 Okay so thank you that was that was great and so so the next session is it's going to be focusing on new developments and methods for calculating spectroscopic properties and this session was nominally chaired by Lucia Reining but unfortunately Lucia couldn't make it this time she got ill at the last minute so I'm going to sub in and this session as you probably noted on your program we discussed earlier this morning also included Frank Neese originally so it's going to start off with Jan Wilhelm and before Jan comes up let me just say a couple of words and then it'll keep it short so that we are we're on track but basically for many properties materials phenomena of interest excited states are are very relevant and important so in other words beyond ground state properties are important so this session is going to deal with in particular charged and neutral excitations those are kinds of excitations that can be measured with say photo emission or scanning tonally microscopy and spectroscopy or by absorption of photons through linear absorption optical spectroscopy and so those in those kinds of methods the formalism that has become increasingly standard in its application in the solid state and condensed phase has been many body perturbation theory and so there the GW that basically is a greens function based formalism that goes that at for charged excitations involves the GW approximation and for neutral two particle excitations the beta-salt-peter equation approach and so a lot of advances in those two methods in the last few years have led to some very interesting calculations and methodologies and yet we're still and you know kind of I think in an early stage in those approaches and so the three talks in this session are going to be covering advances recent advances in our ability to compute accurately and predict these spectroscopic properties and so maybe I'll just mention a couple of things for example in GW it's those calculations are you know tend to be quite accurate and predictive but they're much more computationally demanding than a DFT calculation and that's because you one has to construct the polarizability and that's kind of an end of the four nominally sort of requires and before operations and so one of our speakers is going to be talking about constructing that polarizability at a much lower computational cost another issue in GW and beta-salt-peter calculations right now are the use of pseudo potentials one has to be to use those with great care and construct those with great care and which electrons you treat as valence and which you freeze in the core can affect your calculations and so the second speaker is going to be focusing on using all electron methods for calculating spectroscopic properties that also gives you access to core level excitations which can be measured at most synchrotrons so that's quite quite important and then finally many of the calculations of band gaps and optical properties only indirectly treat the effect of temperature or don't treat it at all and so the final talk in our session is going to be focused on methods to better calculate the effect of temperature on optical excitations and so I think with that I'll pass it to our first speaker who's Jan Wilhelm from BASF and Jan I'll give you I will give you a warning at 20 minutes but you have 25 minutes and then five minutes for questions. Good afternoon everybody and thanks to the organizers for this kind invitation to this conference so all the stuff I will show you about the slow-scaling GW and has been at all the work has been done back at university and in my free time so it's not connected to BASF actually so I would like to start giving a quick introduction into GW it's very sketchy so maybe not really rigorously but maybe you can get some howdy ideas so we are interested in computing energy levels of a molecule or a material and such an energy level is defined as for example bringing here an electron from some states to the vacuum level and the energy and the energy of this level is then this energy difference and also you can there is a definition for unoccupied states the energy is the energy you would get if you would bring an electron from the vacuum level to an unoccupied level so if you now it's a question how you can compute these energy levels of a molecule or a material and you could look in the literature and find the self-consistent field equation of DFT so you see all the molecular wave functions and every wave function is corresponding a corresponded with an eigenvalue epsilon n so you could now take these epsilon n's for the for the energy levels but this is not the correct procedure so there is not a guarantee no theorem that says that these epsilon n's are really connected to energy levels that if you look deeper in the literature and you will find that instead if you put in a self energy sigma which has two space coordinates r and r prime instead of the exchange correlation potential and this energy dependent then use if you solve this equation the Schrodinger type equation you get exact energy level so this is still not for the full truth it's a bit sketchy but you can see difference between these two equations in the literature you will also find a formula for computing sigma these are called Higgins equations but they are extremely complicated to evaluate therefore people normally do approximations to sigma and one very popular approximation as a professor Neaton already said is a GW approximation to sigma it's called it because to evaluate sigma as a product of the Green's function and screen Coulomb interaction the only problem now arises that in G there is an you need all eigenvalues or all energy levels and all the wave functions and the same for W so that means you should also solve this equation here self consistently by just first taking a getting some epsilon n and psi n as input then computing a sigma solve it again and computing a new sigma this is a computation also very expensive therefore people normally do the G-W approximation that means they do a DFT calculation then they get epsilon n's and psi n's so these ones here from DFT they plug in to them to G and to W so here then they get a self energy and then they evaluate these eigenvalues newly and you also take the DFT wave functions from from the SCF so this is also a bit sketchy but yeah as I said in G and W mode you take wave functions and eigenvalues from DFT and you just update them once there are several types of self-consistent G and G-W I will use eigenvalues self-consistent G-W in the following which has been shown to give good results for molecules and in this eigenvalue self-consistent G-W you once compute this G and W and eigenvalues then you plug them again here into W and G you get a new sigma here and then you reevaluate the I the G-W eigenvalues and you do this until you reach convergence. So now as Professor Nitner also already said that the most expensive step in the calculation in a G-W calculation is actually computation of the density response function chi and not in a normal G-W code one is doing that in imaginary frequency and in such or such a computations cases n to the 4 which is with the system size to the following reason so if you double the system size and you have a real space grid all the real space points are doubled this is the same for our prime so you have only n square and then you have to sum over all occupied and overall unoccupied molecular orbitals and each of them are also scaling linearly with the system size if you increase it so in yeah if you add all this up you have our prime i and a it's n to the 4 scaling all following steps computing the W G and the and epsilon and also sigma they are all n to the 4 steps so now it has been already found 20 years ago that there was a better scaling method which is called G W space time method and the time you see here and the reason is you could for your transform this function here from frequency to time and if you do it you see that it's now a product of an eigenvalue epsilon i times function of an eigenvalue of epsilon a that means you can split up the sum here into these two parts because everything is separated and in this way you first can sum over all occupied orbitals this is n to the 3 step because it's number of occupied orbitals r and r prime here are primed are and you can execute a sum over unoccupied orbitals separately each step is n to the 3 and the final summation is here a function of r and r prime another function of r and r prime this is only n square so you brought down the scaling from n took a 4 from here to n took a 3 and then you evaluate or you evaluate this polarizability on several time points and then do you do the back for a transform numerically and then you obtain here the density response in imaginary frequency and in this way you get n took a 3 scaling so now what's there's a bit of an issue if you go to a plane wave basis set where normally GW codes for the solids are done in plane waves the problem is you see here the density response in the plane wave basis set and for this you have to further transform the R index to G so you have here in our index there on our index and if you further transform it you get such matrix element because that's an integral over our and this is this matrix element so you coupled again occupied and unoccupied molecular orbitals and that means you cannot separate this summation anymore although here the function could be separated so in plane waves you actually couldn't implement this space time method in a good scaling way it recently it has this GW space time method has been implemented in bars and they use also real space grids for for the greens function so this is actually this is one greens function this is another one and then compute it then in on a real space grid and do further transform back to get to get a real to get a plane in a chi in plane waves but the problem is that real space grids are not an optimal way for electronic for representing electronic structure calculations and therefore it could be very better to find a better localized basis for for chi for chi where you can which is local so a local basis and still efficient and this could be maybe done by a Gaussian basis set so your all molecular orbital wave functions are expanded in a Gaussian basis so these are atom centered functions and if you then write down all the GW space time method which is very similar in also in Hartree-Fock you get four center Coulomb integrals over Gaussian basis functions so these are all Gaussians and you have to evaluate them and in quantum chemistry there is a very often used trick which is called the resolution of the identity so introduce another Gaussian basis set which is abbreviated as this with pi with P and actually the identity operator is approximated by this Gaussian basis set and there is this inverse overlap matrix appearing because the because the Gaussian basis set is not orthogonal now you insert this identity equation twice in the four center Coulomb integrals once here then you project this new functions onto P this is just this three center overlap integral you get the inverse overlap matrix here then you project Q on the Coulomb operator and then you insert again the identity here between the Coulomb operator and lambda you can get another R I index and inverse overlap matrix and another projection three standard projection so the cool thing is now that this three center projection is sparse in space so that means only if all three Gaussian basis functions are close together then this integral has a value which is not zero but as soon as one of these three big Gaussian basis functions is far away from the others the integral is zero because the Gaussian basis is decaying as e to the minus r square in distance so yeah the integral is zero because you only integrate zeros up here so now the whole algorithm if you use the Gaussian basis set for the molecular orbitals and this resolution of the identity is written here so first you see that you compute one computes the green's function in the gaussian basis in imaginary time then the next step is the computation of density response which is now in this resolution of the identity basis which is local now here it's crucial to have a good scaling and the good scaling you can see in the following so we focus on the sum over nu and first to get an n square scaling because the screens function here has two indices nu and sigma so we already have n square scaling but for every nu here we only have very limited numbers of mu and very limited number of q functions only these functions which are close to which are close to nu only these functions contribute all other integrals are zero and if you increase the system size then you add only functions which are far away from nu so this this one you don't have to consider more mu and q and this means that you only have an n square scaling actually coming from nu and sigma indices it's the same for the sum over lambda and you can also show that the sum over nu and sigma has also n square scaling so all following steps are just simple matrix matrix multiplications and they scale as n took a three with the system size the computation of sigma is again n square if you would look exactly at it then one makes a free transform from time to frequency again one also has to do an analytic continuation from imaginary frequency to energy and then finally one gets the GW and my eigenvalues so now how big can we now go with this algorithm here on the left the homo-lumo gap of such molecules here graphene nano ribbons and they have been recently synthesized on gold services so it's not a read not an not an idealized system one really needs to double the calculations on these types of molecules and on the right you see this the length of the ribbon actually we increase the length of these of these ribbons and shown is is the gap of all transport states in the middle so there are also six such states here which actually our home on do more but I don't I neglect them I only look at the transport gap of middle states and you see the homo-lumo gap here on the left so it slowly converges so one really has to go to large ribbons to actually have a converged homo-lumo gap of these ones and the value where it's converging to is also matching for to a periodic ribbon here that one which has been already published at ten years ago so on the right here you see the computational cost so the execution time is written here node hours so for example here 10 to go 3 node hours means that the computation could be run for example on 100 nodes and for 10 hours the the blue dots here are an or are an end to the for implementation so with imaginary frequency and it's typical that these implementations are limited to several hundreds of atoms and instead the green dots here which are this imaginary time cubic scaling algorithm here I could go to a thousand seven hundred so it's more than here and the reason is that one is an eigenvalue self-consistent GW calculation and here it's only GMO W not and this could be still a forward with GMO W not if you make such a double logarithmic plot so here logarithm here logarithm and you can measure use measure the slope you get the computational scaling and the scaling is actually n to the 2.1 so it's close to n square that means all the cubic scaling steps so all n three steps they have to be cheaper and this is also indeed like this so the brown points are all n to the three scaling steps and they are the computation cost is much below than the n square scaling steps good so some words about the accuracy you could say the other imaginary time and imaginary frequency back transform forth and back could be could introduce some issues so the value of the benchmark has been done for the GW 100 test set which has been published some years ago and it you see here the count the number of molecules which deviate here for example by 0.02 electron volts from reference values and this is done for the homo level in Gingon W not and you see that it would be of course perfect if hundred molecules would be here zero point zero but you actually see that somehow 15 molecules are worse deviating more than 0.06 electron volts and it's mostly due to the imaginary time imaginary frequency transforms but the good thing is you can check it whether and whether you are accurate or not in by just increasing the number of time of frequency points so you can charge record your calculation is good or bad and for the lowest unoccupied molecular orbits it's even a bit better good so far and only talked about molecules and I also did some ideas on periodic GW calculations with this algorithm and for this I would evaluate the greens function at a gamma point and also compute the density response at the gamma point and as soon as you have a very large box due to the locality of the Gaussian basis functions you can reintroduce k points from the gamma only results but this only works if the box is very large and then finally you also include the Coulomb operator with k points and you go through and fire and also the screen Coulomb interaction you get in k points but then you have to do some one has to do some a minimum image convention which is also done in periodic for calculations and one inserted here and this also only works very large supercells so I don't want to go into details here because it's getting very technical and it's not and the code works for five weeks now so it's not that it's super urgent to go into details I just want to show that one can go in principle big with the computer with this algorithm so I picked an interface between an untax one zero zero surface and zero zero one surface it has been disgusting literature that if you take agatas and to tile mixed interfaces to then catalytic activity of this system is much enhanced compared to poor agatas or poor root tile and this interface here has in total thousand atoms I use to the potentials for it 4.4 k point mesh typically one says that in a augment a double-setup basis or in this system or in this case the double-setup basis augmented is converged to converge the gap to 0.05 electron volts it's much electrons and here on the right you see the local density of states of the system computed with GW so one takes the GW not a eigenvalue eigenvalues and then smiths it with a smiths a bit and sums it up and one also projects it then on this on the axis of the interface so it's here this integration and then for example one can see that that if here an electron is excited in agatas here from the occupied states to the valence states then an electron here from root tile can fall into this hole and the hole is here and the electron here so you separate electron and holes and this causes on and now electrons and tolls cannot quickly recombine anymore because they are separated and it enhances and yeah catalytic activity because you have many electrons and many holes in the material so it is so it has been found in experiments that actually this level alignment here between agatas and root tile was 0.5 electron volts so it somehow matched yeah experiments but of course there is much to do so one has to do more efficient k-point integration this is not yet fully converged with k-points also what could do all electron calculations because there is no actually need for pseudo potential yeah one has to do benchmarks how big this cell has to be and finally would be of course cool to have a set of basis sets you can do to do routine calculations so now I would like to show finally an application of GW to a scene molecule so they are still small so the application has been done with the end to the fourth scaling code there is actually a cool rule from organic chemistry for these molecules namely that the resonance structure with the largest number of aromatic pyre sex that is most important for these molecules so what does it mean does it mean if you look at this small molecule called phenan train you draw you can draw many of resonance structures and then you mark the rings where you have three of these bonds so you and then you draw a circle you can do it many ways and you can also do it like this that you have two circles here and now this klar rule says that this structure here with the two rings it's much more important for the properties of this molecule than that one and in chemistry this is then for example you can show or you can measure that if you do want to do a reaction this double bond here is much more reactive than the double bonds in here so this is the foundation for chemistry and in the AC molecules you actually always only can draw one of these ring so in antrasein I show it here you can only draw you can draw the ring on every position and then people say this is a migrating sex that because this sex that here can be on every position and if you make the AC longer and longer it's always the same so you only can draw one of these rings and this can be on every position so now the cool thing is that you can also introduce unpad electrons so like here and then you can draw two of these sexes so one here and one here and now it's the question yeah is it now two sex again two unpad electrons or it can be even four of these sex sets so we don't know or is it maybe even this structure here so close shell without any unpad electrons so this was the motivation and are these asians actually close shell like this or are they open shell with unpad electrons and the problem until now was always that these molecules are very unstable for long asians are very unstable and recently at MPA they have been able to synthesize heptasein and longasein on a gold surface by some fundamental chemistry reaction and now they also can measure the homo-lumo gap of these molecules by scanning tunneling spectroscopy so they make a yeah as also professor Neaton said an experiment and they can probe here the homo level and the lumo level of course it's not extremely extremely well-defined but they can measure here the distance between homo and lumo and in this way they can get the homo lumo gap and now yeah one can plot the homo lumo gap as function of the number of the acing rings so you see here this is the measurement from MPA and this is the other one and also last year luckily there were the acing with 10 and 11 rings was also synthesized on the gold surface so there are also points and now one can do a GW calculation with the closed shell molecule and with an open shell molecule but singlet so you always have a total spin of zero and here you see and it's now a guest phase computation in GW and one takes into account the gold surface by the yeah an image charge model which has also been done by by Neaton and in this way you get so these blue points here are the open shell homo lumo gaps the magenta points are the closed shell ones and you see that the trend is following somehow the open shell gaps so distance is always actually the same and the reason here for this drop is actually a similar change in homo and lumo close to up between 10 and 11 rings and this has been already published before in literature and we would say that this drop is absent in the experiments so we and also the open shell gaps are well matching to the experimental ones so we could have so this could indicate that the acing molecules are actually open shell on the gold surface so I showed you a low-scaling GW implementation which scaled as n to square with the system size one could go to 1,700 atoms and in the last part I showed you the acing example where we thought that the asians are probably open shell on the gold surface so I would like to talk I would like to acknowledge York who supervised my PhD and Dorothea Carlo Roman and Leopold for the nice collaborations on GW implementations and the nano ribbons and acines the funding has been whole or my whole PhD has been funded with Marvel and also several computation time has been funded by Marvel and all has been implicated in CP2k so it's open source and one can use it and I thank you for your kind attention