can apply this to, or you can apply this to new problems you care about. Or you will believe that we're just not there yet and we have to wait a little bit until algorithms, sorry, until appropriate algorithms are produced and we can use quantum machine learning to develop for steels, what do you think about? So in general, I think they use the uterus and development of quantum algorithms is exciting. I mean, there was just a pre-print, I think if we could go on actually using quantum computers to solve the long-range electron correlation problem for and truly oscillators, which is something ever act on for a long time. So I was really excited to see that. And they've done it from the IBM's week. And so they've read, is developed an algorithm to solve coupled to the oscillator is which is not an analytically solvable problem, and that Brantley obtain good results. So, so, so I'm following that sort of at least a bit from distance, but, but, but I think there's a lot of developments in terms of doing quantum machine learning algorithms on quantum computers. I'm not sure how clause VR tool to really have certain breakthroughs. I mean, I do have a more personal story actually I noise startup, which started in that propose in using quantum machine learning for, for drug discovery. But then the end, they ended up doing classical machine learning on quantum data, French what, what type. And that was much more successful. And they actually were recently bought by beak biotech company because that is actually quite exciting. You can do this classical machine learning and data hub. So yup, So I think there's a lot of scope for quantum algorithms, right? And applying them to solving problems. I think they're probably interested in developments going on. Okay. Thank you. Thanks a lot. Any other last questions, maybe? Yeah. So it's getting late and looks and works. So I want to thank Alex again for this amazing talk and nice discussion after it. Thank you very much for the invitation. Thank you. Bye bye. Thank you. Bye-bye. Bye-bye. welcome to Physics Colloquium. We are absolutely delighted to have Alexander had shank or as a speaker. Today, Alexander is a Professor of Theoretical condensed matter physics and the head of theoretical chemical physics group and the head of the department of physics and material science. The University of Luxembourg. Alexander is also distinguished visiting professor at the Technical University in Berlin. Alix received his undergraduate degree in computer science and a PhD in physical chemistry at the Universidad Autonoma Metropolitan that in Mexico City in 2007. From 20082010. He was Alexander Von Humboldt fellow at the Harvard Institute of the Max Planck Society in Berlin. Out of that Alex state at the same institution and lead an independent research group until joining the University of Luxembourg in 2015. In his research, Alex combines quantum mechanics, statistical mechanics, and machine learning to develop accurate and efficient first principles, computational models to study a wide range of complex materials, aiming at qualitative understanding and quantitative prediction of their properties at the atomic scale and beyond. And Alex is one of the leaders in the field. He's extremely productive, published over 180 papers, is ancient, exists 71, with more than 25 thousand citations. Alex is also in the top 1% of highly cited researchers from 2018 to 2020 want. He has also received a number of awards, including a girl for Eric Young Investigator Award of the German Physical Society, Dirac Medal from the World Association of theoretical and computational chemists and a Wander Walls Prius or what, 2021 International Conference on non-covalent interactions. Alex is also fell off of American Physical Society. We're all absolutely happy that Alix accepted our invitation. And without further ado, Alex, please, we're all eager to hear your talk. Thank you very much. And they say for this kind introduction, let me try to share my slides. Okay. Do you see my slides? Yes. Okay. Excellent. Great. So yes, thank you again, say and thanks for for this kind invitation. So as I said, it's a bit late here and in old Europe, but I think I'll manage the first time. I think scientists, they have to stay late work. But I think our work as enjoyable, so on. I'm thank you very much again for the invitation. And they think they hope that I can pass at least part of this enjoyment during my talk. So so I understand this is a broad colloquium. And so I tried to give a broad overview on, on few different topics that forever it can on and find a unified topic. And the unifying topic that I will be discussing here is force field. So, so force fields are some effective representations of the forces that nuclei feel in a certain molecule or material. And this force field, the, the, the, There's a definition for forceful to come off or it's busy and Warner behind approximation. So, so this will be ubiquitously used during my talk. Everything will be born Oppenheimer approximation. And that allows you to define always effective forces for a given nuclear configuration. And the question is, of course, all this forces are coming from electrons, right? So they are coarse-grain electrons and representing them effectively as some interactive and Adams, and the question is, how can we do this effect? So this of course, has been done in the field of computational chemistry and computational biology and material science for a very long time. In fact, for the Nobel Prize in Chemistry in 2013 was avoided for construction of biomolecular for students. A few years ago, new tool came into our toolbox. This is machine learning and machine learning allows the construction of sophisticated and flexible, non-linear forms for this, for students. And so for some time people thought this is sort of a lifesaver right now is machine learning. And we can construct universal force fields for essentially any monocular mature. But of course, once again, those force fields, those atomic forces are coming from interacting lecture. So the question is, when under which conditions we can map interacting electrons into effective for students. And, and I will try to tread on this topic during my talk. So in my group in general, we are interested in quite a complex problem of stops a large systems, large molecules, large materials. And this is a complex problem that involves physics, chemistry, material science, and computer science scientists represented by machinery and so on. People can mean from my group has different backgrounds. They're physicists, chemists, mathematicians, and computer scientists. And there are a few very important people to highlight here. Eager scheme. I'm, I'm, I'm showing you here. Here's a group leader in my group who is leading a small subgroup that works on combining physics and machine learning. And in particular Gregory von Sekhar and financing the lingual. There'll be two people whose work I will mention it. Now. The combination or physics and machinery and require strong experts from the physics side and from computer science side. And so we've established for about 10 years ago, a strong collaboration with a group of close Robert Mueller, who is one of the most renowned machine learners in Germany. He is working at the Technical University of Berlin and in particular to people Stefan Camila and those yellow cells header. Key players also did tremendous contributions to everything I will be describing. So, so a lot of this verb is really a combination between strong expertise and machinery and, and strong expertise in physics and chemistry. So we start from, in our breakfast, start from first principles and for us our standard model, these the Schrodinger equation and in particular born Oppenheimer approximation applied to the Schrodinger equation where we separate the electronic and nuclear degrees of freedom. But they are interested in understanding and solving the Schrodinger equation for large and heterogeneous systems. So for example, proteins, liquids, molecular crystals, or two-dimensional materials. And of course the interactions, the wide range of interactions and all the system's complicated. The solution of the Schrodinger equation because we are talking about thousands or even tens of thousands of interacting electrons. So this is a complicated problem. And you would like to develop approaches, efficient approaches that enable ear increasingly accurate solution of the Schrodinger equation for this complex. So that's our final goal. Of course. This goal of yeah, not the first group overcome this. There are thousands, tens of thousands of groups working on this. And in the modelers toolbox, there is a whole hierarchy of approaches for approximating the solution of the Schrodinger equation. Now it's well-known of course, that exact analytical solutions to the Schrodinger equation exists only for certain model systems or for one electron atoms, like a hydrogenic atom. So when we have more than one electron, which is the case for all systems of our interest, we need to approximate the solution of the Schrodinger equation and particularly to approximate the wavefunction. The most dumpy of approximating it is sort of rate and empirical, but actually the force that's forgetting about all electrons and just say, well, they're effective forces that Adams, you. And this can be done by following the Hellman Feinman theorem of squares. And just write some non-linear function that expressed as the at the, the force that an atom fields in a given confirmation of a molecule or a solid. Going a bit more sophisticated, you can introduce electronic degrees of freedom, for example, why are semi-empirical methods based on density functional theory or quantum chemistry? So you can introduce, for example, a small basis set is more than the basis that you can fit some parameters and get sometimes a reliable ancestral for certain class of systems. The real workhorse in the field of electronic structure theory East density functional theory, because as proven by Hogan broken corn and then constructed effective theory by corn and some density functional theory in principle as an exact theory. But of course, you have to approximate quantum mechanical many-body interactions and hands introduce approximately functionals. And this gives you, of course, errors and pencil. And going up, of course, in principle, we have numerical ways to exactly solve the Schrodinger equation y, a so-called full configuration interaction methods where you write electronic configurations and you write a linear expansion is some coefficients and then you obtain those coefficients. Or you can do Monte Carlo based solutions, so-called quantum Monte Carlo methods. And in principle, if you are lucky and if you have enough flexibility in those wave functions, while you can get, in principle, you can approximate the exact solution to the Schrodinger equation. Now. The nice thing here is that when you go up in this hierarchy, the accuracy of predictive power of your methods increase, but there is a price to pay and the price as computational cost. And another price which is especially important for physicists, is that you lose conceptual insights. Write wavefunctions are extremely high dimensional objects. And getting insights from wavefunctions of say, system, the cells of the electrons is not very easy. And so methods such as DFT or semi-empirical methods actually give you many more insights than methods that are here at the top of this, of this letter. And so the real question, and that's where machine learning comes. How we use the nice ideas, nice conceptual ideas at the lower rungs of this ladder. But we still keep the accuracy that we have and the higher ranks of the ladder, That's ray machinery. But machine learning instead of democratizes this whole hierarchy of methods here because you can use different techniques from different methods and you can combine them in a nice way. For example, you can use aspects of semi-empirical methods for describing a certain molecule, a material, but then train a machine learning method on high level data coming from, for example, quantum, high level quantum mechanical methods. But of course, if your reference data is garbage, right, for example, you took some approximations that are not good enough to describe your system, then machinery will only give you also a garbage, right? And so the question is how to appropriately combine reference data? Which level do you use to produce reference data and which level of theory to use to describe your system. And those are two questions that are still being investigated in our field. So now in the next couple of slides, I would like to delve a bit further into this question of how can we obtain reliable quantum mechanical data and how we can know that we are producing reliable quantum mechanical data for systems of our interests. So I will give you now two examples. One example is of a methodology and approximate methodology, which allows you to obtain very reliable reference data compared to experiment for very complex systems and molecular crystals. And then I will show you a case where you use the highest level of quantum mechanics to different highest levels of quantum mechanics. It turns out that both of them disagree, and this means that one of them or both of them are giving you garbage data, which we cannot actually use for parameterizing machinery and production. So before I started actually machinery numeric, a lot of the work in my group was on developing effective physical methods for describing a long-range electronic correlations. So this are ubiquitous many body effects, right? Where many electrons correlate or large land scales. And you don't want to describe those correlations explicitly, right? Because electro electronic degrees of freedom, because it's just too hard, it's too computationally expensive. So we've developed the so-called MDD, or many-body dispersion method that basically describes the response of electrons in a molecule of material, wire quantum harmonic oscillators and then the coupled or spinlock harmonic oscillators is a long range potential. And we solve the Schrodinger equation for oscillators, not for electrons. And we then couple that energy to a semi local density functional theory functional. And so we get this semi local quantum effects from DFT. We get non-local quantum effects from MBE Hamiltonian. And this is a nice combination of two different methods that we then applied to a variety of molecules and materials. And I will just show one particular obligation of this. And this application conserves, concerns a predictive modelling of so-called, so-called phenomenon of polymorphism in molecular crystals. This phenomenon is ubiquitous phenomenon. So basically, it turns out the Judaic one molecule, for example, this one, this is a drug candidate from actually from Pfizer. And then you try to crystallize it. When you crystallize it in from solution or some other environment, you realize that it can pack in a wide variety of different crystalline arrangement. And that is because there are many types of interactions. Electrostatics, polarization, dispersion, powder repulsion that guide the packing of those molecules in the crystalline phase. And those crystal packets often have almost degenerate lattice energies. So you can have within a window or for, let's say kcal per mole, which is so-called chemical accuracy. You can have 10, 20, 30, 40 of those polymers, right? A huge number, despite the fact that they are. Almost also degenerate. The different polymers can have completely different physical chemical properties. For example, different colors, different solubility is different than cities melting points, conductivities or whatever, whatever property your image. But you really need to know which polymorph is global energy minimum and these polymers or meta-stable states, and this is a very tough problem because we are talking about 1% of the largest temperature, right? That is what determined the differences between this point and this is a very, very tiny energy. And for a long time people thought this problem is completely, it cannot be dealt. Is quantum mechanics simply because the energy difference. And so we've actually applied our methodologist to this problem. And we tried to do this in a blind fashion. So we don't, we don't cheat as, as often we do in theory. The sort of take experimental data and then the calculations. And we then compare back to other experimental data by, by the often biased because we already used experimental data. In this case, what I'm showing you here is a real blind prediction. So, so these are results of so-called blind test of organic crystal structure prediction organized by Cambridge crystallographic data send them. So basically what they do is they collect experimental data, different polymorphs of molecular crystals. They hide this data. You don't know his unpublished data. And they asked experiment, they asked theoretical groups to predict those structures and then they compare the predicted structures which you submit to the experimental ones. And you need to predict both structures, right? Result knowing n structural information on the Norwegian structure of the molecule itself and energies as well, right? And so here I'm showing you overlays between our predict structures legally blind liberty. Rigid crystal structure prediction procedure. We put different crystal groups, we optimize the molecules. And these are optimized, completely geometry optimized structures. And our predictions are colored wildly. Experimental structures are the gray and it's pretty hard to see differences in most cases, the root mean square deviation for 20 molecules and the supercell is about 0.15 angstrom per molecule. It's a really tiny difference. It's mostly invisible here. And so this is, this result can only be obtained when you do density functional theory was a good hybrid functional, been easier or functional, so-called modern empirical hybrid functional. Plus our full many-body description that includes long-range correlations and the full many-body fashion. So here are structural information, so this is pretty good. But of course the question is, are those structures really the global mean? Because experiments often see global minimum. And it turns out that they are when you go to the highest level of theory. So what I'm showing you on this slide, our results for four different molecules. So the molecules they indicated here as this two-dimensional diagrams, the global minimum structures are shown in this unit cell pictures. And what I'm showing you on this diagrams, for example, here on the left, is for different levels of theory. As you move to the right, you increase the sophistication of your level of theory and the accuracy, right? And the there I bought a 100 structures and bottle. That's a 100 polymorphs that we predicted and the experimental structures and rat. And so in the best case, the experimental structure in red should be the global minimum. So it should have a 0 energy on this, on this diagram. And in fact, this is the case for all of this for different systems. When we go to the highest level theory, which includes a high appropriate to be B 0 DFD functional misses a function that describes semi local exchange correlation effects blast the many-body dispersion. So the full many-body treatment of long-range correlations. Glass also vibrational entropy is computed at room temperature. And so as you see here for all these four systems, the, the experimental structure turns out to be the global minimum at our landscapes, which is the best possible prediction you can make. So actually, when we presented this results originally 2016, nature sounds if gene actually nature all this news and views article saying that the volume of prediction problem is solved. I don't really agree with that statement. I think it's not solved. And movie, it's presented really good results. It's surprising results for five different systems. I'm showing four out of five systems. But there's still quite a lot to do. And it took us actually about four years to really finalize everything and writing this paper. Okay, So, so this is an example where Experiment 3 to experimental data. Tells you that your quantum mechanical reference calculations are good enough grade for this particular problem. And this is a very, very tough problem, the problem of prediction problem. But there is also a tremendous problem here because doing all these calculations is computationally very expensive. So I'm showing just part of the results. The total amount of computer time that we had to spend for this study is about 20 million CPU hours. But you can do on, on, on computer is especially in the US, right? If you have access to beak HIPC facilities. But it's not something you want to repeat for every new morning and spill here immediately. The question comes, well, if you have all this data, you could also use this data to construct effective machinery and potentials, for example. And you can learn from increasingly larger chemical space. It says your January data. You can construct those potentials and you can make them more and more general as you produce more when more reliable D. And that's something which has not yet been done in this field in a, in a, in a systematic way, let's say. But the data is in principle, there is just not easy to construct machine learning potentials for this large systems, as I will discuss in the second part of my book. So here's an example of reliable predictions with quantum mechanics, which you can then use for machining. Let me give you now a completely opposite case where, where you cannot decide what quantum mechanics aid and to actually use so, so, you know, in our field of development of quantum mechanical methods, there are two different paradigms to go over. It's heaven, right? Reaches the exact solution to the Schrodinger equation. One is called post Hartree Fock method. This means that you'll construct a Hartree Fock solution which respects anti-symmetry or fermionic, so fermionic statistics of electrons. Then what is missing is so-called the electron correlation energy, which is what I've described already, is the MEG method, which captures long-range correlation energy. But if you want all correlation energy between electrons in an exact way, you can do this wire so-called quantum mechanical methods. In particular, the gold standard in the field, the so-called couple of cluster map, but the single, double and perturbative triple excitations. In fact, this method originally comes from high-energy physics, from nuclear physics. And it was abandoned there because it was not giving good results, but four electrons, strained relations that gives great results. Most of the time they'd been people for that reason really cord goals then. But there's an alternative math, right? So if you have just one that, that you cannot really trust its results because there's just one number and you have to take it for granted. It would be great to have an alternative method. And in fact, there is an alternative method that's called quantum Monte Carlo, which is a completely different way to obtain to approximate an exact solution, I'm afraid your equation. So you write an ansatz for the wave function and you then optimized parameters and it's very flexible ansatz. And the principle of the ansatz flexible and app you get an exact solution and training. And so we've applied this to alternative ways, gold standard ways in quantum chemistry, in quantum physics communities to actually study the interactions between morning, I'm indifferent morning. It's ranging from benzene dimer of year two, this buckyball getchar complex. So this is a C 60 molecule embedded in this cycle of birth and that NRI. And we want to understand the binding energy between the right. And it turns out that when the molecules are small or when interactions are not so strong balls methods. So more gold standard, it's coupled cluster and the quantum Monte Carlo if essentially indistinguishable results. But the surprise is when you go to higher to larger systems and this has simple systems and just non-covalent interactions. There's nothing fancy bulb and it's not strong. Correlations is no oxides are some really strange or Bornstein buttons here. But nevertheless, for such systems, you just increase system size, the interaction, of course, the strength of the interaction increases a bit. You both methods give competitor different reasons and the difference is huge. It's order. Well, I would say, yeah, All order of magnitude more than what one would expect. So, so here the mean difference is eight kcal per mole between the two methods. But the largest difference is 12 kcal per mole. And this is a big surprise. And so we'd be sort of coined this puzzle. And of course now the question is, what do you trust as a reference for machinery? Is that this blue line or is it this red line? Right? And if you put the two different numbers, you will get completely different parameterization for, for, for the machinery enforced. And so, so this two examples sort of GIF. So define the first part of my talk where I wanted to talk about the reference state, okay, So you really have to be critical to your reference date. Sometimes when you use the highest level of quantum mechanics that you have. Disposal, you'll get reference data you can more trust at the moment. While in other cases, for much more complicated examples like molecular crystals, you do have methods that seem to give you reliable and quantitative results which you can use for construction of machinery first. Okay, So, so that's summarized some of the first, or we might talk about reference state and now let me talk about machine. So despite the fact that sometimes we don't, but we cannot produce reliable reference data. Let's say we have cooled reference data. And so we can now produce, for example, energies and forces for molecules as a function of their confirmation degrees of freedom. So we move some functional groups, right? And we know how the forces change on atomic forces change. And that allows us to construct a certain non-linear neural net for poor or current rich regression procedure. To feet, those are reproduced or atomic forces. So of course, we want to really do a complex systems that's where we want to goal and it is full accuracy of quantum mechanics. But at the moment, we are somewhere here, right at present, where machine-learning force fields can be used. Studying smaller organic molecules, I think this is, this part is largely solved or small organic molecules up with maybe three agonist is sort of a soft topic already. Or ordered materials. Are those materials have also been studied by many groups and they're very many. Would machinery methods to construct force was for this things. But if you look at disordered materials or the peptide from biopolymers, they are not there yet and a year classical force fields are still the, the de facto standard. But another thing which is extremely interesting is that children force fields are not, cannot only be used to construct This representations of how atomic forces change with molecular or solid state geometry. But they are becoming new, completely new methodologies in their own right. Because you can study of things which were not possible to study this previous classical force fields. You can study electronic effects. You can start the reactivity, try it so your atoms can change their, their bonding patterns, which was not possible to do this classical force fields. You can construct models for ground state and excited states. And so you can do nonlinear dynamics, you can do optical excitations example. You can easily study nuclear quantum effects, which was not possible to do is classical force fields. Because in their parametrization, people would mix experimental data that includes quantum nuclear effects and theoretical data of each does not those defects and so you cannot mix them. They sat, problem of double counting and so on. And so machinery enforces really enable a much wider set of applications in, in physics, chemistry and chemical physics and physical cans. And this is really where it gets pretty exciting because many of those simulations were simply impossible. Before machine reinforced feels really came into, into the game. Though. When we started working on this field. Aiming at first producing machinery enforced fields for molecules, for small money. That's where we started. We wanted to do something which is quite different to what most people were doing. The sort of put a very challenging problem in front of us. So we wanted to construct a machinery for short, which is general. It can be applied to any potential want to go up to a certain size. It should be transferable, right? It should be scalable and it should represent them all quantum mechanical interactions. So you cannot impose any couples, you cannot predict and the energy of the molecule as some of our atomic energies because this is not possible to move as the Schrodinger equation. And that's what most people were doing before. And so this led us to really reconsider the most basic aspects of all four forces. So what is typically done? They feel that something like this. So you're given a molecule, let's say a benzene molecule like the one shown here as one of the simplest molecules. And you are given the different conformations of the molecule, right? So you have a set of conformations. And of course, different conformations have different atomic forces. And so what we typically do is you write an energy model. And an energy model, right, is written as a sum over atomic energies. And this is already a big problem because Schrodinger equation does not allow you to define it on mechano. She's, the only thing you can do isn't born Oppenheimer approximation is define atomic forces. This is an observable in due to the home and find length here. And so doing this is not allowed by the Schrodinger equation, but nevertheless because of computational. Efficiency and because of permutation symmetries, people do this, but this is wrong. This shouldn't be done prints. Now what we decided to do is different thing. So we start with this confirmations and the right model, a force-field explicitly for atomic forces. And once you write that model, if this model is energy conserving by construction, you can actually integrate it out and get a potential energy surface, right? And the only question is, how do you do this? Energy conservation in the forest them, right? But this is of course well-known because we know how to construct a conservative force fields. You know, the, the curl of the force will have to be 0 there. But it was defined the conservative, conservative forceful. And so what is done in, in, in practice is something like this. So I'm giving you an example, a toy exam. So, so let's say we have this force field, two-dimensional force for this our ground truth. This are two coupled harmonic oscillators are a couple of parameters. And let me just take this and we take six data points at run out of this force here. And we impose the requirement that the curl of the force field has to be 0. By construction, this isn't our machinery model by default. So we work and for his domain. And then we try to reproduce the ground truths to learn from just 66 examples. And we get this field here. So if you compare this conservative fields which you learned to the ground truth, while it has all the features, it's not quantitative, but it's semi-quantitative. But if you'd drop the requirement of energy conservation, so, so you then learn the components of this force, the x and y components, you get this vector field, which is completely nonsensical compared to the ground truth, right? It has a different attractor here and has a completely different for, right? So, so energy conservation in general, in the domain or for force fields, extremely constrained requirement. And it's a requirement that really helps you to learn, right? Then it reduces the need for, for data, for the number of data points that it has a lot of interesting aspects actually that I don't have time to go. And now let's move beyond our toy examples, right, to real morning. So, so now we have a molecule and what we do in our approach, we call it gradient domain machine learning. And S stands for symmetrized gradient domain machinery because we use all the symmetries, global and local symmetries of our system. So global symmetry is this time invariance, which gives you energy conformation, right? And they have of course to rotational and translational invariance and v impulse per mutational and variance, which we discover from in a data-driven way, right? So for example, if, if you have a metal groups which rotates in the dynamics and of course, permuting all the hydrogen atoms on, on, on the methyl group is, is equivariant, right? For the, for the forces and saw the discover those images from the data from the molecular dynamic state. So we produce some liquid and that makes for a given molecule these simple efficient method. We then subsample the recover all the permutation symmetries. We do multi-part. I mentioned there is a lot of Blackmagic going into this, but that's explained in our papers. And then once we do that, we then construct a kernel matrix in the hessian domain because the covariance between 4 atomic forces is given by the Hessian matrix. And then we have a vector of coefficients which is obtained from our training data. Okay? Once we learn this vector of coefficients, this is a convex problem. You can obtain those coefficients by just matrix inversion. You then can integrate this kernel and analytically and get a model for the potential energy surface, right? That's a big sum here, but it doesn't matter. It's an analytic numerically exact solution. So, so then you can plot, for example, potential energy surfaces. And here is one example for one particular molecule shown over here are now this approach is extremely efficient. So for a realistic molecule, such as aspirin, beneath, it has 24 atoms, 60, I think, 68 degrees of freedom, if I remember correctly, we need only about 300 confirmations out of molecular dynamics trajectory to obtain force field, which is accurate to 0.3 kcal per mole, which is really, really accuracy which you can use to run molecular dynamics. And because you only need a very small number of conformations, the reference data can come from the highest level of quantum mechanics. And so we can, for example, train these force fields to couple of class than data, which is, as I said, is a sort of a gold standard for, for small molecules at least. And it works really, really well for those. And once we have obtained this force field. We have now a force-field that includes all the electronic effects within the born Oppenheimer approximation to essentially arbitrary accuracy. So it's almost essentially exact solution of the Schrodinger equation. And then in order to treat quantum mechanics of the nuclei, we use the so-called us integral molecular dynamics. This is based on find one cup plus integral representation of quantum statistics, which in the limit of an infinite number of beads gives you an exact quantiles to this 644 for your quantum particles. And with that we can, we now can really do, I would say embarrassingly quantum simulations because bores our nuclei and our electrons, essentially treated at the exact level of quantum mechanics is in Warner been Homer approximation and of course views in bosonic treatment of the nuclei. And so here is an example of this calculations. This is ethanol molecule, one of our favorite ones. And so it has three different minima, is a so-called trans and gauche minima. And we can calculate, for example, occupation probabilities of those minima. And when we look at our exact simulations and compare experiment essentially get exact results. And this is really resent error bar For experiment. While if you drop, if you, for example, train a force-field at the level of density functional theory, or you do classical molecular dynamics, you will not get this degree. And so say, the agreement is really destroys. You need quantum mechanics or balls, the electrons and the nuclei at the highest level theory. This is just an example of something we can compare to experiment, but they can also do new discoveries. So, so for example, you can compare the effective binding mechanisms to squat. Classical dynamics are the nuclei, are quantum dynamics are the nuclei. And you'll find something very surprising that quantum dynamics often dense to stabilized meta-stable states of molecules. For example, this happens in aspirin, where the global minimum is heavily stabilized. A local delocalization of the nuclei, the molecule is globally standardized and this is actually quite a surprise in fact, and we explain that by fluctuations of negative and positive charges. So call this by star and transitions. And this is the chemical. In chemical. Similar effect happens in this stall when molecule, so Darwin molecule is just a benzene ring of is a methyl group and this methyl group classically is just a broader, it's a free rotor. Classical dynamics just make this, this benzene toluene metal group also lead free. But if you do quantum dynamics, you find that this oscillator here actually starts to localize. And that's again a surprising finding because quantum effects localize this rotor, right? So it essentially just localized on the left side, on the right side. And this is also an electronic, quieter, complex electronic interaction. So this kind of facts that we can find now by this explicit usage or machinery and forceful. So this was not possible to do before result machine learning because those calculations would take essentially decades on, on, on supercomputers if you use this level of theory that we use. But now we can do this calculations and essentially an hour or so or even less. So. So this really demonstrates a huge acceleration that machinery in brains into the field of computational physics and competition against. Okay, So up to now, I've mainly discussed small molecules, but we can do much larger systems now. So of course everyone wants to go to real applications, for example, molecular crystals, D and E nanotubes. And we've actually extended our GDM, our framework by doing, instead of doing exact inversion, we can do precondition into to enable large-scale calculations that we've now extended GDM up to about 400 atoms. We get this double walled knowledge to prevent bliss of unpublished. We are finalizing this week. We've also extended our approach to materials for banks who didn't periodic boundary conditions. We call this Bravais inspired GD and malware big HTML. And all this will be coming out pretty soon. Just an example of an application that can actually do now in a very short time is for exams or the dynamics of a benzene molecule on top the Griffey. So this is fully periodic oscillation graphene and benzene aperiodic systems, right? It's a brute Excel. And we are running the dynamics of this benzene molecule and they're looking at how it fluctuates in terms of the vertical position and in terms of the angle between the vertical and the the plane of the molecule. And what you realize is something again, very, very interesting. Classical electrodynamics, the molecule is delocalized so it's rotating and translating over, over the surface quite widely. While in present ago molecular dynamics. So when you treat the nuclei quantum mechanically, the molecule dense to localize. And this is again counter-intuitive because buzz integral of molecular dynamics delocalize is the nuclei locally. But because the delocalize as nuclear locally, so most carbon distances and carbon-hydrogen distances are larger and effectively, the polarizability of the molecule grows and that increases the funding lines attraction between benzene and graphene. The same thing happens in graphene. The carbon atoms are effectively at larger distances and that increases the polarizability of graphene. And so the fun towards attraction become stronger because of quantum effects. And this is a very counter-intuitive fiend which I would not have predicted result actually running those simulations. So, so this application demonstrates the state of the art that we can do today in the bulk buying this or machine learning force field advance. Okay, So this is all nice and wall and this is a very nice applications I think. And not only ours, but many other groups have demonstrated extremely interesting results for many, many different systems. I would like to spend the last five minutes to talk about challenges. So, so there have been a lot of advancements. But actually I think that we've barely scratched the surface on the field of combining physics, chemistry, and machine learning. And there are many, many challenges and the recently tried to describe them in this prospective article with Igor. The, the main themes are accounting for long-range interactions. So up to now, most people have concentrated on short range chemical effects. The datasets that we have up, it's not really clear how to fully construct them in a systematic way and how to use everything that is there in the data sets. There's still a lot of physics that we have not incorporated into our, I'll get actress. And finally, there are some examples in the recently published literature where people find new phenomena from machine learning. And sometimes this correspond to false discovery simply because you're, you do extrapolation where you shouldn't really be doing. Okay. The 1 they wanted time, which is really close to my heart and that's related to the first part of my talk is how neuroscience it really Electrons are, right? That comes back to the data. Electrons of machinery and forceful. So, so how far away do we need to meet Adams? See rain. So, so what are the whole long range or the contributions to atomic forces from Adam's far away. And this question, of course, has bothered many physicists. So for many, many years. And in fact, the way to corn was a well-known Nobel laureate. Together There's Emily brought down, have written this nice article in PNAS called near sightedness of electronic mail. And many people in computational chemistry side that beeper as a proof that electronic matter is near. Now of course, what is near science? I mean, that is a very strange concept because if you ask someone seated and looking at the window, Well, they see a house far away, right? Which is meaning meters or kilometers away. So for him, maybe near sightedness is a 100 meters. But if you ask, say computational chemist, how neuroscience it is a benzene molecule, maybe they will tell you a few angstrom. So is it really a few angstrom is a 100 angstrom, is it Saul's an angstrom always a damn micro meters or even more and no one really norms. And so this interesting paper sort of setups in an hour based on the simple models, mostly the non-interacting inlet Mongols. And the question is like this. So you have a certain material which is represented here by this cloud. And you have a certain point are 0, and then you have a certain point r prime. And you want to ask a question of whether you can find a critical radius r. Ray fish for all points are 0, would confine all interactions that exist, right? Between our 0 and R prime. And so this means that for every r prime, there is a certain footprint in terms of interactions, right? This region w r prime, which never intersects this sphere via a critical radius r. Now what is the radar is unclear, and this paper has a very interesting last section. This is actually computed section of the paper which talks about interaction from it. So most of this paper is about non-interacting fermions where this radius r is exponentially decay and it's, it's, it's, it's, most of the time it's pretty small. But for interaction fermions of what the corn rates, the following thing. He says, however, charged insulating fermions are classically far sighted in the sense that a sufficiently large distances the fermions see the classical long-range total potential, where rho of t in this integral is the dawdle perturbing charged density, including depolarization. And what this means is that in a periodic materials, the electric field, this typically depolarized and especially involve or written materials because electric fields from different sites on the center of an atom, they can. But in real materials, such as biological molecules, two-dimensional materials, or a liquid, even this is no longer the case. You can have polarization or depolarization in different directions and you electric field is in general delocalized. So if you apply, if you extend this argument to real materials and all materials have insulating charged for nuance. You could say that the interactions there are actually quantum mechanically far-sighted because they also depend on the frequency for the electric field, which is neglected here for, for, for simplicity. And beg them into 1000, five or four is, there are no real calculations to show how I entered the electronic metal is, but now we have the ability to do those calculations. And I will give you two examples of different kinds of fire safety. The first one comes from electronic exchange. So this a hardship for calculation. There is no electronic correlations here for a system of carbon chain terminated with Mason groups. So this is so-called accumulate money. And what I'm doing here is I'm changing the land or this chain and I'm doing or even alternation. So for all even number of carbon atoms, a good this conical shape of the potential energy surface as a function of the rotation angle of one dimensional groups. For an odd number of carbon atoms, I'm getting this parabolic shape and it alternates, right, as I change the number of carbon atoms. So this calculations are pretty easy to do with your favorite hearts before called. Now, if you want to machine learn them, you can use a binary machinery methods. They completely fail because they are unable to describe this non-local you fact and this, this alternation between conical shape and parabolic shape happens because of long-range charge transfer events. And this is absent in all our localized machinery reinforcements, Of course. Now this is quantum exchange effect. Now what about quantum correlation? So we've done this analysis on correlation effects for biological systems. And in particular, the question of how far sighted are fun device I training correlation that lead to find a way it's interactions between the protein and water in wire. And so here I'm showing you calculations using two different approximations to a long-range find a way interactions. And i'm, I'm showing you a radial distribution function for the energy now and I don't have time to read it. See how we compute this for the quantum mechanical case. But there is a way to approximate this pair distribution function. And so here is the protein surface. And, and so if you use a standard pair-wise dispersion models, so for example, using Lennard Jones potential in this case be used so-called Pachinko shuffling about that features it also pairwise aspersion member, all interactions decade above five angstrom away from the surface of the protein. And this is expected, this is r to the minus sixth decade. But if you know what an explicit quantum mechanical many-body calculation using our MVD Hamiltonian, you see that interaction is actually propagate up with five angstrom away from, from the surface. And so this is actually quite far I say Today I will say and provides an illustration of how far sighted balls electron exchange and the electron correlation effects again. And this is of course, still quite a challenge to extract. Now this for aesthetic calculations, but we can prove the same thing for Dynamics. So here is dynamics of two different molecules, you know, build radial distribution function for glycine, which is a small molecule and for ease of benzene, which is a larger molecular switch. And for glycine, everything is localized to five angstrom because it's small molecule. But for ease of benzene interactions propagate up to ten to 12 angstrom. And if you now try to machine learn them, you realize that different machine learning methods for different bytes of the potential energy surface, they have different accuracy is one. Here is another mechanism. And if you look at the errors for different missionary and methods, they are different. And that just reflects the complexity of morbid involves chemical bonds and non-local electronic interactions over large distances. And so this is really an unsolved problem in this field. Okay, That brings me to the end of my talk. So everything that I have described, all the software that we've developed is open source. So Wars, there's TDMA and neural network, but then shows that we've developed are all available online to you. Feel free to download them and play around with them. Always happy to hear feedback or things that work and things that don't work, of course, which is even more important. And finally, I would like to leave you with a challenge slides. So, so I've tried to, first part of my talk, we could discuss how we produce reference data, what reference data is useful, and what reference data is not useful. In a second part, I tried to show how we can use quantum mechanical reference data and develop machine learning force fields to utilize it to the full extent which now have enabled us to really reach exact dynamics is Bohr's quantum electronic and quantum nuclear effects fully captured. But as I sat in the last part of my talk, as I've demonstrated, we still have a lot of challenges to solve. Accounting for long-range interactions is an unsolved problem simply because those long-range interactions involved many interacting electrons with braille large landscapes. In convey to that right, chemical bonds are simple because they involve only a few electrons interacting over at short length scales, right? So, so those short length scales are easy to treat. Long length scales are hard to treat. And in addition, there are many, many other challenges remaining to be solved. Related to data science related construction or descriptor is related to incorporation of different physical laws. And really tight marriage between machine learning and physics, chemistry and that, thank you very much for your time. Thank you, Alex, for a very good talk. Now we'll get some time for questions. Shift up for you and I go, Hey, thank you for the nice talk. And goes like say. So my question is, so what is in your opinion on the, the physical reason for those differences between a couple of class that diffusion Monte-Carlo forms of bigger molecules, dimers. Yeah, so, so we've tried to analyze many possible reasons. In our paper. You've not been able to completely explain them. And I I have two so I have two reasons. One of them to Blaine KMC and funnel them to blame coupled cluster. The way that it's done correctly. So saw on the coupled cluster side, I think that atomic basis sets or localized that plumbing basis sets are a big problem for large systems because they don't have sufficient flexibility to model fluctuations in the vacuum space between the molecules and outside the molecules. The polarizability of those large molecules is very large. And I think the polarizability density, density response is pretty localized. And so that's something that is not easy to treat because even if you put basis functions in vacuum space, which you can do, it's not clear how to do this systematically. And of course, you also get a lot of problems with degeneracies in the Hartree Fock solution when you do so. And hence, this is not a practical solution. So I think on the coupled cluster side, this can be big problem. And, and so the basis that extrapolation procedures that people use I don't think are reliable for this large molecules on the quantum Monte Carlo side, but also the construction of the gestural factor I think is still probably not sufficiently well investigated harm problem aspect in the, in the treatment of many, but I think there could still be issues on that side. So I think Moore's methods have still issues to be solved and I'm not sure which one of them has the largest potential uncertainty. So if I may comment, I agree on COP of class. That'll basically, and what I like about it is, which is already the same thing because you wanted to say that when you do those calculations are big molecules cannot use augmented basis sets. Condition is really important ability and for long-range interactions, you can not doing because you have dependencies. And that's the problem and extrapolation. Now prove the acceleration picks upped up those effects. So that's one thing. But in case of quantum Monte Carlo, I think it's also the node problem. There's no prove the notes are good enough and it may, in some cases, cancel other problems. In some cases, they may have up to larger arrows. And who knows? I mean, you're right, your right leg was known. We know that all beryllium is also of course, enters the gestural factor as well. And yes, sometimes they can compensate, sometimes they can accumulate. That's right, that there's no real numerical proof of that. Yeah. And in the coupled cluster, of course, we used a singly augmented basis sets, right? Read went up to OCC CPV, PV 50, z. But probably you actually need double or triple augmentation, right? And that's impossible to do for the sludge systems as you graduates. Thank you. Any other questions? Maybe from students? I don't see any other questions. Can I ask a question? Yeah, Of course. Yeah, I saw that you had the sun result of fully quantum treatment, lowering the energy of some molecule when compared to classical. And you mentioned this is kind of surprising. Yeah. Yeah. There was a picture like with two curves. So this, the difference between the two curves is basically that you're treating CLI quantum mechanical in the red case. That's right. Yes. Yeah. And so why would this be surprising? I mean, I'm thinking from a different perspective of condensed matter physics, for example, of magnets. So what happens in that case is that what is your new apply would be like a spin. And in physics of magnets there is lecture no army of people are using classical macro magnetics based on the Lipschitz equation, which is the same pretty much as classical molecular dynamics, which creates more visionary snow pliers or a classical Newtonian. Barney again. But then vein. And then if you look at some, you know, if you look at them, Ferro magnets, yeah, it's the same thing in classical quantum usually is very similar, as long as the spin is not 1.5, which is a kind of mass. But then when you go into anything which is not parallel, which means y county fair, I'm arguments. Anything non-colinear, chromiums and things like that. Then every time you touch quantum mechanics, which means you start treating spin as it should be done. Using quantum mechanics operators rather than using and olives shipped equation. Then you always find the quantum mechanics slows down the energy of people. You know, people call this or it's the 0 fluctuations quantum computation. Of course, all these words are kind of watch yours until you start writing equations. Non-linear, slight writing equations. What you see is that it is the superposition of many states which are generating better ground state energies. And I mean, I can even think of the simplest example which is nothing like fancy crystals are just a double well potential. You put a particle in one while and it's classically stock. But if your tunneling and that's actually a very complicated problems. So this one is also sold by the way, like a multiple tunneling to double well, we're taking into account all possible instant. Don't ask the antecedent compares is beyond any standard perturbative treatment that could also lead to a lowering or find them just to somehow kicking in quantum mechanics and superpositions of quantum states in Singapore. Yeah, I would always wore suits, maybe Africa, mystery, but we do not understand the role sort of ammonia Gail. So, so, so what I what I said, it was surprising. I mean, I didn't tell the whole story, but typically what has been found previously by not full dynamics by just include gene for example, vibrational free energies, right? Quantum mechanical free energies or 0 energies, is that quantum mechanical effect destabilize molecules. Now here, this effect really is stabilizing because you go doing full dynamics and including quantum nuclear effects. Dynamics, let's say make this charges five traits. So you have, let's say a positive and a negative charge. They fluctuate, right? Dynamically. Their beach they would do even in classical dynamics. But then in addition, I had zero-point energy is make them correlate in such a way that they actually stabilize the system. And so there are two different file. And then in the end, you have to do the full thing as you correctly say, right? Well, you have to write the equations and decompose terms. But what you, what you see from the full treatment is that compared to classical dynamics, the quantum one stabilized does it while, if you don't do dynamics, but you just compute some effective curves, include in 0 energies, the opposite effect. So, you know, that's real. Lines less than anybody else. I came. Why it's going on. I don't know. It was something else. Something else? Yeah. Okay. So that's so is there or is there a rule I'm just writing today a paper on this stuff. Hml spins how big the spin has to be to shift between quantum and classical. So here's the rule in this world on how big the Notewise should be or how small the NAPLEX should be sorted. You must use quantum mechanics, Burger King, or Newtonian equations. Well, not really because it's not only the mass of the nucleus, but it's also this trend of the forces, right? So if you look at semi-classical Lifshitz like perturbation, know if she's late perturbation theory for quantum effects. Then what you realize is that there's balls, the mass of the particle, and the strength of the force that the important parameters that define the, the, the dullness of your fluctuations. And in so, so for example, you know, if you have hydrogens, they fluctuate more. But in graphene, for example, the quantum of facts and they increase the fluctuations of carbon-carbon bonds by about 30 percent compared to classical dynamics, which is quiet a large effect. And you only get it by Ryan and explicit dynamics because otherwise by symmetry you don't see any, any difference. So going back to burped example, Yoko bridge was benzene molecule for putting on the top or graphene. So this is not power spending a little icon out. That's on our client. Okay. Because I was searching for it, but it didn't show up. Probably google is now focused on selling things rather quickly giving a scientific information. So like if I take a piece of DNA which is actually something quite relevant. Because a decade ago, many people experimentally started looking at whether graphene can sequence DNA by responding to different nucleobases. So what would that example require? Switching to anything to for an apply. If I just put a NACLO base and add the name or guanine on the top of the cases there was a whole show. You drill a hole in graphene and tried to shoot this NACLO basis through the hole to see what is inside them. That's how your sequence. I find Mickey has no clear dynamics would be very important in really dictating the nuclear quantum effects will be important in detergent and dynamics of this, of this process. Because you share the army of people, for example, creator of MIMD would be shooting these things day and night, throw the whole in graphene and looking at all possible orientations. But it was quite massive and you just do pure classical mentoring. And the other thing, the other problem of course, which has nothing to do with no clear is that all the parameterization of force fields, four carbons they use in market dynamics is very far away from solid state physics like they don't know that you are now delocalized. Walk, fades and stuff like that. They basically trip graphene as a bunch of benzene molecules stuck together. So you'll do your thing that, but so would that actually be amenable format to shovel like graphene on something? Well, one nucleobase, of course, is not a big deal, but it would have to be a graphene and NACLO base. And then all the junk around richard gill like water molecules and potassium chloride ions and that kind of stuff. So for that, you need to include long-range effects. I think both electrostatics and, and correlation in, I would say it is physical models. And so that really comes back to mind one of my last points in the training in the current challenges. Also, this will be fun. So problem IDS, I mean, if you want to get. Reliable results. So you can try, you can make localized pretensions and you would get something, but it all depends on how long range You effects are. And even classical electrostatics become squared long-range trade when you have an interface between graphene and mortar, so on. Okay, thanks, or Google's own, fruitful. Thank you. Uh, how we're how we're one of our guests named Henry has raised his hand and Henry want to ask a question. Yes, I word this is the the quantum level stuff is way over my capabilities. But a, B and a euro thing chemists for several, several decades. My question is, on your machine learning a very large molecules, how do you know that you have met the minimum state when you manufacturer may have some sort of internal stress built into the molecule at the end. I can't talk your language so I'm sorry, if it doesn't make sense. So you mean if you want to apply in any machine learning method for a large enough molecule, how do you know that? You can relax that to save some global minimum or some low line? Yes. Yes. Well, I mean, so so depends what large means raid, as I said, currently, is the technology that we have and provided that enough data is there in brands are both treating same molecules up to 100 atoms is visible at all the facts right, is all local, non-local effects. So, so in principle, that should be quite a reliable as long as you can run molecular dynamics or just generate an ensemble of minima that VM on. Let us do that. You can always find another stable or will upon meaning my even. And you can be sort of brothers sure that you are somewhere close to it. But if you're talking about more complex things or are you in periodic materials with some complex unit cells than I think we have. We're not there yet in the sophistication of our methods to really make sure that we have all the required interactions built in. Okay? Yeah. Now, I dealt with 50 thousand molecular weight, your things. We can never give them their loss stability state, right? Right. They would always. The whole dynamics of math, making the molecule was more important thing we could do. You mean kinetics? Kinetics becomes more important basics? Yes, Yeah. Yeah. I mean that's so for this polymorphism problem, that's often also that sometimes for large molecule that's also the case. I mean, exper, experiments often for many systems can get to the global minimum, but not always. And in polymorphism, right, there is a well-known disappearing polymorph problem where suddenly people have produced a polymorph for ten years. And then suddenly to the small change in fabrication conditions, you get to a more, much more stable state. It right? So you find that only after 10 years, don't make me have my nightmares again, right then you produce clones of that material rate and suddenly something happened and everyone, all, all, all, all, you know, batches come out as a new point. And so yeah, that's right, That's unplanned you. But, but so for that, rate, doing prediction is extremely important. Because then you can, for example, you, if you have an experimental structure and you can calculated, but then if you can explore the potential energy surface and you can say a is actually much more stable structure, right? That was really helpful. Yes. Thank you. Any other questions? I want to make sure that Alexander is quite late for you the mind. That's okay. That's okay. No problem. Of course, this is going to be on the, uh, on the machine learning and data science size. And I find it interesting that when in Quantum and condense matter you talk about machine learning. You Qian, very often people just talk about machine learning in general. And I find that it seems to me that the majority of those models or deep neural networks. So and maybe asking some Gaussian process is application. But so this goes back to what you were saying earlier. Like the language is different, right? So can I ask you from your perspective, you had to give it a definition of what is machine learning? How would you define it? And am I right? That primarily it's deep neural networks and the graph networks that are being applied. Or am I missing something? Yet? Been mainly talking, is the kernel, kernel methods like Gaussian process reference, right? And we also use neural net for when we have enough data or when we want to go through chemical space and we have no fit mostly understanding of how to construct a non-linear transformation. Then we just throw the data at a very deep neural network and, and we hope for the best friend and so, so in, in our field, balls approaches are widely used. So most of people who are just interested in, in, in interpolation data is using neural networks. But then even there, there's a lot of interesting work on incorporates in variances and covariances. And so there are this interesting methods that the couple rotation on permutation of degrees of freedom in quiet interesting ways. When you want to describe quantum states, right? So I've talked about force fields, but you can also do work on wave functions, for example, right? And then you have symmetries which have really, really higher level symmetries. And you can build those symmetries in principle directly in neural networks. So, so, so yeah, so most people are using neural networks and as you see, convolutional neural network is a graph neural networks. But people who are in our field who are trained to understand what the LDR trade we extract some in science than the small, sleeker and ridge regression approaches. So just non-linear regression. And then, yeah, and then in principle you can reformulate rate, you can reformulated kernel lake and neural metric. The other way around is a bit harder but, but there is more and more approaches that try to find a sweet spot between how much data you need and how much physics you put in your description of the system. Thanks. Thank you. Any other questions? All right. Someone asked collapsed question. We just actions that are similar to the previous one little bit expanding talk towards a new area. And you feel that's called quantum machine learning is when you use quantum computing algorithms applied to machine learning or develop algorithms for quantum computers to do machine learning. Are you excited about these? So you're following this field, you think where we can apply this to, or you can apply this to new problems you care about. Or you will believe that we're just not there yet and we have to wait a little bit until algorithms, sorry, until appropriate algorithms are produced and we can use quantum machine learning to develop for steels, what do you think about? So in general, I think they use the uterus and development of quantum algorithms is exciting. I mean, there was just a pre-print, I think if we could go on actually using quantum computers to solve the long-range electron correlation problem for and truly oscillators, which is something ever act on for a long time. So I was really excited to see that. And they've done it from the IBM's week. And so they've read, is developed an algorithm to solve coupled to the oscillator is which is not an analytically solvable problem, and that Brantley obtain good results. So, so, so I'm following that sort of at least a bit from distance, but, but, but I think there's a lot of developments in terms of doing quantum machine learning algorithms on quantum computers. I'm not sure how clause VR tool to really have certain breakthroughs. I mean, I do have a more personal story actually I noise startup, which started in that propose in using quantum machine learning for, for drug discovery. But then the end, they ended up doing classical machine learning on quantum data, French what, what type. And that was much more successful. And they actually were recently bought by beak biotech company because that is actually quite exciting. You can do this classical machine learning and data hub. So yup, So I think there's a lot of scope for quantum algorithms, right? And applying them to solving problems. I think they're probably interested in developments going on. Okay. Thank you. Thanks a lot. Any other last questions, maybe? Yeah. So it's getting late and looks and works. So I want to thank Alex again for this amazing talk and nice discussion after it. Thank you very much for the invitation. Thank you. Bye bye. Thank you. Bye-bye. Bye-bye. of Theoretical condensed matter physics and the head of theoretical chemical physics group and the head of the department of physics and material science. The University of Luxembourg. Alexander is also distinguished visiting professor at the Technical University in Berlin. Alix received his undergraduate degree in computer science and a PhD in physical chemistry at the Universidad Autonoma Metropolitan that in Mexico City in 2007. From 20082010. He was Alexander Von Humboldt fellow at the Harvard Institute of the Max Planck Society in Berlin. Out of that Alex state at the same institution and lead an independent research group until joining the University of Luxembourg in 2015. In his research, Alex combines quantum mechanics, statistical mechanics, and machine learning to develop accurate and efficient first principles, computational models to study a wide range of complex materials, aiming at qualitative understanding and quantitative prediction of their properties at the atomic scale and beyond. And Alex is one of the leaders in the field. He's extremely productive, published over 180 papers, is ancient, exists 71, with more than 25 thousand citations. Alex is also in the top 1% of highly cited researchers from 2018 to 2020 want. He has also received a number of awards, including a girl for Eric Young Investigator Award of the German Physical Society, Dirac Medal from the World Association of theoretical and computational chemists and a Wander Walls Prius or what, 2021 International Conference on non-covalent interactions. Alex is also fell off of American Physical Society. We're all absolutely happy that Alix accepted our invitation. And without further ado, Alex, please, we're all eager to hear your talk. Thank you very much. And they say for this kind introduction, let me try to share my slides. Okay. Do you see my slides? Yes. Okay. Excellent. Great. So yes, thank you again, say and thanks for for this kind invitation. So as I said, it's a bit late here and in old Europe, but I think I'll manage the first time. I think scientists, they have to stay late work. But I think our work as enjoyable, so on. I'm thank you very much again for the invitation. And they think they hope that I can pass at least part of this enjoyment during my talk. So so I understand this is a broad colloquium. And so I tried to give a broad overview on, on few different topics that forever it can on and find a unified topic. And the unifying topic that I will be discussing here is force field. So, so force fields are some effective representations of the forces that nuclei feel in a certain molecule or material. And this force field, the, the, the, There's a definition for forceful to come off or it's busy and Warner behind approximation. So, so this will be ubiquitously used during my talk. Everything will be born Oppenheimer approximation. And that allows you to define always effective forces for a given nuclear configuration. And the question is, of course, all this forces are coming from electrons, right? So they are coarse-grain electrons and representing them effectively as some interactive and Adams, and the question is, how can we do this effect? So this of course, has been done in the field of computational chemistry and computational biology and material science for a very long time. In fact, for the Nobel Prize in Chemistry in 2013 was avoided for construction of biomolecular for students. A few years ago, new tool came into our toolbox. This is machine learning and machine learning allows the construction of sophisticated and flexible, non-linear forms for this, for students. And so for some time people thought this is sort of a lifesaver right now is machine learning. And we can construct universal force fields for essentially any monocular mature. But of course, once again, those force fields, those atomic forces are coming from interacting lecture. So the question is, when under which conditions we can map interacting electrons into effective for students. And, and I will try to tread on this topic during my talk. So in my group in general, we are interested in quite a complex problem of stops a large systems, large molecules, large materials. And this is a complex problem that involves physics, chemistry, material science, and computer science scientists represented by machinery and so on. People can mean from my group has different backgrounds. They're physicists, chemists, mathematicians, and computer scientists. And there are a few very important people to highlight here. Eager scheme. I'm, I'm, I'm showing you here. Here's a group leader in my group who is leading a small subgroup that works on combining physics and machine learning. And in particular Gregory von Sekhar and financing the lingual. There'll be two people whose work I will mention it. Now. The combination or physics and machinery and require strong experts from the physics side and from computer science side. And so we've established for about 10 years ago, a strong collaboration with a group of close Robert Mueller, who is one of the most renowned machine learners in Germany. He is working at the Technical University of Berlin and in particular to people Stefan Camila and those yellow cells header. Key players also did tremendous contributions to everything I will be describing. So, so a lot of this verb is really a combination between strong expertise and machinery and, and strong expertise in physics and chemistry. So we start from, in our breakfast, start from first principles and for us our standard model, these the Schrodinger equation and in particular born Oppenheimer approximation applied to the Schrodinger equation where we separate the electronic and nuclear degrees of freedom. But they are interested in understanding and solving the Schrodinger equation for large and heterogeneous systems. So for example, proteins, liquids, molecular crystals, or two-dimensional materials. And of course the interactions, the wide range of interactions and all the system's complicated. The solution of the Schrodinger equation because we are talking about thousands or even tens of thousands of interacting electrons. So this is a complicated problem. And you would like to develop approaches, efficient approaches that enable ear increasingly accurate solution of the Schrodinger equation for this complex. So that's our final goal. Of course. This goal of yeah, not the first group overcome this. There are thousands, tens of thousands of groups working on this. And in the modelers toolbox, there is a whole hierarchy of approaches for approximating the solution of the Schrodinger equation. Now it's well-known of course, that exact analytical solutions to the Schrodinger equation exists only for certain model systems or for one electron atoms, like a hydrogenic atom. So when we have more than one electron, which is the case for all systems of our interest, we need to approximate the solution of the Schrodinger equation and particularly to approximate the wavefunction. The most dumpy of approximating it is sort of rate and empirical, but actually the force that's forgetting about all electrons and just say, well, they're effective forces that Adams, you. And this can be done by following the Hellman Feinman theorem of squares. And just write some non-linear function that expressed as the at the, the force that an atom fields in a given confirmation of a molecule or a solid. Going a bit more sophisticated, you can introduce electronic degrees of freedom, for example, why are semi-empirical methods based on density functional theory or quantum chemistry? So you can introduce, for example, a small basis set is more than the basis that you can fit some parameters and get sometimes a reliable ancestral for certain class of systems. The real workhorse in the field of electronic structure theory East density functional theory, because as proven by Hogan broken corn and then constructed effective theory by corn and some density functional theory in principle as an exact theory. But of course, you have to approximate quantum mechanical many-body interactions and hands introduce approximately functionals. And this gives you, of course, errors and pencil. And going up, of course, in principle, we have numerical ways to exactly solve the Schrodinger equation y, a so-called full configuration interaction methods where you write electronic configurations and you write a linear expansion is some coefficients and then you obtain those coefficients. Or you can do Monte Carlo based solutions, so-called quantum Monte Carlo methods. And in principle, if you are lucky and if you have enough flexibility in those wave functions, while you can get, in principle, you can approximate the exact solution to the Schrodinger equation. Now. The nice thing here is that when you go up in this hierarchy, the accuracy of predictive power of your methods increase, but there is a price to pay and the price as computational cost. And another price which is especially important for physicists, is that you lose conceptual insights. Write wavefunctions are extremely high dimensional objects. And getting insights from wavefunctions of say, system, the cells of the electrons is not very easy. And so methods such as DFT or semi-empirical methods actually give you many more insights than methods that are here at the top of this, of this letter. And so the real question, and that's where machine learning comes. How we use the nice ideas, nice conceptual ideas at the lower rungs of this ladder. But we still keep the accuracy that we have and the higher ranks of the ladder, That's ray machinery. But machine learning instead of democratizes this whole hierarchy of methods here because you can use different techniques from different methods and you can combine them in a nice way. For example, you can use aspects of semi-empirical methods for describing a certain molecule, a material, but then train a machine learning method on high level data coming from, for example, quantum, high level quantum mechanical methods. But of course, if your reference data is garbage, right, for example, you took some approximations that are not good enough to describe your system, then machinery will only give you also a garbage, right? And so the question is how to appropriately combine reference data? Which level do you use to produce reference data and which level of theory to use to describe your system. And those are two questions that are still being investigated in our field. So now in the next couple of slides, I would like to delve a bit further into this question of how can we obtain reliable quantum mechanical data and how we can know that we are producing reliable quantum mechanical data for systems of our interests. So I will give you now two examples. One example is of a methodology and approximate methodology, which allows you to obtain very reliable reference data compared to experiment for very complex systems and molecular crystals. And then I will show you a case where you use the highest level of quantum mechanics to different highest levels of quantum mechanics. It turns out that both of them disagree, and this means that one of them or both of them are giving you garbage data, which we cannot actually use for parameterizing machinery and production. So before I started actually machinery numeric, a lot of the work in my group was on developing effective physical methods for describing a long-range electronic correlations. So this are ubiquitous many body effects, right? Where many electrons correlate or large land scales. And you don't want to describe those correlations explicitly, right? Because electro electronic degrees of freedom, because it's just too hard, it's too computationally expensive. So we've developed the so-called MDD, or many-body dispersion method that basically describes the response of electrons in a molecule of material, wire quantum harmonic oscillators and then the coupled or spinlock harmonic oscillators is a long range potential. And we solve the Schrodinger equation for oscillators, not for electrons. And we then couple that energy to a semi local density functional theory functional. And so we get this semi local quantum effects from DFT. We get non-local quantum effects from MBE Hamiltonian. And this is a nice combination of two different methods that we then applied to a variety of molecules and materials. And I will just show one particular obligation of this. And this application conserves, concerns a predictive modelling of so-called, so-called phenomenon of polymorphism in molecular crystals. This phenomenon is ubiquitous phenomenon. So basically, it turns out the Judaic one molecule, for example, this one, this is a drug candidate from actually from Pfizer. And then you try to crystallize it. When you crystallize it in from solution or some other environment, you realize that it can pack in a wide variety of different crystalline arrangement. And that is because there are many types of interactions. Electrostatics, polarization, dispersion, powder repulsion that guide the packing of those molecules in the crystalline phase. And those crystal packets often have almost degenerate lattice energies. So you can have within a window or for, let's say kcal per mole, which is so-called chemical accuracy. You can have 10, 20, 30, 40 of those polymers, right? A huge number, despite the fact that they are. Almost also degenerate. The different polymers can have completely different physical chemical properties. For example, different colors, different solubility is different than cities melting points, conductivities or whatever, whatever property your image. But you really need to know which polymorph is global energy minimum and these polymers or meta-stable states, and this is a very tough problem because we are talking about 1% of the largest temperature, right? That is what determined the differences between this point and this is a very, very tiny energy. And for a long time people thought this problem is completely, it cannot be dealt. Is quantum mechanics simply because the energy difference. And so we've actually applied our methodologist to this problem. And we tried to do this in a blind fashion. So we don't, we don't cheat as, as often we do in theory. The sort of take experimental data and then the calculations. And we then compare back to other experimental data by, by the often biased because we already used experimental data. In this case, what I'm showing you here is a real blind prediction. So, so these are results of so-called blind test of organic crystal structure prediction organized by Cambridge crystallographic data send them. So basically what they do is they collect experimental data, different polymorphs of molecular crystals. They hide this data. You don't know his unpublished data. And they asked experiment, they asked theoretical groups to predict those structures and then they compare the predicted structures which you submit to the experimental ones. And you need to predict both structures, right? Result knowing n structural information on the Norwegian structure of the molecule itself and energies as well, right? And so here I'm showing you overlays between our predict structures legally blind liberty. Rigid crystal structure prediction procedure. We put different crystal groups, we optimize the molecules. And these are optimized, completely geometry optimized structures. And our predictions are colored wildly. Experimental structures are the gray and it's pretty hard to see differences in most cases, the root mean square deviation for 20 molecules and the supercell is about 0.15 angstrom per molecule. It's a really tiny difference. It's mostly invisible here. And so this is, this result can only be obtained when you do density functional theory was a good hybrid functional, been easier or functional, so-called modern empirical hybrid functional. Plus our full many-body description that includes long-range correlations and the full many-body fashion. So here are structural information, so this is pretty good. But of course the question is, are those structures really the global mean? Because experiments often see global minimum. And it turns out that they are when you go to the highest level of theory. So what I'm showing you on this slide, our results for four different molecules. So the molecules they indicated here as this two-dimensional diagrams, the global minimum structures are shown in this unit cell pictures. And what I'm showing you on this diagrams, for example, here on the left, is for different levels of theory. As you move to the right, you increase the sophistication of your level of theory and the accuracy, right? And the there I bought a 100 structures and bottle. That's a 100 polymorphs that we predicted and the experimental structures and rat. And so in the best case, the experimental structure in red should be the global minimum. So it should have a 0 energy on this, on this diagram. And in fact, this is the case for all of this for different systems. When we go to the highest level theory, which includes a high appropriate to be B 0 DFD functional misses a function that describes semi local exchange correlation effects blast the many-body dispersion. So the full many-body treatment of long-range correlations. Glass also vibrational entropy is computed at room temperature. And so as you see here for all these four systems, the, the experimental structure turns out to be the global minimum at our landscapes, which is the best possible prediction you can make. So actually, when we presented this results originally 2016, nature sounds if gene actually nature all this news and views article saying that the volume of prediction problem is solved. I don't really agree with that statement. I think it's not solved. And movie, it's presented really good results. It's surprising results for five different systems. I'm showing four out of five systems. But there's still quite a lot to do. And it took us actually about four years to really finalize everything and writing this paper. Okay, So, so this is an example where Experiment 3 to experimental data. Tells you that your quantum mechanical reference calculations are good enough grade for this particular problem. And this is a very, very tough problem, the problem of prediction problem. But there is also a tremendous problem here because doing all these calculations is computationally very expensive. So I'm showing just part of the results. The total amount of computer time that we had to spend for this study is about 20 million CPU hours. But you can do on, on, on computer is especially in the US, right? If you have access to beak HIPC facilities. But it's not something you want to repeat for every new morning and spill here immediately. The question comes, well, if you have all this data, you could also use this data to construct effective machinery and potentials, for example. And you can learn from increasingly larger chemical space. It says your January data. You can construct those potentials and you can make them more and more general as you produce more when more reliable D. And that's something which has not yet been done in this field in a, in a, in a systematic way, let's say. But the data is in principle, there is just not easy to construct machine learning potentials for this large systems, as I will discuss in the second part of my book. So here's an example of reliable predictions with quantum mechanics, which you can then use for machining. Let me give you now a completely opposite case where, where you cannot decide what quantum mechanics aid and to actually use so, so, you know, in our field of development of quantum mechanical methods, there are two different paradigms to go over. It's heaven, right? Reaches the exact solution to the Schrodinger equation. One is called post Hartree Fock method. This means that you'll construct a Hartree Fock solution which respects anti-symmetry or fermionic, so fermionic statistics of electrons. Then what is missing is so-called the electron correlation energy, which is what I've described already, is the MEG method, which captures long-range correlation energy. But if you want all correlation energy between electrons in an exact way, you can do this wire so-called quantum mechanical methods. In particular, the gold standard in the field, the so-called couple of cluster map, but the single, double and perturbative triple excitations. In fact, this method originally comes from high-energy physics, from nuclear physics. And it was abandoned there because it was not giving good results, but four electrons, strained relations that gives great results. Most of the time they'd been people for that reason really cord goals then. But there's an alternative math, right? So if you have just one that, that you cannot really trust its results because there's just one number and you have to take it for granted. It would be great to have an alternative method. And in fact, there is an alternative method that's called quantum Monte Carlo, which is a completely different way to obtain to approximate an exact solution, I'm afraid your equation. So you write an ansatz for the wave function and you then optimized parameters and it's very flexible ansatz. And the principle of the ansatz flexible and app you get an exact solution and training. And so we've applied this to alternative ways, gold standard ways in quantum chemistry, in quantum physics communities to actually study the interactions between morning, I'm indifferent morning. It's ranging from benzene dimer of year two, this buckyball getchar complex. So this is a C 60 molecule embedded in this cycle of birth and that NRI. And we want to understand the binding energy between the right. And it turns out that when the molecules are small or when interactions are not so strong balls methods. So more gold standard, it's coupled cluster and the quantum Monte Carlo if essentially indistinguishable results. But the surprise is when you go to higher to larger systems and this has simple systems and just non-covalent interactions. There's nothing fancy bulb and it's not strong. Correlations is no oxides are some really strange or Bornstein buttons here. But nevertheless, for such systems, you just increase system size, the interaction, of course, the strength of the interaction increases a bit. You both methods give competitor different reasons and the difference is huge. It's order. Well, I would say, yeah, All order of magnitude more than what one would expect. So, so here the mean difference is eight kcal per mole between the two methods. But the largest difference is 12 kcal per mole. And this is a big surprise. And so we'd be sort of coined this puzzle. And of course now the question is, what do you trust as a reference for machinery? Is that this blue line or is it this red line? Right? And if you put the two different numbers, you will get completely different parameterization for, for, for the machinery enforced. And so, so this two examples sort of GIF. So define the first part of my talk where I wanted to talk about the reference state, okay, So you really have to be critical to your reference date. Sometimes when you use the highest level of quantum mechanics that you have. Disposal, you'll get reference data you can more trust at the moment. While in other cases, for much more complicated examples like molecular crystals, you do have methods that seem to give you reliable and quantitative results which you can use for construction of machinery first. Okay, So, so that's summarized some of the first, or we might talk about reference state and now let me talk about machine. So despite the fact that sometimes we don't, but we cannot produce reliable reference data. Let's say we have cooled reference data. And so we can now produce, for example, energies and forces for molecules as a function of their confirmation degrees of freedom. So we move some functional groups, right? And we know how the forces change on atomic forces change. And that allows us to construct a certain non-linear neural net for poor or current rich regression procedure. To feet, those are reproduced or atomic forces. So of course, we want to really do a complex systems that's where we want to goal and it is full accuracy of quantum mechanics. But at the moment, we are somewhere here, right at present, where machine-learning force fields can be used. Studying smaller organic molecules, I think this is, this part is largely solved or small organic molecules up with maybe three agonist is sort of a soft topic already. Or ordered materials. Are those materials have also been studied by many groups and they're very many. Would machinery methods to construct force was for this things. But if you look at disordered materials or the peptide from biopolymers, they are not there yet and a year classical force fields are still the, the de facto standard. But another thing which is extremely interesting is that children force fields are not, cannot only be used to construct This representations of how atomic forces change with molecular or solid state geometry. But they are becoming new, completely new methodologies in their own right. Because you can study of things which were not possible to study this previous classical force fields. You can study electronic effects. You can start the reactivity, try it so your atoms can change their, their bonding patterns, which was not possible to do this classical force fields. You can construct models for ground state and excited states. And so you can do nonlinear dynamics, you can do optical excitations example. You can easily study nuclear quantum effects, which was not possible to do is classical force fields. Because in their parametrization, people would mix experimental data that includes quantum nuclear effects and theoretical data of each does not those defects and so you cannot mix them. They sat, problem of double counting and so on. And so machinery enforces really enable a much wider set of applications in, in physics, chemistry and chemical physics and physical cans. And this is really where it gets pretty exciting because many of those simulations were simply impossible. Before machine reinforced feels really came into, into the game. Though. When we started working on this field. Aiming at first producing machinery enforced fields for molecules, for small money. That's where we started. We wanted to do something which is quite different to what most people were doing. The sort of put a very challenging problem in front of us. So we wanted to construct a machinery for short, which is general. It can be applied to any potential want to go up to a certain size. It should be transferable, right? It should be scalable and it should represent them all quantum mechanical interactions. So you cannot impose any couples, you cannot predict and the energy of the molecule as some of our atomic energies because this is not possible to move as the Schrodinger equation. And that's what most people were doing before. And so this led us to really reconsider the most basic aspects of all four forces. So what is typically done? They feel that something like this. So you're given a molecule, let's say a benzene molecule like the one shown here as one of the simplest molecules. And you are given the different conformations of the molecule, right? So you have a set of conformations. And of course, different conformations have different atomic forces. And so what we typically do is you write an energy model. And an energy model, right, is written as a sum over atomic energies. And this is already a big problem because Schrodinger equation does not allow you to define it on mechano. She's, the only thing you can do isn't born Oppenheimer approximation is define atomic forces. This is an observable in due to the home and find length here. And so doing this is not allowed by the Schrodinger equation, but nevertheless because of computational. Efficiency and because of permutation symmetries, people do this, but this is wrong. This shouldn't be done prints. Now what we decided to do is different thing. So we start with this confirmations and the right model, a force-field explicitly for atomic forces. And once you write that model, if this model is energy conserving by construction, you can actually integrate it out and get a potential energy surface, right? And the only question is, how do you do this? Energy conservation in the forest them, right? But this is of course well-known because we know how to construct a conservative force fields. You know, the, the curl of the force will have to be 0 there. But it was defined the conservative, conservative forceful. And so what is done in, in, in practice is something like this. So I'm giving you an example, a toy exam. So, so let's say we have this force field, two-dimensional force for this our ground truth. This are two coupled harmonic oscillators are a couple of parameters. And let me just take this and we take six data points at run out of this force here. And we impose the requirement that the curl of the force field has to be 0. By construction, this isn't our machinery model by default. So we work and for his domain. And then we try to reproduce the ground truths to learn from just 66 examples. And we get this field here. So if you compare this conservative fields which you learned to the ground truth, while it has all the features, it's not quantitative, but it's semi-quantitative. But if you'd drop the requirement of energy conservation, so, so you then learn the components of this force, the x and y components, you get this vector field, which is completely nonsensical compared to the ground truth, right? It has a different attractor here and has a completely different for, right? So, so energy conservation in general, in the domain or for force fields, extremely constrained requirement. And it's a requirement that really helps you to learn, right? Then it reduces the need for, for data, for the number of data points that it has a lot of interesting aspects actually that I don't have time to go. And now let's move beyond our toy examples, right, to real morning. So, so now we have a molecule and what we do in our approach, we call it gradient domain machine learning. And S stands for symmetrized gradient domain machinery because we use all the symmetries, global and local symmetries of our system. So global symmetry is this time invariance, which gives you energy conformation, right? And they have of course to rotational and translational invariance and v impulse per mutational and variance, which we discover from in a data-driven way, right? So for example, if, if you have a metal groups which rotates in the dynamics and of course, permuting all the hydrogen atoms on, on, on the methyl group is, is equivariant, right? For the, for the forces and saw the discover those images from the data from the molecular dynamic state. So we produce some liquid and that makes for a given molecule these simple efficient method. We then subsample the recover all the permutation symmetries. We do multi-part. I mentioned there is a lot of Blackmagic going into this, but that's explained in our papers. And then once we do that, we then construct a kernel matrix in the hessian domain because the covariance between 4 atomic forces is given by the Hessian matrix. And then we have a vector of coefficients which is obtained from our training data. Okay? Once we learn this vector of coefficients, this is a convex problem. You can obtain those coefficients by just matrix inversion. You then can integrate this kernel and analytically and get a model for the potential energy surface, right? That's a big sum here, but it doesn't matter. It's an analytic numerically exact solution. So, so then you can plot, for example, potential energy surfaces. And here is one example for one particular molecule shown over here are now this approach is extremely efficient. So for a realistic molecule, such as aspirin, beneath, it has 24 atoms, 60, I think, 68 degrees of freedom, if I remember correctly, we need only about 300 confirmations out of molecular dynamics trajectory to obtain force field, which is accurate to 0.3 kcal per mole, which is really, really accuracy which you can use to run molecular dynamics. And because you only need a very small number of conformations, the reference data can come from the highest level of quantum mechanics. And so we can, for example, train these force fields to couple of class than data, which is, as I said, is a sort of a gold standard for, for small molecules at least. And it works really, really well for those. And once we have obtained this force field. We have now a force-field that includes all the electronic effects within the born Oppenheimer approximation to essentially arbitrary accuracy. So it's almost essentially exact solution of the Schrodinger equation. And then in order to treat quantum mechanics of the nuclei, we use the so-called us integral molecular dynamics. This is based on find one cup plus integral representation of quantum statistics, which in the limit of an infinite number of beads gives you an exact quantiles to this 644 for your quantum particles. And with that we can, we now can really do, I would say embarrassingly quantum simulations because bores our nuclei and our electrons, essentially treated at the exact level of quantum mechanics is in Warner been Homer approximation and of course views in bosonic treatment of the nuclei. And so here is an example of this calculations. This is ethanol molecule, one of our favorite ones. And so it has three different minima, is a so-called trans and gauche minima. And we can calculate, for example, occupation probabilities of those minima. And when we look at our exact simulations and compare experiment essentially get exact results. And this is really resent error bar For experiment. While if you drop, if you, for example, train a force-field at the level of density functional theory, or you do classical molecular dynamics, you will not get this degree. And so say, the agreement is really destroys. You need quantum mechanics or balls, the electrons and the nuclei at the highest level theory. This is just an example of something we can compare to experiment, but they can also do new discoveries. So, so for example, you can compare the effective binding mechanisms to squat. Classical dynamics are the nuclei, are quantum dynamics are the nuclei. And you'll find something very surprising that quantum dynamics often dense to stabilized meta-stable states of molecules. For example, this happens in aspirin, where the global minimum is heavily stabilized. A local delocalization of the nuclei, the molecule is globally standardized and this is actually quite a surprise in fact, and we explain that by fluctuations of negative and positive charges. So call this by star and transitions. And this is the chemical. In chemical. Similar effect happens in this stall when molecule, so Darwin molecule is just a benzene ring of is a methyl group and this methyl group classically is just a broader, it's a free rotor. Classical dynamics just make this, this benzene toluene metal group also lead free. But if you do quantum dynamics, you find that this oscillator here actually starts to localize. And that's again a surprising finding because quantum effects localize this rotor, right? So it essentially just localized on the left side, on the right side. And this is also an electronic, quieter, complex electronic interaction. So this kind of facts that we can find now by this explicit usage or machinery and forceful. So this was not possible to do before result machine learning because those calculations would take essentially decades on, on, on supercomputers if you use this level of theory that we use. But now we can do this calculations and essentially an hour or so or even less. So. So this really demonstrates a huge acceleration that machinery in brains into the field of computational physics and competition against. Okay, So up to now, I've mainly discussed small molecules, but we can do much larger systems now. So of course everyone wants to go to real applications, for example, molecular crystals, D and E nanotubes. And we've actually extended our GDM, our framework by doing, instead of doing exact inversion, we can do precondition into to enable large-scale calculations that we've now extended GDM up to about 400 atoms. We get this double walled knowledge to prevent bliss of unpublished. We are finalizing this week. We've also extended our approach to materials for banks who didn't periodic boundary conditions. We call this Bravais inspired GD and malware big HTML. And all this will be coming out pretty soon. Just an example of an application that can actually do now in a very short time is for exams or the dynamics of a benzene molecule on top the Griffey. So this is fully periodic oscillation graphene and benzene aperiodic systems, right? It's a brute Excel. And we are running the dynamics of this benzene molecule and they're looking at how it fluctuates in terms of the vertical position and in terms of the angle between the vertical and the the plane of the molecule. And what you realize is something again, very, very interesting. Classical electrodynamics, the molecule is delocalized so it's rotating and translating over, over the surface quite widely. While in present ago molecular dynamics. So when you treat the nuclei quantum mechanically, the molecule dense to localize. And this is again counter-intuitive because buzz integral of molecular dynamics delocalize is the nuclei locally. But because the delocalize as nuclear locally, so most carbon distances and carbon-hydrogen distances are larger and effectively, the polarizability of the molecule grows and that increases the funding lines attraction between benzene and graphene. The same thing happens in graphene. The carbon atoms are effectively at larger distances and that increases the polarizability of graphene. And so the fun towards attraction become stronger because of quantum effects. And this is a very counter-intuitive fiend which I would not have predicted result actually running those simulations. So, so this application demonstrates the state of the art that we can do today in the bulk buying this or machine learning force field advance. Okay, So this is all nice and wall and this is a very nice applications I think. And not only ours, but many other groups have demonstrated extremely interesting results for many, many different systems. I would like to spend the last five minutes to talk about challenges. So, so there have been a lot of advancements. But actually I think that we've barely scratched the surface on the field of combining physics, chemistry, and machine learning. And there are many, many challenges and the recently tried to describe them in this prospective article with Igor. The, the main themes are accounting for long-range interactions. So up to now, most people have concentrated on short range chemical effects. The datasets that we have up, it's not really clear how to fully construct them in a systematic way and how to use everything that is there in the data sets. There's still a lot of physics that we have not incorporated into our, I'll get actress. And finally, there are some examples in the recently published literature where people find new phenomena from machine learning. And sometimes this correspond to false discovery simply because you're, you do extrapolation where you shouldn't really be doing. Okay. The 1 they wanted time, which is really close to my heart and that's related to the first part of my talk is how neuroscience it really Electrons are, right? That comes back to the data. Electrons of machinery and forceful. So, so how far away do we need to meet Adams? See rain. So, so what are the whole long range or the contributions to atomic forces from Adam's far away. And this question, of course, has bothered many physicists. So for many, many years. And in fact, the way to corn was a well-known Nobel laureate. Together There's Emily brought down, have written this nice article in PNAS called near sightedness of electronic mail. And many people in computational chemistry side that beeper as a proof that electronic matter is near. Now of course, what is near science? I mean, that is a very strange concept because if you ask someone seated and looking at the window, Well, they see a house far away, right? Which is meaning meters or kilometers away. So for him, maybe near sightedness is a 100 meters. But if you ask, say computational chemist, how neuroscience it is a benzene molecule, maybe they will tell you a few angstrom. So is it really a few angstrom is a 100 angstrom, is it Saul's an angstrom always a damn micro meters or even more and no one really norms. And so this interesting paper sort of setups in an hour based on the simple models, mostly the non-interacting inlet Mongols. And the question is like this. So you have a certain material which is represented here by this cloud. And you have a certain point are 0, and then you have a certain point r prime. And you want to ask a question of whether you can find a critical radius r. Ray fish for all points are 0, would confine all interactions that exist, right? Between our 0 and R prime. And so this means that for every r prime, there is a certain footprint in terms of interactions, right? This region w r prime, which never intersects this sphere via a critical radius r. Now what is the radar is unclear, and this paper has a very interesting last section. This is actually computed section of the paper which talks about interaction from it. So most of this paper is about non-interacting fermions where this radius r is exponentially decay and it's, it's, it's, it's, most of the time it's pretty small. But for interaction fermions of what the corn rates, the following thing. He says, however, charged insulating fermions are classically far sighted in the sense that a sufficiently large distances the fermions see the classical long-range total potential, where rho of t in this integral is the dawdle perturbing charged density, including depolarization. And what this means is that in a periodic materials, the electric field, this typically depolarized and especially involve or written materials because electric fields from different sites on the center of an atom, they can. But in real materials, such as biological molecules, two-dimensional materials, or a liquid, even this is no longer the case. You can have polarization or depolarization in different directions and you electric field is in general delocalized. So if you apply, if you extend this argument to real materials and all materials have insulating charged for nuance. You could say that the interactions there are actually quantum mechanically far-sighted because they also depend on the frequency for the electric field, which is neglected here for, for, for simplicity. And beg them into 1000, five or four is, there are no real calculations to show how I entered the electronic metal is, but now we have the ability to do those calculations. And I will give you two examples of different kinds of fire safety. The first one comes from electronic exchange. So this a hardship for calculation. There is no electronic correlations here for a system of carbon chain terminated with Mason groups. So this is so-called accumulate money. And what I'm doing here is I'm changing the land or this chain and I'm doing or even alternation. So for all even number of carbon atoms, a good this conical shape of the potential energy surface as a function of the rotation angle of one dimensional groups. For an odd number of carbon atoms, I'm getting this parabolic shape and it alternates, right, as I change the number of carbon atoms. So this calculations are pretty easy to do with your favorite hearts before called. Now, if you want to machine learn them, you can use a binary machinery methods. They completely fail because they are unable to describe this non-local you fact and this, this alternation between conical shape and parabolic shape happens because of long-range charge transfer events. And this is absent in all our localized machinery reinforcements, Of course. Now this is quantum exchange effect. Now what about quantum correlation? So we've done this analysis on correlation effects for biological systems. And in particular, the question of how far sighted are fun device I training correlation that lead to find a way it's interactions between the protein and water in wire. And so here I'm showing you calculations using two different approximations to a long-range find a way interactions. And i'm, I'm showing you a radial distribution function for the energy now and I don't have time to read it. See how we compute this for the quantum mechanical case. But there is a way to approximate this pair distribution function. And so here is the protein surface. And, and so if you use a standard pair-wise dispersion models, so for example, using Lennard Jones potential in this case be used so-called Pachinko shuffling about that features it also pairwise aspersion member, all interactions decade above five angstrom away from the surface of the protein. And this is expected, this is r to the minus sixth decade. But if you know what an explicit quantum mechanical many-body calculation using our MVD Hamiltonian, you see that interaction is actually propagate up with five angstrom away from, from the surface. And so this is actually quite far I say Today I will say and provides an illustration of how far sighted balls electron exchange and the electron correlation effects again. And this is of course, still quite a challenge to extract. Now this for aesthetic calculations, but we can prove the same thing for Dynamics. So here is dynamics of two different molecules, you know, build radial distribution function for glycine, which is a small molecule and for ease of benzene, which is a larger molecular switch. And for glycine, everything is localized to five angstrom because it's small molecule. But for ease of benzene interactions propagate up to ten to 12 angstrom. And if you now try to machine learn them, you realize that different machine learning methods for different bytes of the potential energy surface, they have different accuracy is one. Here is another mechanism. And if you look at the errors for different missionary and methods, they are different. And that just reflects the complexity of morbid involves chemical bonds and non-local electronic interactions over large distances. And so this is really an unsolved problem in this field. Okay, That brings me to the end of my talk. So everything that I have described, all the software that we've developed is open source. So Wars, there's TDMA and neural network, but then shows that we've developed are all available online to you. Feel free to download them and play around with them. Always happy to hear feedback or things that work and things that don't work, of course, which is even more important. And finally, I would like to leave you with a challenge slides. So, so I've tried to, first part of my talk, we could discuss how we produce reference data, what reference data is useful, and what reference data is not useful. In a second part, I tried to show how we can use quantum mechanical reference data and develop machine learning force fields to utilize it to the full extent which now have enabled us to really reach exact dynamics is Bohr's quantum electronic and quantum nuclear effects fully captured. But as I sat in the last part of my talk, as I've demonstrated, we still have a lot of challenges to solve. Accounting for long-range interactions is an unsolved problem simply because those long-range interactions involved many interacting electrons with braille large landscapes. In convey to that right, chemical bonds are simple because they involve only a few electrons interacting over at short length scales, right? So, so those short length scales are easy to treat. Long length scales are hard to treat. And in addition, there are many, many other challenges remaining to be solved. Related to data science related construction or descriptor is related to incorporation of different physical laws. And really tight marriage between machine learning and physics, chemistry and that, thank you very much for your time. Thank you, Alex, for a very good talk. Now we'll get some time for questions. Shift up for you and I go, Hey, thank you for the nice talk. And goes like say. So my question is, so what is in your opinion on the, the physical reason for those differences between a couple of class that diffusion Monte-Carlo forms of bigger molecules, dimers. Yeah, so, so we've tried to analyze many possible reasons. In our paper. You've not been able to completely explain them. And I I have two so I have two reasons. One of them to Blaine KMC and funnel them to blame coupled cluster. The way that it's done correctly. So saw on the coupled cluster side, I think that atomic basis sets or localized that plumbing basis sets are a big problem for large systems because they don't have sufficient flexibility to model fluctuations in the vacuum space between the molecules and outside the molecules. The polarizability of those large molecules is very large. And I think the polarizability density, density response is pretty localized. And so that's something that is not easy to treat because even if you put basis functions in vacuum space, which you can do, it's not clear how to do this systematically. And of course, you also get a lot of problems with degeneracies in the Hartree Fock solution when you do so. And hence, this is not a practical solution. So I think on the coupled cluster side, this can be big problem. And, and so the basis that extrapolation procedures that people use I don't think are reliable for this large molecules on the quantum Monte Carlo side, but also the construction of the gestural factor I think is still probably not sufficiently well investigated harm problem aspect in the, in the treatment of many, but I think there could still be issues on that side. So I think Moore's methods have still issues to be solved and I'm not sure which one of them has the largest potential uncertainty. So if I may comment, I agree on COP of class. That'll basically, and what I like about it is, which is already the same thing because you wanted to say that when you do those calculations are big molecules cannot use augmented basis sets. Condition is really important ability and for long-range interactions, you can not doing because you have dependencies. And that's the problem and extrapolation. Now prove the acceleration picks upped up those effects. So that's one thing. But in case of quantum Monte Carlo, I think it's also the node problem. There's no prove the notes are good enough and it may, in some cases, cancel other problems. In some cases, they may have up to larger arrows. And who knows? I mean, you're right, your right leg was known. We know that all beryllium is also of course, enters the gestural factor as well. And yes, sometimes they can compensate, sometimes they can accumulate. That's right, that there's no real numerical proof of that. Yeah. And in the coupled cluster, of course, we used a singly augmented basis sets, right? Read went up to OCC CPV, PV 50, z. But probably you actually need double or triple augmentation, right? And that's impossible to do for the sludge systems as you graduates. Thank you. Any other questions? Maybe from students? I don't see any other questions. Can I ask a question? Yeah, Of course. Yeah, I saw that you had the sun result of fully quantum treatment, lowering the energy of some molecule when compared to classical. And you mentioned this is kind of surprising. Yeah. Yeah. There was a picture like with two curves. So this, the difference between the two curves is basically that you're treating CLI quantum mechanical in the red case. That's right. Yes. Yeah. And so why would this be surprising? I mean, I'm thinking from a different perspective of condensed matter physics, for example, of magnets. So what happens in that case is that what is your new apply would be like a spin. And in physics of magnets there is lecture no army of people are using classical macro magnetics based on the Lipschitz equation, which is the same pretty much as classical molecular dynamics, which creates more visionary snow pliers or a classical Newtonian. Barney again. But then vein. And then if you look at some, you know, if you look at them, Ferro magnets, yeah, it's the same thing in classical quantum usually is very similar, as long as the spin is not 1.5, which is a kind of mass. But then when you go into anything which is not parallel, which means y county fair, I'm arguments. Anything non-colinear, chromiums and things like that. Then every time you touch quantum mechanics, which means you start treating spin as it should be done. Using quantum mechanics operators rather than using and olives shipped equation. Then you always find the quantum mechanics slows down the energy of people. You know, people call this or it's the 0 fluctuations quantum computation. Of course, all these words are kind of watch yours until you start writing equations. Non-linear, slight writing equations. What you see is that it is the superposition of many states which are generating better ground state energies. And I mean, I can even think of the simplest example which is nothing like fancy crystals are just a double well potential. You put a particle in one while and it's classically stock. But if your tunneling and that's actually a very complicated problems. So this one is also sold by the way, like a multiple tunneling to double well, we're taking into account all possible instant. Don't ask the antecedent compares is beyond any standard perturbative treatment that could also lead to a lowering or find them just to somehow kicking in quantum mechanics and superpositions of quantum states in Singapore. Yeah, I would always wore suits, maybe Africa, mystery, but we do not understand the role sort of ammonia Gail. So, so, so what I what I said, it was surprising. I mean, I didn't tell the whole story, but typically what has been found previously by not full dynamics by just include gene for example, vibrational free energies, right? Quantum mechanical free energies or 0 energies, is that quantum mechanical effect destabilize molecules. Now here, this effect really is stabilizing because you go doing full dynamics and including quantum nuclear effects. Dynamics, let's say make this charges five traits. So you have, let's say a positive and a negative charge. They fluctuate, right? Dynamically. Their beach they would do even in classical dynamics. But then in addition, I had zero-point energy is make them correlate in such a way that they actually stabilize the system. And so there are two different file. And then in the end, you have to do the full thing as you correctly say, right? Well, you have to write the equations and decompose terms. But what you, what you see from the full treatment is that compared to classical dynamics, the quantum one stabilized does it while, if you don't do dynamics, but you just compute some effective curves, include in 0 energies, the opposite effect. So, you know, that's real. Lines less than anybody else. I came. Why it's going on. I don't know. It was something else. Something else? Yeah. Okay. So that's so is there or is there a rule I'm just writing today a paper on this stuff. Hml spins how big the spin has to be to shift between quantum and classical. So here's the rule in this world on how big the Notewise should be or how small the NAPLEX should be sorted. You must use quantum mechanics, Burger King, or Newtonian equations. Well, not really because it's not only the mass of the nucleus, but it's also this trend of the forces, right? So if you look at semi-classical Lifshitz like perturbation, know if she's late perturbation theory for quantum effects. Then what you realize is that there's balls, the mass of the particle, and the strength of the force that the important parameters that define the, the, the dullness of your fluctuations. And in so, so for example, you know, if you have hydrogens, they fluctuate more. But in graphene, for example, the quantum of facts and they increase the fluctuations of carbon-carbon bonds by about 30 percent compared to classical dynamics, which is quiet a large effect. And you only get it by Ryan and explicit dynamics because otherwise by symmetry you don't see any, any difference. So going back to burped example, Yoko bridge was benzene molecule for putting on the top or graphene. So this is not power spending a little icon out. That's on our client. Okay. Because I was searching for it, but it didn't show up. Probably google is now focused on selling things rather quickly giving a scientific information. So like if I take a piece of DNA which is actually something quite relevant. Because a decade ago, many people experimentally started looking at whether graphene can sequence DNA by responding to different nucleobases. So what would that example require? Switching to anything to for an apply. If I just put a NACLO base and add the name or guanine on the top of the cases there was a whole show. You drill a hole in graphene and tried to shoot this NACLO basis through the hole to see what is inside them. That's how your sequence. I find Mickey has no clear dynamics would be very important in really dictating the nuclear quantum effects will be important in detergent and dynamics of this, of this process. Because you share the army of people, for example, creator of MIMD would be shooting these things day and night, throw the whole in graphene and looking at all possible orientations. But it was quite massive and you just do pure classical mentoring. And the other thing, the other problem of course, which has nothing to do with no clear is that all the parameterization of force fields, four carbons they use in market dynamics is very far away from solid state physics like they don't know that you are now delocalized. Walk, fades and stuff like that. They basically trip graphene as a bunch of benzene molecules stuck together. So you'll do your thing that, but so would that actually be amenable format to shovel like graphene on something? Well, one nucleobase, of course, is not a big deal, but it would have to be a graphene and NACLO base. And then all the junk around richard gill like water molecules and potassium chloride ions and that kind of stuff. So for that, you need to include long-range effects. I think both electrostatics and, and correlation in, I would say it is physical models. And so that really comes back to mind one of my last points in the training in the current challenges. Also, this will be fun. So problem IDS, I mean, if you want to get. Reliable results. So you can try, you can make localized pretensions and you would get something, but it all depends on how long range You effects are. And even classical electrostatics become squared long-range trade when you have an interface between graphene and mortar, so on. Okay, thanks, or Google's own, fruitful. Thank you. Uh, how we're how we're one of our guests named Henry has raised his hand and Henry want to ask a question. Yes, I word this is the the quantum level stuff is way over my capabilities. But a, B and a euro thing chemists for several, several decades. My question is, on your machine learning a very large molecules, how do you know that you have met the minimum state when you manufacturer may have some sort of internal stress built into the molecule at the end. I can't talk your language so I'm sorry, if it doesn't make sense. So you mean if you want to apply in any machine learning method for a large enough molecule, how do you know that? You can relax that to save some global minimum or some low line? Yes. Yes. Well, I mean, so so depends what large means raid, as I said, currently, is the technology that we have and provided that enough data is there in brands are both treating same molecules up to 100 atoms is visible at all the facts right, is all local, non-local effects. So, so in principle, that should be quite a reliable as long as you can run molecular dynamics or just generate an ensemble of minima that VM on. Let us do that. You can always find another stable or will upon meaning my even. And you can be sort of brothers sure that you are somewhere close to it. But if you're talking about more complex things or are you in periodic materials with some complex unit cells than I think we have. We're not there yet in the sophistication of our methods to really make sure that we have all the required interactions built in. Okay? Yeah. Now, I dealt with 50 thousand molecular weight, your things. We can never give them their loss stability state, right? Right. They would always. The whole dynamics of math, making the molecule was more important thing we could do. You mean kinetics? Kinetics becomes more important basics? Yes, Yeah. Yeah. I mean that's so for this polymorphism problem, that's often also that sometimes for large molecule that's also the case. I mean, exper, experiments often for many systems can get to the global minimum, but not always. And in polymorphism, right, there is a well-known disappearing polymorph problem where suddenly people have produced a polymorph for ten years. And then suddenly to the small change in fabrication conditions, you get to a more, much more stable state. It right? So you find that only after 10 years, don't make me have my nightmares again, right then you produce clones of that material rate and suddenly something happened and everyone, all, all, all, all, you know, batches come out as a new point. And so yeah, that's right, That's unplanned you. But, but so for that, rate, doing prediction is extremely important. Because then you can, for example, you, if you have an experimental structure and you can calculated, but then if you can explore the potential energy surface and you can say a is actually much more stable structure, right? That was really helpful. Yes. Thank you. Any other questions? I want to make sure that Alexander is quite late for you the mind. That's okay. That's okay. No problem. Of course, this is going to be on the, uh, on the machine learning and data science size. And I find it interesting that when in Quantum and condense matter you talk about machine learning. You Qian, very often people just talk about machine learning in general. And I find that it seems to me that the majority of those models or deep neural networks. So and maybe asking some Gaussian process is application. But so this goes back to what you were saying earlier. Like the language is different, right? So can I ask you from your perspective, you had to give it a definition of what is machine learning? How would you define it? And am I right? That primarily it's deep neural networks and the graph networks that are being applied. Or am I missing something? Yet? Been mainly talking, is the kernel, kernel methods like Gaussian process reference, right? And we also use neural net for when we have enough data or when we want to go through chemical space and we have no fit mostly understanding of how to construct a non-linear transformation. Then we just throw the data at a very deep neural network and, and we hope for the best friend and so, so in, in our field, balls approaches are widely used. So most of people who are just interested in, in, in interpolation data is using neural networks. But then even there, there's a lot of interesting work on incorporates in variances and covariances. And so there are this interesting methods that the couple rotation on permutation of degrees of freedom in quiet interesting ways. When you want to describe quantum states, right? So I've talked about force fields, but you can also do work on wave functions, for example, right? And then you have symmetries which have really, really higher level symmetries. And you can build those symmetries in principle directly in neural networks. So, so, so yeah, so most people are using neural networks and as you see, convolutional neural network is a graph neural networks. But people who are in our field who are trained to understand what the LDR trade we extract some in science than the small, sleeker and ridge regression approaches. So just non-linear regression. And then, yeah, and then in principle you can reformulate rate, you can reformulated kernel lake and neural metric. The other way around is a bit harder but, but there is more and more approaches that try to find a sweet spot between how much data you need and how much physics you put in your description of the system. Thanks. Thank you. Any other questions? All right. Someone asked collapsed question. We just actions that are similar to the previous one little bit expanding talk towards a new area. And you feel that's called quantum machine learning is when you use quantum computing algorithms applied to machine learning or develop algorithms for quantum computers to do machine learning. Are you excited about these? So you're following this field, you think where we can apply this to, or you can apply this to new problems you care about. Or you will believe that we're just not there yet and we have to wait a little bit until algorithms, sorry, until appropriate algorithms are produced and we can use quantum machine learning to develop for steels, what do you think about? So in general, I think they use the uterus and development of quantum algorithms is exciting. I mean, there was just a pre-print, I think if we could go on actually using quantum computers to solve the long-range electron correlation problem for and truly oscillators, which is something ever act on for a long time. So I was really excited to see that. And they've done it from the IBM's week. And so they've read, is developed an algorithm to solve coupled to the oscillator is which is not an analytically solvable problem, and that Brantley obtain good results. So, so, so I'm following that sort of at least a bit from distance, but, but, but I think there's a lot of developments in terms of doing quantum machine learning algorithms on quantum computers. I'm not sure how clause VR tool to really have certain breakthroughs. I mean, I do have a more personal story actually I noise startup, which started in that propose in using quantum machine learning for, for drug discovery. But then the end, they ended up doing classical machine learning on quantum data, French what, what type. And that was much more successful. And they actually were recently bought by beak biotech company because that is actually quite exciting. You can do this classical machine learning and data hub. So yup, So I think there's a lot of scope for quantum algorithms, right? And applying them to solving problems. I think they're probably interested in developments going on. Okay. Thank you. Thanks a lot. Any other last questions, maybe? Yeah. So it's getting late and looks and works. So I want to thank Alex again for this amazing talk and nice discussion after it. Thank you very much for the invitation. Thank you. Bye bye. Thank you. Bye-bye. Bye-bye.
On Electrons and Machine Learning Force Fields | Alexandre Tkatchenko, Université de Luxemburge 11/10/2021
From Zelphia Johnson November 10, 2021
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On Electrons and Machine Learning Force Fields
Machine Learning Force Fields (MLFF) should be accurate, efficient, and applicable to molecules, materials, and interfaces thereof. The first step toward ensuring broad applicability and reliability of MLFFs requires a robust conceptual understanding of how to map interacting electrons to interacting "atoms". Here I discuss two aspects: (1) how electronic interactions are mapped to atoms with a critique of the "electronic nearsightedness" principle, and (2) our developments of symmetry-adapted gradient-domain machine learning (sGDML) framework for MLFFs generally applicable for modeling of molecules, materials, and their interfaces. I highlight the key importance of bridging fundamental physical priors and conservation laws with the flexibility of non-linear ML regressors to achieve the challenging goal of constructing chemically-accurate force fields for a broad set of systems. Applications of sGDML will be presented for small and large (bio/DNA) molecules, pristine and realistic solids, and interfaces between molecules and 2D materials.
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