 Recording in progress e benvenuti a questa seremonia per l'aumento del 2022 valter Korn Pryce per il modello molecculare quantomeccanico che questo anno sarà avverso a Dr. Debashri Ghosh di Kolkata. Voglio andare fuori da Sandro Scandolo, che ci dirà un po' di parole per il IPTP. Grazie, grazie Stefano. E benvenuti a tutti. Siamo qui per l'energia totale e per la seremonia per l'aumento. Questa è la terza edition di Pryce, che, come ricorda, riconosce questa contribuzione nel modello del modello quantomeccanico. È stato istituto jointemente dal IPTP e dalla Fondazione Espresso, e qui Stefano Baroni è rappresentato nella Fondazione Espresso. L'aumento è avverso annualmente, quindi ogni due anni, a un ragazzo, a un adolescente, o direi di più, il scienziato, tra 45, dal counte di sviluppo in cui potete avviare contribuzioni in il modello quantomeccanico e il modello molecculare per la condizionazione del counte di sviluppo o l'economia di emergenza, con ademozia sulle tecniche principali. L'aumento è stato istituito nel 2016, e, secondo me, Stefano avrà raccontato alcune parole per il modo originato, originato in espressione, la connessione di prezzo con Walter Cohn, che, infortunatamente, è passato a via precisamente nel 2016. È, ovviamente, molto supportante della idea, ma non poteva non vedere, infortunatamente, il primo vincente, che era al momento nel 2016, era il professor Jan Mimma, dall'Università G.L.E. L'avorto era giusto in 2008 per Gabriel Merino, dall'Università Mexico, dall'Università Merida. E, infortunatamente, nel 2020, non ci siamo awardati perché di Covid, quindi siamo ora nella terza editione del prezzo. Qui ho solo collettato alcune foto di Walter Cohn a l'ICTP. Se visiti il display diversamente, vedete foto anche qui nel Budinich. Vedete, all'anno, utilizzavamo progettori di overhead, progettori di reale overhead. E la foto qui è con la meeting di Nobel Laureates, con Ahmet Zewail, Rulof Marcus e John Nash. Qui, in realtà, vedete, in compagnia di un formato membro di l'Adviso Scientistico di Tutta l'Energia, il professor Baldirischi. Non credo che il polso sia qui oggi, ma credo che sia una piccola foto. L'avevo preso nel 1986, per l'occasione di un internazionale su la fisica semi-conductora, dove Walter Cohn è piaciuto di dare una risposta historica al campo. E, ovviamente, vedete anche alcuni cacchi di cacchi, in qualche modo lì e sotto, oltre a lì. Allora, grazie molto per essere qui, e ora, Stefano, se potete dire un po' di parole su behalf di la Fondazione Quantumerc Presso. Grazie. Sto ancora un po' di tempo, con alcune recollezioni della mia connessione personale con Walter Kohn e le connessioni di Walter con l'organizzazione più ormai, l'organizzazione prima di questo prezzo. Walter Kohn, ovviamente, è universale conosco come il padre della teoria di funzione densità e come il padre della moda quantomeccanica e materiali di moda, senza lui queste conferenze non existeranno e no novasi potrebbero sfruttare in questo ruolo oggi. Il nome di questa conferenza è molto bizarro che inclusa queste strane parole, tutta l'energia, come se fosse un'energia particolare esiste. È un'allusione, alluzione al paradigma che è introdurato dalla teoria di funzione densità. Perciò la teoria di funzione densità di funzione, la computazione di fisica solidaria era molto concerneda con la calculazione delle energie orbitali, i bandi energiati e i livelli di impurità. Il DFT ha fatto che è possibile ottenere le energie totali di sistemi connessi, intanto con la forza che è attenzione alle atomi individuali, in modo a modellare la stabilità relativamente diversa sulle fasi e strutture di materiali, le reattività chemicali, le dinamiche e tutte le cose che abbiamo avuto una costumazione e che sono visti per il successo di queste conferenze. Come un giudice adolescente, Walter Kohn ha soltanto escapato la ferocità di la persecuzione nazista e ha perduto i suoi parenti e la sua famiglia nel processo. Ha coltivato un'identità molto forte di giudice, ma ha creduto in un'essere personificata di più perversiva che i giudici, i cristiani o i muslimi, per questo punto. Walter Kohn era un uomo e un uomo giovane. Ho chiesto di riportare un'idectote che ha detto a me. Sì dopo che ha avuto il Nobel Prize in Chemistry nel 1998, ha invito a una scuola in Vienna da cui erano espaldi nel 1938, perché i rossini rossini infostrano i nazisti prima di essere in Ostria e per salvare la sua vita nel 1939. Hanno saputo che era costumato per molte scuole austriani per awardare una diplomata matura simbolica e reparatura, che è Baccalo Red. A tutti i giudici che erano espaldi dopo la prossima scuola di Ostria, a Dinas di Germania, ha scoperto questo evento e ha deciso di declamare l'awardo, fino a che l'ospitalità di i giovani ha cambiato il suo mente. Hanno saputo che ha deciso di riportare la sua determinazione, quando il direttore della scuola ha scoperto una diplomata matura non matura, in memoria delle atrocità che ha scoperto da lui, la sua famiglia, e le loro persone, prima e durante la guerra mondiale. Hanno saputo che ha scoperto una diplomata matura non matura, fino alla fine di quei giorni. Walter Kohn era un amico generoso di Trieste e di ICTP, come l'ha detto. He enthusiastically agreed that his name be given to the prize that we are awarding today and corresponded with us while we were organizing its first edition in 2016 till the very end of his days. As Sandro remembered, he couldn't make it to the first award of the prize. Walter Kohn was a man of peace. His advocacy for solar energy and the opposition to the civil use of nuclear technologies was mainly motivated by the knowledge that the line dividing civil and military nuclear technologies is very thin. I'm sure that where he alive today, he would firmly stand by the people who suffered the aggression of foreign powers these days and the tyranny of dictators at home. So I'm done with this very short memory of the men and I would gladly leave the floor to Professor Rod Hoffman who will speak from Cornell University and who will tell us much more about the person and the scientist, the man of Walter Kohn. Please Professor Hoffman. Yes, yes, can you see my presentation? Yes, yes. Very good. So, I'm speaking to you from Cornell University. You see here pictures of Walter Kohn whose name is appropriately attached to this award who from his being a young boy through a scientist and then later on in life. He lived a, as you see from 1923, that his life was indelibly affected by the events of World War II and they led to a progression from Vienna where he was born to the United Kingdom and then to Canada and eventually to USA where he spent most of his life. The those events are part of, of course, of my history as well. I was born in what was then South East Poland but now is the Western Ukraine and we went through many of the same things both in the background and in what we experienced and we both lost his parents and I, my father, to the Nazi obsessions of World War II. I don't want to dwell on those so I do want to vote to you a little piece in the present context from his biographical essay at the time of the Nobel Prize on his teachers at this gymnasium. That's not the one which gave him the non-honorary matura but it was a school that was established for the best Jewish students who were expelled from the state schools and to which he went at age 15 and that's when he got his first exposure to physics and he describes two of those teachers and again the enormity of those events that took place can be appreciated by the fact that those two teachers, Emil Nohel and Victor Saveth, who remain today remembered largely by what he wrote of them, were killed in a Holocaust. He said Nohel was a tall, quiet, noble man who devoted himself to his students. Though I was only 15 going on 16, I already understood due to Nohel's role model and by comparing myself to others what it meant to really comprehend something in physics. This is one of the most important insights for a future theoretical physicist. One reason I tell you this is because we are under a wave of machine learning, neural networks and artificial intelligence and that may not be what is meant by understanding in physics but he already knew that at that time. Saveth was also a fantastic guy. The thing I remember about him is that while he was teaching us he told us about a new book he was reading by Louis de Broglie called Matter and Light. There is a lesson here for us as teachers and that is talk to the students. Tell them what excites you. Tell them about the latest paper that you have read or the book that you are reading. Those were the two lessons I drew from this. Over the right are three books, two of them. He, Walter Kohn, purchased in Canada at age 15-16 some of the first books that he purchased with hard earned money, hard east pure math and John Slater's volume which is a rather compressed volume about electronic structure of matter but also about statistical mechanics. It's interesting to see these books. I'm not going to tell you very much about density functional theory and its evolution first because you know some of it but also there is a very good article written by someone with understanding of the physics and that's Andrew Zangwell's The Education of Walter Kohn and the Creation of Density Functional Theory in a history journal in 2014 just two years before he passed away. What is interesting is what also Zangwell says at some point in this in that Walter Kohn earned the Nobel Prize in Chemistry by asking himself a simple yet deep scientific question He answered that question in an elegant and thoughtful thought provoking manner and then exploited his result to formulate the quantum electron method in a manner which made calculations for real systems computationally feasible. The interesting thing here is the first of three points that I will make in a moment and that is that there are two aspects to the Kohn-Hohenberg-Schamm papers of the early 1960s. One is the simple formulation in an elegant way that connects up to his previous work and use of the variational theorem and in some ways is connected to Kohn's long collaboration with Luttinger in that is his love of mathematics but then he went on to reformulate that theory in a way that you could compute to it. Underneath is a little cartoon of Kohn learning chemistry all this that Walter Kohn received a Nobel Prize in Chemistry together with John Popo is just a testimony to the infinite generosity of chemists it was a very appropriate prize and it was just as appropriate to recognize Kohn for this and recognize this such by the chemical community as it was in another time to recognize Rutherford with the Nobel Prize in Chemistry Oh, if only physicists were as generous they're not I do want to tell you three things about Walter Kohn's science the first is I say here and I've already said that he loved mathematical elegance but he reserved it for situations where it was necessary this is something said by Langer and there is this unusual double development of DFT theory both the theorem and the thought immediately about applications there is also another interesting matter and that is the connection to the Thomas Fermi theory and that is how approximate models which are of no use necessarily computationally to represent reality those models can serve as an impetus for developing something better the second point I want to leave you because I want there to be a little bit of scientific content or some thinking in what I say other than just showing you pictures of Walter Kohn there is this continuing, seeming mystery and that is how it can be that the density a function of just three variables the Cartesian coordinates of the density that this has the same information content as what seems to be a much more complicated function and that is the detailed many electron function for a molecule or a solid where the wave function depends on the coordinates of each electrons there seems to be many electrons there seems to be a reduction of information what's going on I'm not going to tell you my take on this but what I want you to know is from conversations that I had with Walter Kohn this is what this troubled him also the end of his life even as he understood it and the way he explained it is the, well I'm not going to tell you how he explained the other thing that I want to tell you is something interesting that is obvious to you what you should think about it and it has to do with the early history of density function of theory to actually compute anything approximately the density one needs some auxiliary functions for instance basis set orbitals for a molecule, plane waves for a solid these auxiliary functions in the theory were denied any reality they were just what they were mathematical functions but of course they turned out to look like the one electron orbitals or the band structures of solids and I had a paper which is entitled here in that period 1999 where we were trying to understand these things about what do Kohn-Sham orbitals and eigenvalues mean and there is a little drawing here for water of the various molecular Kohn-Sham orbitals at the right and the simplest wave function approximations to them there isn't those things are real and it's important for an understanding of density function to think why those auxiliary functions or how they are related to what are the real wave functions it's the end of my story about Walter Kohn he is, it was a privilege and an honor to know him late in his life to share with him and his second wife Mara to a story because she has a connection to it as well of Europe in that times and it is very appropriate that this award has his name attached to it but now I'm going to switch to something else and that is to saying something about the person being awarded who will be introduced after this and this is the Basri gosh so here is the Basri you will see her in life let me tell you a little, just a little bit about her and her work she ascended the chain of education in the right way meaning that she went to the very best places which include Presidency College of the University of Calcutta and then eventually to Cornell where she got her PhD not too long ago with Garnett Chan who has since departed for California I knew her from that time and we in fact worked on something together on something rather different which is translations of the Bengali poet Joy Goswami she went on to a postdoc at the University of Southern California with Anna Krilov and then began return to India and began her research in a series of institutions that you see which went through the national laboratory chemical laboratory in Pune to the place where she has been for the last five years and that's the Indian Association for the Cultivation of Science where she is a full professor her work has been recognized by a number of awards by just about most awards that young people in theoretical chemistry obtain and one of them that's important is the annual medal of the International Academy of Quantum Molecular Sciences not Arts and Sciences here the work that Debashri has done she will talk about it is both an extension of her work previously in a number of ways with the best methodology for doing calculations but what is also interesting is that one of the main themes of her work is to transform the computational picture of the theoretical chemist imagination to allow the consideration of realistic biological systems in particolar, she has had a strong interest in excited states and excited state properties and to do this she has done everything from the best quantum mechanical calculations that are available to a mixture of those with molecular mechanics type calculations so-called hybrid QMM methods and these are just symbolized by this little picture here the interest in the basic theory that arose from her PhD work was for strongly correlated systems and these occur in chemistry occur in extended systems and perhaps chemists are actually better aware how poor the normal calculations do at going beyond static pictures of correlation and there is a series of studies that she has done about the singlet triplet difference in a group of molecules called polyacines which you see here and some are just long linear chains almost like polyacetylene but some are more kink chains or helical ones and there are interesting differences in the way correlation manifests itself she has also worked on a popular problem in this field and that is triplet the formation of two photons out of one singlet excitation two triplet photons which then propagate and give away of getting higher efficiencies these are in some ways extensions of her work on strongly correlated system but there is another direction in which she has taken this work which goes back to the slide that I showed you about her interest in excited state properties of biological systems and she has now become the world's expert in theoretical framework of melanin melanin is a heterogeneous polymer it is used by the body in protection against the actions of ultraviolet light like anything that is biological it is the product of evolution a chain of evolution and it is not simple it is a polymer that is made up of a number of different monomer units the only thing simple in the world aside from what physicists and chemists do in laboratories is our imagination we have trouble with complexity in general nature does what it has to do so she is very strongly interested and has combined her various interests to give us a picture of the mechanism by which melanin gives us protection this involves first knowing something about the structure of the polymer knowing how it absorbs light and then how it does the photochemistry breaking up into monomer units polymerizing again it is a complicated problem but she has made real inroads in this with that I am glad very happy that one of our best students at Cornell is now in a situation to receive the Walter Kohn prize she deserves it thank you very much so let's thank again Professor Hoffman and let's move on to the actual award of the prize that will be presented by Professor Narasimhan from Bangalore Good afternoon, I'm Shobana Narasimhan from the Jawaharlal Nehru Centre for Advanced Scientific Research in Bangalore, India in my capacity as chair of the jury for the Walter Kohn prize it gives me great pleasure to be here today and to join you in congratulating Debashree Ghosh on being the Walter Kohn Prize Laureate for 2022 we are grateful to ICTP and the Quantum Espresso Foundation for instituting this award and I would also like to thank my fellow members of the jury for the thought and care that they put in into the task of selecting a prize winner the other members of the jury for the prize selection were Nithya Chetty from University of the Witwatersrand Johannesburg, South Africa Rav Kebauer from the Abdul Salam International Centre for Theoretical Physics, Trieste, Italy Ouz Gulceran from Bilkent University, Turkey Belita Koila from the Federal University of Rio de Janeiro, Brazil and Jejun Yu from Seoul National University, Korea we had many excellent nominees for the prize this year we feel that this shows that nowadays excellent work is being done in this field that of the quantum mechanical modeling of materials not only in countries that are economically advanced but also in those parts of the world which are developing countries and emerging economies since promoting science in these countries is a major part of ICTP's mission and has also always been an important priority of the Quantum Espresso Foundation this is particularly encouraging and makes all of us very happy I will now read out the award citation The Walter Kohn Prize for 2022 is awarded to Professor Debashree Ghosh for her path-breaking work in developing novel quantum chemical tools for materials design and the study of biological function Combining techniques from physics, chemistry and biology her work has made important advances in our understanding of strongly correlated materials and complex biological systems Congratulations Debashree Professor Ghosh, the floor is yours for the lecture that you will deliver us Hello Sure Okay, so first let me start by thanking ICTP and the Quantum Espresso Foundation for thinking me worthy of this award Of course the jury members my many supporters who have kind of you know egged me on to do stuff that I wanted to do and I would again start with thanking my students whose hard work I'm going to present today I will have a picture in the end but let me begin by first thanking them so even though Professor Hoffman mentioned about machine learning and how they might not lead to learning I'm going to show how they can lead to learning so let's see and although the title is machine learning the configuration space I'm going to show bits and pieces of various of the research that we do in our group so as was mentioned quite aptly by Professor Hoffman I am interested in excited states of biological systems in their condensed phase in their messy complicated situation and excited states are difficult because they are more diffuse they have charge transfer and so on and there have been talks today and yesterday which has highlighted many of those difficulties to that effect we develop hybrid QMM approaches for these excited states we develop fragment based and machine learning based polarizable force fields because here the environment doesn't get to be a static observer they have to participate to make the biological system so active and interesting we also develop methods that can deal with strong correlation because as I am going to show and as has been shown by many speakers before me excited states are strongly correlated most of the times once we have developed these methods we kind of apply them to understand processes such as photo protection in melanin we look at spectroscopic properties of fluorescent proteins, RNA we have recently started looking at singlet fission and things like that so if I go into the first part of my talk I am going to focus on these strongly correlated systems ok so as was again mentioned by professor Hoffman I don't know how he knew what I am going to talk about because I didn't tell him but well he figured so one of the topics in our group which we are interested in is singlet fission so what happens in these systems is ok if I have two chromophores that are kind of close to each other say a molecular crystal or things like that and if a light kind of can be shine on one of these chromophores they gets excited to a local exciton this local exciton state can then undergo singlet fission to give a coupled triplet state this is actually a really cool innovation in some way which has recently been used as a hybrid material in solar cells where it can mop up the energy that other traditional solar cells cannot so it is indeed increasing the efficiency of solar cells as we know it ok so what do we need to understand the problem that is still existing in this field is these kind of chromophores that have the correct criteria to undergo singlet fission because as you can see the energy of this system has to be higher than the energy of this which means the two triplet states has to be lower in energy than one excited singlet state and this kind of molecules are actually fairly rare they are found in these acines, polyacines and in carotenoids and stuff like that but really they are difficult to synthesize this limit is difficult to achieve so chemists are always looking at newer and newer molecules that can actually achieve this energy criteria furthermore the mechanism of this singlet fission is also quite intriguing because in most of the situations when we look at the coupling between this local excited states and the distributed coupled triplet states the couplings are fairly low so how does it decay from this singlet exciton state to here so that forms another part of our research to understand the mechanism of singlet fission we have recently found out there can be quite a few multiple pathways and how to calculate them and things like that again that will form the next bottleneck of how to design new materials that can achieve good singlet fission so that's one of the problem in our group the other problem as was mentioned is the photo protection in melanin now melanin is a really curious molecule or system I shouldn't call it a molecule because it is many many molecules together so melanin is created of the monomers which are dihydroxyindole DHI mentioned over here that has a nice spectra like you would expect it has its maximum of absorption over here and here however when you put it together in a melanin form which as was mentioned before is a heterogeneous polymer this flat broadband spectra is what happens it's completely monotonic it's completely different from any organic molecule that we know of that's good for us in the sense that it mobs up all the energy that is incident on us as sunlight UV visible you name it it wipes it off but it makes it very difficult to study of late it has been understood that this monotonicity arises from large scale heterogeneity in oxidation states in different ways that they are bonded in how they are aggregated and things like that but we also want to find out what part of the spectrum is due to what kind of molecular structures that's one part of our research the other being okay let's say the melanin absorbs that sunlight now how does it dissipate all of that energy without undergoing any damage in their own structure that's actually quite a complicated pathway that we have come up with and there also we see that heterogeneity plays a very integral role I'll talk about this part in a little bit of a detail towards the end if I can get till there okay so when we are talking about these two quite disparate problems singlet fission on one hand, melanin on another hand how are they related they are related because both of these have excited state processes underneath it and excited state processes kind of tend to look as messy as this you might have your reactant which starts as a nice ground state structure it will absorb light go to its first optically active or optically bright state and from there depending on the gradients of the system it might encounter certain crossing points singlet triplet crossover so on and so forth it might even get into photo product formation or it can come back down either through radiative pathways or non radiative pathways so there's a whole plethora of processes that can happen in excited states and our group tries to find these in real molecules in real systems and we'll see how so of course we first start with the Born-Oppenheimer approximation we are within that limit for now I will show you a few examples where we are not in that limit but for the most of the talk we are in the Born-Oppenheimer approximation and in there we'll of course start with a single reference, a mean field Hartree-Fox solution but let's see how that would work if we take the simple example of water and I'm going to try and pull apart the bonds of water so if I pull apart the bonds of water the exact potential energy surface is this black one over here and if you do methods such as couple cluster which is the gold standard of quantum chemical calculation as has been mentioned quite a few times in other talks or some perturbative approximation such as mp2 you see that the curves are nothing like the exact one in fact they are pretty nonsensical curves the interaction energy should not go up and down like this it never should and the errors are if I plot out the errors it looks even horrible because at bond breaking limit the errors go to minus infinity which is just a disaster for a chemist because I would like to break bonds and make bonds and so on of course this is due to strong correlation of the electrons in those limits and in that and this kind of a phenomena is not just limited to bond breaking it is present in excited states which is going to be my topic of my talk today in radical systems transition metal complexes polyenes, graphene, metal clusters pretty much everything that is interesting in chemistry has this problem and and you see that the traditional quantum chemical methods that we have at our disposal does not work here of course therefore we need something else we need a multi reference or a multi configuration wave function in the valent space what do I mean by that again this has been alluded to in previous talks in many previous talks in this workshop so again as a chemist picture these are the orbitals I have occupied orbitals till the homo and there is the lumo over there and so on now if I have a big gap between the homo-lumo this single reference picture is very nice it follows our principle as we have studied from our bachelor's level classes and however what happens when this delta e or the homo-lumo gap becomes small in those situations the electrons basically do not have a single configuration in other words you don't have a single molecular orbital picture you do not have a single molecular orbital occupation in how to arrange these systems and in this valent space you have either all possible electronic configurations in the valent space or you have to pick and choose the most important ones now I'm going to show you how to pick and choose the most important ones because of course having all the configurations is going to be computationally extremely challenging as it's an exponentially scaling problem and just to give you a small chemical example because here there's a lot of work I mean people have talked about spin systems and so on but let's say I have a molecule with 30 carbon atoms which is a fairly small one at that these are acine systems right so here these are all flat acine systems there if I have only 30 carbon atoms which basically boils down to 30 pz or pi orbitals and 30 electrons in them the configuration space is as large as 10 to the power 33 and of course that's going to be just un feasible to do to compute a Hamiltonian on a diagonalize it or do whatever you want to with it and if you're thinking that ok maybe I will get a very big supercomputer and I'll get it done you know that if you increase the number of orbitals by one more or two more it's going to increase exponentially and you'll never catch up with that so what's the way out here I'm showing why the mass exponential in this crowd I don't need to show this anymore and the exact wave function looks like this in the occupation number formalism in the matrix product notation this is what it looks like where each of these these legs sticking out is basically each of the orbital indices ok so a small short course on matrix product states although last there was a talk yesterday where matrix product state was used quite extensively but still so if I have a real or a complex valued system number it can be denoted as a circle with no legs therefore a vector will have a single leg with an index attached to it the vector index matrix will have two legs a tensor of five dimensions will have five legs so you get the drift and if I were to do a contraction you'll basically get the two legs together and you have a holding hand index which is this this J index over here which is over which you have this summation or contraction and if you were to do a trace of course you have to be have to be left with something which has no legs sticking out so that's it so that's matrix product state in one slide that seems reasonably easy and therefore if I start from this huge answers which we saw was scales as d to the power n for I mean molecular orbital this would be four to the power n because the fox space of each molecular orbital would have four possibilities and now if I were to perform a singular value decomposition on let's say over here along this dimension so when I basically partition this first site and all other sites then I would be left with something that looks like this where I have a matrix multiplied by a diagonal matrix which is for some reason denoted as a diamond shape and then all other indices in one site and I can therefore choose once I do the singular value decomposition you do realize that I don't need to retain all the all the singular values if I only retain the most important singular values and drop out all the rest that might be a nice way of saving the computational cost of this matrix product answers if I keep doing this SBD ad nauseam this is what you will get and lo one behold it looks like I have exponential saving the N which is the system size has come down from the exponent to the mantissa which is all great it looks like we have found our solution but what we have achieved is that we have showed that MPS answers is great but we have still never not optimized MPS answers right and what we know is density matrix to normalization group or DMRG gives us a very good way of finding that answers infatti in my PhD and later what we did is we had coded up my advisor had the first this full molecular Hamiltonian DMRG and then we did the DMRG SCF to actually solve molecular problems now DMRG can quite routinely not very routinely but still quite routinely be used for molecular problems of reasonable size so what it does is if you again go back to this cartoon picture of sites and each site having spins you basically can take two of the sites and find out what is the wave function of on that state in other words you can find the reduced density matrix in that in that system part of the system lattice once you have the reduced density matrix again you basically can retain only the most important singular values and you can drop all other singular values thereby reducing the degrees of freedom you retain the most important degrees of freedom but drop the rest and then again you go to the next site you block and you keep doing this so your system is always scaling never becomes exponential it remains attractible and if I write out the wave function the first equation over here that's what our exact wave function or full C.I. looks like this is what your mean field or Hartree-Fock approximation will look and now what we have is we have added some entanglement between adjacent sites and as I mentioned before DMRG gives us a very good algorithm to determine these these matrix products in this way in this answers that's great but molecular systems are not linear not even by any stretch of imagination a molecule may look like this or even more ugly and the orbitals will look like something like this so how do you arrange them in that linear way because DMRG will go from one to the other to the other to the other like that and for that generally in groups such as ours what we use is some kind of an entanglement measure we look at which of the orbitals are most strongly connected to which other orbital and using that we can arrange them in a linear fashion as best as possible there are some machine learning approaches here that have also come up which are very good at orbital ordering because you can understand the efficiency of DMRG will determine I mean the ordering will determine how efficient DMRG is going to be ok so using that we have we are going to go back to our original problem which was the singlet fission and we will be looking at molecules or trying to discover new molecules that will be good singlet fission material so the parameter that we need to tune over here is the singlet triplet gap and we start with the pure pristine asines which has been studied for quite some time now and we looked at a few alterations to it the reason is again here a chemist intuition comes in quite handy because back a long time back we were taught that these azulean systems you know the 7 membered ring attached to a 5 membered ring these are these have much lower singlet triplet gaps because they are less stable their aromaticity needs to be I mean in order to have their aromaticity there needs to be a huge amount of charge transfer that's involved and so on so that was the logic that was given to us in our undergrads and you see that they were right the singlet triplet gap indeed was quite low but as you come larger azuleans the fall off is not so fast so indeed while we had thought that we might get very low singlet triplet gaps at decent size that's not going to happen with these kind of molecules incidentally these were studied before us by Malryu and co-workers but with the DFT kind of methods we also looked at these fused asine azulean systems these are very recently the kind of systems are being synthesized very recently you know 2012 13, 14 there are and you can papers that are coming up people synthesizing these kind of analogs and here you see you start with the azulean because of course you start with the azulean the 7 and the 5 and then as you attach more 6 membered rings in between there's a very fast drop off in fact there's a singlet triplet crossover so indeed we found the smallest molecule without any hetero atoms by hetero atom to a chemist it means anything other than carbon and hydrogen you can find a singlet triplet crossover so in fact you can get a very high degree of tunability with these small changes to the molecules which is all great but this is like trial and error I'm thinking of molecules coming up with calculations how would I predict it a priori in order to do that we kind of looked at the homo-lumo gap and the occupation number of the LUMO that's generally what's done to tune the singlet triplet gaps or screen for singlet triplet gaps in these molecules and so here I'm showing the correlation or rather the lack of correlation between singlet triplet gap and homo-lumo gap or occupation number of LUMO you see there's no correlation really there's no correlation earlier that this this kind of a measure the computationally affordable homo-lumo gap measure will be good enough to find this correlation does not work and so we kind of went back and we thought about it we were quite confused we came across this paper where they found quantum phases of frustrated two legs spin off ladders with skewed rungs these don't look like molecules right this title doesn't sound like a molecule but if you really look at the connections this is what a skewed rung ladder looks like on the right hand side and the skewed rung ladder if you kind of put this if you put this mapping back this is a polyasoline structure so indeed from this skewed rung or the combinations of skewed rung you can basically get some insight about these different phases that was found by Ram Shesha and co-workers so we went about to create a model Hamiltonian so that we can really look at these systems and of course there's the trusted handy Heisenberg Hamiltonian and we wanted to get appropriate j parameters because I have molecules at hand I can't just tune my j's to whatever and say that that's what's going to happen at j so and so I need to find the correct j's for my molecules so we go back to these Landers interval rules which have been around for a long long time and as you can see these are geomagic calculations of different spin states of this molecule and if you have large enough m states which is the bond orders you can have a very nice agreement of the Landers rule and the j parameters furthermore we can also go back and look at the already existing literature of partitioning Hamiltonians into effective Hamiltonians the simplest one that a chemist thinks about when partitioning comes up is Huckel molecular orbitals where you have chopped off everything and you just have the pi space, the pz space and you have some tunable parameters alpha and beta and still you can say a lot about the chemistry of these systems so that was a really cool kind of a starting point but we need to do a little bit better so we can even kind of think of these partitioning techniques where you separate the Hamiltonian into the most important of the model part and the outer space these are old work long time known and maudru and co-workers have actually applied these to molecular systems in early 2000s so we basically looked at quite a bit of these different model Hamiltonians that are out there and it so happens that we have had experience in using spin flip TDDFT formalisms and there it has been shown by Mehal and also Krilov that using a single spin flip all of these different configurations or different electron arrangements can be reached from a up up up or fully highest spin state so if there are three sides that is what I am showing over here and by looking at the different matrix elements that can arise between these you can find the different J parameters we have done quite a bit of testing with the different kinds of J parameters that are possible anyways to cut a long story short we have used these J parameters and we indeed see that there are signatures of spin frustrated configurations here you can see the spin frustrations where the two same spins come and clump next to each other of course because when you have an odd member dream you don't have any better way to do it and we have also seen how much these frustrati structures contribute to in different systems be it this one, this one or this one and indeed it shows that spin frustration is what is leading to these lowering of singlet triplet gaps of course again me being a chemist I went and looked back for signatures in the molecule and lo and behold if you look at the molecular geometries you will see that wherever there is these spin frustrations signatures of spin frustrations there the bonds are elongated it's like really the spins are there and pushing it apart which makes me very happy because till I don't see it in a molecule I find it a bit hard to believe because I don't know maybe I didn't build my model well or whatever so that's what I always keep suspecting whenever I'm working with model Hamiltonians ok so it's kind of all the stories are saying the same thing that's all good at this point we kind of had that way in that note we basically have a nice way of tuning the singlet triplet gaps of these polyaromatic hydrocarbons there's only carbon and hydrogen in those systems and still you can have a lot of tunability of the singlet triplet gaps you have the design principles in front of you but what if I wanted to extend these systems to do two dimensional systems and we all know that DMRG has a problem with two dimensional systems because of the because of the area law of entanglement right because if you are going to break up the linear system wherever you break the area between the left and the right blocks are going to be the same but if you have a system that is growing in the x and y direction in both the directions when you chop it off and along that area is increasing increasing increasing so two dimensional systems real two dimensional systems will be challenging of course the last talk showed really nice ways of handling the two dimensional systems and I'm going to show some similar systems I wasn't aware of that work but good to know so at that point we were also motivated by that same paper by Carlio and Troyer in science and what they had shown is that the wave function a quantum mechanical wave function can be nicely parametrized as a restricted Boltzmann machine which is a form of a neural network and we were new to this field we didn't know what a neural network was and we just wanted to start with a simple system the simplest that we can think of so what am I doing? I'm trying to rephrase the optimization I'm basically trying to have a different way of optimizing my wave function and to begin with I'm starting with an answers which is the neural network answers so instead of a completely exact full CI wave function I now have a neural network wave function so to say so instead of y of x essentially I have a different form f of x but we are all used to this we take different quantum mechanical answers and we are happy with it so why not an n answers I can do that so that's what I did only thing is here now this f of x is extremely flexible because you can change the number of nodes you can change the activation function you can do many many different experiments with them and I'm going to choose f in such a way that for the training set that's going to be what I'm going to minimize for the training data it's going to be very close to the actual wave function y of x and because I'm a newcomer in this field I'm going to choose the simplest form of f of x so that's what I did so the inputs here are either the spins of each side or they could be the occupation numbers of the orbitals that's what we have taken and instead of minimizing the energy the variational answers which we have all been used to and then variationally optimize it so instead of doing that here what we are doing is we are optimizing the wave function to mimic the data ok but what data am I talking of because I don't have any data to begin with I don't have a wave function if somebody gave me the wave wave function I can give you back the answers I don't have the wave function so I have to get a bunch of these known weights or CI coefficients and that is a problem that was pointed out in the last talk quite appropriately that this is the sticking point even in our calculations but we can find this from initial few runs of Monte Carlo CI it's not really a variational Monte Carlo it's a Monte Carlo CI which was done by Greer and co-workers in the late 1995 6 somewhere like that ok using that data we are basically going to minimize this cost function which is the distance between my f of x and y of x within the data set that I have and what is the benefit of this of course we don't have to compute the energy at which any point which basically means I don't have these contractions to do that's great and what is the flip side of this I will need a lot of data so let's understand the pros and cons and we have constructed a network only thing is you can see over here the number of parameter scales as n squared given that if I have the number of nodes equal to the number of input or number of sites so then the number of parameters that I have or tunable things that I have is n squared which looks great so let's see if it can do anything and indeed it can so we have tested it on dimensionale polyaromatic hydrocarbon systems you may not think it's a very big one it isn't and you may not think it is very two dimensional it isn't but I had to check it with DMRG and I had to check it with a full CI or exact calculation so this is not the bottleneck as in our calculation is not the bottleneck what we check with becomes the bottleneck at that point but we can have variational energies quite accurate with respect to full CI short note very recently we have also tested it on bond breaking problems in this work which is still under revision bond breaking problems are difficult as I showed for even the smallest molecule that one can think about water we didn't do all that great with sophisticated quantum chemical approaches it doesn't work that easily because there's very different kind of correlation in the equilibrium region there are very different kinds when you are breaking the bond the kind of correlation changes and your method has kind of got to adapt to it otherwise you get a non parallelity error and the binding energy that you get is horrible you may have a very good method here very bad there you are doomed vice versa you are still doomed ok so we have tested this on a bunch of these things then we kind of thought what you know kind of like professor Hoffman was alluding to what are these neural networks why do I have that as the answers how is that even meaningful I could use the same technique of machine learning on a MPS answers and if I have the MPS as the answers then the wave function I'll get out of it will be meaningful and around that in the time I came across this paper which is now in neuro IPS they showed a nice way of using MPS to do handwriting recognition and we kind of borrowed from their algorithm which kind of looks very similar to a 2 dot DMRG algorithm so it optimizes two sites at a time and it kind of sweeps through this in a very DMRG like fashion so we have done that just to give you an idea of what might be the benefit our codes are still not very optimized so I can't give you the exact timing and things like that am I running out of time ok ok I had a little bit of a different story in the end but yeah ok so yeah so let's see how at least the formal scaling should work if I were to calculate the energies really calculate the expectation value and stuff then simple 9 MPO based algorithm will scale as k to the power 4 with system size and DMRG we all know scales as k cubed with system size on the other hand MPS if I am going to train it via machine learning the scaling we are going to be linear with k of course there is a nasty NT attached to it and this NT is the amount of training data we have no idea how this grows it grows for sure it grows with system size we have to figure this out in fact I looked at a lot of computer science literature they are also very vague about how NT grows with system size yeah so that's one sticking point still of course data is going to be machine learning but here you can see the variational energies are very good estimates this is the red one is the Monte Carlo CI and we can get much much closer to the exact system than Monte Carlo CI and the reason for this is actually not a mystery it's because if I plot the energy versus the cost function for certain iterations they follow each other quite well so in fact the cost function that we chose is a good proxy of the energy minimization now I am going to switch gears and talk about melanin because that's extremely close to my heart we did a lot of work in that direction but I didn't want to bring too much of it here because that's a lot of chemistry but still I can't stop from sharing those work so what's the melanin it's the material that's present in our skin and there are quite a few different kinds of melanin and it so happens that all of the kinds have this broadband spectra and because the structure of because of this broadband spectra all the structural you know how to find the structure those characterization tools don't work very well they are also not very soluble in water there are real experimental challenges that makes melanin a very hard system to study so what people have done theorists have come up with many many different models of these structures and they have studied you know what is the absorbance in these structures that's one way of going about it that can show how different kinds of structures are possible that can also show how much amount of heterogeneity is required to get back this broadband spectra those have been tackled till now but we are going to ask very specific questions of what are the photo protective pathways in melanin in other words how does it protect us and secondly how does melanin get its color really exact chemical structures not any model nothing like that and we are going to take a bottom up approach this was supposed to be dihydroxyindole I have a dye and a ol on the end but it's dihydroxyindole it doesn't matter it's an indole this thing is called indole with two OH groups which is the dihydroxy so if I look at the spectra in this francondon region or the equilibrium ground state equilibrium region you see there are two states a pi pi star optically active state and another optically dark state which are very close to each other if you so we have tried different modes I am just going to show you the highlights of this work so if I look at the OH bond elongation you basically get what you expect right if you elongate the OH it's the sigma star and the sigma on that OH that's those energies are going to change so it is this dark state that is going to change in energy and come closer to the ground state and the pi pi star optically active state is going to stay as is so if I then create the potential energy surface which is by no means easy task but if you do that what you see is along this reaction coordinate or this the CV kind of a picture if that's the terminology you are used to you see that there you have a low barrier so this is the low barrier over here but even that is pretty that's not that low in the excited state mind you and the energy of the cross section this crossing between the excited and the ground state called the conical intersection is also lower in energy than the starting Franck-Condon region excited state so this is what we get from the static picture now this is where I am going to say that dynamics in these systems become very very important because you might think that you know which are the directions that are most favourable from the normal mode analysis and things like that they don't work that way so if you really have to run dynamics and see where the molecule is taking you and we did that using tally surface hopping codes and we saw that there are two geometries two low line conical intersections that it is achieving one is this one that OH bond elongated I already showed the other is this ring puckered mode and then we went back and looked at both these potential energy surfaces as I mentioned before this planner one has a small barrier but still a barrier and this leads to both photo protection and photo product now this is what stumps us how can a photo product be formed in these melanin systems and we are still alive go out in the sun and we are still alive so that's what's bothering ok the other direction is better because that is completely downhill which is great it's going to happen lot lot faster as I mentioned there's no barrier and it leads only to photo protection so the major channel is great minor channel not so great not that great so we kind of looked at the minor channel once again and we see that the photo products that are formed are actually the hydrogen abstracted or the oxidized form and this is where I did not mention did not get time to mention too much about melanin system in melanin system reduced and the oxidized states all of them are present so these products that we are saying are being formed are also other forms of melanin and these are the oxidized forms mki dki they are also present in melanin and they can give rise to other photo products and all that there's a very complicated pathway but it's a closed loop complicated pathway so all the molecules kind of regenerate with each other in the excited state and melanin never gets to structurally disintegrate which is great for us we can go out into the sun and be fine this idea has now gained some traction which is very heartening to see and I am even more happy because they say computational chemistry is key to understanding the unusual properties of you melanin that's one of the forms of melanin and the reason why computational chemistry is so powerful over here one of the reasons is of course experimental methods here are really really hard so even when with all the computational difficulties we can still give some insight in this direction so in other words structural heterogeneity of melanin has two roles one as I mentioned is to absorb all the sunlight other is to interconvert between different forms and protect itself last slide really I can see people are getting antsy last slide is we have actually just about demystified the color of melanin which means which part of the spectra is from which form which structure of melanin we have been able to say and this of course is from machine learning and tons of data generated using TDDFT calculations the paper is in we are trying to write it up maybe some other time I'll share that story because that's one exciting story so to conclude I have shown you some work on asine systems azuline systems and their fused analogs which shows that we can tune the singletroplet gap quite a lot and there's spin frustration at play which gives us this ability to tune the singletroplet gap we have extended these methods some of these methods to two dimensional systems using neural networks and then we kind of backtracked and used MPS optimization but using machine learning and I hope to have shown you a little glimpse of what we do in these photo protection studies in melanin and melanin structure spectra correlation and so on I haven't talked to you about the singlet fission problem in its coupling terms and things like that but of course there's finite time so some other time these are my students who did all the hard work and some of my former students did some much of the work that I have shown before so thanks to them thanks to them and thanks to the funding agencies for supporting our work and thank you all for listening to me Thanks for an outstanding talk I had a curiosity about the last part so I guess you've already thought about this but what is the role of super molecular assemblies and the environment oh we have done those studies also we have taken small molecules and seen how each of those pathways I've just shown you two pathways different pathways and we have shown how small molecules can tune each of these pathways but because there are so many different pathways at least one or the other always remained ultra fast so melanin gets to deactivate next thing we also looked at dimers and we have some tetra more calculations in the it's going on forever but we we have seen some excited state proton transfer pathways which are coming about when we have dimers and we expect that these will again be quite important in higher oligomers ok, thank you I understand you correctly the MPS optimization and the result you showed actually for a four member ring right? I showed you for a four member ring yes, we have gone up to six so how does the scaling really go since there are a bunch of physicists is there any hope it can be applied in a condensed matter system? you mean NT? here I have to say this so there are some difficulties of small systems as well you know whenever you have edges things become quite complicated so if you have really a infinite system for example infinite DMRG is easier than finite DMRG so those are also going to kick in but of course you are well aware that I work only in these Gaussian basis forms but yeah, maybe we can extend it to plane waves and give it a go I don't see that there will be significant difficulties there there might be some simplicities also there ok, so looking forward to talking to you more on this Ralph, thank you very much for this very nice and inspiring talk in the introduction to your prize we all talked about Volta Cogni density function theory so the question kind of is in the areas can one kind of mix your matrix product methods with some kind of density function theory approach I don't is there any way of a hybrid approach where one could read the hard stuff with the people have thought about it but there's generally a lot of double counting of the correlation that happens and that's what makes it really messy to handle ok, so this is still messy it is still very messy and because you kind of lose handle on what is what which error is coming and cancelling or which error is coming and kind of blowing things up it gets really confusing that's the I mean the little experience in that direction that I can tell you but here I should mention that there are some you know if you have orbitals with ligands there people have tried DFT and from that DFT orbitals they would do a kind of DMRG or MRCI those kind of things but they always add some empirical corrections and things like that in the end which makes me a bit yeah, get carried thank you for your talk I just would like to precise about all your calculations of the azuleans in dolls or a molecular compounds did you take into account that these molecules were isolated once or you had some agglomerations we look at some isolated but as I was mentioning for his question that there when we look at environment effects there we use QMM there we do use QMM but the results I presented today is mostly just QM but in general for your study it's important to have the solvent effects it is, it should be but those are the next steps so once we have the pathways we generally look at how does those pathways change so we look at the environment as a perturbation always I see, thank you other questions if not I may have a general one which I don't know as I may have any actual answer so near a conical intersection I would expect that correlations get more important because different configurations approach when changing the geometry but at the same time the Born-Oppenheimer approximation would break and coherence would be lost so how do I take care of it how can we combine all these difficult effects in a unified picture so we generally start with in the Born-Oppenheimer approximation itself we create those regions where the, and we use multi reference methods to calculate of course because that takes care of the correlation part now once we have those crossings in those crossings we calculated the non adiabatic coupling elements and using that we diabetize the wave function in there to figure out what would happen after that so there those non adiabatic couplings become difficult and we do calculate them only big approximation that we have over here in the interest of full disclosure is we use those surface hopping algorithms of John Tully for the dynamics which is a classical analog of quantum dynamics so what it does is it throws many many trajectories and when it encounters one of those conical intersection it does a probabilistic way of how many of those trajectories hop into the other surface or not ok we can thank again and conclude in the session on behalf of the quantum espresso foundation let me invite all of you to the refreshments that will be served in the lobby just outside this room these you probably already knew one thing that probably very few of you know is what motivated the refreshment the offering of the refreshment it was not only the celebration of the prize but also the 20th anniversary of the quantum espresso project in one week in one week 20 years back so the 19th century the 19th of January 2003 the first commit to the quantum espresso repository was struck so enjoy the refreshment and happy birthday quantum espresso