 Well, good morning everybody. My name is Nicola Corona from Paul Sharon Institute in Switzerland. And first of all I would like to thank the organizer for the invitation for having me here. And actually to open these one year 90 developers meeting. I will call myself a developer in the 90. I'm more a user than still I'm very, very happy to be here and looking forward for discussion because now it's better. Yeah, I was saying because I'm very happy to be here because what I'm going to present now is a is a work we have been doing in in Los Angeles since a few years now. And it's slightly related to, to the money, when you function money and 90 in particular, and this is about a spectacular spectacular functional approach to spectroscopy that we name kubman compliance function. And in particular, it's. And in particular it's implementation in in quantum express so and the connection with the 90. So I first just give you a brief introduction on kubman spectral function what they are and what are the basic assumption behind and then I show you some benchmark to prove that this is indeed a very effective approach. And then I go to the central part of the presentation that is the application presented system where the connection with my new function is made up parent and, and the interface with 90 code is key for this development. And the central quantity we want to target our charge of citation, you are very familiar with this essentially. This is the, the best structure of your material and it's not the ground state property sorry principle density functional theory. So in this, in this respect, still you want to like to be able to actually reproduce this quantity essentially because they are connected with with the experiment like director inverse for the mission spectroscopy or angle result for the mission spectroscopy. So then the question is how do we simulate those those quantity. So for what concerns and system brings function meter that is considered to be a good compromise between accuracy and computational cost. And indeed for many weekly to moderate the material that this function theory already within the so called double approximation, give very accurate result for many, many material here you see just an example for silicon, in particular you see that the PEN gap is is correctly reproduced. Now the price you pay is that you have to to work with an unlocal and frequency dependent object, which is the one body with this function. And this is way more complex than what we are probably used to this density functional theory where the basic variable is the ground state that. So if if I do a step backward to density functional theory and I take the connection structure now I know this has no obvious connection with the actual been structural material, nevertheless, the, the, the quality, at least the qualitative agreement with that actually is quite remarkable. And the, the well known and unfamous underestimation of the, of the band gap. So, so the question is, can we have just something in between those two approaches trying to match the efficiency of a functional approach like density functional theory and the accuracy of functional theory. So our answer to this question is actually a cool ones puncture that are based on a very simple idea on the observation that essentially, what is missing in approximate density functional theory is the fact that the single particular value you're going to show energy, actually on a high here doesn't really match with the definition of a charge excitation that is the energy differences between the system and the system with plus or minus one, one electron. And this is with this function theory where this is enforced by construction, the pole of the one body response from actually are the single them charge excitation of your system. And the reason why this is missing in density functional theory is essentially because the energy as a spurious almost quadratic behavior on the occupation of the, of the orbit. If you remember, you know, I tell you the game value is nothing but the derivative of the energy with respect to the occupation number so essentially this cartoon here. The game value is nothing but the tangent to the to the red curve that represent a typical local senior condensate function. And now you see that these these are here the derivative doesn't really point toward the, the energy of a system with a minus one. The basic idea is to revert the spurious quadratic behavior into what we call movement compliant behavior, this blue line here, and now you see that you're, if you're able to do that, then the, the again value so the derivative will correctly give you the, the total energy differences between the new term the system with plus or minus one. So, this is very simple and actually. Yeah, just let me say that this is not, not new actually in a reading the FT you have something similar, you might be familiar. You might know this is the well known piecewise linearity condition and that's it. But this apply only to the energy as a function of the total number of electron, or if you want as a function of the occupation of the ice molecular occupation of the ice molecular orbit. And this in an original way to all the electron in the system and toward the occupation number so we are more general the density functional theory in this respect. And the nice thing is that you can do this with very simple correction to your density functional that here I call PI KC coupon compliant that actually turns out to depend on the orbital density. So this is, of course, the generalization of the FT as I was saying, but still way simpler than this function theory because now you're central variable central quantity of the orbital density so and local and real real objects. Now, I don't have time to go into the detail I just want to mention that this correction are actually devised and forcing the linearity condition I was explaining the slide. You end up with the very simple expression that are actually given in terms of the art extreme and correlation energy of your underlined that functions. And here we just to set the momentum that will we refer to KI is the black term here, which is the simplest correction we have and then we have a more advanced one that we call KI PC where we are the next term in right here. That is inspired by the set interaction correction by doing zoomer, and with this extra term the approach become exact for any one electron system so this would give you the right the exact solution for any one electron system. Now, these these expressions are quite simple but essentially are derived in a very strong approximation essentially that is that when we add or remove one particle and we analyze the energy, we assume that you're not readjust. And this is just to work out explicitly the expression is very simple and compact form. But of course he is a strong approximation if you want this would be the analogues of coupon theorem in art before where you have the linearity but working in a frozen art feature. So what you're missing is relaxation screen effect that actually are central to correctly described charge excitation. And we introduced this with some orbital density dependent screen coefficient that can be computed fully ab initio during the year we develop several ways to get this screen coefficient, probably the most general one and what we are happy with that the moment is is given here in this formula, it's a well defined average of the microscope microscopic the electric function of your system. Again, if you want to know more I will be more than happy to show you the detail where this come from but essentially you are robbing the response of the system. And finally, in addition of a tiny fraction of an electron in the in the in the system, and the numerator is when you account for the response of the system the denominator is what you don't, and the ratio between the two, give you a measure of the importance of this. And what is important, especially in this context and with connection with my new function is the third property of this class of functional that is the localization of the variation. Actually, because of these orbital dependent term up here, the, the function is no more unit are invariant under unit rotation of your mind for. And this means that the minimization drives you toward the unique set of what we call minimizing or additional orbital, that actually are typically very localized and resemble boys orbital molecule or maximum of high spending function in the standard system. And by the function itself. So at the end of the minimization we have this set of orbital here you see two of them for the police police yet in the chain. And once you reach the minimum, you typically take your matrix and multiply that we used to keep the orthogonality during the musician you diagonalize it and you get the canonical orbital and again value that actually has a direct connection with the experiment. So, like, I don't know if it's function or charging situation. Okay, this is a very brief summary of one. But as I was saying at the beginning that now we have a more general thing with the NC functional theory now the basic variable of the density and another striking different with respect to standard connection is that now we have one potential for each for each So this is clearly more more general. So it's also reminiscent of quasi particle approximation in this function theory where we have one self energy at the given value of the frequency for each. And, and I will show you that this is enough to to actually describe. charge at the system. So the first thing we did was actually to take a large set of a standardized set of molecules this is the GW 100 set you might be familiar with these. So these two benchmark and validate different GW implementation. And for this reason we have actually quantum chemistry result experiment, but also many different results for different and from different approaches ranging from simple correction to the empty like I'm just going to add the one off and then article can and different GW depending on the starting point or self consistent GW was a part of self consistent. And here I look at the, we look at the mean absolute terror for the first utilization potential evaluated as minus the energy of the homo again value. So I, I like the, the, the coupons function here you see KIPC that I show you in the previous slide and intermediate version where we apply in a perturbative fashion the KIPC I'm going to talk about the ground state. And as you can see the performance is quite remarkable we are in line with the, or even better than most of the GW result. But now, and we are almost as good as the best GW which in this case, or at least the last time I checked was you know that we're not on top of. And this despite the fact that this is quite a simple, simple approach, I, I like this down here, again, where we essentially deal with local independent. Now I have to be fair and just to say that this is exactly true but but you need these extra computational cost, given by the fact that you have to calculate the screen coefficient. If you want, as an analogy, this is pretty much like in the ft plus you. This is a very small overhead on density functional theory but still you need to compute the, the value of the you parameter and this might require additional calculation. This is another example to show that not only the first utilization potential but also other single party colleague in value are correctly reproduced here we took a set of 27 small molecules that are relevant for photovoltaic. You see the, the fuller in the scene. And again, this is the average performance of KI in blue and please in red, compared to the state of the art in GW. And you see again we are in line with this function theory or even slightly better especially for KPC. For both the first organization potential and the electric community, a game evaluated as miles the energy of the game. And also just want to mention that also deeper state are correctly produced. Here we computed the theoretical for the mission experiment for this is an example for C 60 fuller in. And you see that that KPC is remarkably good agreement with with with the experiment. And this is actually true for all the system we looked at so. And if you want all the details on how these are for the mission. You can check out this, this reference down here. Okay, and now just want to go to the central part of the presentation that is how do we extend it for these two periodic system or crystalline system. And this is where the localization of the variation of it and actually the connection with a new function is apparent and it's key to the success of the coupon function. And in order to show you this in some detail, I start with this with this light, essentially, I probably mentioned this or not but I just want to say that in a nutshell what kuban's function. It's actually enforcing a function for the concept of Delta CF. So the single particle again value as is replaced by a total energy differences between the neutral system and the system with plus or minus one. Now, you might know these, but it's well known that standard Delta CF on top of local semi local function is quite good for small molecule, but it's bound to fail in the thermodynamic needs. We did this computational experiment, we take a chain of a chain chain and we made, we made it increasingly longer and longer toward the thermodynamic limit represented by the polyacetylene chain. And we look at the first ionization potential again estimating different way down here in black triangle you see that the Homo from PV and you know this is completely wrong both for small molecule and you have to compare with this star here, the star and this red star here that represent the experiment or quantum chemistry calculation for small molecule. So you really look at Delta CF so you really do a to CF calculation with the system with an electron one for the system with an electron, and this is well known it's quite good for small molecule. But it goes back to the Homo to be when you approach the thermodynamic thing. And the reason for this failure is a combination of two fact the first one is that you're using the local function. The second one is that you are removing your electron from a from a block state or a canonical state that becomes more and more delocalized as you approach the thermodynamic link. So the solution is either you go for a highly non local functional or you remove the, the, the constraint on the, the localization of the chronicle. And this is actually what coupon does essentially they impose it as yet still working on with the local similar to that function but we force this delta CF on a set of vanilla like object that are presented here for those are two of them for the for the chain. And the reason we have a finite correction both for for small molecule and in the terminal clean to very specially KPC recover extremely good agreement with with the experiment. So this just say that the localization of the rationality is a key to get accurate correction also for for a standard system. This was a toy model we have we apply these to a set of 30 semi conductor for which we looked at the band gap and seven surface seven ionization potential from seven services. And again, we compare with the experiment and with this function theory here in the table you see the average performance of the function. So we find it's, it's quite remarkable the the accuracy of especially KPC and even more remarkable is the fact that the performance is consistent for both the band gap and the ionization potential which is not the case in this function theory so the quasi part of your self consistent GW gives a very good estimation of the band gap but the absolute position of the band edges is not very accurate and the opposite is true for for genome that we know so non-self consistent. And it's quite impressive and remarkable that KPC can do both job at the same time with the very same level of accuracy. But now let me just mention something that was some kind of headache for us for a few months essentially the fact that we are. We need to work with a set of localized that will apparently break the the transition symmetry of the of the system essentially you have to think of this kind of a defect in your system so we are adding a charge in a very localized state. This is called the natural way to address these it's in a supercell and indeed this is what we did up to now working in a supercell even if the system is perfect. And the question is, do we have block symmetry. Even if we're working with this set of localized and the answer is actually yes and this is the work done by Ricardo Genari at DPSL. And the key observation is that actually the variation of the one that comes out from the musician actually are by me like and by when you like and they satisfy some sort of probability that that is you can reconstruct all the. And this is the only thing you have to notice and if you use these are then you can prove that the coupon potential actually commute with all the translational operator. The committee said and this means we are a block compliant and this means that we have a best structure underlying even if you're working in a supercell. This is more conceptual than practical, because with that, that stage we still have to do a calculation in a supercell because this is pretty easy to get forward to do but then we can unfold the best structure. And then the entire best structure for instance of silicon in the primitive primitive brilliant zone. And this is important, especially if you have a system with an indirect gap where the three cents in silicon that the bottom of the conduction band is between gamma and X at some random point. And this again is done by Ricardo Genaro. Again, here the agreement with experiment is extremely, extremely good. And I would so complete the structure of the material. And last step, and this is where actually connection between 90 is even more important is essentially then the question is, so if we have translational symmetry. Can we just exploit them from the beginning and directly work in in a primitive cell and the answer again is yes. It's not as trivial as if you were working with the canonical condition state, but still you can do that. And the key observation is again that the basic quantity again at the orbital density. And those are if you want a new density by definition periodic on the supercell commensurate with the number of key points you want to, you want to have the same thing of the primitive cell in one zone. But the key observation is that given the fact that the variation orbital are like, so they have this translational product you can rewrite these objects as a sum of quantity that are periodic on the primitive cells simply motivated by a phase factor. And this is all you need to know to recast a problem whose national dimension is the supercell into a primitive cell plus the same thing of the brilliant zone. So as an analogy, this is pretty much the same that happened in phone on calculation, you can either do a frozen phone calculation where you build up a supercell that is commensurate with the wavelength you want to have the perturbation that you want to study, or do you use the machinery of density function perturbation theory where you decompose the perturbation into a sum of monochromatic one in the primitive cell, and you use a primitive cell approach and the same thing of the supercell. Of course, the, the, the, the advantage is from a computational point of view is, is tremendous because now you can work with a small, a small cell, you can, in principle, parallelize over two points in principle, space group symmetry of the system. And in quantum espresso, this stage as a as a post processing essentially the basic assumption is that now our variation a lot that actually coincide with maximum guys by new functions so we skip the minimization and we use a simply maximized by new functional obtained from a money and 90 calculation so but everything start with the pwc at calculation, this is the LBA best structure of the mass and I, then we use the money and 90 code to obtain the funny a function and we have to do these procedures so we want to rise separately occupied and empty many for this to have meaningful localized orbital for a charge excitation processing. And then, as I was saying, we have used these as a proxy for variational orbital and most of the case, this is an extremely good approximation so the minimization really doesn't modify much the, the, the, the maximum function. And then we implement the interface with money and 90, and this is the coupon code where essentially we take the output of the wcf, essentially the condition state, the output of money 90 essentially the rotational matrix that allows to go from the block representation to the to the money gauge for the connection state, and then you have to build up the basic ingredient that are the periodic part of the money density which is given simply by these, these, these objects here. And once you have this you can build up the ingredient needed for the equipment functional, first of all, you have to compute the screening coefficient and this is the real bottleneck of the of the calculation, because essentially this require a linear response calculation essentially you have to, to compute the action of these electric markets on some perturbation that you can imagine this as we are perturbing slightly perturbing the system adding a tiny fraction of an electron into a function. Essentially the perturbation it's something that looks like this is the art of exchange and correlation potential due to the, to the function, but the nice thing is that you can recast these into a sum of monochromatic contribution. You have to work within the primitive cell, and this is implemented with the machinery of density function perturbation theory so a split is some of empty state for the calculation weapon is, is, is not needed. And this is everything is well known for those of you that are not familiar essentially you have to solve a set of self consistent equation that are very similar to the standard one in a ground state calculation. So this is for for DFT but now instead of looking for the self consistent child density you look for the self consistent the self consistent variation of the child density due to this particular perturbation up here. In fact, you can build up the hook my name is Tony and, and this is a competition very cheap compared to the creation of the screen for patient. But the nice thing is that now you have it in a in a vanier representation so you can do all the post processing tool that you can imagine and that I love quite advanced looking at the talk of the summer school last week. The physical point of view what happened is that essentially the band deviance band is pushed downward the conduction then is pushed upward a bit and these results in a band gap that is extremely good agreement with with with experiment. And here I just show you some more example, again this gallium arsenide on the right here AI, and I compare with the standard idea or quite common approach that is this HSE I did function, and I compare with experiment these horizontal dashed line represent the band gap in green. The, the bandwidth of the balance band in blue and the position of the states in red out here. We know that the typical failure of the HSE correct for the band gap. A bit also for the position of the state, but wasn't there. The bandwidth and key items to these orbital dependent correction can reproduce correctly, the band gap improves a lot the description of the state and the bandwidth, at least unchanged. This to show that it's this approach is. In the quality is not a system dependent as it happens for hybrid function where you tune this missing parameter once for all and this is the case of HSE but this parameter might be an individual or a system dependent on the other side for a wide band gap it's later HSE is not. It's not good anymore, while AI because of these screening coefficient correctly produced the electric response of your system and also in this case an accurate estimation of the band gap once you remove the zero point contribution from the experiment. And this is a more challenging the case of the thing outside which is well known to be challenging also for GW calculation and again, here. The failure of a day is even, even more remarkable essentially because this stays down here from thinker to high energy and this push up the oxygen state and this closer, even more the band gap. The HSE quite good job goes in the right direction and AI is, is even better and almost better than you would expect. Okay, and with this I conclude, I hope I convince you that now we have a functional approach to get accurate charge the creation in a finite and standard system. The complexity of the approach actually is very appealing and promising for automated approach in particular with the automated magnetization. It's open source it will be released soon with quantum, quantum express and the basic idea is that we can have this can be used as a code pillar for a computational infrastructure that can be accessible to a broad audience. I want to acknowledge people because I'm not the only one working on this, because I was leading the project and that's a great use one of the first developer to be smiling at them. And then, then we have a formal postdoc and the cabinet in our case, but present. And many other people that contributed to the project. I should be open for question, but I might start with some questions for you essentially to streamline the situation actually we would like to have a robust and automatic linearization and I learned from the summer school that we have something already in place with just the CDM meeting also we have the automatic approach. And the other important thing is that we need to have a separate linearization for provide an empty manifold. So, this would be great. If I can discuss with someone you in particular. This morning saying that he's actually working on these and has some nice idea to get these working. So the computational point of view is it would be extremely relevant for us to be able to work on the irreducible bill and wedge of the Cape on it in the middle and so on essentially because where the image itself is not it's not the deal but the calculation of the screen requires actually a double sum over over Cape on so we would really benefit from the use of groups. Okay, and with this I thank you for the attention like open for question. Maybe first we answer a question was asked by Sergei on zoom. Sergei asked what is the relation between maximalization or position by Kubman's functional for instance for some topological ideas when your functionalities cannot be looked at. It's hard to position one of the reaction are Kubman's arm it has always been right. Now this is a very, very good question typically or for the system we used to we looked up to now that essentially are 3d periodic system with no trivial topology. The variation of the actually are very similar to funny function that I the basic idea is that actually what Kubman's function. The minimization is driven by a set factor determine and you know from chemistry at least that this is one of the different way you can get localized or so maximizing the set factory. Now I don't remember the name for this localization procedure but this is one of the possibility and all this localization procedure produce a very similar function is the reason why. So maximizing our square or maximizing the set factory is pretty much the same. But so I would expect that we have the same, the same limitation as you have in maximum has been a function for the system you were mentioning, but this is something we never really tried and it would be extremely. Nice to see. Thank you. I have two questions. So, in the result that you are showing at the end so you get amazing agreement with experiments, just to confirm so the experiment you subtract the zero point motion. Yes. Okay, yeah. Yes. For medium flow, right. Yes. Zinc oxide I'm not sure probably know something to check. I don't know. I mean if you have any idea how important it is for Zinc oxide very happy to hear if you have some references. And for gallium arsenide also we added the spin orbit effect because this is not in the implementation yet so we are for a movie 0.1 from the from our calculation to account for this. And also the PR. If for going tonight. No, I think it shouldn't be there. And the other question is now that you have both implementation so supercell and primitive cell. Have you done any comparison for example for get a mastermind. And particularly I'm interested in the convergence rate. So like to get the same value. Do you have some blood do you know how fast or slow, the supercell converge to the single cell guy result for the same guy. So, so there are two things here so in this in this implementation done with the primitive cell plus the brilliant zone. We did some extra approximation time approximation on the actual form of function so there's no one to one correspondence between this implementation and the supercell one. But this is a typically is a very good approximation in principle you would expect to see exactly the same result because it's really just a writing of your problem in supercell in a primitive cell to a center of the apart from the smaller one implementation, the convergence is something we didn't check but actually be the screen or carefully let's say. So in principle the two has to converge in the very same way. So the size of the supercell is exactly the same converging parameter number of k point in your presentation. And the screen coefficient converge. I think, well, you should converge very, very easily in semiconductor, you know you don't need that very large. So in terms of k mesh to convert the electric project like the microscopic function for metal so when they get those. So in terms of q grid. Is it like 444. Yeah, so in this, in this application is a six by six by six supercell and this is already enough for to have a decent interpolation of the bands because again, now you can. Those are converges out but I think even four by four by four for the screen. It's something. Thank you. Any other questions. Yes. Thank you very much for the talk. And I want was wondering, looking at your final result about linear response. If there is any way to compute, for example, vibrational properties, or any other linear response properties with this kind of data. Thank you. And so you're asking if you can use these as a, let's say that the starting point for a phone on calculation or. So, not at this stage. And now everything is implemented. If you want to like energy not that you're not so it's really not fully self consistent so. But in principle, you, you, I don't see any, any, any real obstacle to these. Well, So, not with any response but maybe with a certain for an approach for sure, you will be doing a supercell and you compute. So, I think it's doable. And maybe a quick comment on this in the sense that the KI functional as the exactly the same total energy of the base function you start with. So it's not giving you improved energetics from LDA or PV or PV so. So the AI PC functional ads are this Purdue Zunger self interaction correction with a screening coefficient that comes if you want from imposing a spectral property imposing a linearization. This seems to be working well so it's basically a local screen the focal term. Okay, we have only one case where we looked at this that was some of the DNA and RNA basis, and that term was giving the right portion of a certain angle that wouldn't be. But it's not that we expect particularly exciting results from the total energy and does the phone also, apart from the fact that you have consistently in KI busy a screen focus change that at the end is the same thing that that hybrid functionally different labels are giving so my feet also. Okay, for KI is absolutely the same. I mean, and KI PC would be similar to a hybrid with just a different flavor of a screened for exchange. But again to do phone also. I think it would be simpler to do a finite differences with phone or my than trying to do a question on top of that. Exactly as also in the FT plus you. I mean there are phone also in the FT plus you with the response. That is so much easier to do them by finding differences. If you want there is one additional concept that is this screening coefficient is a configuration dependent. So if you take the first of the second derivative of the total energy, you should take in principle into account that also the screening coefficient is configuration dependent so it contributes to the frequency, and that makes itself a little bit more complicated. Okay, yeah. Other questions. Yes, I'll say. Very quickly so for, for empty states, but so the, how does your result depend on the, on the disentanglement window. Now, good, good, very good question so this is something that we need to explore more systematically would say, but there is of course dependence because now your function depends on the actual shape of the, of the orbital density of the plug in so of course I mean the modification is dramatic, then, then you would expect to have also sensible changes in the gap or the property. But if the disentanglement and now here I'm not an expert but if it's just to give similar function just more localized than I would expect that the dependence is not dramatic but in principle yes we have. And this is also for, for the, for the occupied man for if you get different kind of organization. Actually, this is counterbanz but the screen coefficient that depends actually on the shape of the contract, but we have these. But in principle we have minimization we know which is the right. This is for occupied for empty. Maybe I have a question then so the, the, you mentioned that implementation is done with the FPD and so with Q points. So it's also the vanuization part is done in the primitive cell not in the supercell. Yeah, here in this workflow everything is done in a previous cell, so there's, I mean it's really like a standard calculation. And the only thing you have to do is this, the FPD that process is quite complexion intense but it's like the competition on the you with the. But it's intensive in terms of time or in terms of memory. In terms of computational time in the sense that, that this is the real bottleneck of the calculation, because it's, I mean it's a linear response so in principle you would need to solve a problem that is like standard the CF in the FD but for for each of non equivalent all of them are identical you get once, and that's all but these are an extra competition of course that you have to perform. No more questions, I think we can thank you to the next speaker. So, next week we saw some you. So for those who are connected online we have a half an hour break and then we resume with our schedule right over here.