 Okay, thank you, Jeff, for the kind introduction. Sorry for this minutes of delay. So it's my pleasure to talk to you about some recent results about optical and core spectroscopy with many body perturbation theory. So as it's clear from the title, we are going to talk about light matter interaction. And I suppose that most of you, when I say light matter interaction, have in mind a picture like this. So with our favorite material, impinged by, for instance, solar light. So this is the realm of optical excitations that more or less occupies the visible and ultraviolet range. So I located it between 1.5 and 10 EV just to give you an order of magnitude. Probably this is a bit generous in terms of energy. And most importantly, we are thinking about transitions between valence and conduction states. This is in opposition to another regime, which is the regime of core excitations. So in this case, the source of our radiation is not supposedly the sun or a laser in the visible frequency range, but X-ray radiation. In this case, excitations are from the core states. So we are no longer talking about this narrow visible range, but a huge energy range between, let's say 0.1 to 50 kev, but of course we can go even deeper. I'm talking just to, again, to give you an order of magnitude. And in this case, the transitions that matter, that drive the physics of the problem, are transition between core to conduction states. So of course, our intention to study these problems on the same footing raises this fundamental question about the methodology. So which methodology can we use to treat these two problems on the same footing? So let's put it in a sort of wish list. So we want a methodology which is ab initio because it's parameter free, because it gives us insight about the electronic structure of the material and any material can be in principle treated. We want to deal explicitly with many body effects. So we are not satisfied of just a mean field picture. We want to take into account electron-electron correlation effects as well as electron-all interactions. And last but not least, we want a non-electron formalism because we want to treat explicitly core electrons. So we are not satisfied of having them, let's say, treated approximately as in a pseudo-potential form. We want to treat them explicitly. So for this purpose, we have to use, let's say a specific formalism, a non-electron formalism, but I will come to this in a second. First, I would like to sketch very briefly and very schematically the workflow of our calculation for theoretical spectroscopy. We start, of course, from DFT, which give us the ground state information about the system, also give us a sort of qualitative picture of the electronic structure. This cartoon is supposed to represent a band structure. This band gap is wrong. We know that. And this is why the next step is to do the GW approximation, to get a quantitative picture of the electronic structure, which is represented here in this cartoon by an upshift of the LUMO level, which is typically what we get by doing GW. And finally, to get access to the optical spectra, or if you want to the electron-hole interaction, since optical in the context of core spectroscopy is not appropriate, we need to solve the beta-salpeter equation. So in this way, and this is what this cartoon represents, we get an optical spectrum, or a core spectrum, with, let's say, sharp peaks that are supposed to represent excitons, if any, in the system, and also with an explicit description of electron-hole pairs. Let me also specify that while this is the common, I would say, the state-of-the-art workflow for theoretical spectroscopy calculation in the realm of optical excitations, for core excitation, we typically skip the GW step, and we do simply beta-salpeter on top of density functional theory, correcting the band structure from DFT with a scissors operator. The reason why we do that, but for time constraints, I don't have the possibility to go deeper into that, is the fact that GW would indeed correct the, sorry, the conduction states, but is really ineffective for core excitation. So for this reason, we just skip the step and we simply correct with a scissors operator, our spectra. So, but as I anticipated already, to do that, to follow this workflow and to do with the, let's say to fulfill the wish list, I showed you a couple of slides before, we want to use all electron DFT. So what we do is obviously to solve the Consham equation, so far, nothing new. Let me also specify that in the results that I will present you next, I make use of a semi-local exchange correlation function, so really quite basics. What I would like to emphasize here is the fact that this is done indeed in the framework of an olelectron-full potential. So what is really crucial here is the basis set that we adopt to represent the Consham states. So, and then, let's say the method that we use is the so-called linearized augmented plane waves method plus local orbitals. In a nutshell, this method is most easily represented in this way. Suppose this is the region of space that is given by your material or by the atoms in your unit cell. So the red spheres, also called muffin-tin spheres, represent the region surrounding the nuclei. They have different size because our material can have different atomic species and each atomic species may have a different effective radius. So in this region, and this is indicated here, our basis function is essentially given as a product of a radial function, a spherical harmonics and an augmentation factor that connects, let's say, this function with the boundary at the so-called interstitial region. This is the region further away from the nuclei where our wave function is essentially given by a plane wave. So then we are somehow just treating the electrons as plane waves. I will skip the GW part because we had a very nice introduction in the talk before mine and because in the end, let me just say that we also used the G0W0 approximation, I would like instead to spend a couple of slides discussing about the beta-salpator equation. What I wrote here on the top of my slide is this Dyson-like equation for the two-particle or the electron-hole correlation function. The L0, so the one with the subscript, represents the, let's say, non-interacting Ks. In red with K, I indicated the electron-hole Coulomb kernel. So this is the formal wave, very compact wave, Dyson-like equation to write down the beta-salpator equation. In practice, what we do, we actually map this problem into an effective Hamiltonian, such that in the end, we have to solve an eigenvalue problem, the problem that you see here on the slide, which is essentially an effective two-particle Schrodinger equation. We get from the solution of this equation, in particular you can recognize here the eigenvectors of this equation act as weighting coefficients for the two-particles wave function, which I emphasize here is a six-dimensional object that depends explicitly on the electron and the hole coordinate. We also get information, this is what, I mean, what I emphasized at the beginning, this is how we get optical or core absorption spectra by the calculation of the imaginary part of the macroscopic dielectric function. In the square models here, you recognize the matrix elements and once again, the BSc eigenvectors that act as a weighting coefficient. I would like to go a little bit deeper into the structure of the beta-salpator Hamiltonian, or if you want of the kernel of this electron-hole equation. So here I write the beta-salpator Hamiltonian as a sum of three terms. The first one is trivial, it's just a diagonal term that takes into account the energy difference for independent particles or quasi-particles if we do GW in between. The second term is the so-called exchange term. You can see by the implicit plus sign here that is a repulsive term. It contains, this is the kernel part, it contains the bare short-range part of the Coulomb potential, and it takes into account the local field effects. I will come back to this during the results part. And finally, the third term is the so-called direct term which is an attractive term that takes into account the attraction between the positively charged hole and the negatively charged electron in this sort of semi-classical picture. The kernel here is given by the screen Coulomb potential W. So the main difference between these two terms, one is repulsive, the other is attractive, and most importantly, this term includes the screening from the material. Okay, so all this theory is implemented in the exciting code. This is the first one for the moment is the reference paper for the optical spectroscopy part. We are about to submit an updated version of this paper. In the middle you find the reference for the core spectroscopy. So the advantage of our approach once again is that, indeed, to come back to our wish list, it provides us with an ab initio approach which is parameter free and allows us to study any kind of material without any a priori knowledge or consideration. It offers all the many body formalism that we are seeking, meaning that we have a beta-salpator formalism that is naturally extended to core excitations, and we have included electronic correlation and excitonic effects that are so relevant to discuss about spectroscopy. Last but not least, this is an electron formalism, and I showed you, that allows us to treat optical and core spectroscopy on the same footing which is, indeed, our aim. And the core states, so about the core states, this I didn't mention, any core state can be treated in principle, so we have no restriction as long as it is a core state, and this includes, natively, so to say, the spin orbit coupling of core states. So I would like to show the capabilities of this approach with a couple of examples. The first example will be about optical and core spectroscopy in this sort of organic, actually strictly speaking, this is a hybrid system formed by, as a benzene functionalized self-assembled monolayer on gold surfaces. And the second example is about, again, optical and core spectroscopy of multi-alkalian Timonites for photocathode application. But let me start immediately with the first example, as a benzene functionalized self-assembled monolayer. I showed you already this cartoon picture. This was actually the topic of a collaborative research center that ended in 2017, so there were like 20 groups involved in the Berlin area studying these type of systems. Why are these systems so interesting? Well, this system, so these self-assembled monolayers of alkyl chains functionalizing these gold surfaces are by themselves functionalized by these molecular switches. So the idea is that these are very fascinating systems because they are well-ordered in principle functional architectures on surfaces. So they can be deposited, they can be controlled, they can be monitored, they can be probed. However, very soon in the project, it was realized that these type of systems, especially when they are so closely packed on the surface, they have hindered photo switching capabilities. And this, of course, is a huge drawback if you want to use this system as photo switches. In the first experimental papers studying these materials, this was ascribed to static effects in first place and in second place to a very strong and pronounced intermolecular and exidonic coupling. But yet, before, let's say, we started our investigation, the reason for these effects was not really well explained. So the way we tackled the problem was the following. We forgot about the substrate. We just consider the, let's say, azobenzene molecule. We started from the isolated azobenzene. Let me just mention that in order to take a little bit into account the environment of this molecule, we actually consider this oxygen bridge with a material functional group attached just to reproduce a little bit the, let's say, the coordination with the alkyl chain. And we actually studied the isolated molecule and then we consider two more models system, namely what we define as a diluted sample. So here I show you the unit cell viewed from the top, which is essentially given by one molecule in this unit cell and then this sister structure, which we call the packed sample because we have in the same unit cell two molecules. And from now on I will refer to this as the D-SAM and the P-SAM. Okay, so we started, we studied the optical spectroscopy of the system and this is the results for the three prototypical system we are investigating. So of course in the experiment we are just considering these packed samples, but our analysis on these three model systems is aimed to rationalize this behavior. So these are the spectra in the case of the periodic system, so the D and the P-SAM, we actually have two direction depending, let's say, if it's perpendicular to this AB plane or if it's parallel to it. Okay, let's have a look at this excitation. So I have marked already in the spectrum the most relevant ones. The first, the lowest energy one is dipole forbidden. This is well known for those of you who are familiar with the azobenzene molecule. This is the homo-lumotransition, which is an N-pi-star transition, which is obviously dipole forbidden. And this somehow stays forbidden in the molecule and in the diluted SAM, not really in the packed SAM. The second transition, which in the isolated molecule gives rise to this strong peak here, is given by the homo-1-2-lumotransition, which is a pi-pi-star transition, so obviously this is dipole allowed and even quite intense. In the diluted SAM, this is actually the picture that I provide in analogy to this, so we don't have molecular orbiters, we have bands. This is the band structure of the system and this is referred to as one here and this is referred to as two here. What you see, so the green lines are actually the band structure, the red dots represents this, let's say, beta-salpator coefficients. These are the a-coefficient of the beta-salpator equation projected on the band structure. So we typically name them as the weighting coefficients. So the diameter of these circles represent the contribution and as you can see, the first one is essentially given by the homo-lumotransition once again and the second one is given by the homo-1-2-lumotransition. Let's have a look what happens in the P-SAM, in the packed SAM. Well, in this case, of course, we have a much more complicated band structure because we have two molecules in the unit cell, so obviously we have some band dispersion in some direction, but what is really striking is the following. Once again, the first excitation, which is the dipole-forbidden one, even though in this case it's not really fully dipole-forbidden, yet it is still stemming from the highest occupied bands to the lowest unoccupied ones. On the other hand, this S2 excitation, which is here, actually at 4EV, so well above the band gap, is actually given by a quite complicated mixture of transition. You see, we have contribution up to these bands down here. Okay, so if we want to summarize a little bit all this visual information that we got, let me list it a little bit. So we find in this, by comparing the spectra, we find quite some similar spectral features in the molecule and in the diluted SAM, which seems to be quite promising in the sense that it seems to be, let's say, enough to dilute the monolayer in order to have good switching capabilities. While we see that indeed when we increase the packing density of the monolayer, we actually reduce the binding energy. I mean, the band gap reduces and so does the binding energy as well. Concerning the packed SAM, we also, so as I anticipated already, the first transition, S1, is actually activated, is not bright, but is definitely not dipole-forbidden. And the absorption spectrum above the onset is significantly blue-shifted and also quenched. I mean, these peaks are in absolute values, quite smaller, quite reduced compared to the isolated system and the D-SAM. And consequently, the spectral density in the P-SAM is also sizably blue-shifted above the gap. So the question that we faced when we got this result was, okay, what is the reason? What is the driving force that affects so significantly the spectrum of the packed monolayer? And after some investigation, we actually realized that it was local field effects. So to do that, so we proved in a sort of inductive way doing a computational experiment. So we solved the beta-salpeter equation. Strictly speaking, this would be the beta-salpeter Hamiltonian for triplet excitation, including only the diagonal term, which is this trivial contribution from, let's say, energy differences, and only the direct contribution. So we neglected the repulsive term. And this is the result that we got. So the blue lines are indeed this beta-salpeter without local field effects. Strictly speaking is the triplet, but of course, experimental is to don't understand spectra with triplet excitations. And the gray area is the so-called independent particle approximation. So this would be just the diagonal term neglecting also the direct term. Okay, so what you immediately notice in this case that all spectra, including the one of the packed SAM, have this sharp and strong peak representing the absorption onset. So there is no significant difference between the three spectra. The binding energy, which we can say roughly estimate as the difference between this dash line, which is the fundamental gap, and the first bright excitation is significantly reduced in the P SAM. And evidently, this is clear that it is local field effects which promote the mixing between the transition that we have seen in the previous slide, sorry. The point is the following, that we have the contribution from these excitations here. This is, again, dark. T1 is as dark as forbidden as S1. And indeed, it comes again from this excitation. And T2 is indeed much more similar to this homo minus one, two-lumor transition that we identified for the molecule and the P SAM. The good agreement with experiment is confirmed in this slide. These spectra actually look a little bit different from the ones that you have seen in the previous slide because we actually post-processed them in order to take into account the effect of the gold substrate and also to take into account the polarization that was used in the experiment. This was done by interfacing our exciting code with this post-processing tool called Layer Optics. The functionalization of the SAM didn't change the picture. In this case, we also included this isolated dimer, but somehow the picture is the same. So even if we included this methyl fluorinated, this CF3, and also this CN, the picture doesn't change. And this is actually summarized in this other paper. But now I would like to discuss a little bit about core spectroscopy. We investigated the excitation from the nitrogen K edge, so we studied the transition from the nitrogen 1S electrons. So these are again the results for the molecule, the diluted SAM, and the packed SAM. So the first thing that you should notice is that core spectra are really dominated by exotonic effect. In this case, we make this comparison with, let's say, by considering the energy difference between these peaks, basically the first peak in the spectrum given by the shaded area, this is again without exotonic effect, and these solid lines. And indeed, it turns out that the first excitation is targeting the LUMO, the second one, B targets the LUMO plus three, and the third C targets the LUMO plus seven. The binding energies range from six electron volts in the molecule, so they are really huge, to four electron volts in both monolayers. And we also notice that essentially the beta-cell pater doesn't only give us information about the binding energy, but it also correctly reproduces the relative weight of the peak compared to the experiment. Here we also have the results for the other molecules, so the one with the functionalization. Again, we notice that as in the optical excitation, also in this case, the spectral features are preserved upon functionalization, and in terms of binding energy, the presence of the functional group on the molecule as a marker just affects the binding energy of the order of 0.2EV, but in this regime this is really negligible. So to summarize this first part, let me say that we have indeed demonstrated that these densely packed self-assembled monolayers of azubenzene are indeed characterized by pronounced intermolecular coupling that is ruled by local field effects that dominate the absorption by quenching the band which is responsible for the photoisomerization. Core excitation, as I've shown in the last couple of slides, have also huge binding energy, very, very large, ranging from four to six electron volts, and excitonic effects have a crucial influence to determine the relative energy and intensity of the peaks, and this was all confirmed by the very good agreement with experiment. So now I have to rush a little bit in the second part, but I still want to show you the highlights of these results. This is a recent project that I started in collaboration with colleagues from the Elmwood Centre in Berlin, which is just opposite side of the street compared to my institute. As many of you know, this institute hosts the Bessie Synchrotron, so maybe some of you have collaborators who do experiments there, but probably what you, I don't know if you're aware of the fact that they are now working for a renovation of this facility, and one of the crucial points in order to improve also the quality of the beam line is to use very sharp beams. And to do that, an important part is to have very good particle accelerators and in particular photocatholes. And this is what this Berlin Pro project is all about, is it is to design the new generation of particle accelerator, including new photocathode materials. The most important point for these materials is to have high quantum efficiency and low mean transverse emittance, meaning that the beam should be very focused. And the most relevant candidates for this application are multi-alkali-antimonides material. So we can visualize them in the periodic table. This is actually already the example of the material that I studied, cesium-potassium-antimonide. You see, potassium and cesium are over there, so these are the alkaline metals. Antimony is over there. This is the geometry of the system. This is an FCC crystal, so very, very simple, with this cesium atom in the middle and this potassium atom over there. This is the band structure of the material that I investigated, both with PVE and GW. So far, so good. The GW gap is 1.62 EV, which is a very good news for experimentalists who wants to have this absorbing visible light and is almost rigidly shifted compared to DFT. This is the projected density of state just to give you a flavor of the composition of the state. So the valence band is dominated by this antimony P state, these magenta peaks that are partially cut and the conduction band is dominated by C state, mainly from cesium and antimony. They are very weak here because it's very parabolic. You will see in a second another picture. Concerning the optical spectrum, so here I'm showing you again the results from the BSE. This is the red line. The vertical bars are the solutions, so really the discrete peaks. And the shaded area is the independent quasi-particle, again for our analysis purposes. So this material absorbs in the visible region. This is very good news because this is what our colleagues are aiming for. They want to shine the cathode with a visible laser. So this is very good news. Exitonic effects that we can appreciate it by comparing the red curve and the shaded area. Well, of course we have a slight red shift of about 150 to 100 milliV, which is essentially the value of our binding energy. 120 is for the lowest energy one and a redistribution of the oscillator strength towards lower energy. We can discuss a little bit about the composition of the excitation. Again, I'm showing you here these excitonic weights. So basically the projection of the beta-salt-patter eigenvectors onto the band structure. You can notice that these A, B and C excitons, so basically they are represented here. They are all targeting, let's say, transition from the top of the valence band. This is really at the gamma point or close to the gamma point or in its close vicinity. This higher energy peak, it's actually a bit shifted from there and this is quite remarkable. The last slide about core spectroscopy. We investigated the L3 edge, meaning transition from 2P, 3.5 electrons. So this is the first peak. We have a very strong excitonic peak. This is again clear with the comparison between the solid line and the shaded area. We have 16 excitations comprised within this peak. I'm just showing the first two who are very close to each other in energy and they have binding energy of 150 and 200 milliV. Let me just remind you the composition of the conduction band. So we have the bottom of the conduction band which is S states from cesium and then we have here higher energy, the D states from cesium. But interestingly enough, we have already contribution to this X point. And indeed, if we analyze the contribution to these two peaks, we notice that they are very close to each other but one is actually targeting, so is targeting from the 2P, 3.5 electrons, the bottom of the conduction band with S character. This here is actually targeting the D band. So both are allowed, but within really a few hundred of milliV we have these two different kind of transitions. So this is basically the end of my talk. In the second part, I showed you this incoming project. We actually just published the paper. This was an invited contribution. We got information about both optical and coarse petroscopy that is relevant for our experimental colleague and in particular, I hope I give you as a general message the fact that, yes, many body perturbation theory is expensive but gives you really unprecedented insight and analysis tool for fingerprinting the materials. With this, I would like to thank my collaborator and of course you for your kind attention and sorry for the delay.