 I will basically be short and introduce you to a part of a session that focused on advanced methods in ground and excited state computations and Professor Nice's expertise is in quantum chemistry and particular wave function based methods and he's been doing some very exciting calculations at the frontier of using couple cluster methods, sort of higher level gold standard quantum chemistry, wave function quantum chemistry on systems in the solid state in the condensed phase. And so this is a very exciting area in our community for both validation of say plain wave density functional theory advanced methods but also opening up new avenues for exploring the phenomena of complex materials. So I'll let Frank tell you more about it. Frank please floor is yours and I'll give you a warning at five minutes about 25 minute talk. Thank you very much for the kind invitation to come here and I'm very sorry for the confusion that I caused it was a family tragedy this morning and I have to add out. But I nevertheless want to embrace the opportunity to tell us a little bit what we did in the field of solids and surfaces and I do it from the perspective of molecular quantum chemistry if I come across a bit amateurishly during the talk that's the truth. So let's look at a molecule or molecular system or maybe also solid through the eyes of physicists and it's nothing else but a collection of positively charged nuclei assumed at rest and the moving electrons and what I always find of hypnotic attraction in that field is that a single physical law named the Coulomb's law should be able to account for all of the complexity of the material world or nearly all of the complexity of the material world. And of course as we all know since Newton's days the many body problem is a hard one in classical physics and it's even harder in quantum mechanics and when we talk about first principle wave function approaches we approach that typically in two stages and first solving the mean field Hartree-Fock equations that give about 99.8% of the correct energy and introducing the idea of each electron moving in the average field of the other electron and the nuclei and what's missing from that is just 0.2% of the total energy it's frustrating that 99.8% isn't good enough but basically the last 80 years of molecular quantum chemistry has been an uphill battle against the missing 0.2% of the energy and that is so-called dynamic electron correlation basically the instantaneous interaction between electrons when they bump into each other they come in two flavors the same spin correlation or Fermi correlation and the opposite spin correlation namely the Coulomb correlation and the Fermi correlation is relatively easy because part of it is in the Hartree-Fock and what's really hard is to treat the Coulomb correlation correctly. And how to do that and how to do that without introducing screening functions or u-parameters and all of these things that is the subject of Appianichal quantum chemistry and what has been found to be the most successful method here originated in nuclear physics where it is less successful than in chemistry and that is a couple cluster and that's where the wave function is written as an exponential of an operator T acting on the Hartree-Fock reference wave function and the operator T comes in terms of excitation classes and these excitations are promoting 1, 2, 3, 4 particles at a time from occupied Hartree-Fock orbitals into virtual orbitals and it is very fortunate by construction it is size consistent at any level of truncation of the cluster operator and in chemistry we are very lucky that we can essentially truncate the cluster excitation operator after the second or most the third term. Now if you expand the exponential of course then you get the linear terms here in those operators and then you get products of these excitation operators and they describe disconnected excitations meaning statistically uncorrelated events in electron correlation. The couple cluster calculation method is not variational but it is solved by a projection technique that leads to non-linear equation set that is not hard to solve and contains up to the fourth power of the excitation amplitudes and it is a gold standard method where CCSD parenthesis T where parenthesis T accounts in a perturbative way for the triple excitations and that has been tested at Libertum in molecular quantum chemistry and has been found to be a really very accurate method and if you capitalize on couple cluster theory you can go crazy accurate in these calculations. This is calculation a method, a compound method of my colleague Jan Martin and it is based on couple cluster theory and he shows in that was more than 10 years ago that relative to the most accurate thermochemical data available, gas phase thermochemical data available, he reaches an accuracy of 0.1 kilocalories per mole and this is an absolute accuracy. There is no rolling dice here, there is no fitting there, no parametres, this is just simply natural constants and the Schrödinger equation and this is what couple cluster theory then gives you, it gives you a systematic way to really solve the many particle Schrödinger equation to an accuracy of about 0.1 ppm parts per million and that is amazing. For very small system you can go even more accurate but like couple cluster theory it is about really solving the Schrödinger equation to that accuracy with no strings attached. Now what's wrong of course about couple cluster theory and you all know that is that it scales very unfavorably with system size namely CCSD parenthesis t scales as n to the seventh meaning if you want to treat a system that's twice as large you have to invest 128 times the computational resource in terms of CPU time, disk and memory and that of course many people, I'm very surprised always how many people give this answer to that problem. Computers, computers, computers and more computers but with an n power seven scaling this in my opinion clearly is a losing proposition and supercomputers don't solve the problem but instead I always felt very strongly that what one should do is to invent intelligent approximations that like bring down the computational effort so that these calculations become feasible and it is surprisingly hard to do that without spoiling the accuracy of the parent method so there have been many many many many approximations to the couple cluster equations but many of them were of a kind that they introduced errors that were far too large to be tolerable and then couple cluster theory is lost. So essentially there are three things to be exploited here. The first thing to be exploited is sparsity and in the self-consistent field there is sparsity and by Kuhn's conjecture the density matrix is falling off exponentially however very slowly stop and in the correlation energy there is a lot of sparsity and so here you look at pair correlation energy so these are increments of the correlation energy brought in by pairs of electrons and you can always write the exact correlation energy as a sum of pair correlation energies and they fall off extremely quickly with distance so after about two bonds like the energy contribution is zero then there is a wonder valve tail and then and then you forget it so there is very quickly a linear scaling number of significant electron pairs that contribute to the correlation energy and that is of course the basis for local correlation theory and that alone is not enough however and that is where we come in that the next thing you need to do is to compress data unfortunately I don't have time to go into much detail but rather the idea is rather than to operate on large matrices that are densely filled with small numbers you invent a transformation that gives you a small block of the matrix with large numbers that is densely filled and the rest is zero and then you truncate so it's basically kind of G-zip operation on the quantum chemical information content and these are the three principles that we have utilized and we have invented a method that's so called DLP and O CCSD parenthesis T and the DLP and O stands for domain-based local pair natural orbital theory and if I would explain that to you the entire talk would be about that but I want to go to the applications and what it gives you is linear scaling with respect to system size so that would be the canonical couple classroom method that is the system size here is the number of atoms and that is the computational effort of DLP and O CCSD parenthesis scales linearly with system size and with a small pre-factor and so that means instead of being able to treat 10 atoms you're able to treat hundreds of atoms with that method and it is now probably the most accurate method that you can apply routinely to molecules and we have worked on this with an entire group for about 10 years this was the first paper and since then the citations here are exponentially rising and it's on a good way to become one of the really substantially used quantum chemical methods in computational chemistry and it's easy to use it's black box just in the same way that DFT is oops sorry you can treat ginormous molecules with that that was from 2013 was the first time an entire protein has been treated with couple cluster theory so that was an all electron CCSD parenthesis T level calculation on an entire protein we didn't really learn anything from it other than that we were able to finish the calculation but it shows that that these calculations can be done that had been 640 atoms and 12,000 basis functions that was the first calculation on a molecule over a thousand atoms and the last thing we did last year was a big drug that contained 22,000 basis functions and 2,400 atoms so basically the curse of the bad scaling has definitively been overcome with that development and if you subject that now to the standard quantum chemistry test set so in quantum chemistry the culture is that you have a laboratory test set containing like hundreds or thousands of data points of high accuracy thermo chemical or other data that people run their methods through in order to get error statistics and if you if you see how how we're doing that so DLP and all CCSD T in these tests do with an average error of about 1 k cal per mole and so that is chemical accuracy and this is not by chance this is by construction and all DFT and these are don't rule us own test set so right I'm not cheating then is these are don't rule us on test set and it outperforms now how can we do solids and surfaces with that of course the proper way to do that would be to go to full periodic implementation of that and that is scary then as I've witnessed I've I've seen I've observed people doing couple cluster theory on solids and it scares me and and so what we're doing is I think the pedestrian way we treat them the retreat the solid or the surface just like a large molecule and since we're able to do a few hundred atoms we can go to very large embedded cluster models so what we do then is to take the solid or surface and then we cut out a quantum region and that quantum region can be pretty large it can be like a few hundred atoms then we kept that with capping ECPs it's all standard technology and then we embedded in the field of a couple of tens of thousands of point charges and so basically we it's very similar to doing a calculator QMM calculation on an enzyme so basically that is the way we do it now of course you tell me that such an embedded cluster is not a solid and I understand that and and I know that there are limitations but there are things you can do with it and in order to convince ourselves that we're not doing nonsense what we typically do is the following we do periodic DFT calculation on the system and then we vary the cluster size and we do we use the same functional as in the periodic DFT calculation and then we observe that the cluster embedded cluster results converge towards the periodic DFT results using the same functional right and if that is the case and typically it is a case in the overwhelming majority of cases that we studied we really were able to converge the cluster calculation towards the tube periodic result at the DFT level and then we feel entitled to use that converged cluster and apply couple clusters theory to it and the first study we have done there is a couple of years ago together with colleagues from the TUM Munich from cast and Reuter and we have studied small molecule binding to TI02 surfaces and my colleague Robert Schlügel tells me that the experimental data on these systems isn't very reliable but it's the only thing that we found and so it's it's what we what we connect to and so there is data for water for methanol for CO2 for ammonia and for and for methane and for all of these the binding energies cup calculated with the DLP and OCC STT is within 1 k cal of the experiment so that is the best comparison we can offer and the same is obviously not true for DFT that is varying all over the place here for example here in the water molecule so that is the experimental result here is the DLP and OCC STT and then depending on the functional dispersion corrected or not you can get all kinds of results from 10 k cal error to relatively close here that would be be to peel up a double hybrid functional that is not really cheaper than the DLP and OCC STT so so I guess PB0 D3 would be more something that that is known to that community and that has an error of about 4 k cal or so so it's it's it's quite significant for the case of the CO2 adduct I think it's it's well known that DFT always wants the tilted conformation to be lost in energy but the experiment shows that the parallel conformation is lower than energy and that is also what the DLP and O gives you so it's it's in substantial agreement with experiment so going through a list of functional there were always a few functions that were relatively close to the DLP and OCC STT for one system but then not for the next or second next system so there was not one functional that uniformly performed good now one nice thing about the couple cluster energy that that I cannot get from the DFT is I can understand it I can break it down in digestible chunks and one thing that we have come up with here so-called local energy decomposition and the local energy decomposition what that gives you is say you have an interaction between two two systems whether that's a solid as surface or an enzyme and a risk and an effector or a drug it doesn't matter and so you have these contact points between these two interacting systems and now the total interaction energy is then our total binding energy is then just the sum of the interaction energy as these contact points and the local energy decomposition allows you at each of these points to decompose it into electrostatic contributions dispersion energy contributions and exchange contributions and that is very very powerful we've been using it in molecular chemistry all the time and in terms of the surfaces you can see that and that is certainly not surprising if you bind water to the TIO two surface then the binding is predominantly electrostatic and if you bind methane to the TIO two surface the binding is predominantly dispersion controlled and quite typically DFT does relatively well if the binding energy is is electrostatic and it varies all over the map if it's dispersion even if you include the grimmer dispersion correction then then you see here for the dispersion like the results are very variable in electrostatics is better but also you have some really bad results for example here with PBE so that is the story on on binding energies and just to give you an idea of course you pay for it it's not for free on one point of the largest cluster we've been treating the PBE calculation takes 30 minutes the PBE zero calculation takes five hours the double hybrid calculation takes 12 hours and the DLP and O calculation takes four days it is more expensive there is no doubt about it but it's still efficient enough to do it in production mode you just wait a bit longer but you're rewarded with a systematically accurate result now we've been trying to extend that whole scheme to excited states and that was a was a very substantial struggle I think we've made quite some progress along the way and I want to show you here for the first time what we've very stand with respect to band gaps so the band gap is defined as the difference between the ionization potential and the electron affinity and an alternative definition is the first optical excitation energy and of course these things are related and for semiconductors the band gap and the optical band gap they are fairly similar now I can wrap my head around an excitation energy fairly well as a molecular chemist and and then many of the things you guys are talking about is a bit beyond me but of course we can approach it this way now here's one thing that always confused me and and that is very many times you see in that literature that people equate band gives with orbital energy differences right from the corn charm orbital energy differences and then they are happy if like they add hard to fork exchange and it gets larger but I don't really know what that means and look at this here this is interesting and I have the PBE functional that doesn't have hard to fork exchange and the orbital energy difference between the Homo and the Lumo is 2.06 electron volts and if I do a delta SCF calculation by moving an electron and reconverging I get practically the same and if I calculate to use TDDFT and calculate the first singlet and triplet and then take the average I also get practically the same so things are completely fine here and then it's absolutely okay to use these orbital energy differences as a measure for that for that excitation however as soon as you add hard to fork exchange that's no longer true here then the orbital energy difference is 3.5 electron volts and the delta SCF is totally different and it's and it's the same as the average between the singlet and the triplet excitation energy and that's okay because in the TDDFT response equation there is that term here the fractional hard to fork exchange CHF times that integral IAA which is not small five minutes fine and of course if you don't take that into account that is not a physical number here right this is a physical number this is a physical number the most physical numbers are singlet and triplet excitation energies so one really should look at the states and not at the orbitals and that's why I would never call an orbital state then the state is many particle object and orbitals one particle object and it's it's absolutely the same as true for for solid so if you look at things sulphide here or lithium chloride and that is the difference between the orbital excite the orbital energy difference and the excitation energy and it's several electron volts large and of course that is exactly the way it should be so now couple just a theory for excited states that is a complicated subject it's the equation of motion couple cluster in the interest of time I don't go into it and there are technical challenges that we needed to overcome and we ended up with a scheme that's a so-called similarity transformed equation of motion couple cluster that's an ingenious invention by Marcel Noyan and what Marcel has shown if you apply a second similarity transformation to the similarity transformed Hamiltonian and get the amplitudes from the separate equation of motion IP and EA problems you can eliminate the the singles doubles block of the transformed Hamiltonian and then you only have to solve a CI singles basically a particle whole dimension problem in order to get a fully correlated results and that is absolutely beautiful and it's a very accurate method that has an average error and excitation energy molecular test set of about 0.1 electron volts and we've been able to implement that in a near linear scaling fashion and so we now can apply that to a whole range of semiconductors here and so you see that is our range and this is a range of of band gaps that has been calculated for them and again we do the cluster thing and we see that in the majority of the cases our calculations really our DFT calculations are converging to the periodic result and the couple cluster calculations are converging to the experimental result and that is quite beautiful so if you look at it so here is our for the range of systems these are the Hartree-Fock meaning CI singles results they have a big error of more than one electron volts then we do the stem couple cluster that goes point two to point three and once we had the spin orbit coupling we go go to an error of below point two electron volts and compared to DFT it's it's way more accurate than DFT that depending on the functional the DGA functions have errors of more than one electron volt hybrid functionals 0.5 electron volts double hybrids are a bit better but the couple cluster is by far the most accurate so that is all I had to say I hope you found it a bit interesting and what I've talked about is it correlated ab initio quantum chemistry can now be applied to systems containing hundreds of atoms and that allows us to treat large cluster systems and the results of these couple cluster calculations so far I think have been quite encouraging and they do outperform DFT I'm aware that the cluster models do not solve all the problems in solid state and materials chemistry but I think there's a lot you can do with it thank you