 project already 20 years ago yes 20 years ago and so actually most of the the other organizers got stuck because the airport was closed because of fog so yes so we are only few good and so I hope they will they will do it because I mean one guy had promised so I'm ready to do another lecture yes I had to do another lecture for this guy this afternoon and I hope that they will arrive because the way they have to do all the lectures of the school so I mean three lectures is already enough so I is the school organized so I mean it's not job I will tell you in the introduction it's not job because it's like a one has to go from zero to infinity in five days velocity is infinity of course and so the idea is that in the morning we will do theoretical lectures and also there we will try to introduce a few concepts but not everything because it will be impossible you need a course and then in the afternoon we will do ensign so you will see those things in practice using yambo of course during the school you will see only bits and it's just I mean I invite to just go back and learn more so but the structure is exactly this we have theories in the morning and practical lectures in the afternoon all developers will be just around I mean I'm staying in this guest house so whatever you need just come to us for installation and problems and theory and everything just come to us and then we we can discuss okay so let me open officially the school with a small lecture about the perspective on material science that is given by yambo so if you look at material sense for yambo what do you see I think that the perspective of yambo is just a perspective of materials community in the sense that you see all critical aspects and features and needs and problems that you encounter in doing computational physics okay so material science is a very large word there are many different communities inside and actually I'm a theoretician originally personally so my background is in quantum field theory originally then I moved to condenser matter so I come from this part theoretical physics and then I started writing the code because I needed to do I need numbers just numbers fine but the point is that along the years in the last 20 years the word around the theoretical physics increased enormously and now there are communities that themselves have an entire literature and research and so on and so forth things that are very far from our background I know about your background with chemistry of physics but there are things I just trust me in this theoretical computer science in computer engineering that I understand nothing I mean it's like if someone talks to me in Arabic no way but at the end of the story I have to take care of all this because the codes like yambo have been involved in all different community in all these communities this is a really source a lot of complications for me and also for you as users I mean it's not that you install yambo and then this afternoon you'd be we'd be able to run on 60,000 cores no way I mean it takes some time it's all straightforward okay so there are different actors in this word material science so there are experimentalists theoreticians and what I say run this I mean so just run on computers so the radical physics this is the sort that what we will learn in the morning the problem is very actually is very very old and very well known you're in Newtonian as a body-body interaction column interaction is not seeing a body object as many body objects so whatever you want to do you have to take in consideration the effects on all the electrons together so how do you solve this many body problem this is the threat what this is what is solved in theoretical part of the story so you need to find methods like fancy functional theory or many body rotation theory or beyond I mean we will just tell you about few methods this is not not all the methods have been developed we will not talk about for example dynamic I mean field theory we will not talk about that so we will just talk about the tools and the approaches used by the code and so the first part is yes how do we solve it and then once we find a way to solve it how do we implement it so we have some equations to solve and then some approximations to do and moreover the kind of theory that we want I'm just giving you an overview I mean don't understand everything the kind of theory that you need depends on the physics it's not that you do theory yourself I mean an absolute way it depends on what you need to calculate if you need to calculate current or voltage or a charge migration or polarization and absorption or gap you name it and then we have to sit together and see what is the theory needed to evaluate it and depending on the kind of physics you may need to introduce more complex and advanced methods that can be TDDFT many body or even more complex methods like non-equilibrium Green's function theory this is what I'm doing at the moment for example I'm working in equilibrium Green's function theory world good then once you write your beautiful piece of code and this is what it was done myself in 2000 actually I started writing it was not yambo was name of self and I did it for my PhD I needed a tool to calculate the numbers in my PhD but along the years many people contributed to the code and it grown and grown and now we are version 4.5 I think and and it along the years they got a lot of more things that were calculated with the code now I mean we stopped in 2009 so that still 10 years there are so many things and then you can get a clue an idea just for the fact that at the beginning in the first paper that we published when the code was made GPL in 2009 we were 4 now we are 20 in the last papers we published last year we are 20 okay you will see a lot about yambo yambo can calculate several things I mean it is feeded by by a DFT grand state calculation at the moment we support pwcf and abinit so you do your system with those two codes and then you are ready to to calculate to start yambo and then we young we young we can calculate plenty things and and then there are several libraries that they are they are released with the code so in general we try to use it to use it the most user friendly as possible in the compilation installation even if my students say that this is something that only I it's friendly only for me it's true I mean but we can do it together and many people and then actually it has grown in the years and now it's not only a code only as a community so we have we have been doing schools in the last 20 years and yambo has I think has traveled I think I think I think I miss Australia I think Australia because China Japan Africa United States North South Europe I think everywhere maybe Russia maybe Russia maybe we miss Russia maybe no for us as we really what it has been told all over I also thanks to CTP we participated too many schools organized by a CTP and there is a forum there is a wiki page that is the one you will use to do tutorials where there is there are all informations about the code this is the educational part yambo so there are how to use about the tutorials theories and so on and so forth and the source is open and is also legit repository so if you want to contribute or to get the latest snapshot of the code you can use if you able to use jit you can use jit if you don't know what is jit just ask us we will tell you and it has been applied I mean there are around we are around 6600 publications then be done using yambo and there are particle about everything from molecules to solace nanostructures surfaces actually I don't even know all the system it has been applied to being a community it also part it has several interactions with funding it has been source of funding received funding at the moment there is in 2h 2020 projects and and lately we have been a lot concerned about performance because you know that now computers as in the material science word I mean the part relative to computers has grown enormously and also the technology and computers across enormously so for example now the latest machine and I will tell you more the lens machine the most I mean expensive and fast and enormous that the moment is not only CPUs it's probably is naively machine where there are CPUs and GPUs video cars you know the one used for gaming I bought a PC to do to do coding on zip on GPUs and my my my sons that I like they like very much the fortnight they saw it said wow but this is great to do to play for that because actually we are using the technology developed for gaming I made as video cars and so performance is an issue especially for us that you are traditions I mean I didn't have any idea what is an even a GPU so yes we are many we had a t-shirt even if most of them lost it but it's t-shirt yes and so we are many we had several schools around and this is the last one I went in Cameroon in last November and there is this school then this year again we will go in Africa again in Wanda in summer and but there are many I mean 20 years there are really many then we are educational okay just as the last words about the the performance so what makes you more specific is the fact that among all the codes that were I mean what when I did my PhD there are many people writing codes but a certain point where does super computers entered in the in the business lots of codes did we're not able to cope with it and we're not able to run on those machines because actually you need sometimes to rewrite entire parts of the code yambo for some reason was able to do it I mean was rewritten I mean between version one two and three what was completely rewritten then now is not possible anymore it's too large there's no way to rewrite yambo now you can write parts but not the entire code and and this is possible because the code was a modular I can tell you I mean there is also some theory of coding I mean it is not that you do coding I mean just that's it and one of the key things to be able to evolve is to be modular if you're modular they are pieces that are as much as independent as possible then you are most probably to be successful as I told you in the years we managed to export yambo on CPUs and GPUs and this is the latest development that I mean the latest release only is the first one the 4.5 is the only one that may release with GPU support then thanks to this kind of coding we were able this is actually already old the result able to run up to 60,000 but I mean actually yambo at the moment is pretty good in performance we didn't manage to see a saturation of the code and indeed in one of the eight projects where this in is a project for exascade transition how to bring those machine those codes to exascade machines okay so again MPI when CPUs you will be told how to use a CPUs both as MPI or open MP two different methods to use the CPUs while GPUs there is only one method and this is performance by GPUs I don't want to mention about this okay yambo is pretty much used among the codes in the praise and the end of this H220 max project and was the second after quantum espresso and then yes I want to just to say a few words about it something that for me is really important I mean a super good situation is super complex right so theory and coding is a big jump then how do we do it I mean how do you do it how do you find yourself your path in this in this walk so I would I suggest after many years of teaching is that you have to use a gradual procedure but you have to be careful that he is here so you have a physical phenomenon that can be among the ones calculated by yambo or another one it's possible that you came here because you want to calculate for example change migration at the moment yambo yambo you cannot have electrons moving in space let's talk about it then physical phenomenon you need to first of all read and study so if you run the code this week everything will be I mean just reshuffle because of the time when you go back don't run before reading it's completely useless then you feel the form of which questions are completely nonsense so you have to theory study and then the simulation is that the end because between the theory and the the simulation there is one important step is discretization computer discrete objects computer is not continuous objects so if you have an inter-referential equation you cannot put it as it is on a computer you have to discretize and in this discretization there is is the source of most of the parameters so you study the the phenomenon you connect it to the microscopic world and through the theory then you understand which kind of numerical methods are used and then again you simulate so from this you can get you can approach in a proper way and some tutorials understanding the parameters the way to to choose them and I mean it's important that you understand because there is in the tutorial there is more than one example that if you don't change properly they computer they permit us you will stuck the machine in Cameroon Dapton to me that's the point people say oh my computer does not reply and it's not answering more it's completely frozen I said yes because you didn't change that number so yambo can kill your machine yes okay that oh then maybe okay because that is the point everyone asking you what why you are austere why it's an oyster that then yambo doesn't mean anything so it was Conor Rogan that to make joke of me said it yet not a many body code by young boy doesn't mean anything it's just I mean in Africa in some in Swahili yambo means hello that's why the oyster the oyster is because when I started writing this yambo when I met actually meter this one is the founder of the code I was working with vacuum paration diagrams I had those diagrams all around I mean I was just crazy with those diagrams for me because I couldn't find the solution to the problem and then I published I found the solution because I published paper but then she turned the oyster the vacuum parization diagram the second order vacuum parization diagram in an oyster and this is why yambo is as an oyster that's it okay so yeah that's the easy part no equations good now I was sorry we have in the program there is a really many body okay so do you have questions about this you have to wake up at a certain point let me just just inform you okay so let's go to the to the to the real job now we do many body okay what time is it now are we on time I was quick okay because in general I'm not quick I'm very slow okay so let's now do with the many body okay so at the very core of yambo is quantum mechanics is there any one of you that doesn't know what is a bra or a cat just to know as chemists I mean how would you how you are distributed and the chemist just can raise the hand chemist all the others are physicists it is an engineering physicists all the physicists raise the hand okay so chemists in physics I'm very minority of chemists okay we'll be not not live for you I know I know for the chemists but I will let you anyway okay so but chemists I mean you do brackets right yeah so actually fuck yes actually fuck is fine the problem is after Artifuck Artifuck you go for MP whatever we go for for for GW I know I know okay but I mean let's do now a quick review of quantum mechanics the easy things that we need for for yambo and then we will introduce many body in our in a realistic way so a simplified way okay so quantum mechanics make sure then the many body problem and Artifuck why actually fuck because I think that Artifuck just can give you a very good insight about the different paths you can take to solve the problem in a weekly correlated case okay so the problem we need to solve is to create a micromarker connection so you have you're a mctonian that actually this is a mctonian is is just the poor electronic one but in general there are a lot of a lot of other actors entering the mctonian like phonons or spins or magnetic fields electric fields and so on and so forth but I mean the the core of the many body problem is already inside electronic case so now you need to find a connection through between this and mctonian and the observables in this case there are three observers that you can calculate with yambo you can calculate bunch structures you can calculate with of the structures positions optical absorption including temperature you can include temperature with yambo with an electron phone interaction and you can also calculate time-dependent quantities in this case is polarization time-dependent polarization through many body and also through the berry how do we do it that the each of this somehow is an observable in the easy cases you can really write it as an as an operator that can be you know the current the current of depolarization and also the bands that they can be connected to averages of operators so you introduce this space of states so given the mctonian the eigenvalues of this and they can vectors define a space this is not a normally complete space on which you can calculate averages and also time-dependent averages so you can introduce a time-dependent operator switch down an interaction and this system will start oscillating and on the basis of these oscillations you can calculate quantities then the very job is to rewrite this very compact problem to expand the problem because I mean when you define the observable as an average of an operator you are condensed as a simple as super simple it's just one line but to calculate it and to discretize it you have to make it explicit this is our work of theoretical physics to write this condensate average in terms of something that can be calculated one way is through diagrams this guy is Freeman Dyson Dyson equation and the Dyson equation is a way to rewrite specific case of specific average in terms of a series of which you can calculate analytically the terms and then you're done if you manage to sum this series you are done you can really calculate at the end get a number that's the point now what is the complicated part about this term and you will see in a second this first part you see is a summation over the the electronic states the electron the electron sorry I is an electron you have an onion of the single electron so this first part represents an electron moving along if the electrons moving moves along then the solution is just to find the spectrum of this amitone and but this is the beast because it will just feel electrons moving reciprocously so this means actually that in this room in independent particle approximation if some of you well the fun of some of you will ring the others will not care we'll not see we'll not hear anything they will just look at me instead the many but interaction will do in such a way that if your phone will ring some hands with some head will turn and actually the heads will turn depending on the distance unfortunately the column interaction is really a beast because it's very slowly decaying potential very slowly I mean there is that I mean in transform moment in transfer space goes like one over two square is even divergent so slow to be divergent in when you do the footage as warm this is also a lot of problems actually it's also source a lot of physics I mean natural works I mean if you look at nature from from math you see that the most interesting things in nature in math are divergences like one over q square so your plasmons because of the one over q square okay so the many body problem is the problem of connecting the against states of the full amitone to the against states of the single particle part so we define this lower case and other against states of 8 of small h of single particle part and an uppercase and the against states of the wall of Newtonian then again you have a cat that is a state and the bra is the adjoint this is fine right yeah this is okay okay this all you know yes and then you also know that if this operator commutates commutates with the Newtonian then it's stationary and then the average is just simply the corresponding against state good okay now the easiest way we can do is just just to neglect the interaction if we neglect the interaction then we approximate amitone with only the independent particle port so in this simple cartoon the interaction are those lines every electron is this yellow sphere and the interaction are the lines if you remove the lines then the solution is trivial because the state the exact against state of the full amitone and is the exact against states of n independent electrons this is just a product of the single electron states this product is averaged with a function representing the level of excited state in the ground state we are all sitting now in the first excited state some of you are just happened here so it's just a way of counting the single particle levels it's trivial I mean if you have a finite temporal system we will be the waiting function yes if you have excited state of an electronic independent electronic system at high temperature or this is the function it has two names one is Italian and the other is Polish I mean if if they are bosons if they are not electrons of our boson the function is of the name of an very important Indian guy yes the boss answer is for yeah for fermions yes yes we'll be a formidable function so independent particle approximation to excited states in the sense of temperature will be a formidable rock so yeah so in this case you can we'll write this air complex average as a functional of the averages in the free single particle states for example the amitone of the ground state is the sum of the occupied energy levels that's it it's easy and then you will see that we will show you how to calculate several quantities it's independent particle approximation it's easy everything is practically analytical and okay then I mean one important point then you will see along the the lectures why I mean is it always so bad independent particle approximation well depends indeed first you have to understand the physics we go back to the original argument we have to understand the physics and then compare what you're calculating with what you're interested in and see the level of approximation unless you don't have formal proofs that the approach we're using is the exact one you have to use this let's say validation with check with experiment you understand more about this but actually for I think that 99% of the things that we are gonna talk about we don't have formal justifications good now in the real world the amitone includes several effects that we will neglect for the moment because in the full amitone and there is also temperature there are phonons there are also other kind of actas can be manians can be spins indeed and every of this element introduces an additional interaction term in a million so for the moment we neglected fully electronic we stick to the zero temperature so what I will talk to you today is zero temperature problem there's a finite template that the tools change and also we will use a static amitone for the moment we will not introduce a time-dependent fields and we will proceed to the ground state okay so in this case the the core of the many body problem is the following as originally introduced by Landau so you have those three electrons are there and then you have the full interacting problem is there any way to replace the single actos the single electrons with something that is slightly modified but still weakly interacting so if you want yes if the phone will ring we will all turn our head but if the the person with the phone has an overcoat you know or a big pullover that is actually shielding the phone then the the sound the music will be weaker right and then maybe only a few persons around will turn head this pullover is a way to dress the electron so how do I define and how do I know if it exists such a representation so in the many body methods the idea is from a forbidden point of view is to replace this amitone and not with the free one but with a free one with in addition a many body potential it's a single particle many body potential that is not produced by nature is something that you introduce mathematically and then you require to this potential to satisfy some condition to reproduce something of the full amitone what now we see then with the mitone will also introduce in the case of time dependent amitone and our time evolution by this let me skip it for a moment I will go back to this later one problem how do you how do you approach this this problem or define this potential who of you doesn't know anything about the FT little so little little okay yes okay that's good and all the rest you know what is the FT it's okay and it's important for us because then if I give the FT for given then you understand nothing wow only one only one doesn't know how number one theorem would you be able to tell at least what is it talking about what for you for me student I mean you should know come on I will ask you later it's a number one theorem who has nothing who doesn't know it no okay only one okay so you just a little bit okay that's fine so density function theory is a method to define this potential and it's a variational method so one way is a variational way and I will just mention it but the straightforward method that you will find on a textbook is use perturbation theory this is the the poor man approach you say oh look I multiplied interaction with a pre-factor and then I do an expansion I assume that I can expand the agonist aid in powers and then I defined the coefficients in such a way that to a given level of approximation the two states are the same this is perturbation theory if you do with two level problems you can have this is the true level independent particle part then you are the potential that just mixes one and two two levels one and two this is very sturdy for you can do it I mean it just do the expansion you can solve exactly and find this but then you can also take this sorry this thing and then expand of powers of of lambda when when you multiply v by a lambda and then you get that you can expand the exact agon states in powers of lambda now of course in this case you solve exactly the problems 2 by 2 they multiply v by lambda and you do power expansion and you see yes I could just expand in powers the many body problems that is a case where you cannot solve exactly the problem because you cannot solve exactly the full Hamiltonian so in that case you use perturbation theory and perturbation theory is trivial you expand the agon states and then you are required the theory you are what required the expansion to give this is the agon state agon value problem explicit then you expand in powers left right hand side and you compare term by term by comparing term by term you find an expansion for the agon values for the agon states this is the static perturbation theory and again using study perturbation theory applied on the 2 by 2 level system you just get this expansion again we are not at the point of getting a potential we are seeing that with which study perturbation theory given a certain perturbation this will modify the state and the energy but then you may wonder where is the potential now to introduce the potential we use at refoc I think at refoc as gives at the end to interesting concepts that can be used in general very very much beyond at refoc so what is at refoc at refoc as a way to solve the many body problem within certain stringent approximations assumptions in the case and then you can introduce at refoc in two ways one is with the perturbative approach and the other is with the variation approach if you do it with the perturbative approach yeah I mean at refoc is just easy because you take the independent particle part then the ground state of this emiltonian independent particle part is just a product of states and the agon function is as later determinant and then exactly like in the two body in the two-level problems you do perturbation theory calculating just averages exactly like a study perturbation theory you go in powers of the interaction so at the first order you have the correction and the second order you have the second order correction now when you solve the I mean I don't want you to get all the math because it would be impossible just get the ideas you do perturbation theory then you correct the energies then you go and look at the definition of the ground state energy at this within this approximation you see that again is a sum of single particle energies in our true folk if you do what you fuck you do the math you realize that you can rewrite the ground state energy with the interaction treated at the first order so you take the interaction you treated it to the first order then you realize that your total energy is a sum of single particle energies but they are now modified so this change in a single particle energy can be written as an average of a potential you can introduce the potential in such a way to give the change of the single particle energies within second order perturbation theory this potential is composed of two pieces one is this part that we call archery and the other is this other part we call exchange the archery part is something you should have expected from simple physical arguments because the archery part is just a potential produced by the density of the system beyond the single particle approximation where you have only the kinetic part the first term that appears is just the standard electrostatic potential this comes out so normally naturally in the vertebrative approach in addition there's another term that is the fuck term this fuck term is instead induced by the form of your egg acids that is just literally germinant the B and T symmetric it just avoids electrons to feel ferments to overfill a single state so it's possible for two ferments to be in the same position so it's Paul exclusion what is really important of this approach is that you have even if within severe approximations out to fuck we're written the many body problem as a single particle problem under modified potential you can actually we found archery folk through a variational approach completely different in nature where you actually assume that all that the ground state of this Hamiltonian will be a superposition of the German and you find this position such a way to minimize the energy if you do it use the Lagrangian approach then again you find an equation for the single particle states of the ground state that solve an equation that is the archery folk equation where again you find the archery and the fuck potential now there is a big difference with the petrified approach in the petrified approach these states that enter in the potential itself are bare because it's perturbation theory so you take your system that is not interacting with this non-interacting system when functions I have energies you build the potential that will normalize the lexons themselves so you see this not is the bear level entered in the potential and this potential will change the energy of this bear level so the change of my energy depends on myself depends on myself and depends on all the others is a self-consistent problem so again in the simple example I gave before in the pullover of the lady we are all involved in creating this pullover so but we must be dressed as well so we are bad we build a first version of the pullover for all of us then again with the now with the pullover version one we build up another pullover version two this is a self-consistent cycle that archery folk as built in it is important concept because you see that in many body if you do perturbation theory you are bare objects inside definition of the potential if you do with the variation instead the objects inside the potential are already dressed so take a more message in archery folk so you have archery folk and this is pauli so in the archery folk problem you have just physically a simple introduction of electrostatic and exclusion exclusion principle so not very much not not very much fancy but there are important properties that we must take home for going beyond first is that the particular approach in the particular approach if introduce that fuck with the particular approach like energies and when functions sorry and this will change about when functions will not change inside the potential in a variation approach everything must be fun self consistently but again in both cases the folk potential defines a potential effective potential that exactly gives the single particle levels that correspond to a variation on minimum in a variational approach or to a second order perturbation perturbative correction in the perturbative approach say now wow much of it's great then you apply archery folk and you get that the gaps of your systems are systemally overestimated leading for rather think it's like 5 EV you are above of 5 EV you are completely off no way I mean but this is something expectable I mean actually chemistry will tell me no archery folk is not so bad yes yes it's true if you take a systems very tiny some solids if you take a system that is only few elections then there are effects important so in the case of few elections then archery folk is particularly fitting because in that case what really makes a lot of difference in self-interaction so we only few that this I can explain you but I mean anyway archery folk for few few elections is particularly much more more effective than in the case of extended system for extended system is pretty bad so this means they are missing we are missing something while we are missing and this is fine one because what we are missing actually is easily connected to form and diagram we miss correlation we miss correlation so correlation is what is missing when you do just archery folk I mean the point is that physically now we are permanent because how would we introduce a conceptually in a conceptually simple way correlation now we are just introducing as something that is just missing now in the next lecture we take two minutes break in the next lecture I will try to introduce correlation in a simple way with a realistic approach without even we don't use in diagrams or something like that but at the moment what is important of this first part of the lecture is that they come messages that in many body really the problem that we have to solve is to define in as much as easy possible an effective amiltonian effective potential and effective whatever that still keeps my solution my property to the level of a single particle problem of course this potential have to be careful because in archery folk this potential there is no way it is defined by the method itself when we we need to do this correlation we need to be careful in the sense of filling this potential with properties that are interesting for our problem but still the problem will be to introduce a potential that will embody within some ways the many body properties okay so now what time is it okay now I I don't want to do a 40 minutes lecture I prefer to do smaller lectures so we will do correlation after this and now we like to have discussions so if you have questions if you don't understand anything if you want to rest five minutes this first part is done also so this way I think you would be more awake if you do like one hour lecture in general also me after one hour lecture after the I just decay I just sleep 20 minutes then yes yes okay yeah sure it's yeah I mean oh and I can tell you even more and you want to comment on the self-interaction expert so I think that there's a very different case for what concerns density functional theory in many body perturbation theory and in a sense the case of many body perturbation theory somehow easier since if you have a five month diagrams somehow you you see exactly what happens there in the electron-electro interaction by this I mean that typically so if you start from expectation values of the electron-electro interaction operator which has four field operators in that we direct and exchange terms that when applied to same single particle state basically would cancel out so somehow in this respect the art refocus prototypical you have the cancellation of the art tree term with the exchange term and somehow so one of the definitions of self interaction is exactly when you go to higher levels or higher orders of theory the fact that in some cases you miss some of these exchange diagrams that may cancel out the corresponding direct diagrams and this is exactly what happens by the way in the GW case so in the GW case you have screened interaction and the diagrams you miss are already there at the second order in GW mix the second order exchange diagram and in fact you suffer of self-interaction that kicks in via the screening the RPA screen that is also well known in chemistry to be not self-interaction free and actually have what is self- screening within GW this was documented both theoretically and computation things are instead different if you think at the case of density functional theory where you don't have such information of diagrams so somehow you have the hood of your car that is closed and you cannot access that piece of information and in in that case you have to refer to other definitions of self-interaction one of these was the basically relying on the an exact property of the total energy as a function of the fractional number of electrons that is piecewise linearity of the total energy that is somehow connected since the derivative of the total energy with the occupation is somehow related to an effective eigenvalue single particle eigenvalue so somehow the fact that total energy is piecewise linear means that these eigenvalues do not depend on their own occupation that again is concept related to self-interaction still is not the very same definition such that the art refoc that is totally totally self-interaction free from a diagrammatic point of view is not self-interaction free in the sense of piecewise linearity still in density functional theories somehow the only thing you can do you can only define total energy self-interaction in in that framework in general as this was referred by I think Purdue groups at least as many body and body self-interaction freedom and to me that is the proper definition density functional tier of self-interaction is still an open options there are several proposals there if I may add a very simple old man's compliment what not very very rigorous very theoretical but to me the self-interaction error is the name you give to the feature of your theory that makes the energy of the hydrogen atom different from one readberg so if you have a complex theory such as many body theory the minimum requirement of the warm density functional theory or whatever quantum chemistry you name it couple clusters anything the minimum requirement you have with such a complex theory is that it can solve the problems that you could solve without that theory unfortunately none of those complex theory can solve one body problems you don't need them in those cases but it would be relieving if you could and so this is not a definition but but if you do density functional theory for ordina of course Hohenberg and Kohn say that you do density functional theory for one electron it gives the right result it's a theorem but current implementations of density functional theory applied to one body problems to one electron problems give the wrong the wrong energy the name you give to the mistake you make is a self interaction error so a little bit a step further in elaboration is coming to what the other Andrea said in his lecture that this this theory is Hartree-Fock and density functional like are mean field theory or mean field like Hartree-Fock is indeed mean field density functional is not but it has the form of of a mean field theory which means that you can attribute physical properties to individual electrons which you cannot in a truly interacting system so that you can you can speak of properties of individual electrons in mean field theories so you are tempted to treat the one electron at a time as you would do in for a nitrogen atom for a one electron formally mathematically they are the same elaborating a little bit more so the self interaction error in density functional theory and in many body perturbation theory and in any sophisticated theory is the relic the relics what remains of the original scene of those theories that fail for the hydrogen atom okay so how do we do I mean I have to do correlation then it takes 50 minutes to correlation then we go for the coffee break because now is it's 10 30 now 30 always the plan of a break we do coffee break and then we do correlation