So, good morning everybody. I will be chairing the session today up to the coffee break and let me go straight to the first speaker who is Stephen Louis who doesn't need any presentation in this community and he will tell us about election correlation in multi-particle excitations in time-dependent phenomena and superconductivity in materials. Is this on? Could you hear me? Thank you very much for the introduction Amelia and first of all, I'd like to thank all the organizers for inviting me to give this morning's talk. So what I would like to do today is to share with you some of our recent work using many body perturbation theory to study electron correlations in a couple of topics, multi-particle excitations, time-dependent phenomena and superconductivity in some materials. So this is going to be the outline of the talk. I will begin with looking at interaction and time-dependent phenomena in photo physics of atomic wave thin 2D crystals. That will include looking at correlated multi-particle excitations such as trions and bi excitons and exciton-enhanced nonlinear optical responses such as Schiffkern and then we will look at how correlation influence experiments such as results from experiments such as pump probe transient optics and time-dependent angle result folding emission spectroscopy. And finally, as the last topic, I will look at the role of self-energy effects in the electron phonon coupling and superconductivity. So let me begin with this topic of try to calculate from first principle using many body perturbation theory of non-equilibrium phenomena and excitations go beyond one of two particle excitations. So if you want to look at this kind of phenomena, one has to go beyond the standard GW and GW beta-sculptor equation approaches. For example, if we're interested, oops, let's see, if you're interested in correlated high number of particle excitations such as trions and bi excitons, then one has to actually investigate the interacting three and four particle GWINs functions. And if you're interested in time-dependent and high-fuel phenomena such as those measured in pump probe experiments, nonlinear optics, or even fuel-driven transitions, then one has to look at the time, explicit time propagation of the GWINs function. For example, looking at GW approach and then look at this time propagation using the non-equilibrium GWINs function formalism. So let me begin by looking at correlated multi-particle excitations in 2D systems. As you all know, interaction is enhanced in one and two dimension. So it's not surprising, experimentally, one find that multi-particle excitations are actually prominent in those measurement of those systems. The example I give you is bi exciton on monolayer tungsten disilinide. Plotted here is the photoluminescent spectrum, and what you see here is this this peak label XX, which actually grows with the intensity of the excitatation light. And this peak has been identified as a bi exciton, a combination of two excitons, and it has been well studied experimentally. And this kind of phenomenon, in fact, are of fundamental and practical interest in a number of other areas, such as exciton condensate and deficient of a single exciton into two excitons in organic crystals for photovoltaic applications. So in terms of theoretical approaches, you were interested in the quasi-particle excitations, you had to look at the single particle GWINs function, say within the real approach that you solve this single Feynman diagram where that dashed line is the screen-codown interaction. For optical property, including electron hole interactions, then one has to solve two dot Feynman diagrams using the beta-sulphide equation approach. For bi excitons, which is a four-particle excitation, then, in fact, one has to look at soft something like diagrams that look like this, and there are 36 such diagrams involving four particle lines and their interactions. This looks formidable, but in fact, recently we were able to formulate it and develop the computer code to do such calculations. So let me give you some results. This is to look at trions and bi excitons in monolayer tungsten diselinae, which is a semiconductor and the low-energy excitations in this semiconductors are at the K and K prime valley, just like graphene. Here are the calculated results compared to experiments for the binding energy of a negative trion and bi exciton. So there are no adjustable parameters in the calculation, and you see that they are actually rather good agreement between theory and experiment. In fact, these are the first fully-abinitional many-body calculation of this kind of excitations. Our results shows that there's a very rich energy and spin valley level structure for these excitations. They are rather high-energy phenomena because the binding energy is in the order of a few tens of non-electron volts. The results are recently experimental observations and in fact give some new predictions. So for example, for the bi exciton in this system, traditionally it has been thought as an exciton, which is a combination of a intra-valley bright exciton and an intra-valley dark exciton. However, from our calculation what we find that's really not the case. The bi exciton that was measured here, in fact, is an exciton, bi exciton that combining an intra-valley bright exciton and an intra-valley dark exciton. And this kind of configuration was ignored previously because of the neglect of important electron hole exchange, the effect that come in on all those diagrams, 36 diagrams. Now, let me turn to time-dependent and nonlinear phenomena. Here, we have to look at non-equilibrium grid function and solve it in the time domain using the CalDIS control. For the experts in the audience the method we use is one we developed with a time-dependent GW that is within the adiabatic approximation for the self-energy and propagating it in real time. With the density matrix approach. Now, the advantage of this approach is that it makes the calculation much more doable. It captures the self-energy and excitonic effects. We expected it to be relatively accurate in the weak and moderate field regime. Within linear response, it is equivalent to the beta-soprita equation approach in which we test that, in fact, is the case. However, if you do time propagation, then you get our nonlinear responses and time-resolved phenomena including excitonic effects. And I will show some example of this. Because of this approximation, we can now perform the time propagation with a single time variable as opposed to time to the third power in the full Katerynov Bay equation approach. So, let me use shift current as an example. Shift currents are photo-induced DC current in a non-centrosymmetric crystal without having a PN junction. It is a second-order optical response that is with an incoming AC field, you could generate a DC current, and it is related to band topology, that is the shift of the inter-shell corner of the electron from the optical excitations. Now, previously one could do an independent inter-band transition type of theory for this kind of effect, but for 2D materials excitons are so important that we decided to use this time-dependent GW approach to look at the problem. So, here is some results we obtained for shift currents in monolayer germanium sulfide. Plotted here is one of the coefficients here that relates the optical field to the DC current, sigma yxx. So, the blue curve is when we turn off electron-hole interaction in the time-dependent GW approach, and then the red curve is when we include the electron-hole interaction. So, you see that there are dramatic changes in the spectrum. Exotonic effect in this material enhance the shift current at certain frequencies by orders of magnitude and completely changes the shape of the spectrum. This is quite interesting because exotonic effect is so important in 2D materials. One would expect that this kind of effect to be very large in any kind of 2D semiconductor, and in fact, we also find that for nonlinear response such as some frequency or this harmonic generations, you can also get auto-magnitude enhancement. Another very interesting result is that that you get DC charge transport with illumination inside frequency, inside the gaps. So this phenomena would be extraordinarily interesting and important in possible photovoltaic applications. Here's an example of second harmonic generation for the same system. What's plotted is chi 2, and again, the blue curve is without including electron-hole interaction, and the red curve is including exotonic effects. So again, you see that there can be orders of magnitude enhancement in the nonlinear optical response. Now, let me turn to field-driven phenomena within time-dependent operas. Normally, you think of probing exotons by optical means, but recently, we and others have realized that you could also probe them using time-dependent operas. The idea here is that you excite the light with a pump, optical photon, so you put the system in a non-ecoribidium state, and then later you probe it with operas. So here's an example. For the case, again, monolayer germinium sulfide. What we do here is to simulate this pump-hole experiment by shining light first with a frequency that corresponds to the permanent first exciton, excitation energy of the system, and then we probe this spectral function after a certain delay time. So on the left here is the operas spectrum when we neglect electron-hole interaction in the calculation. So what you see is as expected, these are the occupied bands, and you also see some of the unoccupied conduction bands because the pump photons. When we turn on the electron-hole interaction, then what you see is this spectrum, which is quite different. You see some novel features now in the unoccupied state energy regime, and in fact, you see several, oops, wrong direction. Several series of features, new features, and those are excitonic features, and by reading out the energy precision, you get out the exciton, excitation energy, and the spread of the intensity here, in fact, give you information on the wave function of the exciton in case space. That is, you could think of an exciton as a linear combination of free electron-holes, and this intensity here, in fact, is related to this coefficient here. And this kind of experiment, in fact, has been, is now doable in the last few years, and people have seen that experimentally. So by doing this kind of calculation, you could directly get out the exciton energy and its wave function. Another interesting feature is that you could see renormalization of the bands due to photon excitation, and if you increase the intensity of the pump light, you could see more dramatic renormalization. And this is given by this example here, looking at the same time-dependent opus for the case of a monodermal disulfide. The A exciton, the permanent exciton in this system is at 1.8 electron-hole. Here, we pump the system with frequency, photon frequency, at 1.7 electron-hole, which is slightly off-resonance, and you do see this excitonic feature, and this gives you the exciton excitation energy, and not much happened at the top of the valence band. But if we now do the same simulation and use frequency exactly at resonance, then you see again this excitonic feature, but the dispersion now changes in the top of the valence band. In fact, it's also changed dramatically, and this kind of camelback feature that you see both on the top of the valence band, and that of the excitonic features, in fact, is a exciton polarization driven exciton 4k effect in this system. Now, let me talk to you about another very interesting optical phenomena in 2D materials. Now, we look at bilayer system. Here is, for the case of molititums, selenide, and tungsten selenide, and what happened here is experimentally, what one finds is that your photo-excite layer, two-layer layer A, then you actually could influence the optical response of layer B in a very, very quick time scale. So the time scale, in fact, is in the order of hundreds of femtoseconds, and traditionally in the literature, this has to be interpreted as a single particle transfer, a charge transfer mechanism. That is, when you do this excitation, you create holes here, and this two systems form the type 2 band-alignment system. The hole gets transferred here, and then when you try to probe layer B, that will be influenced. And it turns out that if you do a DFT calculation, the coupling between the top of the valence band of layer A and B are actually very, very weak. And it cannot give you this fast-time scale, and you have to invoke phonons. But even with phonons, it's still quite slow. And this got us to think that maybe exotonic effects is important, because exoton is so dominant in those two systems. So what we did is to apply this kind of, okay, to this system, the TDAGW method. And the reason is that if you create an excitation in layer A, then there are actually a continuum, a bunch of interlayer exotons that are in resonance with the excitation in one of the layers. So you could quickly transfer intralayer exotons to an interlayer exoton, and that can lead to a change in the optical response of the unpumped layer. And I won't have time to go into the details, but basically, by calculating the time propagation of the Grinch function, you could get out the optical response. And when we do that, what you find is the diagonal element of the density matrix, which corresponds to the occupation of the single particle state, has a very slow time scale as a function of time after the pump. But the electron hole coherence of diagonal elements of the density matrix, which describes the transfer of an interlayer exoton to the interlayer exoton, actually go through a very fast time scale. And if you look at directly what the calculated change in the absorption of the system, that is you pump layer A and then you measure layer B, then what you find is that there is a very fast change in the absorption when you include the full electron hole interaction effects. And if you do the same calculation within TD heart-treat, then you don't find any change at all in this time scale. And the rise time that we calculated from our approach is in the order of 300 femtoseconds, which agrees quite well with experiment about 200 femtoseconds. So this is an alternative explanation in addition to the phonon charge transfer, induced charge transfer mechanism. Now let me spend the next three minutes maybe to talk about electron phonon coupling. So as we all know, most of the calculation for electron phonon nowadays are done within DFT, which are basically describing the coupling of the Kong-Sham electrons with the phonon field. This had worked very well for many materials, but it failed for some. And what we have done recently is to develop a method to increase self-energy effects at the GW level to the electron phonon coupling using a linear response theory similar to the density functional perturbation theory. So basically what you do is you, for the electron phonon matrix experiment, you take away the turn that involved in Vxc and replace that one turn involved with the self-energy within linear response. And what you find is in fact that correlation effects, self-energy effects, can change G by as large as a factor two in some materials. So here's some results we have obtained for some metals, sorry metals, series of metals. For simple normal metals, EFPT and GWPT basically give you similar results. However, for some metal oxides like this one, you could have a difference of a factor of two in the coupling constant lambda. And this change enhancement in lambda by factor two, in fact, explains the very large TC of this bismuth potassium, barium bismuth potassium material and whereas DFT cannot explain TC at all. And similarly, self-energy enhancement of the electron phonon coupling could also explain the king that one sees in the photo emission experiment of the couplet plate. And that enhances the king by a factor of three. In terms of a very recent example in the case of superconductivity in the neck plate, and this is a system people are very interested in because it's an analog of the couplet plate. And if one can make it and make it a superconductor, then you might find another system with unconventional superconductivity. However, while this has been done very recently in the last four years or so, three years, and what's fine is TC in this material is quite high, 23 degree. But if you do DFT and the BCS type of phonon induce the superconductivity, the predicted lambda is 0.2 and TC is much less than 1. I see that the chairman is getting nervous. So basically, I just give you a very brief version of what happened here. What happened is very interesting. It turns out the neck plate is very different from the couplet plates. It's a two-band system. It has the nickel D band near the fermion energy, but also there's a rare earth band near the fermion energy. So the band structure within DFT is given by here. If you do a GW calculation, those two bands swap in position and changes the fermion surface dramatically and also the electron phonon coupling constant. And here is the LLS equation calculated with DFT and also with this GWPT. And what you see is a factor of 5.5 enhancement in the coupling constant.  And then we solve the k-dependent LLS equation and find out a predicted a very interesting superconductivity in this material. And we're actually sticking our neck out now. We're making this prediction that this material is a two-gap S-way superconductor. Here is a distributional gap at low temperature. For the rare earth band, it's very high, the gap, but for the nickel band, it's very low. And in fact, the gap distribution of a functional temperature is given here, and we have a TC about 22 degrees, which is very close to the experiment. And we also, so it's very, very different from the cube plate. And our results could also explain the tunneling experiment data. The tunneling data for the clean sample give you something like that, clearly shows two gaps.  But it turns out you take this two-gap model and broaden it with impurity, scattering effects, then you get the v-shape. So I think over time, let me leave you with this message saying that many body prohibition theory with screen-column interaction to the n-particle-greens function can be a powerful versatile approach for understanding and prediction of a variety of spectroscopic properties and field-driven time-dependent phenomena for real material, but you have to treat the interaction appropriately for appropriate phenomena that you're interested in. So as the very last slide, I want to acknowledge my excellent postdoc and student who did all the work, and I leave you look at this slide. Thank you very much for your attention. Thank you very much for this fascinating talk. So we have time for a few questions. Yes. Yeah, you have this two-gap, as you said, but the symmetry of both the gaps according to you are a swift, right? That's correct. But if I understand correctly, one of the band is actually coming from nickel x-square minus y-square, so the expectation was that will be d-wave. So do you have any comments on it? Of course you say that the v-shape comes from the disorder and etc. Right. What happened is that according to our calculation, there's no opposite experiment yet, and there's no real detail of tunneling with a phase experiment measurement. So according to our calculation, superconductivity is driven by the rare earth band, and that has a very strong electron-phonal coupling due to the fact that the self-energy effects bring it to the family level, family surface, that band, and also enhances the electron-phonal coupling. So the driving force is the rare earth band, and that's why I give you a two-gap s-wave and large Tc. So all these predictions remain to be verified by experiment. Thank you. Thank you. And thank you very much also for my side. It's a very beautiful talk and very, very clear. Very nice. Let me continue on the news question, because I was also curious about the doped neodymium nickelate. If I remember correctly, experimentally, the whole coefficient changes sign as a function of temperature, right? Suggesting that the carriers actually change from electron-like to hole-like. Do you have a view on this in this context? We have not looked into that very carefully, but there are many pockets in the system, there are electron and hole pockets and so on. So it might be reasonable using the kind of band structure we have with the GW approximation to analyze that, but we haven't done that. So question here. Thank you very nice talk. Thank you for your very nice talk. I have a question about your correlation effect of the shift current. It's a germanium sulfide. I saw that the enhancement is okay, but there are some sign change if you include the exotonic impact. Do you know why? It's very strange. In general, there will be sign changes even in the independent particle picture of shift currents. Depending on the frequency of light, even with the same polarization, you could change the direction of the current, and that's related to the shift vector in the band structure, which is related to the very connections and so on. So that's not surprising because you see that even in the independent particle picture. Now, the two dominant peaks below the gap in the plot that I saw you change the sign, and that's related to the nature of the two excitons. One is the A exciton, the other is the B exciton. And again, if you change the polarization of the light, you could actually change the sign of the coefficient. And that's very exciting because one of the things that we are doing now is with Mike Cromby, where he could try to measure the current on 2D material and by changing the frequency of light, we may be able to see this. Well, I think we have to move on for the interest of time. Thank you very much against it. Our next speaker is Johannes Lischner from Imperial College, and he will tell us about large metallic nanoparticles. Thank you very much. And I also would like to start by thanking the organizing committee for this opportunity to present the research of my group on modeling the hot carrier generation in large metallic and nanoparticles. So this is a talk about so-called nanoplasmonic hot carriers where one exploits the capability of metallic nanoparticles such as a gold nanoparticle to convert the energy of light into energetic or hot electrons and holes. And what we mean by hot is typically a large energy compared to the thermal energy. And such hot carriers can be very useful for energy conversion applications such as photo catalysis, photovoltaics, also in sensing and there are many other applications. So here you see just one example where one basically uses a gold nanoparticle to convert light into holes and electrons. The holes can do an oxygen evolution reaction. The electrons can be transferred to a titanium nanoparticle and then do a hydrogen evolution reaction with basically what's happening is water is split into oxygen and hydrogen. So this is one of the ideas where these nanoplasmonic hot carriers can be very useful. So where does this ability of the metallic nanoparticles come from? And that has a lot to do with this concept of a localized surface plasma. So a localized surface plasma is a collective oscillations of all the conduction electrons inside the nanoparticle and it is responsible for the very large absorption cross sections that we find in metallic nanoparticles when the frequency of the light is resonant with this natural oscillation frequency of the electrons and you get a big peak in the absorption spectrum and very large light absorption. But what happens much like in a pendulum that sort of slowly loses energy due to various damping mechanisms is that also this collective oscillations of all the electrons is a damped oscillation and what is happening is that the energy is converted from the collective motion of the electrons into single whole pairs by something that is known as the land-out damping mechanism and we can visualize it in the following way. So here we see sort of the electrons are sort of pushed down by the applied electric field of the light and that creates an internal field and this internal field in terms of gives rise to excitations of electron whole pairs which then constitute the stamping channel and just as sort of a concrete experimental example. So here is a work from from the Halus group at Rice University who demonstrated that they can use these hot carriers to dissociate hydrogen on a gold nanoparticle. So here is the gold nanoparticle and what's happening they claim is that the hydrogen molecule adsorbs to the surface and then hot electrons tunnel or hop onto the hydrogen and that then gives rise to the dissociation and this is a chemical reaction that is very difficult to induce by other means. Okay, so this is sort of the experimental motivation. Now of course what I would like to do is develop a way to model these kind of hot carrier generation processes. So how do we go about doing that? So the first thing we do is we map this very complicated problem of interacting electrons onto a problem of non-interacting electrons moving in an effective potential which of course is very familiar to all of you but this effective potential is slightly different from what you're used to. So of course there will be a potential arising from the illumination. This is just the electric field from the light which polarizes the electrons in the nanoparticle and this polarization just rise to restoring force arising from electron-electron interactions and so this gives them rise to an induced electric field inside the material and we can calculate the total potential arising from these two contributions using electrodynamics and here for example for the special case of a spherical nanoparticle one can solve the Maxwell equations within the so-called quasi-static approximation analytically and gets a solution for the potential which is shown here which involves the dielectric function of the bulk material which we for simplicity just take from experiment. Okay so once we have the effective potential in which the electrons move we can then go ahead and calculate the rate at which hot carriers are generated simply by evaluating Fermi's golden rule which is shown here so here we calculate the rate of electrons with energy E that are generated by photons of frequency omega and this has all the usual ingredients there's a matrix element squared of the effective potential an energy conserving delta function some occupancy factors and there's some delta function which basically tests if the electron that is generated has the energy that we're interested in so fairly standard textbook stuff. Now to evaluate this expression all we need of course are wave function and energies of electronic states in a nanoparticle and to get those of course what we need to do is do some quantum mechanics and solve the Schrodinger equation which is shown up here which means we have to diagonalize a Hamiltonian which typically scales like the third power of the linear dimension of the Hamiltonian but the problem that we're running into very quickly is that the linear extension of the Hamiltonian the size of the Hamiltonian increases very rapidly with the size of the nanoparticle so if you do you know standard atomistic approaches like ab initio density functional theory you can get to nanoparticles with maybe a few thousand atoms maybe ten thousand atoms but you know experimentally relevant nanoparticles in this field of nanoplasmonics typically contain millions of atoms so there's a big gap between what we can simulate and what's being what's being relevant to experimentalists and this is why many researchers in this field actually use non-atomistic approaches so gelium or spherical well models which you can solve for much larger nanoparticles but these come of course with a lot of problems you don't really have material specific band structures no d bands you can't really describe the different facets that that the nanoparticle can have so so very a lot of limitations so there's a problem how can we bridge this gap between you know and model the electronic structure of large metallic nanoparticles and the way we we tackle this problem is with a set of methods which are which are known as a spectral method and I'll try to explain briefly what those are so we go back to to Fermi's golden rule which I'm just you know copied here exactly what I showed you a couple slides ago and we rewrite it a little bit so what we do is we insert two delta functions and we also add two integrals so we haven't done anything so nothing's changed but now we can define this function phi here which is sort of a sum over all the transitions some matrix elements and some delta functions and this function phi contains all the information about the electronic structure of the nanoparticle the rest is just delta functions and occupancy factors now phi we can now expand in terms of a series of chevy chev polinomials so it will look like this so there's two two energy arguments so we'll get sort of two chevy chev polina products of two chevy chev polinomials and there'll be sort of some coefficients mu mn which will be frequency dependent and it turns out that we can write these coefficients in the following way as a trace of four operators two of these operators are chevy chev polinomials of the Hamiltonian and the other two operators are the effective potentials so this is what we need to evaluate and to do that we use a fairly well known trick where we approximate the trace by the expectation value of a random vector which becomes more and more accurate as the nanoparticle gets bigger and bigger all right so we need to evaluate this expectation value of these four operators between a random vector how can how can this be done so to do this we basically exploit the recursion relation of the chevy chev polinomials and we define this vector vn which is the random vector acted upon by the potential and the chevy chev polinomial of the Hamiltonian and if we have vn then the coefficient that we want to calculate is just the overlap of vn and vm and so here is basically how we calculate these vectors and this is just using the recurrence recursion relation of the chevy chev Hamiltonians so what we need to do then to generate these coefficients is basically to act repeatedly on the random vector with the Hamiltonian and this is very efficient if the Hamiltonian is sparse so what we do then is to use a tight binding with hopping integrals fitted to ab initio band structures um and we use a model where we have nine orbitals per atom so for the case if we want to model a silver nanoparticle it'll be five four d orbitals one five s and the three five p orbitals and that will give us a relatively sparse representation and this then allows us to do nano to model hot carrier generation rates and nanoparticles containing millions of atoms so let me show you some results that we can obtain with this method the simplest kind of system that we can look at are spherical nanoparticles so here we're looking at spherical gold nanoparticles and look at the size dependence of the hot carrier generation rates so here on the x-axis you have the electron energy zero is the Fermi level the blue curves are the the the generation rates of the holes and the red ones are the generation rates of the electrons and the different panels are the different diameters of the nanoparticles two four and eight and we're looking at light at the plasma frequency of a gold nanoparticle in vacuum this is the absorption spectrum here and we're looking at the peak and what we can see immediately is that for the smaller nanoparticles which contain a few thousand atoms there's a lot of peaks which arise from quantum size effects so what this tells us is the nanoparticles that we can typically model with ab initio methods suffer quite severely from these finite size effects and only if we go to bigger systems containing about 10 000 atoms or more do these you know peaky distributions merge into something relatively smooth how do we understand these more smooth distributions for the bigger nanoparticles uh for that we quickly need to remind ourselves of the band structure of gold which has sort of a set of uh bands with sp characters which are dispersive and cross the Fermi level and there's another set of less dispersive d-bands which start about two ed below the Fermi level so with this in mind we can now and try to understand these hot carrier generation curves so there's one set of peaks which are sort of indicated by these green arrows here which arise from interband transitions which are transitions from a d-band to an sp band and and you can see that these interband transitions generate very energetic holes but the electrons are very close to the Fermi level which means they're not very energetic but there's another set of peaks which are indicated by these orange arrows and these arise from what's called what's known as intra band transitions so these are transitions starting in the sp band and ending up in the sp band and these transitions are forbidden in the bulk but in a nanoparticle because you have a surface that breaks translational invariance they are allowed and they give rise to energetic electrons but relatively un energetic un energetic holes we can also look at the frequency dependence so here we're just flexing our muscle a little bit and look at a nanoparticle that now contains more than a million atoms and we can basically see as we have more energy available and higher frequency photons we can excite sort of a broader range of hot electrons and hot holes we can also look at other materials so here we're looking at a silver a nanoparticle and because the d-bands and silver are further from the Fermi level than a goal you can see that the peak from the interband transitions is as far away from the Fermi level but otherwise it's it's quite similar okay so far I have told you about spherical nanoparticles but one of the sort of cool thing about the nanoscale is that you can make nanoparticles in many different shapes so here I'm showing you some experimental images from my collaborator Emiliano Cortes in Munich where he's prepared nanocubes of gold rhombic dotted cathedra and octahedra of gold and what is interesting is that these different shapes also expose different facets of the so you can see that the nanocubes expose a 200 facet the rhombic dotted cathedra expose a 110 facet and the octahedra expose a 111 facet so there's a close connection between nanoparticle shape and the exposed facet and then what they did is they use these nanoparticles to reduce carbon dioxide electrocatalytically so here's the experimental setup it's quite complicated but we don't need to understand all the ins and outs so what they do is they feed some co2 into the chamber this is our working electrode where the gold nanoparticles are located and then they basically convert the co2 with some electrons into co and then the co is sort of analyzed in a gas chromatograph and everything is connected essentially to a battery and they can do these experiment with a lamp on or in the dark so first let's look at what happens in the dark so on the x-axis here is the applied potential and on the y-axis is essentially the efficiency of co2 conversion and what they see is that the best conversion rate is for the rhombic dotted cathedra while it's somewhat lower for the cubes and the octahedra and this is consistent with what's known both from experiments and and dft calculations that the smallest activation energy for co2 reduction is on the 110 surface okay but this is in the dark so now let's see what happens when they turn on the light and what they see are these red curves and basically you always see an enhancement but this enhancement is much much stronger for the cubes and the octahedra and only relatively little for the rhombic dotted cathedra so this is something that we wanted to understand and what we did is we carried out some calculation where we created some models of cubes octahedra and the rhombic dotted cathedra each containing about 200 000 atoms now of course we can't solve the Maxwell equations analytically anymore as we could for the spherical nanoparticles so we use the finite element method as implemented in the commsol package and then we calculate the hot carrier generation rates for these different shapes and this is what we get yes so just by looking at these hot carrier generation rates it's very obvious that there's large generation rates for the cubes and the octahedra and significantly smaller generation rates for the dotted cathedra so this is consistent with the experimental findings and when we integrate these curves and look at the total number of hot electrons that are generated in these different systems again we see similar and large excitation rates for the octahedra and the cubes and much smaller generation rates in the rhombic dotted cathedra so this is basically consistent with experiments and if you want to understand where this difference is coming from this is essentially we're still working on sort of figuring out in detail but a big part of the story is the electric field enhancement that you get in the different shapes so here is our plots of the electric field enhancement in the different systems so each graph is a cut through a different slice of these cubes but the bottom line is you see a lot of red which corresponds to high electric fields for the for the nano cubes and also the dotted cathedra but much less red for the rhombic dotted cathedra so the electric field enhancement is much larger for the top and the bottom row which then translates into higher electron hot electron generation rates the last part of the story that I want to tell is to look at more complex more complicated architectures at the nano scale so beyond just looking at different shapes you can play even more complex games and try to create different nano architectures by combining two different materials in particular one idea is to combine a plosmonic material like gold with a good catalyst like palladium and look and look at these systems for the conversion of formic acid into hydrogen in particular these guys in munich looked at four different architectures two of them are core shell nano particles where the gold is in the middle and it's surrounded by a thin shell of the catalyst and either it's the pure catalyst or an alloy of the of golden palladium or the second class of systems are these so-called satellite systems where they have a big gold nanoparticle that is decorated by little nanoparticles of the catalyst or in fact little little nanoparticles which themselves are core shell nanoparticles and then they play the same type of game and look at the enhancement of the chemical activity in the light and they see the biggest enhancement for the satellite systems and much smaller enhancement for the core shell nanoparticle so again this is something that we wanted to study and so we we looked at these four different systems here just a plain palladium nanosphere, a gold palladium core shell nanoparticle, a satellite system and then a satellite where the small nanoparticle is itself a core shell system and we modeled these again we calculated the quasi-static potential using the finite element method for the full system consisting of both the palladium and the gold part but then for the hot carrier generation part we only evaluated the hot carriers that are generated in the palladium and this is our result so it's very obvious that the largest generation rates are obtained for the two satellite systems so the biggest generation rate is where the satellite is itself a core shell nanoparticle the second one is the simple satellite systems and the pure palladium nanoparticle and the core shell are down there so much much smaller and again this is at least this trend is consistent with what they see for the experimental enhancements when they turn on the light and again we can ask ourselves where are these enhancements coming from and again a large part of the story is electric field enhancements because you get very large electric fields when you have small gaps so here you have in the in one satellite you have a small gap between the the palladium nanoparticle and the gold nanoparticle and for this other system you could say that the palladium is sort of in a gap between two sort of gold antennas which leads to an even larger electric field enhancement which again then translates into high hot carrier generation rates all right so this was all I wanted to say so I've shown you a new atomistic approach that allows us to look at hot carrier generation in large in large metallic nanoparticles and I applied this method to three different systems the first one were spherical nanoparticles of gold and silver where we looked at the competition of interband and intraband transitions as function of the nanoparticle size then we looked at the effect of the shape of gold nanoparticle on carbon dioxide reduction and finally at hot carrier generation in these gold palladium nano architectures for hydrogen production finally I want to acknowledge the team that's done the work most of it is done by Hanwen Jin who is an excellent PhD student and imperial and I also want to thank you for your attention thank you thank you very much Johannes for this very interesting talk I'm sure there are questions hi Johannes thanks for the nice talk I have two questions in fact first one is that with your methods you don't really see the plasmon right so in the sense that you see single particle excitations you don't see the many body excitation that is associated with the plasmonic effects and the second question is when you have the satellite that is a core shell structure by itself is this stable so is a so you you already as that your platinum palladium is covering all the gold structure is this through the descales or do you you have a separation of something like Janos particles that are you know how is the coverage in this case okay let me answer your second question first I mean these are all system these are all basically motivated by the experiments right so so we haven't studied so we were assuming that they're stable because the experimentalist tell us just as a word of sort of so what's actually happening in the real world is that these nanoparticles are covered by ligands and so these ligands are very important in stabilizing the nanoparticles but I mean thermodynamic stability is a problem so for example the experimentalist actually wanted one set out to make alloy satellites like they did the core shell satellites but what ended up happening is that the electron that the satellite nanoparticles ended up being core shell type so it's a complicated question that that we're not that we're not answering to answer your to go into your first question you're right that we evaluate Fermi's golden rule which doesn't capture electron electron interactions but the perturbation that we use is from a solution of Maxwell's equation and Maxwell's equation does capture the plasmon peak so in that sense we do have the electric field of the plasmon as input into our Fermi's golden rule so in that sense we do capture the plasmon if you know what I mean thank you any other question hi the chemical reaction takes place on the surface so whereas you're computing the carry generation in all your object uh what are we diffusion so so is this a realistic uh thing so should you consider that only part of electron generated participate to the chemical chemistry at the surface uh that's a really good question um so at this point our method gives us the full hot carrier generation rate and doesn't give us spatial resolution um the thing that I do know is that um intra band transitions are enabled by the surface so they only happen at the surface inter band transitions happen everywhere so we know that we already know that intra band transition electrons are rising from intra band transitions must be at the surface but of course you raise a very very good point and that is the point of relaxation and diffusion and all of these important effects which uh which are which are not included this is just hot carrier excitation and there's a lot of discussion about how quickly relaxation happens and you know do they relax before they can participate in chemical reactions all of that all of that isn't isn't included yet but for future work definitely anything else I think so my question is about the shape dependent um so um does it mean does it mean that the field enhancement depends basically on how sharp the corners are of the the the more roundish the shape the less enhancement you have hey exactly in a nutshell that's okay if you if you have like a lot of people are interested in sort of nano starts very spiky things and then you have lots of lots of people okay I think we have to move on again thank you very much for this talk and uh so a previous session that was on time dependent phenomena to another one on Harvard U treatment in these materials simulations and so we start with the talk this session will bridge over the over the coffee break so the first talk will be now and it is by young woo son from the korean institute of advanced studies and he was going to tell us of efficient ab initio methods to extend for extended habits interactions okay uh first of all I thank organizers for giving me a chance to present uh my groups their recent uh efforts to implement it uh extended how about the interactions in the phantom espresso so uh this is my post up then who uh contributed this project so it's doctor sound need this to remove back mood to the samsung and uh dr will young and other other post up here okay so I don't need the introduction here for the disc community because everybody knows that you know it's uh actually lda or pve doesn't uh uh kind of uh designed to give a uh uh quasi particle energy gap even though if you practically people many people computed uh gap for the disc uh semi local local local approximation for the exchange correlation that for the uh prototypical covalent material or zinc oxide or two-dimensional multidisciplinary or even crepe that uh all key uh group uh quasi particle uh all gap or its group velocity is uh is not uh agree where we uh do not agree where we the experimental barrier and moreover sometimes it's very qualitatively not good in some sense that indium arsenide actually if you computed the fd gga it's a topological insulator but it's just a typical normal insulator if you compute it uh including the correlation effect very well also put that cobalt oxide you need the u to compute the energy gap and moreover for some complicated systems such as molecular junction if you use uh land power formula or non-equivalent green function technique if you do not include the cyber interaction correction that actually the lda current you know almost uh uh kind of uh if you you don't if you should not have a current in some sense but you have a lots of current here so kind of qualitative error so uh there are many uh kind of uh apples to overcome that in the Hamiltonian uh level so for example uh Steve already introduced that this kind of uh diagrammatic approaches of jg double approximation and the local self-intention error correction through the u including the u or hybrid positional and dynamic mean field theory and so and so forth so there's a lots of effort so uh the one thing i want to address in this talk is that all these things are very good but for example if you want to do a many calculation in a very fast uh then for example high throughput walks or database driven research openly this kind of uh accurate computational method is quite expensive and very hard to do that because of the a lot of resources you need more over for example the hybrid function or mvj lda uh functional method actually has some intrinsic errors when there is kind of uh uh some specific system that was not uh designed well for the application of this function error and also the u value actually uh sometimes people use an empirical uh correction but you know if you do a lot of uh database or large uh system actually you need some way to calculate it uh u value right so this is a topic so how to implement it local and non-local self interaction and as correction sorry self interaction error correction without any impure season with very fast calculation uh simultaneously achieving the kind of uh accuracy comparable to the gw okay so uh this is how about Hamiltonian then this is a do that a good form of the DFTU formulation then this is the tensed matrices projected on the some localized orbital here is the i th atom is m m prime so to compute the the some empirical values and also linear response theory developed by this uh uh koko chiyon and zero curly uh zero curly long time ago and also and the momentum space uh recently uh uh team rope and company uh developed the dense function perturbation way is a momentum space formalism to compute the u and also there is another way is that the kind of evaluating the u value uh from the unrestricted heart repop formalism so actually we focus on the the last one is developed by recently in this agabito and the other co-workers because uh as i mentioned before the original purpose of this work is to compute it uh very uh many system with very fast time so we want to compute the u value within a self-consistent loop we don't want to do the other another additional computational routine so we think that this is good so let me introduce a little bit about that so uh i think actually original idea was developed by mosey and carter uh uh in 2007 this piv paper that they look at the molecular system that actually the u and j or hobart Hamiltonian actually can be think of what kind of a projected pairwise heart repop interaction uh computed by uh some other functionality a functional so uh hcv and zero functional is nothing but an extension of this molecular system ideas to the block wave function so so this is heart repop representation so here this is just the bare electron repulsion integral so this is just a bare interruption for the given uh one atoms for i here then m is a different orbital so so inter-orbital uh prolonged repulsion representation and this p is a key idea here so when you uh projected your wave function is a density matrix uh to the some submanifold of this m and n prime orbiters you scale this with this uh value of n what is n this n is uh just the weight of the total blow wave function uh so projected total blow wave function to the the interested molecular orbital so when this is becomes to be zero that the expression becomes to be uh lda or pbe when it becomes to be one it's just a heart repop so if you do some calculation that it should have some value it depends on your system and also this is also position dependent because it's the index of the eye okay so this is the renormalized occupancies control this self-energy or u-value of system so if you equate of this expression to the uh how about the Hamiltonian that actually you end up with some kind of uh hybrid type expression so do you have a better column interaction with the weight here for the u and j okay this is nice so uh this but this is still dft plus u formalism so you can computed within a self-consistent rule uh with uh unrestricted heart attack uh formalism so this even though this is very nice when you calculate the u within your self-consistent loops this still has a lot of problem that dft plus u has for example so the you know semiconductor is it you cannot describe very well and also the many metal oxide compound is also over localization so electron get to the uh strongly localized of the orbiters and also if you have strong PD hybridization that uh it's very hard to compute it and also there should be no local correlation you cannot deal with it so uh if you decompose a full-length interaction so this is very general expression then uh let's focus on the single orbiter uh problem here so we drop the all orbital index so just the site index and ikr then you know everything is the same then it goes to the Harvard interaction then actually the this is the uh hierarchy of size then then if ik is equal and jr is equal both both are not equal to together then this is uh inter-side of the interaction then the next one is correlated hoping through the bond charge then the fourth one is peromagneticism right so this is a decomposition of colloid interaction so uh it's uh almost 10 years ago uh Coco Chihon is developed the you know this kind of uh including inter-side of an interaction within a DFT formalism so everything is ready so this is DFT plus U formalism then you include the B term actually uh you end up with this then actually this is uh just uh like uh you then fully localized limit consideration that this is just a double counting for the DFT so we just uh deleted that this is final expression for the DFT plus U plus V formalism in a density representation so you can immediately notice that this is very interesting because as already very well known that this U uh functional actually force the the integer feeling for the specific localized orbital for the eye right however this inter-side orbital actually pushed away from the electron from localized side actually to the bond side so this is controlling the bond interaction so this is actually competing as we expected right so from this formalism okay so we now combine those two ideas together so how you can do that so inter-side of our uh interaction as I showed before this is already written in the Coco Chihon the paper then this uh ij means that uh this is the we just consider the pair of atom i and j located different position within a given cutoff so this is only parameters in our formalism so you can set up the how much pairs you do you need so and this is nothing but uh kind of a dense matrix so you we use the reading also normalized projector uh yeah you can use anything you want then we write down the ACV and zero right expression for the inter-side interaction so because of uh kind of double counting is that one port and here is the generalized projector for the display interaction looks like that then this is just a cool long interaction to to accelerate the computing time we just using the three gaussian feeding for the given projectors so it's just almost analytical so it's very quick if you have a given position and orbiters and this one is the controlling this is a decisive one so this is a project generalized pairwise dense matrices then this n value here looks like that so this n is our uh hypothesis or unjust so this renormalized occupation actually controlled the inter-side interaction we consider that there is many way but there is no justification this is my unjust so we consider that uh inter-side current interaction uh will be controlled by the charges located both sides as well as charges located in between them so we're just adding up the projected density for the located for the ice electron and jet electron okay so if this goes to the zero then all calculation goes to the lda or pbe original exchange correlation functional if it goes to one it's called the the hot reply okay then using this all this expression that equating everything uh you end up with a kind of a pseudo hybrid functional for the inter-side current interaction so we implemented this one is quantum express of seven zero version and in our home institution said n looks very simple actually if you if you have a dense matrix and projected pairwise n value then you can compute it in the within your self consistent loops so actually the computational time compared with the pbe it doesn't increase much it's it's the same because every density matrix is solved within your self consistent loops right so so you kind of converged this matrix and these function are simultaneously in your self consistent loop then all calculations have been done uh within a very short time so this is the result so we computed this 20 23 different three-dimensional solid from a simple cobalt semiconductor and two five three five and two two six and zinc compound ionic compound some oxide so this is theory and experiment uh curve so this is uh line then this is pbe and this is hsc and this is gw so gw is a little bit overshoot and hsc is a little bit under the line and pbe is quite below the line and this is our one so you compared everything together then actually we are on a very satisfactory in the sense that uh so for example this is uh uh little fluoride so gw is here and the hsc and this is pbe and our one is here and then magnation upside no method uh algorithmic experiment so magnation upside is very notorious very difficult then any other things are like that okay so this is a projector you need a projector so we use a projector uh inside in the pseudo potential so we just extracted the ready and also normalize uh project uh orbiters within the pseudo potential so there is a kind of dependency on pseudo potential we tested two databases not so much but there are dependencies then uh band gap only very well and the important thing is that it's very fast okay so this is some example so the silicon is about the 116 percent and zinc oxide is almost already very well as I mentioned the lithium fluoride is kind of 100 percent and moreover graphene group velocity is almost the same as gw or experiment and moreover this is important this is a low dimensional material for example it's a black phosphorus so black phosphorus as you see that this is a phosphorine has corrugated uh structure so there are strong mixing between s and p orbital here then and the low dimension is two dimension this is number of layer and this is computed energy gap and gga is quite uh off from the experiment so this is a quasi particle gap for the single layer then and as you see that this is hybrid function hsc is 06 and this is dft plus u on a p orbital okay so this is ac ben 0 and this yellow triangle is mb j lda so as you can see that all those are actually on top of the kind of exotonic gap so this is bsc calculation then uh gw 0 calculation is this and gw 0 calculation is this so the hour one is blue or dark is on just on top of the gw 0 calculation so i'm sorry so so it's okay so it's a low dimensional system actually the gw calculation you need a very high cutoff uh there is now there's some nice technique developed by steve's world accelerated calculation but essentially our calculation computation time is the same as the pbe and moreover then is there well known uh well pointed out the manish and steve's paper in prl in the 10 years ago that hybrid functioner is not good yeah not good for this kind of reconstructed system then this silicon one on one two by one construction that bulk semiconducting gap and there is a one-dimensional chain this is also semiconductor so this is uh very old r-press and inverse r-press data and this line is our calculation so uh our calculation also agree very well is gw's calculation because in our calculation intersite her body interaction and u interaction actually changes depending on the position because it reflects the local screening through the number variation of the projected density p and the magnet moment is also good okay so okay uh for silicon actually our one is the 100 times faster than hsc so and also you don't need the resources you can do it in the laptop then uh any other things yeah because this is the function error the single particle function error you can also do the uh kind of opponent calculation as steve introduced very well then his achievement is very nice one is the gw df pt so actually we think okay this one is uh recently people consider the correlation effect on the ponon for example this is nickel oxide lda you know optical ponon is this dot is the experiment and this pure the circle is computed by lda it's quite different than the sabra supplement cotelia show that if you include the dmft calculation dw is very well and also steve introduced that this chart is for for national system for example barium bismuth oxide you need the gw so as i mentioned before it's very nice but it needs a lot of resources so uh our one is just the hover the interaction so it's the onsite and intersite so you're just using the chain rule then you can compute it the force directly uh fortunately the next speaker and team look developed the prulae forces for this uh uh density variation so we're just using it and the the other one is very straightforward to compute so this is the result we first tested uh silicon uh diamond and germanium you can see that this is uh uh what's that let this constant variation with respect to uh deviation with respect to the experiment so this is percent you can see that lda is tends to be smaller than experiment and pbe is expansion and pbe sore is okay and hsc and this and our one is this so lda pbe is era is about one one to two percent and pbe sore and hsc and our one is plus minus point five for the here then bulk modulus it's more dramatic as you can see that uh all those things are very bad that including pbe sore then hsc and ours is about five percent and this is optical pendant then you can see that the uh this is error with respect to the experiment then this is a functional for the exchange correlation and this is a symmetric point of optical pendant that it's okay but silicon is our one is plus minus one point one point five and moreover actually this is much better this is greenizing parameters then uh this line is our one and dot is the experiment so the mode dependent greenizing parameters our calculation is very nice so a lot others so nickel oxide then you can see that pbe is uh this dot is the experiment so usually as i mentioned before the oxide if you include the dft plus u is that considered determined u typically over localized so the optical uh frequency is very hard compared to hardened compared with the experiment so you can see that this one's upshifted then this uh intersite interaction is a counter balancing of that that then you can see that uh our calculation is uh very very well with the experiment it's very comparable to actually more than the dft and this is baron viscous oxide system because of time limitation uh this is summary so this study the experiment for the dope system and uh blue one is pbe and red one is our calculation the key critical pendant mode is m and r as treating as treating mode so as a function of the doping it becomes to be charged this way to the superconducting transition at the doping about 40 percent of the potassium here so this line this is doping of potassium here and this is a summary of frequency of those two poor critical pendant mode so the negative means that it's a cdw state and becomes to be hardened because it becomes a superconductor so if you compute the gga then all those phonons still are negative means that still and cdw phase then if you compute it including plus u for the all orbiters necessarily that it predicts that the there should be cdw to superconductor transition around 30 percent and this is our calculation if you're including the b that our calculations exactly match the experimental observation okay so let me conclude we developed and implemented the extended how about functional formalism in the quantum espresso and this can be done in the within a self-considered loop so the time consuming the calculation is exactly almost the same not exactly same as semi local approximation for the exchange correlation then everything you can do with the dft plus u or semi local approximation actually you can do with these formalism thank you thank you very much that was really impressive results you have here any questions okay whatever uh yeah thank you very much uh i actually have two questions uh the first question is about your double counting correction uh yeah that as you know as a practitioner it's a very tricky thing i think you use the fully localized limit uh does it work in every case actually we do not test it very well about that uh approximation we just using it then the tested every other's then there are some errors as you can see that there i don't know whether error comes from that bill then approximation or the other there are so many other answers there so which one contributed error we don't test it rigorously but as you you crack this is not a fully localized limit right surely so we need to consider it more okay and the second question is do you understand what is so uh you know really particular about magnesium oxide that nothing works is the nature of bonding or i don't know i don't know okay i don't know we just quickly surveyed every us only 23 is very quickly so we do not focus everything tells everything thank you very much for the very very interesting talk um and since the new share two questions i will also take two the second one will be very short um but the first one is maybe a bit more extensive and also maybe to the gw experts in the audience because i'm confused about one point um i understand that conventional methods to calculate u and also u and v actually uh have two ingredients one is coming essentially from matrix elements overlaps of different orbitals and representations and so on and that's important but there's a second one which is essentially assessing the screening and uh in other methods this is very explicit for example in the constrained random phase approximation techniques you can even choose the channels that you would like to screen but also for example in the methods that matthew koko choney put up that you cited you have this linear response actually essentially determining the screening the response of the system so now in in your technique i saw the matrix element and all the overlaps but i didn't understand how you include screening so i kind of for myself figured out that your scope is a bit different that you essentially are aiming to parameterize the heartary fork Hamiltonian which is a different thing than the u of lda plus u but then on the other hand your results should essentially reproduce the heartary fork which doesn't seem to be happening so i'm a bit puzzled about this yes and then the the second question is very short it's just a technical one when you talk about the nickel oxide and you're referring to the v do you mean the v between two nickel or the v between nickel and oxygen so is it's a ligand the second is very it's straight nickel and oxygen okay yes here v is the nickel and oxygen and and the first one is also is thank you very much we have very much thought about it very long time actually so this is a matrix element impact is a straightforward in this formalism the screening that actually as i show you before that we constructed kind of a function error form for the v it involves the kind of projected electron for the given uh uh atoms participating the intersects prolong interaction that we waited them proportional to the charge among within the unicellar that how much charge proportion participate in the bonding so we waited them with some proportion that's a kind of a kind of free factor for the heart effect so that's the reason why we go we do not go back to the heart effect because we always has kind of waiting factor with respect to the whole charges so it kind of is sensing in some sense of screening because every in the whole charge in within the unicellar how much charge for participating the bonding okay so that's uh that's still we do not know the answer but somehow it's very remarkably reproduced the gw result i actually frankly we still do not know the exact thing but the unjust it's just resuming of the all charges participating that uh procedure yeah that's all we know because this is unjust we just write down okay this may be better okay so so result looks like that so frankly speaking i don't know yeah yeah okay thank you is there any other quick question riko thanks for the nice talk um you compare your results with uh band structure calculation and did you also try optical response um uh yeah yeah that's a very nice question so so but you know the optical you need a uh electron-horror pair interactions as a better circuit equation as Steve already demonstrated so our contribution maybe you can bypass the gw but all the other coolant matrix elements you need to compute the electron-horror pair interactions so we maybe improved marginally the computational speed but we tested it i don't have it sorry because i converted it to the pdf file but we tested it and put silicon silicon and uh black phosphorus then our calculation is quite agree very well with gw better circuit equation okay thank you very much and uh well there's a quick question by francesco last time because i mean indeed the the critical things is this effective screening hc hc also has a with a very mixing parameter somehow a screen that is somehow hidden in the calculation a critical case to prove these is an heterostructure between the material with high electric constant the low electric constant and the binary alignment between the two hc these fail totally and gw taking account so probably this is the best test so you have to take an intelligent with a low yeah semi-conductor i get semi-conductor and see if you get the bad alignment of gw that is a probably okay thank you yeah thank you very nice comment actually we will try that's a list uh yeah that's a list okay thank you thank you very much okay thanks a lot we thank the speakers of this morning session again and now i remind you of course i remind you there is coffee but uh that needs no reminding but there is the the photograph for the workshop happening now and otherwise please come back here by 20 past the hour please the photograph will happen here so if you can stay please for the photograph so please all come down we will the photographer will will stay there we will be here down so okay here he is yeah in front and in the back so he will be above so he will see both lines so please so please form a further line in front those on the on the tails please come to the center we are too too broad so i promise this is the most difficult part of the workshop everything else thank you so coffee is in the entrance hall so and please for the speakers please come for the speaker of the next session please come down so we can test the the presentation Sa, sa, sa, test, test, test, sa, sa, test, test, test, sa, ok, I feel it well like this, I don't feel it at all, I feel it quite present, ok, thank you guys, wait up, test, test, test, hello, hello, hello, hello, hello, hello, hello, hello, hello, hello, hello, hello, hello, hello, ok maybe we can get started with the second part of the morning This is Nicola Marzari from EPFL in Lausanne and the Paul Scherer Institute. So I'll introduce the speaker of the second part of the previous session. So we have Yuri Timrov from EPFL on actual electronic properties and the intercalation voltages of lithium ion battery cathode materials from extended Hubbard functional. Yuri Flores, yours I give you a sign five minutes before. Thank you, Nicola, for the introduction. Good morning to everyone. So first of all, I would like to thank the organizers for having given me the opportunity to present my work today. And it's really my great pleasure and honor to present my work here. OK, so let's start with the self-interaction error or the localization error in approximate DFT. So let's consider the simplest case, the dissociation of the H2 plus molecule. So here on this figure, I show on the top the charge density distribution of an electron in green for the H2 plus molecule. So the interesting thing happens when we are actually pulling apart two hydrogen ions. So in approximate DFT, what you find is that the electronic charge density is split equally between two ions. So we have half an electron on the left and half of an electron on the right. And this is the only solution in DFT. But then if you solve the Schrodinger equation exactly for this problem, you will actually realize that there are an infinite number of solutions. One of the solutions is that you have one electron on the left and zero on the right. Or you have one electron on the right and zero on the left. So this is the so-called, and these solutions are actually orthogonal to each other and degenerate. So this is the so-called left-right degeneracy. And actually, linear combination of these two orthogonal solutions is also a good solution. So why in approximate DFT, we obtain only one solution where you have half an electron on the left and half on the right? And this is exactly because of so-called self-interaction errors. So and there is a link actually between this problem and the so-called spurious quadratic energy change when we are adding or removing a fraction of an electron to the system. So in this figure, I show the energy error as a function of the fractional charge for the H atom. So if we use Hartree-Fock, which is free from self-interaction errors, we will see that the error is 0. It's because of the linearity of the energy, because of the so-called piecewise linearity of the total energy with respect to the number of electrons. If instead we use approximate DFT with LDA or even hybrid functional B3D, we will see that actually energy changes in a quadratic fashion and so there is a deviation from the exact solution due to the localization error or self-interaction error. So electron is actually spread around and that's why we have half an electron on the left and half on the right. But actually if we come back to our problem on the left and actually we can, in approximate DFT, we can impose the piecewise linearity and by doing so we can restore the left, right degeneracy. And actually what we will obtain is that the energy cost of removing of an electron from the left ion is equal to the energy that we are gaining when we are putting the same fraction of charge on the right. And this allows us to restore the piecewise linearity. And so this problem of the H2 plus is actually of self-interactions in 2 plus is actually found also in the mixed valence materials. So if we go to the next slide, so if we consider this casted material, so the correct solution is actually that we have two types of irons, one in the oxidation state 2 plus and another in the oxidation state 3 plus. But if we use approximate DFT with LDA or GA functionals, what we will find is actually the average oxidation state of 2.5 plus. And this is exactly due to self-interaction errors of approximate DFT. So what happens is that the iron 3D electrons are delocalized and they're spread around, so you have the equal number of charge on all iron irons. And that's why we have 2.5 plus oxidation state. And we can make again a link with the energetics. So we have the spurious quadratic energy change when we are adding or removing a fraction of an electron to iron. So in this figure, we see the exact solution that must be piecewise linear is a function of the number of electrons. But when we use approximate DFT, we have some quadratic-like behavior which is wrong. Okay, now let's talk about DFT plus U because it's one of the methods to cure self-interaction errors. So DFT plus U was introduced in the early 90s by Anisimov and coworkers. And then later on Liechtenstein, Duderov and others introduced other formulations of DFT plus U. So the idea was just to take DFT on one hand, take Hubbard model on the other hand. So since Hubbard model was developed to work with strongly correlated materials, so people initially thought that actually DFT plus U is the method to deal with strong correlations. But later, people actually realized that what you actually cure with the plus U correction is not strong correlations but self-interactions like in the H2 plus molecule. So this is the energy expression for in DFT plus U. I want to stress that this is heuristic. There is no theorem or proof of this. And this Hubbard functional is actually not variational with respect to Hubbard U. So far there is no any theorem or proof. And in the previous talk, already Jung will explain about this functional. I don't want to spend much detail, but what we have, we have DFT total energy which is augmented with the Hubbard correction. And here N are the so-called occupation matrices which are defined by taking a constraint of a function psi and projecting them on the atom-centered localized functions phi. And F are some Fermi Dirac distributions. This is well-known. And in 2010, as Jung mentioned, Matteo Coccioni and Campo, they introduced an extension of DFT plus U. It's called DFT plus U plus V where we have not only the on-site Hubbard correction which favors integer occupations and that pushes your electron to be more localized, but you have a second correction, the inter-side Hubbard correction which actually favors hybridizations between transition metal and ligands. And so these two terms are actually competing with each other. So it's important to have the balance of the two to have the accurate description of the system. And this is just a picture showing that plus U wants to localize electron on the transition metal atom while plus V actually restores back the hybridization with, let's say, oxygen ions around.  So on the one hand, we have Hubbard parameters, U and V, which are unknown. And on the other hand, we have this localized atom-centered function phi. So it's actually, one can wonder that they are independent objects, but actually it's completely the opposite. They are dependent on each other. So depending on which type of Hubbard projector functions you choose, you will need different values of Hubbard, U and V to get the correct energies. So let's talk more about Hubbard parameters. Already a lot was said in the previous talk, but I would like to summarize after the coffee break. So we don't know Hubbard parameters, so we need somehow to determine them. And there are two strategies. One is to use the semi-empirical values by tuning Hubbard U to reproduce some properties of interest, let's say, band gaps, magnetic moments, you name it. But for this, we really need to have experimental data as a reference. And on the other hand, we have first principles methods like CDFT, CRPA, Hartree-Fogg-based approach like ACBN0 and linear response. So in the previous talk, Yanggu nicely explained about the ACBN0 functional. And the topic of this talk is actually linear response theory. Hubbard parameters are not universal. What does this mean? So when we compute Hubbard parameters using ab initio methods, let's say linear response, we will find that Hubbard parameters are not unique. They depend on many properties. So one is, which Hubbard projectors do we use? So there can be atomic or octagonalized atomic, maximum localized of any functions. These are those localized functions highlighted in yellow. Then the value of Hubbard U depends on the oxidation state of the studized atom, in other words, on the pseudo potential, simply speaking. Also, the Hubbard U depends on the exchange collation function, albeit LDA or GGA. And also on the way you compute them, the self-consistency, there is one short way of computing Hubbard parameters or self-consistent. I will say more about this later in my talk. So how to compute Hubbard parameters within linear response theory? So let's start with the definition of the Hubbard energy. This is the Hubbard correction. For simplicity, I consider only one transition metal, so I don't have the summation of our atoms. And here N is computed by taking a trace of the matrix N, so it's just a number of electrons in the Hubbard manifold. Then we remind ourselves the problem, so the exact total energy must be piecewise linear is a function of the number of electrons in the Hubbard manifold, while approximate DFT gives quadratic behavior, which is what we don't like. So we don't like this curvature, so we simply can impose the condition that the second derivative of the total energy with respect to the number of electrons in the Hubbard manifold is zero. So this way allows us to get rid of the curvature and restore the piecewise linearity. So what we do is simply take the definition of the energy, compute the second derivative, it's a very simple task. And what you will readily obtain is that U is actually the second derivative of the DFT total energy, as simple as that. There is a more rigorous mathematical proof in this paper by Matteo Coccioni and Stefano DiGironcoli, and I would like to stress that there is no theorem for the piecewise linearity of the total energy in the Hubbard manifold, only with respect to the total number of electrons. So it's heuristic. How to use linear response theory in practice? We need to take our concept equation, we modify it a little bit by putting inside some small perturbation, so lambda is the strength of the perturbation and V is the perturbing potential, which is simply the projector on the localized manifold. And then we need to construct supercells and perturb atoms one at a time. Since we're using periodic boundary condition, the perturbed atom will interact with its periodic replicas, so that's why we need to use supercells large enough to get rid of this unphysical interaction between perturbed atom and its replicas. So we solve this modified equation for several values of lambda. This way we can measure the response of the system to the perturbation, which is the change of the occupations, delta N, and we divide it by delta lambda, which is the change in the strength. And this gives us the object which is called response matrix, chi. We take the inverse of this matrix, then we compute the chi not, which is the object analogous to chi, but chi's self-consistent value while chi not is the non-interacting or bare response. Then we take the difference of the two, we obtain a matrix. On the diagonal of that matrix, we obtain on-side-hubbard view corrections, and on the off-side of the diagonal, we obtain the inter-side-hubbard view parameters. So this method works very well. It was applied to many problems. However, there are a number of drawbacks, the computational cost, of course, then possible convergence issues, and it's not always easy to use it in practice, so quite low user friendliness. So we actually asked ourselves, can we have a better or more efficient reformulation of the same theory, but using more effective methods? And actually, we did it several years ago with Matteo Coccioni and Nicola Marzari. So I will show that we can go from supercells to primitive unit cells. So what do we do? We start with our modified quantum equations. I say that this is a small perturbation, which allows us to expand all quantities in Taylor series. Then we cut off those Taylor series at first order, so we keep on the first order quantities. And by doing so, we will actually, we can show that this modified equation will be actually a linearized quantum equation, also known as Stein-Heimer equation. So we can solve this equation, and moreover, we use the fact that the potential in a supercell can be decomposed as a sum of the Q points in the primitive cell. And by doing so, instead of using finite differences in the supercell, we're actually having an analytical formula in the primitive cell, where we need to sum up over Q points, which are different modulations of different monochromatic perturbations. We have a phase factor, and delta Qn are the responses of occupations to different monochromatic Q-modulated perturbations. And then we do the same post-processing step as before to obtain how about the UND parameters. So this is nothing but density functional perturbation theory that was, it is known for three decades. So it was used for phonons by Stefano Baroni, Stefano DeGeroncoli, Andrea Del Corso, and Paolo Giannozzi. So it's computationally much less expensive than using supercells like frozen phonon. It's easier to converge and user-friendly and autonomous. We implemented DFPT for computing how about parameters in quantum espresso, the corresponding code HP, it's public open source distributed with quantum espresso. On the left, I show you the scaling. In black, I show you the old supercell approach with finite differences in red is DFPT with primitive cells. So you will see enormous speed up. This is thanks in particular to symmetry because by using symmetry, we can reduce number of cue points. While in supercells, we can use the same trick. We can't reduce number of atoms. So we gain really a lot due to this. And on the right in the table, I show you the numerical comparison of the old linear response for supercells with DFPT and we see really remarkable agreement. The residual errors are just numerical noise. We can further reduce them. And then I also mentioned about Haber projectors there are really many choices in different electronic structure codes to have different types of Haber projectors. In quantum espresso, we have in particular non-autogonalized atomic orbitals, phi, which are provided with pseudo-potentials. However, disadvantage or drawback of these projectors is that a duplication of Haber view is actually twice in the overlap regions here, which is not wanted. So we can use octogonalized atomic orbitals instead, which is compute overlap matrices, invert them, and we construct these objects using loading octogonalization method. By this way, we get rid of this double counting or double application of Haber corrections in the overlap regions. Another very good option is to use maximally localized linear functions. This also, we're actually working on this, and but for us, the standard and the most accurate is the octogonalized atomic orbitals. And finally, we use the self-called self-consistent procedure when we're computing Haber parameters within DFT plus U plus V. How does it work? We start with initial structure, let's say experimental geometry, or you take it from some database.  With some initial guess of U and V, this could be zero if you don't have any clue, or it can be some good initial guess. Then we do ground state ECF calculation, and on top we compute Haber parameters using DFT. Then we check whether the Haber parameters are converged and if the geometry is converged. If not, we go back and we repeat this cycle until we get to the point where we reach the full self-consistency that is to say that the Haber parameters don't change, the geometry doesn't change, the electronic structure doesn't change. So all is consistent. And what we find in practice that this is the Haber view is a function of this number of iterations or cycles. If we do just one iteration is the one short calculation, we get something like slightly higher than five EV. But if we do this self-consistent cycle, we will find actually that the Haber view changes, in this case to 4.3. So there is a non-negligible change which really highlights that it's important to use this consistency. But I would like to mention that here we need to do structural optimization which requires Haber forces and stresses. So let me mention quickly, Yang Wu already mentioned in his talk previously, but what we do is we use the orthogonalized atomic orbitals and that our goal is to compute Haber forces and stresses. I don't have time to go into detail, but in a nutshell, we simply take the derivative of the Haber corrective energy with respect to atomic displacement style and this all boils down to the derivative of the occupations with respect to atomic displacements and this instead depends on the derivative of the square root of the overlap matrix which is not a trivial object to compute. It's not a function, it's a matrix to the power of minus one-half. And we have shown that it's actually known that one has to solve the Sylvester or it's also called Lyapunov equation. It's a non-trivial task, but actually we managed to find exact solution which can be written in a compact four over here. And we implemented in quantum espresso and benchmark with finite differences here and you see in the last column that the agreement between our analytical formula and finite difference is really good which confirms the accuracy and correctness on the derivation and implementation. So now let's switch to applications. So in my talk, the title you saw, it's all about lithium ion batteries. So let's try and use DFT plus U to lithium ion batteries. We know that our energy demands are growing due to the growing population and we no longer can continue using conventional sources because of pollution and global warming. We urgently need to do something with this. One solution is to use green or renewable sources like hydro, solar, wind. But for this we need storage energy systems like batteries on the large scale. However, the current batteries are great but there are safety issues as you can see on the examples here. So we need to search for newer, more efficient, safer lithium ion batteries. So let's try to use DFT plus U plus V. On the left I show you the lithium ion battery. We have negative electrode which is called anode and on the right we have positive electrode which is called cathode. Here it can be let's say graphite and here there are many options for cathodes. And one can do high throughput to look for good cathodes. And in between anode and cathode you have liquid electrolyte. And during the discharging process you have lithium plus ions going from the left to the right and electrons go in the opposite direction. So what happens at the cathode? So in the fully charged battery we have this compound. It's just an example but we have iron. All irons are in the same oxidation state 3 plus. And when we fully discharge the system we have this compound where we have iron and 2 plus oxidation state. And the interesting thing happens in between where we have the mixed valence compound with iron in 2 plus and 3 plus oxidation state. And I would like to stress that it's really important to have a very accurate method that gives us reliable energetics and electronic structure of these complex materials. And Hubbard functionals is one of the methods that can be used for these problems. We start with the self consistent solution of Hubbard parameters using linear response theory. So this is our simulation cell for this cathode material. We have four transition metal ions in this system. This can be all manganese atoms or all iron or it can be mixture of both. So we compute the Hubbard parameters. So here I report Hubbard values for four types of manganese at concentration X equal to zero, so no lithium. So we report U which are all the same values of Hubbard U and V is in some certain range of values. Yep, thanks. So then if we increase the concentration of lithium in the system we will notice that actually the first three manganese don't change much but the last manganese actually changed abruptly. The Hubbard U value for this manganese changed abruptly. We also computed the Hubbard parameters for the other concentrations and we can also check how Hubbard parameter changes for all transition metal atoms. We did the same type of calculations for the iron or the V, but the bottom line is that the Hubbard parameters are site dependent and they change upon lithiation or dilation. So what people commonly use they use empirical U the global value across all lithium concentrations for all transition metal ions, but actually what we can do and what we actually see that Hubbard U is not global it actually depends on the transition metal ion and it does change upon lithiation or dilation. We computed many properties that I would like to show you the most interesting. So let's consider atomic loading populations. Here I show three panels. The top panel corresponds to DFT and PB Sol. The middle panel hybrid HSC06 and the bottom DFT plus U plus V. On the Y axis I show you the 3D shell occupations of transition metal ions, manganese in this case. And the X axis is the lithium concentration and for each concentration we have four bars and each bar corresponds to four types of manganese. So with concentration of zero we have all manganese in the same oxidation state three plus and at concentration one all of those ions are in oxidation state two plus. When we're adding lithium one by one we see that only one transition metal changes occupations at a time. So we see this very clean and clear digital changes occupations. If you use hybrid functionally also observe the same trend, but if you use DFT and we know that there are self interaction errors we see that all occupations of all atoms change in the same manner because the electronic charge is delocalized and spread around equally on all atoms. So that's why you have, you see that you don't recover these digital changes occupations. We did the same analysis for iron. Again you see that DFT plus U plus V works very well. Instead here hybrid tries to do the good job but it's actually not as accurate as DFT plus U plus V because you don't really see the very clean and clear digital changes occupations. And again DFT fails like in a manganese or living case because of self interactions. We also studied another mixed valence material where we have manganese and iron. Again we can see the same trend that DFT plus U plus V works well. Hybrid also good but not as accurate as DFT plus U plus V while DFT fails. Also I would like to mention that for the concentration from zero to one half is the manganese that is redox active and then from one half to one is actually the iron which is redox active. So the bottom line is that DFT plus U plus V is very accurate to reproduce the digital changes in occupations which are really critical to recover experimentally observed redox plateaus in voltages. We also computed lithium and decalation voltages so all what we need is to use this thermodynamic equation. This is a total energy at lithium concentration X2 minus total energy concentration X1 minus energy of bulk lithium. It's a total energy workshop so all what we need is just total energies. And this is the result. We see that the last bar is the experimental voltage. DFT largely underestimates the voltage. Hybrid and DFT plus U add corrections. They overshoot over correct and only DFT plus U plus V is in a very good agreement with experimental voltages. We also did the same analysis for other cathode materials. We always find that DFT plus U plus V is the most accurate for computing voltages. We also check spin polarized projected density of states at concentration X0. We see that DFT plus U plus V and HSC06, they are very similar while DFT fails. When we start increasing the concentration of lithium, we see again that DFT plus U plus V has very similar trends to hybrid functionals while DFT fails. And also for other concentrations over and over we see the same trends that DFT plus U plus V mimics very nicely hybrid functional. We studied also other families of cathode materials. This is the so-called spin-all cathode materials. On the left we have anti-ferromagnetic insulator. On the right, ferrimagnetic insulator. Both have 56 atoms in the supercell to accommodate these complicated magnetic spin configurations. And the bottom line is that hybrid functionals are expensive, computationally expensive of these kind of systems and less accurate while DFT plus U plus V has a moderate cost. We computed different properties. I would like to show you just voltages. The same trend is in the previous phospholivine cathodes. DFT plus U plus V is in a very good agreement with experimental voltages. I'm coming to conclusions, but before I finish my talk, I would like to mention briefly about computational cost. So when we know U and V, DFT plus U plus V is actually only marginally more expensive than DFT. Computing these parameters using DFT is about 20 times more expensive than DFT, so it's not negligible. U and V from DFT allows us to generate some databases, and we can use those and use machine learning then to predict inexpensively hybrid parameters. So in collaboration with Martin, Urien, and other coworkers, we developed a machine learning model and on the Y axis is the predicted values on the horizontal one. It's the one we compute with DFT, and we see really good agreement. And finally, if you compare the DFT cost of computing hybrid parameters, which is HSE06, you will see in the last column that still the ratio of the timing, still DFT for computing U is cheaper than using hybrid functionals. And another slide, very important, there are some limitations and open questions in all this. So first is that linear response theory for closed shell systems gives very large values of hybrid view parameters, which is, we need to find a solution to this problem. Then U and V are position dependent, so we need to have these derivatives of hybrid parameters. I forgot to mention, but in our case, we neglect these derivatives, but in principle, one has to include them, as Jung will mention in the previous talk. Hybrid functions are not variation with respect to hybrid parameters, no proof of theorem. And DFT plus U plus V is a mean field, a single determinant approach, so no correlations, one has to use multi-determinant methods instead. And finally, the piecewise linearity in the Hubbard manifold is heuristic, there is no proof of theorem. And with this, I would like to conclude my talk. I've shown you that DFT plus U is really robust and accurate. It can be broadly applied to mixed valence functional materials. We compute U and V using linear response theory. And in the case, on the example of lithium ion batteries, I've shown you that the computed properties, electronic, electrochemical, are in very good agreement with experiments. And with this, I would like to thank my collaborators, Nikola Mordzari, Matteo Cococcioni, is also in the audience, Michele Cotilga, Francesca Coulante, our sponsors Marvel SNSF. Of course, thank you for your attention. And finally, I would like to briefly mention about the advanced quantum espresso school that will take place at the end of August this year in Pavia. If you're interested, please stay tuned on the PsiKi mailing list for more information. Thank you. Great. Thank you. Thank you, Yuri, and we are open for questions. If I understand correctly, as was, you know, replied in the earlier talk, the V is actually between the transition metal and the oxygen. Correct. So suppose I'm doing a calculation at the model level, which is, for example, if you take a cuprate, just a one-band Hamiltonian. Okay. Then, of course, you know, the oxygen degrees of freedom are integrated out. Then the, actually, the V term should be included in the effective view you are thinking about. So did you have any attempt of calculating that? And will that, I think that was the question asked by Zilke. So will there be some effective V, which actually, in terms of Hubbard model, that's the V between the transition metals? Okay. So V between transition metals? In our, from my experience, we have those Vs also, but they're actually vanishing. They're very small. So computing, we have them, but they're vanishing. No, no, but the point is, if you really down-fold or integrate out the oxygen degrees of freedom, they will show up in the one-band limit. We haven't done this, but it could be interesting to check. Let me take the microphone on the way. So we actually computed those from CRPA, and we also confirmed that the UPD, the interaction between ligand and D, is actually large. And then the question you're asking is can we actually down-fold or not, right? Other questions? When you use machine learning methods, can you choose the local environment of your atoms? So for example, in the lithium-ion battery you were showing, you see that the parameters depends on how much lithium is around. Can you do this also at the machine learning level, or you have enough data to do this, or you need to implement your algorithms in that case? Yes, yes. So the answer is yes. So in our model, we use occupation matrices as descriptors. So with the projection of contemporary functions on a localized orbital, this are the main objects. And so we do take into account these changes in the local chemistry. So what we need to provide to our model are these occupation matrices. So what you will see that when you change concentration of lithium, the occupations on transition metals change, and so we give this to the model, and the model realizes this, and gives on the output the respective changes in the Haber parameters. So yes, our model is sensitive to this local chemistry. Yeah, so we use how to build the database. We use DFPT, we apply it to a number of systems, we predict Haber parameters, and we also have the respective occupations. So we provide all this to the machine learning model. So the model sees, okay, for these occupations, I should have these values of Haber parameters. So you train it, and then let's say you take a new system for which we don't know anything. And what you need is just to compute occupations, and then you put this in the model, say, okay, now I have these occupations. What would be the Haber view? And the model gives you this certain value of the Haber view. Okay, thank you very much for the nice lecture. I see it is impacted on this lithium, and tachylation, voltage, and other electronic structure. But what do you think on other electrochemical properties like energy body or ionic diffusion, because we wanted to study this charge transport right and these cut-off materials? Yeah, it's a very good question. I think we just need to try. We haven't tried the, for those examples that you mentioned, but I think this method is generic, is general. We can apply it to any problem. So it's an open source. You can just, if you're interested, you can give it a try and see if it works or not. Yeah. Okay, thanks, Yuri, for the talk. Thank you. And so the next speaker will be Nong Arthrit from Utrecht University, and it will be about accelerating the construction of machine learning inter-atomic potentials using surrogate models. And we tried already, but... Okay, help is at hand. Okay, first of all, thanks a lot, Nikola, for the kind introductions and also many thanks to the organizers for inviting me here. Actually, my talk, it's slightly different from the rest of the talks from the communities or from this conference, but I'm really happy to be here. So my work mainly, we are developing machine learning models, try to understand the complex energy materials. And today I will focus on how we accelerate how to construct the machine learning potentials using surrogate models. And we develop our own machine learning model tools and also database, and we also share with the scientific communities. So the software package that we develop is the Atomic Energy Network. It is an open and free software package. It is really nice that the previous talk already introduced and give introduction on batteries, but I just wanted to repeat again that actually atomic simulation to understand batteries is really very complex and complicated, but understand many properties of material as atomic scale is very important. For example, the properties of interface and also nano transports according to interface is very important. And you can see that on the left-hand side, the interface of a solid state batteries that contain the order of lithium-cobal oxide, like you can see here, and also the interface of the electrolytes. This is like a disorder of lithium-cobal oxides or even the electrolyte, the light point here, and also the anode. And another size, this is the anode, lithium silicon. This is kind of like a amorphous structures of the lithium silicon, but what we are trying to understand the complex because it's so important at atomic scale. For example, the important domain like a nano size, like you can see here, or even interfaces and also amorphous phases. So what we like to do, we would like to make use of accurate and also reliable of first principles or the DFT that we can generate atomic structure at realistic and larger scale like this. So together with Columbia Center for Computational Electrochemistry, we also started to combine atomic simulation and also machine learning to develop database and also make use of machine learning try to understand such a complex interface. For example, in this cartoon that I draw. So we try to understand and characterization of interface which is like a resistance and also artificial like a degradation for example here. So and also many other parts as already you mentioned that cathode material also very complicated. What we do or what our work that we try to develop machine learning models that are based on learn from accurate and reliable electronic theories. For example, DFT how to learn the atomic interact. So we develop very reliable and accurate for example quantum mechanics or the DFT database and then we interpolate and also use machine learning models to learn and to construct efficient and accurate machine learning models so that we can really learn from the DFT database and then we get really efficient and accurate energies that we can use in application for example in Monte Carlo simulation and also can get accurate forces that we can use in realistic and larger scales in molecular dynamics simulations. So the model that I'm going to talk and discuss today so we use artificial neural network for the interpolation and is it really easy to use and also based on only atomic positions and it's also can really reference once we train and we fit it can get the results as accurate as for example DFT. This is the whole workflow of our work. So as a practice that you can see here so we need to get really reliable and also accurate database and then we select the data that we hope that it can really capture the application that we are interested in that we construct like a full potential energy surface and once we get the data and then we can select like a model selections and then model trainings and then we start to do model validation that you can see here and if we validate our model already if it's working or not we start to test by looking at the complex model that we're looking at in this case I show like the interface between solid and liquid for example if our machine learning model or machine learning potential is accurate enough it should be able to work directly as our intended applications but if it doesn't work we can also use another workflow of Fletcher assist active learning so that it can help to find and capture what the structures not include or not seen in the training set so we do this iterative refinement and maybe this is quite like a very abstract let's look at one concrete example we are using like a water model as example here as active learning construct such a training set which is also very important first we have initial data set and then we construct the neural potentials and then we fit and then we use the neural potential in the application for example MD simulation and then you can see that in X axis this is our structures along the MD trajectory that you can see here and we detect the binding energy on the DFT reference data in the red cross here and also our neural potentials along MD trajectories in the blank so we take a look at the errors between our reference data and your network you can see there's still quite high errors so the criteria is also depending on your application you can set up as you wish to have and then you can see that some structure if it's not close to the DFT reference data then we can include them in the training set and then we do like this iterative refinement so we implemented our models in the atomic energy network if you are interested in, this is the website we also plug it in and we have the ended library that can use directly in the many applications of software package for example like ASE, LEM and also Tinker also the L-Poly this is the references if you are interested in so let's take a look how we apply and also construct machine learning model for example to understand the Liam transport or more of a silicon for high energy density batteries as already showed before that batteries are really complex is for the positive electrode and also electrolytes and also negative electrode they are not the static, it's dynamics so the number of atom is changing all the time while the battery is short and this short like you can see here so we are trying to understand and try to optimize the composition so that we can find what is the best performance of materials so the first example we try to draw the full phase diagram of for example lithium silicon so this is the whole workflow sorry is it kind of like complicated but we would like to overall if we don't have data we cannot have machine learning models so the most important is that we generate DFT database so this is the initial that we can start for example we get the structure from crystal structures and then run some short AMD simulations and also distort structures by scaling the structure that we have and then we construct the primary results of neural potentials and then in the same time that you can also use the genetic engullitum to help to find a new phases by make use of the accurate neural potential that we have and we increase the temperatures that we are running also AMD simulation between 700 to 1500 Kelvin is depending on also materials and then we can also estimate the conductivities by using the linear plots and also can draw the phase diagram and also do structure analysis for example let's take a look at the first example this is a lithium silicon and for lithium ion batteries so we construct like a large DFT database of the lithium silicon that you can see here on the right on the left hand side this is a computed phase diagram that you can see both from the... this is the lithium in the silicon layer you can see so our reference data and neural network prediction is the same so in this plot I only show the DFT computed phase diagram so our NN potentials and also DFT can predict like both crystal structures of the lithium silicon and also high energy amorphous structures that completes the phase diagram the formation energies that you can see here and then in the same time we also compare the one test provides the blue that here this is as a room temperature and our one test provided predicted also include agreement with experimental measurement but we show is it in a few compositions based on the convex house that you can see here and to understand the lithium transport so we have also to make sure that our potentials or neural potentials really accurate for diffusion so we also create a model that can represent that different compositions neural network can predict the diffusion part accurately so I show only two examples the lithium 3.75 silicon and lithium 2.5 silicon here to show and the two parts here the X-axis is the NEV images of the part that it can move the lithium from A to B side so you can see that the two structures that we independent not include in training set that neural potential can really represent DFT a result accurately and then we use the neural potential to run long time MD simulation with different compositions that you can see and also from the beginning until long time MD simulation like two nanoseconds so neural network potential represents the DFT reference data accurately so this is really nice that we have efficient and accurate in potentials and then we can understand the compositions while we are running the MD simulation also different compositions and to make it more realistic we also looking at like the nanoparticles that you can see on the top of the figures and we also estimate the conductivities or the activation energies using the linear plots with different compositions so you can see that we can identify the atomic structures of different compositions and also how atomic rearrange and we also can learn that the diffusities that we can predict from neural potentials that can also provide the atomic structures so overall that we see that our neural potential can also predict the diffusities close to experimental measurements like you can see from the reference on the left hand side here and we can identify that the highest diffusities is between the lithium 1.0 2225 for example so once we learn this we can also optimize or try to find what composition is the best for our materials and not only that we also looking at a more complex interface for example our students and post of Chen Wang and how are you looking at a more fast like a lithium phosphorous sulfide and also anicate and also in one looking at the interface between lithium anode and also the electrolyte ethylene carbonate let's take a look at the first phase diagram by how you and also change so we also draw the phase diagram of the lithium phosphorous sulfide or LPS so we see that we use the same technique and once we use our machine learning models and also can map the compositions between the material like a P2S5 and also lithium 2S and we can draw so the blue one is the crystal structures but in realistic right when the batteries it is a moving like a charge and discharge the composition is slightly changing but it's not very easy to understand the properties so then we try to find the relationship between structure, stability and conductivities and this is the structure that we can extract from in this case I show as the crystal structures in the graph that you can see here but then we also want to understand the amorphous structures or aggressive ceramics like you can see here so when we know this type of structure already and then we can also estimate the activation energies like you can see that the composition that we found this is slightly closer to the parent's crystal structures on the left is the lithium PS3 and on the right the lithium 4P2S7 and in these structures and let's take a look because it's so many structure in our database so we also make use of another machine learning model like clustering, try to learn what is similar to the lithium environment and close to the parent's crystal structures and then we find the relationship between the structures of the amorphous structure here and I don't talk about the local environment here because we also take the structures to calculate for example spectroscopies and then we can also understand the oxygen state of like sulfur and also phosphorus but today I will only show the conductivities and compare with experimental measurements so to identify the new structure that we get from glassy ceramics it is also a compare like a reference with the previous work that done with the crystal structures like you can see it is a compare with experimental measurement but our work with the format of phase diagram we could identify the amorphous structures and then we found that it is have a higher conductivity than the perfect crystal structures so if I have enough time so far I only discuss like between database only energy only and we generate really large and big database but for the beginner sometimes how to start to develop your own neural potentials maybe it is easier to have some efficient tool so in 2020 together with April Cooper we propose one way that how to construct new potentials that include atomic forces for example in this case wire tail expansion so just to brief because I also discussed this in 2021 in this workshop already so as you know that the more data points include the training set you will get really accurate target potential energy surface in this simple linear zone energies in the gray region here of the hydrogen dimer as you can see and the data original symbol is the DFT the more data points you have you will get closer to the target like a linear zone energy so but we don't get large data set directly right when we start to construct our neural potentials how to do that this is also another visualization to show also for water that you can see that if you have more data points you will really have really accurate energy and forces that you can see here in this demonstration that you can see but most of the time or sometime that including forces in the training set is quite expensive and also take a lot of CPU time that's why we introduce another method by including approximate forces information which is kind of like a linear approximations by introducing include like a linear tail expansion you don't need to do new DFT data set but you introduce small displacements and then estimate the energies where the displacement that you have and include in a training set so like you can see here that if you have for example the blue one this is seven data points if you train your neural potential sometime you miss like the atomic energies they slightly predict inaccurate but when you include more data points here the cross like a minus x or plus x in this case the hydrogen dimer so you get more data points and then you construct a linear potential while use more data point from tail expansion and then you get the right energies and also the right structures again if you can using all force information direct force that you can generate from your first principle calculation that is the best way to do but it's just more expensive in this case we also demonstrate for water six molecules that you can see if you use all information like the force information as direct force training you get really very accurate forces like the absolute other forces it's really nice and perfect but it takes like eight times more expensive than include like a force information while tail expansion like you can see but using tail expansion very efficient but also improve the force information too this is for a molecular system I also did benchmark for a solid the cattle the combination of lithium and also some tantrum metals oxides like you can see that when we include the force information while tail expansion is also include or improve the force information and we also test sorry sorry so we also test by right in this simulation by using two type of calculation the first one only energy only so you can see that sometime the MD simulation also explore but include force information is this kind of very stable right so but in realistic we would like to look at interface right so you have more complicated system like a solid here as a lithium anode and also the molecules like a solid as a electrolyte so when we use for example tail expansion as a approximation is kind of like a difficult sometime is also too large and is also make a kind of like a not very easy to predict when you have like a complicated system that's why we are thinking that maybe include the same idea but include like a non-linear like Gaussian process regression that could help so we make use of by introduce or additional more data points by introduce non-linear Gaussian process regression that we can introduce more data points by getting the learning from the delivery values that you can see here and then we test this model again with hydrogen dimer on the left hand side this is the linear tailors but we introduce the displacements in many different regions of different displacements sometime with small displacements and also large displacements so sometime is also fail to predict the linear zone potentials but for the GPR model as you can see here that is fit perfectly this is just to explain what I just explained in the previous slides when we have like a very small displacements like a 0.03 angstrom so both metals are tailor additional data and also additional data from non-linear GPR both work very well but then when we include larger distances the tailor expansion slightly fail but for GPR it's working really very nicely and then we also extend this method model to our interface between the ethylene carbonates as the molecules and also the lithium anode so with the other distributions of you can see that with the forces that you can see by using the GPR model it gets much lower and using the tailor expansion also improve a little bit but only use PLDFT data points have a higher errors so both energy and forces show that using our additional data points include in the training set improve the quality or accuracy of the forces which can be really a good way to get accurate forces for our machine learning models in the future so this is my last slide that I just explained so we are still do benchmark on how to run MD simulations by getting more data points from the non-linear GPR models but in summary that we want to construct machine learning potentials to make use of the force information so you can see that we can reduce the reference data use less DFT data by actual DFT calculation but get more data points from tailor expansion and also non-linear GPR and in this case that we use more data set it also allows us to run stable or long MD simulations which it also will be good for materials prediction or to understand material properties so I hope that I could demonstrate that training machine learning models on data from simulation which is useful for accelerating the computational material discovery and also validate your machine learning model is very important especially compared with more accurate data or together with experimental measurement and also sharing your model and database it will be beneficial for scientific communities thank you very much thank you Nonga nice talk and perfect timing so we have time for questions let me run up there thank you for your very interesting talk I have two very quick questions the first thing is as I heard that you use artificial neural networks if I'm correct you mean multilayer perceptions have you compared this multilayer perception based like models to graph-based models if you know the crystal some very popular things called crystal, graph, convolutional neural network and a lot of things that are based on that have you compared it? the second one is I heard that you use it for molecular dynamics if you want to predict the dynamics you need a very precise potential energy surface have you do this before do the molecular dynamics before you test it's something like a NERGIST elastic band or dimer method to test if your potentials have the same potential surface as the DFT one and you have the same set of points I'm serious about this because it's very seldom to hear it somewhere you use multilayer perceptions in this field thank you for your talk thank you very much for the question the first question that you asked no, I haven't constructed or developed the graph network as a descriptor yet so the descriptor that we use here is based on the two-body and three-body like a local atomic environment so that develops first is it with the Baylor and Palinero and then we extend it to more easy to use by including the chip-shaped polynomials so that it is more easy to use by having many more order so you still bring a lot of prior knowledge to your network you're still okay yeah, thank you not the graph network but then the second question your question asks like is it okay to compare my DFT and neural network here then to see if it's accurate to use in MD simulations, right? the answer is that I just wanted to make sure that if the neural network potential that I construct is it really also work for the diffusing part or not as you can see that the activation energy is really very high here because this is not really optimized but just to see the part to get the images from the NEB calculation and then we just predict the structure that we get with alien potentials so and this is really just to show that it's really capture the structure that really not include in the training set yeah, thank you so much for your answer okay, thank you very much for the nice work and presentation so if I correctly understood it you said that it's possible to model this electrolyte interfaces using this machine this method coupling with DFT for this DFT or machine-lead MD so my point is what do you think about the stability issue when modeling these interfaces either in the anode or cathode parts? so this is quite complicated, right? this is just to demonstrate that you have really a mixed bond between solid that you have like a lithium is it like a solid? but our molecules like ethylene carbonate for example, in this cartoon they have mixed bond like oxygen and hydrogen or carbon and hydrogen here so we cannot, I mean it is nice that you can develop big data from the DFT directly but it will be really a lot and big data because this is also not accurate by GGA, by PBE plus one in a while that we already test so we need more accurate methods maybe hybrid functional which is very, very expensive because we check, of course we cannot find the experimental measurement to confirm so we try to look at formation energies or binding energies but there is no experimental measurement to validate our prediction that's why we try to develop really very large and efficient to get the method like a very efficient by generate like let's say artificial new structures but not doing the DFT by itself so this is the idea just try to use not too many accurate DFT or even hybrid functional DFT calculation but we derive more data or more structures by using like expand by Taylor expansions or expand by Gaussian process regression to get new structure and new energy and new forces that we can include in the training set so this is just the idea Thanks for the very nice talk I have two questions a little bit following up previous question so my understanding is that your training data set basically your training data points configurations of your system that you put into the neural network so in your slide 12 we are showing like a time dependent simulation so do you have like training data point for each of those times or these are predicted you train at a time and then you predict the time evolution so that's the first question I'm not sure if I understood your question so you see like if I predict also the time so in your slide 12 Okay 12 Yes so each of the red dots which are understand comes from the as general network are predicted at different times right so for each of those times do you have like training data points that you learn or you learn a time I don't know zero and then you predict a time as the times goes so in this case so we run long in the simulation with new network potentials and then we select the frame that we get from new network potentials and then recalculate with DFT so this is we get the red one so because we know that we construct neural potential based on DFT right Yes and then we use the neural potentials run long MD simulation like a five nanosecond or two nanosecond and then we select the frame from the A and M D and then we recalculate the DFT with that structure so you have new sam